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67780e9e6dde43c90831f476 | 29 | The density of states (DOS) analysis for Pt-doped pyrene (Figure ), showing a cluster of high bands around the Fermi level, signifies a material with enhanced electronic density near the Fermi energy. This feature suggests a quasi-metallic or semi-metallic nature, characterized by a high density of electronic states available for conduction at minimal energy input . The clustering of bands around the Fermi region implies delocalized electronic states, which facilitate efficient charge carrier transport and improved electrical conductivity. |
67780e9e6dde43c90831f476 | 30 | Such a band structure is indicative of strong electronic interactions and overlapping energy levels, likely arising from the synergy between the platinum dopants and the phenalene matrix. The proximity of these bands to the Fermi level also enables facile electron excitation, contributing to the material's exceptional electrochemical and catalytic properties. This electronic architecture positions the material as an ideal candidate for applications requiring high charge mobility and robust electronic interactions, such as in advanced energy storage systems, electrocatalysis, and optoelectronics. |
67780e9e6dde43c90831f476 | 31 | Mulliken Electrophilc Indices: The Mulliken electrophilic indices (Figure ) reveal that platinum in the Pt-doped phenalene (Table ) carries a partial positive charge of 0.101, whereas the bonding carbons (C3, C5, and C7) have much smaller partial charges of 0.017. This charge disparity plays a crucial role in enhancing the catalytic efficiency of the system. The relatively higher positive charge on platinum indicates that it acts as a strong electrophile, effectively attracting electron density from the nearby carbons. This promotes the activation of adsorbed hydrogen atoms during the HER, facilitating efficient proton reduction. The electron density withdrawal from the carbon atoms makes them slightly more nucleophilic, creating a synergistic interaction with platinum, which enhances the overall catalytic activity by lowering the energy barrier for hydrogen desorption. This electrostatic configuration significantly improves the catalyst's performance, allowing for a lower overpotential and higher current densities in HER. |
67780e9e6dde43c90831f476 | 32 | Regarding electron recombination, the charge distribution in the Pt-doped phenalene also plays a pivotal role in minimizing this detrimental effect. The higher positive charge on platinum creates an electron-deficient site that promotes charge separation upon excitation. This strong electrophilic character encourages the effective transfer of electrons from the adsorbate to the platinum center, reducing the likelihood of charge pair recombination. The bonding carbons (C3, C5, and C7), with their smaller partial charges, act as electron-rich centers that stabilize the electron density during the reaction. This stabilization, combined with the electrostatic interaction between the platinum and carbon atoms, prevents the recombination of electrons and holes, thereby enhancing the charge carrier lifetime. As a result, the Pt-doped phenalene maintains efficient electron flow, which is crucial for sustaining high catalytic activity and achieving long-term stability in electrochemical applications. |
67780e9e6dde43c90831f476 | 33 | The observed Gibbs free energy values for Hβ (-0.24157 eV) and HβΊ (-0.11589 eV) highlight the thermodynamic landscape of Pt-doped phenalene for HER. A material's efficiency for HER is significantly influenced by its ability to mediate proton adsorption, electron transfer, and molecular hydrogen desorption with minimal energy barriers. The relatively low Gibbs free energy for HβΊ suggests that the material facilitates favorable adsorption of protons, an essential initial step in HER. Concurrently, the negative Gibbs free energy for Hβ indicates efficient desorption dynamics, crucial for sustaining catalytic turnover and preventing active site saturation. |
67780e9e6dde43c90831f476 | 34 | The moderate disparity between the free energy values for HβΊ and Hβ reflects a balanced adsorption-desorption process, a hallmark of an efficient HER catalyst. This balance minimizes the overpotential required for the reaction, enhancing the thermodynamic efficiency of hydrogen evolution. The synergy between the platinum dopant and the phenalene matrix likely optimizes the electronic structure and active site distribution, ensuring that the Gibbs free energy aligns closely with the thermoneutral value (ideal ΞG β 0 eV) for hydrogen adsorption. These properties underscore the material's promise as a highly effective electrocatalyst for hydrogen evolution, combining favorable thermodynamics with robust catalytic activity. |
67780e9e6dde43c90831f476 | 35 | Where Ξ· is the overpotential, which represents the additional energy required for the reaction to occur beyond the ideal thermoneutral condition. ΞGact is the Gibbs free energy for the actual step in the HER process (either proton adsorption or hydrogen molecule desorption). ΞGthermoneutral is the Gibbs free energy at the thermoneutral point. |
67780e9e6dde43c90831f476 | 36 | The calculated overpotentials for the HER based on the Gibbs free energies of -0.11589 eV for HβΊ and -0.24157 eV for Hβ provide critical insight into the electrocatalytic efficiency of the Pt-doped phenalene material (Figure ). The overpotentials for both proton adsorption and hydrogen desorption are relatively low, suggesting that the material facilitates favorable proton adsorption at its surface and efficient hydrogen molecule desorption. A low overpotential is crucial because it indicates minimal energy losses during the HER process, thereby enhancing the overall efficiency of the reaction. Specifically, the moderate overpotentials reflect a balanced adsorptiondesorption mechanism, reducing the need for excessive energy input and optimizing the catalytic activity. These properties align closely with ideal HER performance, where the Gibbs free energies approach the thermoneutral value (0 eV), minimizing overpotentials. As such, Pt-doped pyrene demonstrates considerable promise as an efficient electrocatalyst for HER, capable of achieving high catalytic turnover with lower energy consumption, making it a potential candidate for sustainable hydrogen production in electrochemical energy conversion systems. |
67780e9e6dde43c90831f476 | 37 | In conclusion, the model demonstrated a comparable Gibbs free energy and overpotential, indicating its potential for efficient catalytic performance. The electron density analysis revealed significant and effective charge redistribution, further supporting the enhanced reactivity of the system. Additionally, the Fukui indices confirmed that the model exhibits a stable and ideal electronic profile, capable of minimizing electron recombination, which is crucial for maintaining high catalytic efficiency over extended periods. The presence of multiple optical absorption peaks and a favorable HOMO-LUMO gap underscores the material's suitability for photocatalytic applications, where effective charge separation and light absorption are key to promoting efficient photocatalysis. |
67780e9e6dde43c90831f476 | 38 | Moreover, the strategically positioned adsorption bands within the visible and near-infrared ranges place the model as an ideal solution to the persistent challenge of charge recombination, ensuring superior carrier dynamics and sustained reactivity. These spectral features not only enhance lightharvesting efficiency but also open avenues for overcoming limitations in current catalytic designs, thereby setting the stage for breakthroughs in scaling hydrogen evolution technologies. |
6627d1f9418a5379b07ed59f | 0 | Global anthropogenic CO2 equivalent (CO2e) emissions continue to rise year on year, resulting in a predicted global surface temperature rise of 3.2 o C (2.2 -3.5 o C) by 2100 if all implemented climate policy targets are reached , the Sixth Assessment Report by the International Panel on Climate Change (IPCC) states that "All global modelled pathways that limit warming to 1.5Β°C (>50%) with no or limited overshoot, and those that limit warming to 2Β°C (>67%), involve rapid and deep and, in most cases, immediate greenhouse gas emissions reductions in all sectors this decade". Within the global emissions scenarios considered within the sixth assessment report, those that have a greater than 67% chance of limiting global temperature rise to less than 2 o C include between 196 -280 Gt of sequestered CO2 from fossil CO2 alone by 2100 , not including atmospheric CO2 removal via bioenergy with CCS (BECCS) or direct air CO2 capture and storage (DACCS). The International Energy Agency's (IEA) Sustainable Development Scenario, in which global emissions from the energy sector reach net zero by 2070, includes 240 Gt CO2 sequestered by 2070, accounting for 15% of emission reductions . As of 2023, around 40 carbon capture and storage (CCS) facilities are in operation globally, capturing approximately 0.045GtCO2/pa, with an additional 50 planned to come online by 2030, capturing an additional 0.125GtCO2/pa . Although ambitious, this is an order of magnitude short of the approximate 1.2GtCO2/pa capacity needed in the Sustainable Development Scenario, highlighting the wide gap between aspirations and actions. It is clear that if CCS is to contribute significantly to global climate change mitigation efforts, a rapid increase in the deployment of CCS facilities is required. Post-combustion capture (PCC) encompasses any technology that separates CO2 from a gas mixture downstream of an industrial process. Typically, this is a high-volume flow rate of combustion products and possibly additional CO2 released from process materials, e.g. limestone, at atmospheric pressure, containing mainly nitrogen, water, and oxygen, with varying quantities of CO2 . Depending on the process, the flue gas to be treated may contain trace impurities to varying degrees, including CO, NOx, SOx, volatile organic compounds (VOCs) and ammonia (NH3), to name a few. Potential applications for PCC deployment cover all facets of the industrial decarbonisation landscape, from the energy sector by decarbonising critical dispatchable power infrastructure such as combined cycle gas turbines (CCGT) and coal-fired power plants and decarbonising home heating and transport with blue hydrogen production to raw material production such as cement, glass and metal. Additional cross-industry applications lie in waste and biogenic fuel combustion, contributing to energy production, waste management, raw material recovery and negative emissions. Numerous technologies are under consideration for large-scale post-combustion capture, including solid adsorption, CO2 selective membranes, and cryogenic separation; however, the most technologically and commercially mature and the focus of this manuscript is amine-based CO2 capture. Amine-based post-combustion CO2 capture functions on the principle that amine groups will bond with acid gases, such as CO2, to form a carbamate or bicarbamate compound in a temperature-reversible reaction and, as such, can be used to separate acid gases from a dilute gas stream in a two-step absorption and desorption thermal swing process. Absorption typically occurs in a packed bed absorber column at close to atmospheric conditions. Within this column, the flue gas contacts in a counter-current fashion with descending CO2 lean liquid solvent, transferring CO2 in the gas phase to the amine solution as it travels up through the column. For a given liquid to gas ratio the residence time of the liquid solvent in the packed bed absorber column, and so also the duration of exposure of the liquid solvent to the gases, in particular CO2, O2, NOx and combustion impurities, contained in the flue gas, is proportional to the packing height. CO2 lean flue gas leaves the top of the absorber column after emission control techniques to minimise unwanted carryover of amine and amine-derived products, while CO2-rich liquid solvent leaves the bottom of the column for regeneration. Regeneration occurs in a separate pressurised desorber or "stripper" packed bed column; CO2-rich solvent descends through the stripper and condenses steam, which has been generated at the bottom of the column. As the steam condenses, it heats the rich solvent and reverses the carbamate/bicarbamate forming reaction, liberating CO2. Mostly, CO2 lean solvent exits the stripper packing and passes through a reboiler, where a thermal energy source heats the solvent, further liberating CO2 and generating the stripping steam. The highest temperature in the post-combustion capture process occurs in the reboiler. CO2/H2O vapour leaves the top of the desorber column for drying, conditioning and compression for export while the now CO2 lean solvent is returned to the absorber. At all stages the steam also provides a stripping function, by reducing the partial pressure of the CO2; the ratio of CO2 to H2O vapour at equilibrium with the solvent depends on total pressure, solvent loading and temperature. Amine CO2 capture solvents are ammonia (NH3) derivatives where a substituent, such as an alkyl or aryl group, has replaced one or more hydrogen atoms. They can be broadly characterised into primary (with monoethanolamine (MEA) being the most widely known example for CCS applications), secondary and tertiary amines, representing how many hydrogen atoms have been substituted for alkyl or aryl groups. Due to its reactivity, low cost and ease of reclamation, MEA continues to serve as a viable solution for CO2 capture from low-concentration CO2 flue gases. Stainless steel construction or corrosion inhibitors for carbon steel constructions can mitigate the corrosion concerns present for higher concentration solutions, while advanced configurations and control processes continually improve thermodynamic efficiency, particularly at high CO2 capture fractions. Historically, CO2 capture fractions, defined as the mass of CO2 exported divided by the mass of CO2 entering the absorber, of 90% were targeted. However, in recent years, net-zero commitments have challenged this assumption's viability, as 10% residual emissions from PCC is clearly incompatible with these goals unless some form of permanent negative CO2 emission technology is concurrently employed to recapture the residual emissions. The economically optimal CO2 capture fraction will be the point at which the marginal cost of increasing the CO2 capture fraction is more than the lowest cost permanent negative CO2 emission technology that is available to recapture and permanently store the emitted CO2 (a point that will change as both technologies are deployed at scale). In the absence of a definitive economic optimum, the CO2 capture fraction that results in no net addition of CO2 to the atmosphere is considered for this work. This CO2 capture fraction is dependent on the ratio of atmospheric CO2 entering the boundary of the facility with atmospheric air (typically used for combustion) and the added CO2 generated by that combustion or other processes within the facility, and, as such, varies from application to application (see Eq 1). However, it typically falls between 99.2% for a CCGT up to 99.8% for a steam methane reformer (SMR). Mullen et al. term this CO2 capture fraction as 100% fossil CO2 capture however 100% added CO2 will be use in this manuscript to account for biogenic CO2. This terminology will be adopted throughout this manuscript, while capture fractions below this will be reported as gross CO2 capture fractions, as is typical for the industry. |
6627d1f9418a5379b07ed59f | 1 | Increasingly, CO2 capture fractions above 95% up to, or slightly above, 100% added CO2 capture is the focus of emerging research. Mullen et al. provide a detailed analysis of the currently available literature, critically assessing seven modelling studies and six pilot plant facilities where CO2 capture fractions over 95% were achieved. The authors identify lean loading as the critical factor to ensure thermodynamically efficient operation at increased CO2 capture fractions. Lean loading must be sufficiently low to provide a strong driving force of absorption at the top of the absorber despite decreased CO2 concentrations, a consideration typically absent or insufficiently considered in the current literature. As well as increasing the absorption rate throughout the absorber, low lean loadings facilitate increased cyclic capacity of the solvent (CO2 absorbed per unit of solvent), minimising the quantity of water to be moved through the system and maximising rich loading. These factors will contribute to a decreased energy requirement for solvent regeneration, and, as will be explained later, higher regeneration pressures will reduce compression duties. Where the importance of low lean loadings was recognised, solvent regeneration to the loadings required is typically mismanaged. Michailos and Gibbins describe what has been termed the desorber "inflection point". They present a modelling study using a 35% wt. MEA solution on a flue gas representative of a commercial CCGT and study 95% and 99% gross CO2 capture fractions over a range of lean loadings and absorber packing heights. They show that as lean loadings decrease under constant stripper pressure and incoming rich loading conditions, the energy requirement for regeneration per unit of CO2 captured, known as the specific reboiler duty (SRD), increases exponentially below a low loading value that depend on the specific conditions. This phenomena has historically led to the conclusion reducing lean loadings and, by extension, increasing CO2 capture fractions will result in exponential increases in SRDs. However, Michailos and Gibbins showed that the inflection point can be shifted to lower lean loadings by increasing the stripper pressure, noting, though, that reboiler temperatures will increase proportionately as a result. This change in inflection point loading arises because the rapid increase in SRD corresponds to the point where the water vapour to CO2 ratio in the reboiler rises to a level at which it cannot be condensed to near-equilibrium partial pressure and temperature with the incoming rich solvent at the top of the stripper column. This leads to increasing levels of water vapour in the CO2 at the top of the column, representing a significant heat loss. An increase in stripper pressure shifts the vapour liquid equilibrium (VLE) in the reboiler towards lower vater vapour/CO2 ratios for a given lean loading, at the expense of higher reboiler temperatures. Mullen et al. build upon the work of Michailos and Gibbins by completing an in-depth techno-economic assessment on 100% added CO2 capture for both an SMR and a CCGT using a 35% wt. MEA solution. They find that, although the thermal efficiency of the process decreases and the cost of the product increases relative to achieving 95% CO2 capture fractions, the effect is modest and is primarily due to the increase in the absolute quantity of CO2 captured rather than any non-linearity in the specific cost to capture CO2 as the CO2 capture fraction increases. The authors further conclude that, for the assumed conditions of this study, unless the cost of negative emission technologies with permanent CO2 storage falls below 184 Β£/tCO2, increasing CO2 capture fractions to 100% of the added CO2 is the most economical method of fully decarbonising a CCGT. Mullen et al. also show that the CO2 intensity of the counterfactual to hydrogen combustion, i.e. natural gas combustion, means that the cost of CO2 avoided falls as the CO2 capture fraction increases for the SMR process considered, despite the increase in product cost. Mullen et al. suggest two design changes to achieve 100% added CO2 capture: increased reboiler operating pressures and, by extension, temperatures, which facilitate efficient solvent regeneration for low lean loadings, and, in the CCGT case, a moderately increased absorber packing height, from 20m to 24m, to increase the mass transfer area. Although moderate from a process and technological perspective, these two design changes will expose the solvent to previously largely unexplored process conditions, with higher regeneration temperatures, lower lean loadings and increased duration of exposure to the oxygen content of the flue gas. Each of these process modifications may lead to an increase in specific solvent degradation rates. Mullen et al. note that this is a knowledge gap and assumes an MEA consumption rate of 2 kg/tCO2, quoting experience from MEA-based pilot plant studies, which report a range of 0.17 -1.5kg/tCO2 . This manuscript uses emerging models developed by Braakhuis and Knuutila, two co-authors, to shed light on the effect on MEA degradation rates of the process conditions thought to be thermodynamically beneficial when operating at 100% added CO2 capture. MEA will degrade when exposed to oxygen-rich atmospheres (oxidative degradation) or high temperatures (thermal degradation) . Unless effectively controlled, solvent degradation products in the circulating solvent can reduce CO2 capture performance, increase atmospheric emissions and operational costs and accelerate equipment corrosion . Degradation causes a loss of solvent directly while further solvent losses may occur as part of solvent reclaiming, which is required for sustained operation to remove all degradation products at the rate they are formed and maintain constent solvent health. One of the main degradation mechanisms for MEA is carbamate polymerisation, often referred to as thermal degradation. This mostly occurs at elevated temperatures within the CO2 capture process, most notably within the stripper sump and reboiler, where temperatures often exceed 120 o C for extended periods. It also occurs when the solvent is descending through the stripper packing and during pre-heating of the solvent, albeit for relatively short periods and at lower temperatures than the reboiler. When the carbamate, formed when CO2 reacts with MEA, is subjected to increased temperatures ring closure and dehydration occur to form 2-oxazolidinone (OZD). OZD is sensitive to nucleophilic attacks and reacts with MEA, forming dimers, oligomers, imidazolidinones, and other cyclic compounds. The cyclisation of the carbamate leading to the formation of OZD is the rate-limiting reaction. This rate was found to be dependent on both temperature and CO2 loading. Higher CO2 loadings have been shown to increase degradation rates, possibly by forming more of the carbamate or increasing the availability of proton donors, which can catalyse dehydration. A detailed review of thermal degradation methods is available in Braakhuis et al. . |
6627d1f9418a5379b07ed59f | 2 | Oxidative degradation of an amine is a two-step process involving the dissolution of O2 from the flue gas into the solvent, followed by a liquid phase reaction between the dissolved O2 and the amine. The observed amine degradation rate is thus a function of O2 solubility, mass transfer resistances, and kinetic reaction parameters. Process parameters, such as temperature, O2 partial pressure, amine concentration, and CO2 loading, influence each of these mechanisms. A detailed review of oxidative degradation methods is available in Braakhuis et al. . Braakhuis et al. define two categories of oxidative degradation: direct and indirect. Direct oxidative degradation occurs within the absorber where the solvent is in direct contact with the flue gas, and the quantity of dissolved oxygen is replaced while consumed. The magnitude of this effect is a function of the rate of mass transfer of O2 from the gas phase to the liquid phase and is expected to vary depending on the location within the absorber as the bulk temperature and the solvent loading change. Indirect degradation happens downstream of the absorber, where no further contact with an oxygen-rich flue gas occurs; in this case, the degree of oxidative degradation is limited to the quantity of dissolved oxygen in the solvent when no longer in contact with the flue gas. This can be mitigated with process modifications that reduce the quantity of dissolved O2 that is carried over to the absorber sump, for example, flashing or N2 sparging of rich solvent. The process considerations proposed by Mullen et al. for 100% added CO2 capture might be expected to adversely affect the degree of MEA degradation within post-combustion CO2 capture plants. Higher reboiler temperatures will obviously increase the degree of thermal degradation, all other things being equal. However, the associated reduced loading (i.e., carbamate concentration) in the reboiler may somewhat mitigate this. Concurrently, a reduced average loading in the absorber may increase the solubility of O2 overall and lead to increased oxidative degradation. Additional packing, the inclusion or absence of intercooling, and liquid-to-gas ratios will also all contribute to the uncertainty surrounding MEA degradation rates at 100% added CO2 capture fractions. This work applies the oxidative (Braakhuis and Knuutila ) and thermal degradation (Braakhuis et al. ) models for an MEA solvent with process modelling completed by Mullen et al. to compare the specific quantity of MEA degradation for three industrial flue gas sources (CCGT, EfW and SMR processes) at two distinct CO2 capture fractions (95% gross CO2 capture & 100% added CO2 capture), with the inclusion or not of intercooling serving as a third variable. For the first time, we quantify the expected additional solvent degradation rate when operating at a 100% added CO2 capture fraction, facilitating an assessment of the resulting impact on process economics. It is important to note that the operational conditions proposed for 100% added CO2 capture operation would also provide a reduced energy penalty for lower CO2 capture fraction operation should the resulting solvent degradation rates be deemed economically acceptable. Likewise, if solvent degradation is more critical to a project than thermal efficiency, lean loadings sufficient to achieve high CO2 capture fractions can be achieved at lower temperature regeneration conditions. This work aims to compare the solvent degradation rates at proposed design points for the considered CO2 capture fractions that the authors consider to be valid and viable, acknowledging that such design points are project-specific and do not represent an absolute economic optimum, as no such point can exist except for specific project conditions. |
6627d1f9418a5379b07ed59f | 3 | This study serves as a first step towards quantifying the effect of achieving 100% added CO2 capture in post-combustion CO2 capture plants using an MEA solvent solution. However, limitations of this study remain; the degradation framework provides only the instantaneous predicted MEA consumption rate of the system at a point in time. As such, it does not consider the effect of cumulative production of degradation compounds within the solvent as the operation continues over an extended period and their concentrations balance with removals by reclaiming; degradation compounds within the solvent may catalyse MEA degradation and thus accelerate the reaction. Additionally, although thermal and oxidative degradation mechanisms are considered in the framework, they are considered independent, and no interactions between the respective degradation compounds are accounted for. Finally, this study does not consider the catalytic effect of corrosion compounds on solvent degradation due to the complexity of the reaction mechanisms and the limited experimental data; these will also rise until balanced by removals in reclaiming. Considering the limitations highlighted above, the results presented in this manuscript should be considered predictive only for a perfectly clean solvent. Over an extended period of operation, actual MEA degradation rates are expected to diverge from those predicted by the framework, likely trending towards increasing degradation, unless contaminants within the solvent are maintained at a very low level through a high rate of solvent reclaiming. Additionally, the cases presented here are not intended to represent an optimum for CO2 capture fraction, thermodynamic performance or solvent degradation but merely to demonstrate the effect process parameters can have on each of the above. Case-by-case optimisation will be required on a project basis. However, the results presented in this work can serve to advise designers on methods of reducing or controlling solvent degradation rates. |
6627d1f9418a5379b07ed59f | 4 | Process modelling for CO2 capture The process modelling of the CO2 capture plant is conducted using an open-source MEA model funded by the US Department of Energy and developed by the Carbon Capture Simulation for Industry Impact (CCSI) in ASPEN PLUS . This model is validated against pilot-scale data from the US National Carbon Capture Centre (NCCC) . The reader is referred to Mullen et al. for a detailed description of the process modelling. However, the process does not notably differ from that of a traditional amine CO2 capture plant. Three distinct CO2 capture applications covering a range of CO2 flue gas concentrations have been considered for this work. A GE H-Class 1 X 1 combined cycle gas turbine (GE 9HA.01) with a rated thermal efficiency of 63.5% (LHV) serving a CCGT application, A 500 t/day of municipal solid waste (MSW) moving grate plant serving as the energy from waste (EfW) application and a 1000 MWhth (HHV) steam methane reformer (SMR) for hydrogen production as the final case. Two CO2 capture fractions were considered for each case, 95% (gross) and 100% (added), and two lean loadings of 0.1 and 0.2 mol/mol. Intercooling was included since it was found to be effective in counteracting oxidative degradation even when not required to avoid absorber 'pinching'. An additional CCGT case was considered where 95% CO2 capture was achieved at low lean loading and increased absorber packing to illustrate the energy-saving potential of these design modifications irrespective of CO2 capture fractions. This leads to a total of 11 cases assessed in this work (see Table ). A 35% wt. MEA solution was used in all cases. Flue gas compositions and flow rates were extracted from previously completed works by Mullen et al. and Su et al. . For each of the cases described in Table , the stripper pressure is modified to ensure that the inflection point described in Michailos and Gibbins is not passed. This leads to variable desorber operational pressures and, by extension, solvent regeneration temperature. Plated heat exchangers were assumed for all heat exchangers within the system, with holdup volume and residence time calculated using Eq 2. |
6627d1f9418a5379b07ed59f | 5 | Where π Μ is the lean solvent volumetric flow rate, LMTD is the log mean temperature difference, and k is the thermal conductivity. Surface compactness is assumed to be 150m 2 /m 3 as per Zohuri , while thermal conductivity values of 3894w/m 2 .K for the reboiler and 1932w/m 2 .K for the cross heat exchanger were taken from Woods . Log mean temperature difference (LMTD) was maintained at 6 o C for the reboiler and a minimum approach temperature of 5 o C was applied for the cross HX, leading to an LMTD of circa 7 -8.5 o C in all cases. Should high residence times in these pieces of equipment be found to increase degradation excessively, this can be mitigated by increasing the LMTD at the cost of increased irreversibility in the system, however this may results in adverse effects due to higher metal skin temperatures as only bulk liquid temperatures were considered in this analysis. Absorber and desorber sump levels were taken at 1.1 and 5m, respectively, as per Elliot et al. . A flooding limit of 80% of the flooding value was imposed on all columns, and the total solvent inventory was assumed to be 150% of the summation of all equipment volumes and packing holdup. A complete list of model assumptions and equipment residence times is available in Appendix A. |
6627d1f9418a5379b07ed59f | 6 | The kinetic degradation models for MEA used in this work have been adapted from previously developed oxidative and thermal degradation models described in Braakhuis et al. & Braakhuis and Knuutila . The kinetic rate constants in both models are defined using the adjusted form of the Arrhenius equation shown in Eq. 3. The equations use a reference temperature and reaction rate coefficient at this temperature, simplifying the parameter fitting and optimisation. |
6627d1f9418a5379b07ed59f | 7 | The thermal degradation model for MEA describes the consumption of the solvent and the formation of intermediates and degradation products. The model is developed for 30 wt% MEA and is valid at loadings between 0.1 -0.5 mol CO2/mol MEA and temperatures up to 160Β°C. This model has been extrapolated to apply to a 35 wt% solution, as similar degradation rates are expected, as reported by HΓΈisaeter et al. . Although no experimental data was available below 100 Β°C, the predicted reaction rates are insignificant at these temperatures, and the model can be extrapolated . The modelled degradation reactions, reaction rate equations, and fitted parameters are given in Table . The free concentration of CO2 in the solvent is used as a surrogate for the concentration of the intermediate 2-oxazolidinone (OZD), a key reactant in carbamate polymerisation. |
6627d1f9418a5379b07ed59f | 8 | There was insufficient experimental data to effectively assess the formation of 1,3-Bis(2-hydroxyethyl)urea (BHEU) at various temperatures, and it was impossible to determine this reaction's activation energy accurately. The reaction mechanisms for forming BHEU are expected to resemble those of HEEDA (reaction no. 1) closely. Therefore, Braakhuis et al. consider it reasonable to assume that the activation energies for both reactions are similar. As such, the same activation energy is applied to model the formation of BHEU. |
6627d1f9418a5379b07ed59f | 9 | The kinetic model for oxidative degradation of MEA has been adapted from the work by Braakhuis et al. . The model is developed using experimental data produced by Vevelstad et al. , who used an agitated bubble reactor at temperatures between 55 Β°C and 75 Β°C and gas phase oxygen concentrations between 6 vol-% and 98 vol-% . Liquid phase mass transfer resistances for O2 were expected to be present in the agitated bubble reactor, especially at higher temperatures. This would reduce the availability of dissolved O2 and limit the overall degradation rate. Therefore, mass transfer resistances have been approximated and accounted for during the development of the degradation model . |
6627d1f9418a5379b07ed59f | 10 | The oxygen solubility model by Buvik et al. is used in this work. This novel solubility model considers the effects of temperature and concentration of ionic species in the solvent and thus accounts for reduced solubilities in CO2-loaded solvents. Dissolved metals, such as iron and copper, have been shown to catalyse the degradation reaction significantly . However, dissolved metals were not present during the degradation experiments used in the model development . |
6627d1f9418a5379b07ed59f | 11 | The outputs of the process modelling are described in section 3.1 are detailed in Table . As previously described by Mullen et al. and Su et al. , when lean loading is reduced accordingly as CO2 capture fraction increases and regeneration conditions are optimised, minimal differences in the specific energy requirements are observed, and in some cases, a reduction is seen. This is most pronounced in the CCGT case as the driving force of absorption at the top of the absorber is still moderately low, even for a 95% CO2 capture rate at a lean loading of 0.2 mol/mol. A reduced SRD is predicted in all 95% CO2 capture cases if lean loading is reduced below 0.2 mol/mol, as per Mullen et al. and Su et al. However, this research aims not to optimise thermal efficiency but to compare solvent degradation rates at typical operational conditions with those considered beneficial when achieving 100% added CO2 capture. Nonetheless, an additional case was included where a 95% CO2 capture rate was achieved for a CCGT flue gas at 0.1 mol/mol lean loading and 24m of absorber packing. A 15.3% reduction in SRD was observed, representing a substantial energy saving at the expense of a 23.7% increase in solvent degradation rates, which is discussed in section 3.2, and an undetermined effect on plant CAPEX and CO2 compressor power. This demonstrates that the energy benefits of low lean loading operation aren't specific to high CO2 capture fractions and must be a project-by-project cost optimisation decision. Indeed, if solvent degradation is more critical to a project than thermal efficiency, lean loadings sufficient to achieve high CO2 capture fractions can be achieved at lower pressure/temperature regeneration conditions. |
6627d1f9418a5379b07ed59f | 12 | Reaction rate [molβ
m The inclusion or otherwise of an intercooler had minimal effect on CO2 capture in the CCGT cases. Due to the low concentration of CO2 in the flue gas, the quantity of heat released in the exothermic reaction is not sufficient to increase the bulk gas temperature to the degree that the driving force of absorption is reduced sufficiently to necessitate intercooling. This is not the case for the EfW and SMR 100% added CO2 capture cases. The reduced solvent flow rate (due to the reduced lean loading) coupled with the increase in CO2 concentration in the flue gases leads to absorber pinching, where low/no mass transfer occurs. As a result, 100% added CO2 capture is not achievable for these specific design cases without intercooling. |
6627d1f9418a5379b07ed59f | 13 | Intercooling appears to have a minimal or negative effect on thermal efficiency for the 95% CO2 capture cases as the driving force limiting higher temperatures are pushed to the top of the absorber; further optimisation of return temperatures, intercooler location or additional packing beds may mitigate this. However, this is beyond the scope of this work. It should also be noted that, for simplicity, in the CCGT cases with 24m meters of packing, the intercooler location was maintained at the centre of the absorber. In reality, this is unlikely as it does not relate to an interbed location where the installation of intercooling would be most simple; as this case represents a 3 bed x 8m packing absorber, an intercooler would be situated between one or both of the liquid collection/redistribution sections between each bed. Additionally, in situ absorber intercooling was assumed within the degradation framework with no residence time or hold-up volume ascribed to the intercoolers; this may result in an underestimation of the oxidative degradation rates in the intercooler cases. However, this effect is expected to be minor if residence times and intercooler return temperatures are low. |
6627d1f9418a5379b07ed59f | 14 | Figure to Figure show the profiles of O2 concentration and CO2 loading of the solvent along the absorber length for each case, along with bulk temperature and the predicted oxidative MEA degradation rate. The results presented are intersection averages of each modelled absorber section (1 to 100). The high O2 concentration seen at the top of the absorber occurs due to the rapid dissolution of O2 into the liquid phase over the final section of the absorber. A lower lean loading in itself does not appear to largely affect oxidative degradation rates. This is due to the order of the degradation reaction with respect to O2 being low at 0.47, so an increase in the concentration of dissolved O2 will have a progressively smaller impact on the degradation rate and the subtle effect of increased solubility and unloaded MEA concentration at lower lean loadings appears eclipsed by the much more dominant effect temperature has on the reaction rate. More critically, and an entirely novel observation, is that, by the same virtue, total MEA degradation rates within the absorber are approximately comparable over the range of flue gas O2 concentration studied. While increasing O2 concentration will increase the concentration of O2 in the solvent, the resulting increase in MEA degradation is muted by the low reaction order. However, O2 leaner flue gases have increased concentrations of CO2 in post-combustion applications; in the absence of intercooling, the high CO2 concentration will tend to lead to higher temperatures in the absorber as more energy is released by the exothermic reaction between MEA and CO2 per unit of flue gas processed. As the oxidative degradation reaction is strongly influenced by temperature, the increase in bulk temperature throughout the absorber present in low O2/high CO2 concentration flue gases appears to, at least partially, offset the effect of decreased dissolved O2 concentrations; this is clearly illustrated in Figure . This is most prominently observed in the cases with intercooling included, with a 30-80% decrease in oxidative degradation predicted. This indicates that regardless of the CO2 capture rate or loading, intercooling can be an effective measure for reducing solvent degradation rates. This must, however, be considered in conjunction with the increased CAPEX and operational requirements that result from including intercooling. Notably, a 43% increase in oxidative degradation in the absorber packing is seen when comparing the 100% added capture and 95% gross capture CCGT cases at 0.1 mol/mol lean loading without intercooling in both cases. This is the result of increased temperatures in the absorber at the higher CO2 capture fractions. Comparable degradation rates can be seen between the same 95% case and the 100% added capture case (with intercooling), a novel conclusion which indicates that intercooling may be a particularly potent mechanism for reducing solvent degradation in CCGTs at high CO2 capture fractions despite giving a minor increase in SRD in the cases presented in Table (likely due to decreased reaction rates at lower solvent temperatures). Likewise, the intercooler arrangment presented here does not represent an optimum; further benefits may be observed by revising return temperatures or the inclusion of an additional intercooler, which may have benefits outwith reducing oxidative degradation as this optimisation may allow a marginally higher lean loading to be utilised while maintaining the same CO2 capture performance, reducing thermal degradation. Figure and Table detail the predicted total and location-specific MEA degradation rates in the CO2 capture process. As MEA reacts rapidly with oxygen, the majority of the oxidative degradation occurs within the absorber internals, with the absorber sump and downstream equipment contributing minimally as the remaining dissolved O2 in the solvent is consumed. The effect is more prominent in O2-rich flue gases as a higher concentration of dissolved O2 is carried over into the absorber sump. For the 100% added CO2 capture cases, i.e. lean loadings of 0.1 mol/mol, thermal degradation increases by a factor of 3 to 4 due to the increased temperatures experienced by the solvent in the regeneration system. The increase in reaction rate due to increased temperatures outstrips the decrease from the reduced carbamate concentration in leaner solutions, resulting in the net increase in degradation seen, albeit dampened to some degree. This indicates that a designer should utilise the lowest regeneration pressure that will achieve the required trade-offs between solvent degradation, energy efficiency and CAPEX. This is clearly shown in Figure which details the distribution of MEA thermal degradation at key plant locations. A grouping of degradation profiles by lean loading is immediately apparent, with minimal difference seen between the three processes analysed. The assumed residence times for each piece of equipment are available in Appendix A. Figure Illustrates the consumption of O2 dissolved within the solvent once direct contact with the flue gas ceases. The degradation framework assumes that once the solvent exits the absorber packing and enters the sump (modelled as a continuously stirred tank reactor), it is no longer in contact with O2 from the flue gas. From this point onward, degradation occurs indirectly through previously dissolved O2. For clarity, only the CCGT cases are shown; however, the EfW and SMR cases follow similar trends and can be seen in Appendix B. |
6627d1f9418a5379b07ed59f | 15 | In reality, it is anticipated that the solvent in the absorber sump will still have some exposure to the flue gas, either through contact at the interface or due to the introduction of entrained bubbles resulting from the downcoming solvent. To assess the impact of this kind of exposure on the degradation rate, we predicted the degradation rates under a worst-case scenario by assuming that the solvent in the sump is fully saturated with O2 throughout the residence time, see Figure . Therefore, the solvent leaving the sump is also fully saturated with O2. In this case, the total MEA degradation rate is increased from the baseline 256.9 g/tCO2 to 291.3g/tCO2, a 13.4% increase. However, it is unlikely that the solvent will be entirely saturated with O2 in the absorber sump, as previous oxidative degradation experiments conducted in agitated bubble reactors found that mass transfer limitations for O2 are present . Nevertheless, it is essential to consider this effect, especially when operating with long sump residence times or flue gases rich in O2, resulting in high dissolved O2 concentrations. Process modifications that mitigate prolonged contact between the solvent and the flue gas may be beneficial, as also discussed in . Likewise, process modifications that remove dissolved O2 from the solvent solution, either prior to or post sump, i.e. flashing or sparging, should reduce indirect oxidative degradation proportional to its removal efficiency. |
6627d1f9418a5379b07ed59f | 16 | Minimal MEA consumption occurs in the cold-rich solvent pipeline to the heat exchanger (both pipework and heat exchangers are modelled as plug flow reactors) due to the low residence time and temperature. Within the heat exchanger, dissolved O2 consumption increases rapidly due to the increased reaction rate stemming from the increased temperatures. By the time the solvent reaches the stripper column, O2 is predicted to have been entirely consumed in all cases, as also seen in previous work . Minimal O2 in the export CO2 stream is a crucial CO2 pipeline specification due to downstream pipeline integrity concerns. As a result, deoxygenation systems are often included in the design downstream of the stripper at considerable capital expenditure. That being the case, confirmation of total O2 consumption in the solvent prior to the stripper through pilot or operational studies may allow the omission or reduction in the capacity of the deoxygenation system, leading to a reduction in capital and operational expenditure for systems using aqueous MEA as solvent. This may not be the case for an alternativesolvents with greater resistance to oxidative degradation. |
6627d1f9418a5379b07ed59f | 17 | A design variable available to designers is the hold-up volume of solvent in column sumps. Having a high volume of hold-ups can buffer against operational upsets but comes with the cost of increased solvent exposure to degradation conditions as residence times increase. To investigate the magnitude of this effect, a sensitivity study was conducted wherein the residence time in both the absorber and stripper sumps was varied independently; the results are presented in Figure . |
6627d1f9418a5379b07ed59f | 18 | When considering the absorber sump, the sensitivity of the stored rich solvent is highly dependent on the assumptions made regarding the degree of O2 mass transfer into the rich solvent. Where no mass transfer of O2 occurs, analogous to an independent storage system with minimal contact with atmospheric air or gas capping, no increase in oxidative degradation occurs as the degradation reaction quickly reaches equilibrium as the dissolved O2 in the solvent is consumed. However, if the stored solvent remains saturated with O2, the increase in degradation is linear with residence time. As previously mentioned, the likely effect is somewhere between these two extremes; however, the reduction of absorber sump residence times with independent rich solvent storage systems may provide a benefit if longer-term storage is required. |
6627d1f9418a5379b07ed59f | 19 | For the stripper sump, the degree of expected thermal degradation experienced by the solvent per cycle increases linearly with residence time. This is particularly critical at higher temperatures as the slope of the additional degradation is increased due to the less favourable conditions. A buffer store of lean and rich solvent can aid in operational flexibility by enabling the rapid response to changing absorber conditions without the delay of producing additional lean solvent. However, the results presented here indicate that utilising the stripper sump to provide this storage capacity will lead to excessive thermal degradation. Storage of any lean solvent in excess of the minimum level required by the regeneration system in a separate storage tank after the cross-heat exchanger (i.e. ambient storage) could mitigate this by minimising the holdup time in the stripper sump. Table details the absolute and relative change in MEA degradation rates predicted to occur when transitioning from 95% gross CO2 capture to 100% added CO2 capture for the design points presented in this work. The increase ranges between 21% and 112%, primarily due to the increased rate of thermal degradation in the regeneration section. Solvent replacement OPEX is a function of solvent consumption rate and solvent cost and, therefore, Table can indicate OPEX incurred as a result of replacing this degraded solvent. To provide economic context, using a representative cost for an MEA solvent of 0.5 -5Β£/kg MEA results in an increased OPEX of between 0.02 -0.38Β£/tCO2. However, the cost indication provided here does not include any additional costs associated with the increased intensity of emission mitigation or solvent management (i.e. increased rates of thermal reclaiming) that are likely if solvent degradation increases, or any increase in volatile solvent losses due to the lower lean loading or higher absorber exit temperatures -these considerations are beyond the scope of this work. |
6627d1f9418a5379b07ed59f | 20 | This article presents, for the first time, an assessment of monoethanolamine (MEA) degradation rates when capturing 100% of the added CO2 produced as part of three distinct energy production processes fitted with a post-combustion CO2 capture (PCC) process utilising a 35% wt. MEA solvent. The three processes considered, a combined cycle gas turbine (CCGT), energy from the waste facility (EfW) and a steam methane reformer (SMR), cover the expected range of O2 (1.2 -11.0 % vol) and CO2 concentrations (4.7 -19.5 % vol) within industrial flue gases likely to be relevant in PCC applications. Thus, the MEA degradation rates presented can form a likely range for PCC systems using an MEA solvent within the bounds of the study limitations highlighted throughout. Flue gas conditions are extracted from the previously published works of Mullen et al. and Su et al. and form the input to the process model of the CO2 capture plant, which uses an open-source model developed by the Carbon Capture Simulation for Industry Impact (CCSI) in ASPEN PLUS . For each process, two distinct CO2 capture fractions are considered: 95% gross CO2 capture, which forms the basis for comparison and a CO2 capture fraction resulting in the capture of 100% of the added CO2 produced by the process (99.2, 99.6 & 99.7% for the CCGT, EfW and SMR respectively). The process modifications used to achieve 100% added CO2 capture have previously been described by Mullen et al. and involve the reduction of the solvent lean loading from the typical value of circa 0.2 mol/mol to circa 0.1 mol/mol and, in the case of the CCGT, 4m of additional packing within the absorber column. Mullen et al. have shown that the additional specific thermodynamic penalty of operating at 100% added CO2 capture is minimal if these process modifications are implemented and conclude that to operate efficiently at the reduced lean solvent loading, an increase in stripper operational pressure is required to suppress the production of surplus steam within the regeneration system and minimise energy losses. This increase in operating pressure necessitates an increase in regeneration temperature within the reboiler, a process modification that the authors suggest may increase the thermal degradation of the solvent. Concurrently, a reduced average loading in the absorber may increase the solubility of O2 overall and, coupled with increased residence time due to the increased packing height, may lead to increased oxidative degradation. This study applies thermal and oxidative degradation models developed by Braakhuis et al. to investigate how these process modifications affect the predicted MEA degradation rates compared to operational conditions, which achieve a gross 95% CO2 capture fraction. Additionally, we investigate the effect absorber intercooling, sump O2 dissolution and residence times rates have on total degradation. Initially, we show that for an MEA solvent, oxidative degradation primarily occurs within the absorber packing and that, while the solubility of O2 into the solvent and the partial pressure of O2 in the flue gas will affect total oxidative degradation rates, the effect is dampened by the low order of reaction relative to O2 concentration. In the absence of intercooling, higher CO2 concentrations in the flue gas will tend to lead to higher temperatures in the absorber, as more energy is released by the exothermic reaction between MEA and CO2 per unit of flue gas processed. As the oxidative degradation reaction is strongly influenced by temperature, the increase in flue gas temperature present in low O2/high CO2 concentration flue gases appears to, at least partially, offset the effect of decreased dissolved O2 concentrations. We find that, for the conditions analysed in this work and for equivalent intercooling regimes, oxidative degradation rates within the absorber packing are approximately equal over the three processes analysed, as decreased dissolved O2 concentrations are offset by increased temperatures. The inclusion of intercooling consistently reduces total oxidative degradation rates as the bulk temperature within the absorber is reduced, and the reaction rate is proportionately reduced. This effect is predicted to result in a 30-70% reduction in oxidative degradation within the absorber packing. This indicates that, regardless of CO2 capture fraction or loading, intercooling can be an effective measure for reducing solvent degradation rates. This must, however, be considered in conjunction with the increased CAPEX and operational complexity of including intercooling plus possibly a slight reduction in rich loading. Notably, a 43% increase in oxidative degradation in the absorber packing is seen when comparing the 100% added capture and 95% gross capture CCGT cases at 0.1 mol/mol lean loading (both without intercooling). This is the result of a compounded effect of increased temperatures in the absorber at the higher CO2 capture fraction and the 20m to 24m increase in absorber packing height, increasing residence times. But comparable degradation rates can be seen between the same 95% case and the 100% added capture case when intercooling is included. This novel conclusion indicates that intercooling may be a particularly potent mechanism for reducing solvent degradation in CCGTs at high CO2 capture fractions. |
6627d1f9418a5379b07ed59f | 21 | The degradation framework assumes that once the solvent exits the absorber packing and enters the sump it is no longer in contact with O2 from the flue gas. The authors consider this assumption optimistic as, in reality, the solvent in the absorber sump will still have some exposure to the flue gas or downcoming solvent, replacing the consumed O2 to some degree. To investigate the magnitude of this effect, a sensitivity analysis shows that when a continually O2-saturated sump is assumed, the magnitude of total MEA degradation within the system for the CCGT case with 100% added CO2 capture increases by 13.4%, placing an upper bound on the magnitude of this effect as it expected that dissolved O2 in the sump is unlikely to be entirely replaced by the stated mechanisms. Likewise, process modifications that remove dissolved O2 from the solvent solution, either prior to or post sump, i.e. flashing or sparging, should reduce indirect oxidative degradation proportional to its removal efficiency. Due to the increased temperatures seen in the cross-heat exchanger, by the time the solvent reaches the stripper column, the dissolved O2 is predicted to have been entirely consumed in all cases. Reduced O2 concentration in the export CO2 stream is a crucial CO2 pipeline specification due to downstream pipeline integrity concerns. As a result, deoxygenation systems are often included in the design downstream of the stripper at considerable capital expenditure. That being the case, should this be confirmed through pilot or operational studies, it may allow the omission or reduction in the capacity of the deoxygenation system, leading to a reduction in capital and operational expenditure. This may not be the case for alternative, less reactive, solvents. When considering thermal degradation, a pronounced effect is evident. Despite the decreased carbamate concentration in the leaner solvent reducing the rate of thermal degradation at a given temperature, the increased regeneration temperature required to achieve a lower lean loading outstrips this limiting effect, resulting in a 3 to 4-fold increase in thermal degradation when regeneration pressure (and temperature as a result) is increased to efficiently produce a solvent with a lean loading of 0.1mol/mol vs 0.2mol/mol. This appears to be an unavoidable consequence of operating at higher regeneration pressures and indicates that a designer should utilise the lowest regeneration pressure, and hence temperature, that will achieve the required trade-offs between solvent degradation, energy efficiency and CAPEX while being aware of the increased degradation rate and adjusting the solvent management regime accordingly. This work highlights stripper sump residence time as a key design variable for minimising thermal degradation. A buffer store of lean solvent can aid in operational flexibility by enabling the rapid response to changing absorber conditions without the delay of producing additional lean solvent. However, utilising the stripper sump to provide this storage capacity will lead to excessive thermal degradation. Storage of cold lean solvent after the cross-heat exchanger could mitigate this. Some key limitations apply to this study. The degradation framework used in this work does not consider the effect of longterm degradation compound accumulation and removal within the circulating solvent, interactions between the thermal and oxidative degradation compounds or the catalytic effect of corrosion compounds on solvent degradation. As such, the results presented in this manuscript should be considered predictive only for a perfectly clean solvent. Over an extended period of operation, actual MEA consumption rates are expected to diverge from those predicted by the framework, particularly as dissolved metals catalyse oxidative degradation, likely trending towards increasing consumption unless contaminants within the solvent are maintained at a low level via an effective solvent reclamation system. Also, we do not consider the effect any additional solvent degradation will have on atmospheric emissions or the associated control techniques, solvent management regimes or waste production. Additionally, the operational conditions proposed for 100% added CO2 capture operation would also provide a reduced energy penalty for lower CO2 capture fraction operation should the resulting solvent degradation rates be deemed economically acceptable. Likewise, if solvent degradation is more critical to a project than thermal efficiency, lean loadings sufficient to achieve high CO2 capture fractions can be achieved at lower temperature regeneration conditions. Finally, the intercooler arrangements presented here are not considered optimum, and it is likely that further benefits, both thermodynamic and degradation-related, could be achieved with a dedicated optimisation effort. This work aims to compare the solvent degradation rates at proposed design points for the considered CO2 capture fractions that the authors consider to be valid and viable, acknowledging that such design points are project-specific and do not represent an absolute economic optimum, as no such point can exist. Even so, this study serves as a first step towards quantifying the effect increasing CO2 capture fractions in post-combustion CO2 capture plants will have on solvent degradation. We identify key areas for further study and validation in test facilities as well as design considerations that may help mitigate solvent degradation. The learnings presented here can serve to advise project designs and researchers alike when considering operating at 100% added CO2 capture, a development the authors believe to be critical if post-combustion CO2 capture is to be compatible with a Net Zero world. |
646c8f15ccabde9f6e390fe8 | 0 | Nitric oxide (NO) is an important endogenously produced signaling molecule . This gaseous messenger is critical for the regulation of vascular and muscle tone, neurotransmission, wound healing, platelet aggregation and many other physiological processes. Furthermore, nitric oxide plays a significant role in tumor biology participating in cell death, angiogenesis, and antitumoral immune response . Dysregulation of NO production leads to various pathological processes. For instance, impaired NO production causes diabetic vascular complications . |
646c8f15ccabde9f6e390fe8 | 1 | Therefore, precise control of NO concentration opens promising possibilities for target therapy including anticancer therapy. For controlled delivery of nitric oxide, extensive efforts are being made to develop novel NO-releasing materials such as liposomes, nanoparticles, macromolecules. Short lifetime (~5s) in living tissues and limited diffusion range of nitric oxide imply the use of methodologies which rely on the triggering of NO release using external stimulus, for example, light radiation , X-ray radiation , or ultrasound . Visible and NIR light represents a smart fine-tunable and non-invasive tool for practical usage due to deeper penetration in biological tissues. Therefore, development of such photoactivatable NO-donors is highly desirable. |
646c8f15ccabde9f6e390fe8 | 2 | In recent years, several general approaches toward such molecules were established. Briefly, one of the common methodologies is based on photolysis of metal nitrosyl complexes . The main restrictions of this approach are potential difficulties of structure modifications and possible metal ions toxicity. Metal-free photoactivatable NO-donors often utilize homolysis of N-NO fragment or nitro-nitrite photorearrangement in sterically hindered nitroarenes followed by homolysis of O-NO bond. Typically, visible light absorbance of this molecules is reached by conjugation of NO-releasing moiety with chromophores such as rosamine and rhodamine ,. Si-rhodamine and other. The antenna (chromophore) with high fluorescence quantum yield can be used for the optical calibration of the NO release dosage . BODIPY difluoro-4-bora-3a,4a-diaza-S-indacene) chromophore could be also useful as antenna due to unique photochemical properties, such as narrow absorption bands with tunable wavelength, which provides successful usage of these dyes in various scientific areas, from optoelectronics to life sciences (see and references therein). First BODIPY-based NO photodonor (NOBL-1) utilizing N-NO bond homolysis has been reported by Nakagawa group . Extended work on BODIPY-based NO-releasing molecules was made by Sortino group. Cupferron conjugated with BODIPY-based photoremovable group was reported to underwent rapid deprotection under green light irradiation yielding free cupferron, which fast hydrolysis led to NO generation. |
646c8f15ccabde9f6e390fe8 | 3 | Another donor is based on N-nitroso-4-nitro-3-(trifluoromethyl)aniline N-substituted with BODIPY-containing fragment . Both compounds demonstrate relatively high quantum yield of NO generation (Ξ¦NO) and excellent quantum efficiency (ΡΦNO). Iodinated BODIPY molecules demonstrate the ability of singlet oxygen ( 1 O2) generation under irradiation with high quantum yields (Ξ¦Ξ) . Simultaneous generation of NO and 1 O2 may lead to promising synergetic effect on photodynamic therapy efficiency cancer and bacterial infections treatment. Recently, several molecular hybrids combining NO-releasing moiety and iodinated BODIPY has been reported by Sortino group . |
646c8f15ccabde9f6e390fe8 | 4 | In the present work, we search for simply synthesizable small-molecule NO photodonors with intense absorption in visible region. Several BODIPY-based NO photodonors have been already reported, as mentioned above. We have previously studied several hindered nitrobenzenes, linked to the BODIPY core in meso-position , but the NO release was undetectable. Mesomethylene BODIPYs have especially remarkable properties and have been used in various applications, including photolabile protecting groups . We hypothesized that this scaffold could be superior as light-harvesting moiety for N-Nitroso NO photodonors. |
646c8f15ccabde9f6e390fe8 | 5 | Herein, we present BODIPY-NODsa family of simply synthesizable NO photodonors based on meso-methyl-BODIPY core. We report the efficiency of NO photorelease, photoinduced 1 O2 generation and fluorescence quantum yields. The proportion of NO and 1 O2 can be tuned by introduction of substituents into the chromophore core, from the sole photorelease of NO with barely detectable 1 O2 to the opposite (no NO / high 1 O2). These compounds and their future derivatives are promising for the development of light-controllable smart therapies, including the photodynamic therapy of cancer. |
646c8f15ccabde9f6e390fe8 | 6 | To measure in EtOH, we used 1,3-diphenylisobenzofuran (DPBF) as a singlet oxygen scavenger as described in with methylene blue as a standard (Ξ¦β=0.50 ). The initial absorbance of DPBF (at 410 nm) was matched to ~0.84, whereas the absorbance of dyes was matched to ~0.03 at 500 nm. In both experiments, single 500 nm LED was used. The results were corrected for the non-zero width of excitation spectrum. |
646c8f15ccabde9f6e390fe8 | 7 | Quantum chemical calculations of the adiabatic potential energy surface (PES) profiles for the studied molecules were carried out in the DFT approach using CAM-B3LYP functional, implemented in the GAMESS program package. As shown in , energy levels and related parameters can be estimated more accurately with M06-2X functional, so we tested all the obtained parameters using this functional. PES calculations included the localization of stationary structures and the determination of their type based on the analysis of normal vibrations. The 6-31 + G* basis set was used for BODIPY-NODs which do not contain iodine atoms, whereas SPK-DZP was used for others. The influence of "environment" was considered by the polarizable continuum model (PCM). Excited state calculations were carried out using TD-DFT method. |
646c8f15ccabde9f6e390fe8 | 8 | The fasting blood samples were obtained from the cubital veins of healthy volunteer with informed consent. The sample were collected in the vacuum tube containing sodium citrate as anticoagulant (9βΆ1). After collection, the sample was kept at room temperature for an hour to obtain a layer of plasma containing platelets. In the next step, the sample was labeled with fluorescent calcium probe Fluo-4-AM (Thermo Fisher Scientific, USA). The stock solution (1 mM) of Fluo-4-AM was diluted 62.5 times in phosphate buffered saline (PBS) and mixed 1:1 with blood plasma. After incubation for 30 minutes in the dark, the sample was 10 times diluted in PBS with or without compound 2a or 2b, placed in a well of 96-well plate and allowed to rest for another 30 minutes before experiments. Calcium signaling in individual platelets was recorded using CarlZeiss AxioVert.A1 fluorescence microscope with 20x objective. |
646c8f15ccabde9f6e390fe8 | 9 | 3.1. Synthesis of NO photodonors Different mechanisms of NO release were reported, including intramolecular charge transfer (ICT) , photoinduced electron transfer (PET) , or homolythic fission with the formation of aminium radicals . BODIPY-based N-NO photodonors reported previously contain extended linker connecting BODIPY and NO-releasing moiety. On the other hand, N-NO group in several cases was directly attached to a chromophore . We decided to use short methylene linkage between BODIPY and N-NO. Such compounds are easily available starting from meso-CH2Cl-BODIPY 1a (Scheme 1). Substitution of Cl with I followed with reaction with primary amine (i-propylamine or aniline, respectively) gives amines 2a,b, whose nitrosation leads to N-nitroso donors BODIPY-NOD-1 and BODIPY-NOD-2. |
646c8f15ccabde9f6e390fe8 | 10 | Interesting feature of some BODIPY NO-photodonors is the ability to generate 1 O2 under light, which could be enhanced by introduction of iodine atoms in the BODIPY core . Simultaneous generation of NO and 1 O2 demonstrates synergetic effect and results in increased photocytotoxicity. For this purpose, we synthesized the iodinated derivative BODIPY-NOD-3. |
646c8f15ccabde9f6e390fe8 | 11 | Analogously, we prepared BODIPY-NOD-4 and BODIPY-NOD-5 to study the effect of boron methylation (Scheme 1C). Compounds 2b and 3 reacted with freshly prepared MeMgI, giving products 4 and 5, respectively. After that, obtained compounds were nitrosated, using sodium nitrite and CH2Cl2/THF/AcOH mixture, to get final N-nitroso compounds BODIPY-NOD-4 and BODIPY-NOD-5. When working with iodinated and/or boron methylated compounds, we had to use milder conditions, due to the tendency of starting and target compounds to decompose under heating. |
646c8f15ccabde9f6e390fe8 | 12 | In this section we compare the obtained molecules in terms of photophysical properties and NO generation efficiency. Figure shows the normalized absorption spectra in ethanol. All compounds have high molar extinction coefficient at ~510-520 nm (ΠΡΠΈΠ±ΠΊΠ°! ΠΡΡΠΎΡΠ½ΠΈΠΊ ΡΡΡΠ»ΠΊΠΈ Π½Π΅ Π½Π°ΠΉΠ΄Π΅Π½.). A slight hypochromic shift is observed upon boron methylation. The fastest and the most efficient NO photorelease is observed for BODIPY-NOD-2 (~20% total for 2 min), whereas BODIPY-NOD-4 shows the same speed but lower total yield (~4% total for 2 min). Compound 2b (the photoproduct of BODIPY-NOD-2) was photostable in EtOH, and the fluorescence of DAR-2 probe did not change upon its illumination. |
646c8f15ccabde9f6e390fe8 | 13 | It should be noted that NO quantification using DAR-2 may lead to inaccurate results if the absorption spectrum of the photodonor changes significantly at the probe excitation wavelength (540 nm) during photolysis. Another possible error source is the intrinsic fluorescence of the molecules under study, which could also change during photolysis. An alternative method is needed to confirm the NO photorelease. For this purpose and also to account for NO that is not trapped by DAR-2 but undergoes reaction with oxygen, we performed experiments with Griess assay as described in Supplementary materials. The Griess assay allows to measure the concentration of nitrites. The amount of nitrites after 10 minutes of photolysis (12 Β΅M) was ~80% of the initial concentration of BODIPY-NOD-2 (15 Β΅M), which is consistent with the total conversion to 2b visible by the change of absorption spectrum. |
646c8f15ccabde9f6e390fe8 | 14 | Surprisingly, the absorption spectrum of the photoproduct of BODIPY-NOD-1 does not coincide with its counterpart 2a: it has an additional red-shifted peak at about 550 nm (Figure ). However, the formation of 2a during photolysis is visible with HPLC, whereas the unknown photoproduct absorbing at 500 and 550 nm has much lower retention time (Figure ). |
646c8f15ccabde9f6e390fe8 | 15 | Measurements of NO photorelease for BODIPY-NOD-1 are obstructed because the absorption spectrum of this photoproduct overlaps with that of DAR-2 probe. It results in the background fluorescence increase during photolysis; however, the fluorescence of DAR-2 probe did not significantly exceed the background level, therefore we conclude that BODIPY-NOD-1 has low efficiency of NO photorelease. |
646c8f15ccabde9f6e390fe8 | 16 | The absence of fluorescence turn-on behavior may lead to the conclusion that PET does not occur in BODIPY-NODs. To additionally confirm this fact, we measured the fluorescence QY in a series of solvents having different polarity (Table ). A library of meso-substituted BODIPYs was studied in , and it was showed that their fluorescence, if quenched in polar solvents due to PET, turns on in non-polar solvents. In contrast, our results imply that the probability of PET is low. To analyze the NO release mechanism, we performed quantum chemical calculations for the singlet, triplet, and excited states of all compounds. The calculations were carried out in two functionals (CAMB3LYP, M06-2X) using different basis sets (6-31+G*, 6-311+G*, SPK-DZP). |
646c8f15ccabde9f6e390fe8 | 17 | For the compounds under study, there were no significant differences from the choice of calculation parameters. The obtained molecular orbitals (with computational parameters corresponding to H2O) are shown in Figure . No profound relocation of charge density from BODIPY core to the substituent is visible (which would indicate PET-like behaviour). However, some charge is transferred to the nitrogen atom, possibly weakening the N-NO bond. The absence of PET is especially surprising because NO releaser described in , based on the same dye and N-nitroso bond as well, acts via PET mechanism. According to the authors, NO release process includes PET from the fragment containing N-NO to the BODIPY core and the formation of a radical pair. |
646c8f15ccabde9f6e390fe8 | 18 | We believe that PET do occur and is the principal mechanism of NO photorelease, but is not visible in fluorescence and in calculations due to its low probability. Indeed, the estimated QY of NO photorelease, Ξ¦NO, is 5.5Γ10 -4 for BODIPY-NOD-2. This value was obtained by using 488 nm laser and measuring the absorbed power and the amount of released NO. This value of Ξ¦NO is indeed much smaller than the Ξ¦F. Similar value for Ξ¦NO (1.9Γ10 -3 ) was reported for NOBL-1 , which was successfully used for the photomanupulation of vasodilation. In contrast, fluorescence turn-on behavior was reported for photodonors having much higher Ξ¦NO, for instance, Ξ¦NO = 0.15 in . |
646c8f15ccabde9f6e390fe8 | 19 | Photoinduced singlet oxygen ( 1 O2) generation is an intrinsic property of many dyes, including BODIPYs. Simultaneous production of 1 O2 and NO is of interest for the development of hybrid photodynamic therapy . The iodinated derivatives BODIPY-NOD-3 and BODIPY-NOD-5 are promising in this respect. The normalized absorption spectra and photophysical properties of iodinated compounds are shown in the Figure . Absorption spectra are red-shifted shifted by ~30 nm for the diiodinesubstituted BODIPY compounds due to its electron-acceptor nature, in accordance with previously published data on similar compounds. Fluorescence for these compounds are weak (QYs are 0.015 and 0.003, respectively), probably due to the enhanced conversion into triplet state. Interestingly, BODIPY-NOD-3 is also capable of NO photorelease, as shown in Figure . Despite relatively low speed and total yield (cf. Figure ), it could greatly enhance the action of 1 O2 as photodynamic agent. In contrast, the release of NO is not detected for BODIPY-NOD-5. |
646c8f15ccabde9f6e390fe8 | 20 | To evaluate the efficiency of 1 O2 generation, we measured its luminescence spectrum around 1270 nm. Figure ,D shows the luminescence intensity relative to the absorbance at the excitation wavelength (500 nm). As expected, relative luminescence intensity is approximately 200-times higher for BODIPY-NOD-3 than for BODIPY-NOD-2 which does not contain heavy atoms. Surprisingly, its boron-alkylated analogue BODIPY-NOD-5 exhibits ~100-times lower relative luminescence compared to BODIPY-NOD-3. We conclude that exchange of fluorine atoms for methyl groups result in significant reduction of 1 O2 generation efficiency. |
646c8f15ccabde9f6e390fe8 | 21 | Accordingly, the luminescence for BODIPY-NOD-4 was not detected. The quantum yield of 1 O2 generation Ξ¦β in CCl4 was determined by comparison with 2I-meso-phenyl-BODIPY for which the QY was reported to be 0.81 (in toluene; compound I2-BDP in ). Results are shown in Table . We also determined Ξ¦β in EtOH by the diappearance of 1,3diphenylisobenzofuran (DPBF) absorption at 410 nm as described in using methylene blue as a standard (Ξ¦β=0.50 ). The results are shown in Table and are largely the same up to the experimental uncertainty, whereas the experimental data are presented in Supplementary materials. |
646c8f15ccabde9f6e390fe8 | 22 | To sum up, we present a family of compounds with NO-releasing ability and singlet oxygen formation. The maximal NO yield and the release speed was observed for BODIPY-NOD-2, whereas maximal 1 O2 generation was detected for BODIPY-NOD-3. Observed low efficiency of NO photorelease in the case of significant 1 O2 generation could be also explained by the reaction with oxygen with the formation of peroxynitrite . This process is an alternative to the reaction with DAR-2 probe, which reduces its apparent fluorescence. Still, these experimental results show that the introduction of heavy atoms into the BODIPY core does not enhance the photorelease of NO, indicating that the latter proceeds from the singlet state. |
646c8f15ccabde9f6e390fe8 | 23 | Blood platelets are the foundation of hemostasis and also contribute to a variety of other normal and pathological processes, including thrombosis, inflammation, and tumor development . The hemostatic function of platelets is closely related to their ability to change physical properties in response to vessel wall injury . The first step of this process is platelet activation, which comprises a series of prothrombotic events, triggered by the increase of intracellular calcium . Abnormal platelet activation is considered as a cornerstone in pathogenesis of atherosclerotic cardiovascular diseases , which are the principal cause of mortality globally. Therefore, it is highly anticipated that in-depth study of platelet activation and development of advanced methods for its assessment could contribute to further progress in cardiovascular medicine. |
646c8f15ccabde9f6e390fe8 | 24 | Despite novel methods are being developed , they usually rely on in vitro measurements, which is far from physiological conditions: in normal vessels, platelet activation is constantly inhibited, primarily by NO constantly released by endothelial cells. Concentration of NO as low as 3-90 nM effectively inhibits platelet activation , and attempts to study platelet activation using exogenous NO donors were made . Light-activatable NO donors are promising in this respect because they provide steady and controllable release. In this study, we used compound BODIPY-NOD-2 as NO photodonor. |
646c8f15ccabde9f6e390fe8 | 25 | In this paper, we presented novel BODIPY dyes containing N-Nitroso moiety and showed the photoinduced generation of NO. We showed that for photodonors containing the phenyl ring (BODIPY-NOD-2,3,4,5) the maximal NO yield is observed for unsubstituted BODIPY, whereas boron alkylation and the introduction of the iodine atoms reduces the efficiency, although influence the singlet oxygen generation. For the isopropyl-containing photodonor BODIPY-NOD-1 the photorelease of NO was not detected. Using the developed NO photodonors, we demonstrated efficient light-dependent inhibition of platelet activation in vitro. We also show that some compounds could additionally generate singlet oxygen, which is promising for the photodynamic therapy. The presented compounds could be used in biological research and serve as the basis for the development of novel hybrid therapeutic methods. |
6331ea3fe665bd2ec8139e52 | 0 | In predictive ab initio spectroscopy, the use of high-level theory and large basis sets makes each energy calculation computationally expensive. As a result, the energy points are not computed on a fine mesh. Continuous Born-Oppenheimer potential-energy functions are generated by a smoothing procedure. For example, cubic splines are used in the VIBROT/MOLCAS program and high-order polynomials are used in the MOLPRO program. Several smoothing options are available in the popular LEVEL program, by the late R. J. LeRoy. Different smoothing procedures produce different spectroscopic results. Even within a single model, such as splines, interpolation error may be significant for vibrational eigenvalues. The choice of grid points may also affect the results. For sparse data, which is a common situation, the differences between smoothing methods can be surprisingly large, as shown by the examples below. Here we propose a strategy to reduce this variability. |
6331ea3fe665bd2ec8139e52 | 1 | It should be noted that model dependence is also problematic in the reduction of data from experimental spectroscopy. Different models produce different values of meaningful parameters, and analytical functions may fail to reproduce experimental data, despite their great proliferation known as "potentiology." Polyatomic potential-energy functions have a separate literature for smoothing functions, as a result of their greater dimensionality. Here we only note that the polyatomic strategy by Fu et al. is most closely related to the present suggestion. |
6331ea3fe665bd2ec8139e52 | 2 | When predictions are intended to be quantitative, it is important to report the uncertainties associated with those predictions. In any application for which the values are important, the reliability of those values is also important. Reliability is usually expressed as an uncertainty statement. The uncertainties should reflect variations in the method of data analysis, in the selection of data points, in the choice of energy levels used to obtain spectroscopic constants, and uncertainty in the data themselves deriving from physical and mathematical approximations. Note that noise in energy calculations is not restricted to stochastic methods of electronic structure. For example, basis-set extrapolation carries uncertainty as well. The present strategy is helpful for reducing the uncertainties in predicted energy levels. In other words, the strategy improves the precision of predictions. |
6331ea3fe665bd2ec8139e52 | 3 | where E is potential energy, R is the internuclear distance, and fM(R) is a continuous model function. The model function is fitted to the ab initio data, which are a small set of pairs of distances and energies, (Ri, Ei). Polynomials remain a popular choice of model function. In the present strategy, we include a high-resolution potential energy function computed using a less expensive, presumably lower-level theoretical method. This provides the physics used to guide the interpolation of the high-level data. The low-level data are converted to continuous form, g(R), using spline interpolation. The low-level grid should be dense, so that interpolations are short and the method of interpolation does not matter. We replace eq. ( ) by |
6331ea3fe665bd2ec8139e52 | 4 | where g(R) is the continuous "guiding potential" derived from the low-level data. This reduces to eq. ( ) in the case g(R) = 0. As in eq. ( ), the parameters of fM(R) are fitted to the high-level data. However, now they are only required to reproduce the difference in energy between the high-level and low-level data, which usually displays weaker structure and smaller magnitude than the high-level data alone. |
6331ea3fe665bd2ec8139e52 | 5 | Note that the result of eq. ( ) is not a "dual-level" potential energy curve because the low-level method does not contribute directly to the energy. E(R) is the high-level potential with interpolation and possibly extrapolation. The low-level guiding potential, g(R), although lacking adjustable parameters, contributes in the same way as the model function, fM(R). Unlike the model function, g(R) is derived from the electronic structure of the molecule under study. This strategy is described as "physics-guided" because the guiding potential is from actual calculations on the molecule of interest. No feasible calculation contains "all" the physics, but quite a bit can be captured using a low-cost guiding potential. In contrast, mathematical forms such as splines, polynomials, and Morse functions are not based upon any physical laws. Such functions are still required for fitting the energy differences, but their numerical influence is diminished, compared with direct fitting of raw data. The examples presented here are simple: covalently-bonded molecules composed of light elements and closed-shell ( 1 ο ο« ), single-well electronic ground states. Such simple potentials are the easiest to fit using conventional, direct fitting, eq. ( ). |
6331ea3fe665bd2ec8139e52 | 6 | Vibrational eigenvalues are computed using the Fourier-grid Hamiltonian (FGH) method with 501 grid points. FGH has periodic boundary conditions, so a padding interval, equal in width to the data set, is added to the left and right sides of the potential to suppress periodic artifacts. Each padding interval is filled with a constant (flat) potential defined by its nearest computed value. To test for periodicity artifacts, the unsigned sum of wavefunction amplitudes at the left and right edges is divided by the maximum amplitude. If that ratio exceeds 10 -6 , the padding interval is increased. The high-resolution, low-level potential is interpolated using cubic splines to yield the function g(R). |
6331ea3fe665bd2ec8139e52 | 7 | For F2, the high-resolution grid has 221 points from R = (1.1 to 2.2) Γ
, a spacing of 0.005 Γ
. The coarse, irregular grid consists of the nine points with R = 1.28, 1.30, 1.32, 1.36, 1.42, 1.48, 1.54, 1.58 and 1.63 Γ
, which are close to the energy minimum and the classical turning points (on the high-level potential) for v = 0, 1, 2, and 3. Low-level methods are HF/6-31G*, B3LYP/6-31G*, fcMP2/cc-pVDZ and fcCCSD/cc-pVDZ, all spin-restricted, where the prefix "fc" indicates that core electrons are left uncorrelated ("frozen"). The high-level method is RHF-CCSDT/aug-cc-pwCVTZ with all electrons correlated. We are testing procedures, so a high-resolution grid is also computed at the high level to provide access to "correct" values. All calculations are done using Gaussian09 except for CCSDT, which is done using the CFOUR programs. For CO, the high-resolution grid has 201 points from R = (0.8 to 1.8) Γ
, a spacing of 0.005 Γ
. Guiding potentials are computed at: CASPT3(10,8)/aug-cc-pwCVTZ (third-order multireference perturbation theory ), icMRCI(10,8)+Q /aug-cc-pwCV5Z (internally contracted multireference singles and doubles configuration interaction with Davidson correction for additional correlation), and UHF-fcCCSD/aug-cc-pVQZ. The CCSD calculations are done using Gaussian09 and the multireference calculations are done using MOLPRO. For C2, the high-level data from Boschen et al. span a wide range, from 0.9 to 20 Γ
. Here, only distances up to 6 Γ
are considered. The high-resolution grid is from 0.9 to 6.0 Γ
in steps of 0.005 Γ
(1021 points). Inexpensive guiding potentials are CASSCF(8,8)/cc-pVTZ and icMRCI +Q/aug-cc-pwCVTZ using three-state-averaged orbitals. The X state is identified as the lower of the ο = 0 states in the CASSCF, and as the icMRCI state dominated by that CASSCF reference. Abrams and Sherrill obtained a correctly shaped potential from RHF-fcFCI (full configuration interaction) using a small basis set. However, this is costly (about 100 times more than the present MRCI and 10 4 times more than the present CASSCF), so for this method we use a superposition of three grids: from 0.9 to 1.9 (οR = 0.005 Γ
), from 1.9 to 3.2 (οR = 0.02 Γ
), and from 3.2 to 6.0 (οR = 0.1 Γ
) for a total of 294 points. We solve for the three lowest states (of irrep Ag in D2h), to get beyond the curve crossing near 1.7 Γ
while obtaining values for X Ξ£ . The X state in the FCI calculations is identified by requiring smoothness in the energy and in the components of the quadrupole moment, although it is not always clear. These calculations, including the FCI, are done using MOLPRO. Data analysis, including splining and polynomial fitting, is done in Python using the standard Scipy and Numpy libraries. |
6331ea3fe665bd2ec8139e52 | 8 | In the subsection about guided point-selection, the high-level method for F2 is the same as described above, to allow comparison with "correct" results. The high-level method for C2 is CCSDT(Q) with all electrons correlated. Correlation energies are extrapolated to the basis-set limit, assuming n -3 dependence, from calculations using the aug-cc-pwCVTZ and aug-cc-pwCVQZ basis sets. Hartree-Fock energies are obtained using the aug-cc-pwCV6Z basis sets, without extrapolation. These calculations on C2 are done using CFOUR. |
6331ea3fe665bd2ec8139e52 | 9 | Testing on F 2 . Difluorine has only a formal single bond, but is an anomalous molecule with strong dynamical electron correlation. To determine the distance resolution needed to exceed wavenumber precision, a uniform grid of 2201 points (from R = 1.1 to 2.1 Γ
; resolution = 0.0005 Γ
) is computed at the fcCCSD/cc-pVDZ level. The ground vibrational level, E0, is computed along with the first four intervals: πΈ , πΈ , πΈ and πΈ . The numerical values are affected by the choice of spline interpolation method. The difference between cubic and linear splines indicates how much information originates in the fitting procedure, instead of the quantum theory. This difference is computed for each of the energy quantities as a function of grid resolution. The value of E0 is the most sensitive to the grid resolution, by far. A grid resolution of 0.0075 Γ
is needed to converge E0 to a precision of 1 cm -1 . A resolution of 0.035 Γ
is adequate for the four energy intervals. Throughout the present report, a resolution of 0.005 Γ
is used for "high-resolution" grids, except as noted in the Computational Details. |
6331ea3fe665bd2ec8139e52 | 10 | From a high-resolution, high-level dataset we obtain reference, "correct" values for the vibrational energy levels (using the cubic spline). These "correct" values are E0 = 457.58 cm -1 and the successive vibrational intervals πΈ = 898.08 cm -1 , πΈ = 874.22 cm -1 , πΈ = 849.85 cm -1 , and πΈ = 824.93 cm -1 . The "correct" values do not represent experimental data except to the extent that the high-level method represents reality. However, they are the appropriate benchmarks for testing the fitting procedures. Note that the v = 4 level depends upon parts of the potential beyond the sparse high-level data (see Computational Details), and therefore reflects the accuracy of extrapolation. We expect the guiding potentials to improve the quality of extrapolation because the guiding potentials extend beyond the range of the nine high-level points. |
6331ea3fe665bd2ec8139e52 | 11 | Figure illustrates the difference in structure between the high-level, sparse data and their differences from each of the four guiding potentials. The task of the model function, fM(R), is to fit the points in each plot. For some of the guiding potentials, the range of the energy differences is larger than that of the high-level data themselves. However, the differences are more nearly linear and might be more accurately fitted by the model function, fM(R). To explore the helpfulness of a guiding potential, we start with an unusually simple model function, a linear polynomial of degree 1. Fitting it to the points in Fig. , as described by eq. ( ), or by eq. ( ), using the four guiding potentials, results in the potential curves shown in Figure . The curves obtained via eq. ( ) are qualitatively correct, while that from eq. ( ) is of course useless. The quantitative performance of these curves is shown in Table . Accuracy improves along with the quality of the guiding potential. The highest-level guiding potential used here, fcCCSD/cc-pVDZ, reproduces the vibrational fundamental within 1.1 %. The level v = 4 relies upon parts of the potential that must be extrapolated beyond the sparse, high-level data used in the fitting. Despite extrapolation, the errors in the 4-3 interval are no worse than expected from the errors in the lower intervals. fcCCSD/cc-pVDZ 0.00 0.00 -0.00 0.01 0.05 a The highest interval requires the v=4 level, whose turning points lie beyond the range of the high-level data and therefore rely upon extrapolation of the fitted potential. b Fitted curve truncated to eliminate turnover. |
6331ea3fe665bd2ec8139e52 | 12 | Although a linear model function will seldom be the best choice, there are at least two situations in which it could be: (1) when only two data points are available, presumably from an extremely costly method, and (2) when more than two data points are available but they contain noise that must be mitigated by an averaging process such as least-squares fitting. Situation #2 is especially relevant for stochastic methods of electronic structure. Note that the energy minimum, Ee, and its location, Re, can also be determined from only two points by using eq. ( ). |
6331ea3fe665bd2ec8139e52 | 13 | Next we try a quadratic polynomial of degree 2 for fM(). The resulting fitted curves are shown in the Supporting Information. Compared with Figure , the agreement with the reference potentials is improved. The quantitative performance, shown in Table , is markedly better than for the linear model function. Errors for the extrapolated interval (πΈ ) are different from expected by extrapolating the errors in the lower intervals. Surprisingly, the highest-level guiding potential now shows the worst performance. Of course, eq. ( ) yields only a harmonic potential with this model function. |
6331ea3fe665bd2ec8139e52 | 14 | A quadratic function is typically used when only three points are available and a harmonic result is acceptable. In that case, one chooses the three points of lowest energy, to estimate the curvature at the energy minimum. If we do that here, the results from eq. ( ) are improved. For example, the error in the fundamental transition is reduced to 16.50 cm -1 . However, that still exceeds the errors from using eq. ( ). |
6331ea3fe665bd2ec8139e52 | 15 | A cubic polynomial of order 3 is the simplest polynomial that can provide anharmonic results via eq. ( ). The resulting fitted curves are shown in the Supporting Information. As expected, the errors are smaller with the cubic model function than with the quadratic. The choice of guiding potential has a correspondingly smaller effect. The guided results are markedly better than unguided. For a quartic polynomial (order 4) the fitted curves are plotted in the Supporting Information and the quantitative errors are listed in Table . For the guided fitting, results are noticeably improved only for the extrapolated interval. The results are markedly improved for the direct fitting of eq. ( ). Result for higher-order polynomials are plotted in the Supporting Information and summarized in Table . Errors generally decline for all fitting methods, as expected. |
6331ea3fe665bd2ec8139e52 | 16 | In this test, nine data points are included: near the energy minimum and near the classical turning points for the four lowest vibrational levels. These points were selected in the intuitive belief that they are good for reproducing the vibrational levels. Polynomials are used to interpolate and to extrapolate the data. With low-order polynomials, using a guiding potential improves accuracy substantially. Except for the lowest-order polynomials, different guiding potentials provide similar accuracy. These trends may be understood by considering eq. ( ). Low-order polynomials, fM(), recover less information from the high-level data than high-order polynomials recover, leading to heavier reliance upon the information in the guiding potential, g(). |
6331ea3fe665bd2ec8139e52 | 17 | Application to CO. Powell and Dawes have published sparse potential energy curves for carbon monoxide computed using a quantum Monte Carlo (QMC) method. To obtain spectroscopic constants, they fitted selected points from their data to a Morse function. The authors had difficulty with the curve-fitting, reporting that the Morse potential cannot fit the data over their full range. Note that a Morse potential unphysically truncates all anharmonicity at the first constant (ο·exe). Here, we restrict our attention to the most expensive calculations, Table in ref. , and to the four QMC points that are relevant for the lower vibrational levels. These points lie at R/Γ
= 0.9, 1.0, 1.1 and 1.3. (The next point is at 2.6 Γ
.) 0.9 Γ
is close to the inner classical turning point for v = 24, for which the outer turning point is near 1.655 Γ
. Figure shows the sparse QMC data and their differences with the guiding potentials. The differences between QMC and the multireference methods are nearly linear. The uncertainties for the data points are not all the same, so the model function must be fitted using a weighted procedure. We choose each weight to be the inverse square of its stated uncertainty. Starting with fM() as a linear function, we obtain spectroscopic constants as shown in Table . (Potential energy curves are shown in the Supporting Information.) Experimental values are shown in the first row of Table for reference, but we can only expect to match them to the extent that the QMC data are accurate. |
6331ea3fe665bd2ec8139e52 | 18 | Thorough uncertainty analysis is beyond the scope of this report. However, we can use straightforward Monte Carlo propagation (500 samples) of the reported energy uncertainties to obtain that major component of uncertainty. The results are included in Table between parentheses, and refer to the least significant digits. For example, using the icMRCI+Q guiding potential and quadratic model function yields standard deviations (in cm -1 ) of 6.6, 0.21, 0.0026, 0.001, 0.0002 and 0.03e-6 for the constants ο·e, ο·exe, ο·eye, Be, ο‘e and De, respectively. The propagated uncertainties mostly increase with the order of the fitting polynomial, as expected from the corresponding reduction in noise averaging. In this case, we do not know the "correct" results because we do not have a highresolution grid of QMC data. From the F2 test we expect that higher-order polynomials will give more accurate results. (This expectation is supported by the increasing similarity among the alternatively guided potentials for CO as the polynomial degree is increased-see Supporting Information.) Greater precision is associated with a smaller variation of results from different guiding potentials. Considering the values of ο·e in Table , the spreads are 33 cm -1 from a linear model function, 1.3 cm -1 from a quadratic, and 1.4 cm -1 from a cubic. For ο·exe, the spreads are 1.02, 0.14 and 0.24 cm -1 from linear, quadratic and cubic, respectively. The results appear reasonably converged with the quadratic model function. Since the highest-level guiding potential is from icMRCI+Q, and it shows small and near-linear differences (Fig. ), we might favor the results from that guiding potential and the quadratic model function (boldface in Table ). Note that a cubic function fits the four data points exactly, which means that the statistical noise in the data will not be canceled at all (by least-squares averaging). |
6331ea3fe665bd2ec8139e52 | 19 | Application to C 2 . Dicarbon is well-known for its challenging electronic structure. Here, we focus on the spectroscopic constants as determined by fitting the high-level CEEIS (correlation energy extrapolation by intrinsic scaling) data by Boschen et al. The authors reported difficulty fitting the data to a continuous form, which they ascribed to an avoided crossing near 1.7 Γ
. In the end they used a cubic spline. Here we re-analyze their 43 data points (up to R = 6 Γ
) using guided fitting. Abrams and Sherrill reported correctly-shaped curves at the fcFCI/6-31G* level, so we use it here as a guiding potential. We also use guiding potentials from CASSCF/cc-pVTZ and icMRCI+Q/aug-cc-pwCVTZ (active core), which are far less expensive than FCI despite the larger basis sets. |
6331ea3fe665bd2ec8139e52 | 20 | First, we note that direct analysis of the high-level data from Boschen et al., using eq. ( ), gives results that depend upon the method of interpolation used to smooth the potential. Table lists the first six vibrational intervals and the ground (zero-point) energy relative to the (interpolated) minimum. The variability with splining method, an arbitrary choice, is shown in the last column. The high variability indicates that the data, of themselves, do not contain enough information to define vibrational levels to wavenumber precision. Alternatively, a physically derived guiding function may reduce the demands placed upon the model function, thus reducing the variability (i.e., uncertainty) from the arbitrary choice of splining method. By making this comparison, we are not suggesting that a linear spline is a good choice of model function. We are showing that the information carried by the model function has a significant impact on the spectroscopic results. Table . Vibrational intervals (cm -1 ) of C2 as computed from high-level data by Boschen et al. using different splining methods. |
6331ea3fe665bd2ec8139e52 | 21 | Figure shows the differences between the (relatively) sparse CEEIS data and three choices of guiding potential. As before, the differences have weaker structure than the raw data. However, structure here is more noticeable than in the previous examples. For each of the three guiding potentials as g(R), we apply the four splining methods used in Table as fM(R). All results are listed in the Supporting Information. The variabilities and the results from the cubic spline are shown in Table . The most consistent results, with little dependence upon the choice of splining method, are obtained when guided by the icMRCI+Q potential. However, all the guiding potentials lead to marked improvement over the unguided results in Table , and the results from the different guiding potentials (Table ) are in mutual agreement. The closest agreement across guiding potentials, to all digits displayed in Table , is obtained from the cubic spline. Tables and consider the uncertainty arising from the choice of splining procedure, and show that it is significantly reduced by using guided fitting, instead of direct fitting with eq. ( ). One may also consider uncertainty arising from the data themselves. In this case, the CEEIS energies do not carry statistical uncertainties, as in QMC calculations. However, the selection of data points (i.e., values of R) affects the results. For example, if additional data were collected, the results would be somewhat different. This effect can be estimated from the existing data by subsampling. We take a random subset of 41 of the 43 points from Boschen et al. and analyze them using a cubic spline and either eq. (1) or eq. . Repeating this 500 times, the resulting standard deviation for the fundamental frequency is 0.79 cm -1 from direct fitting and 0.51, 0.52 and 0.52 cm -1 using the CASSCF, MRCI+Q and FCI guiding potentials, respectively. Standard deviations for the other vibrational quantities of Table are listed in the Supporting Information. Except for the experimentally unobservable ground-state energy, the standard deviations are all less than 1 cm -1 , suggesting that Boschen's dataset is large enough. |
6331ea3fe665bd2ec8139e52 | 22 | It is seldom obvious which values of R should be computed at the highest level. Thus, in careful work there is the tendency to compute more points than necessary, leading to reduced efficiency. We seek to construct a dataset that yields results that are not sensitive to the choice of guiding potential. Thus, we compare the potentials, E1(R) and E2(R), obtained by using eq. ( ) with two guiding potentials, g1(R) and g2(R), in turn. The value of R with the largest discrepancy in energy, |πΈ π
πΈ π
|, is a logical choice for the next highlevel point. We illustrate the technique using the C2 molecule and the CASSCF and MRCI+Q guiding potentials, described above, as g1(R) and g2(R), respectively. The high-level method is CCSDT(Q)/aug-cc-pwCV Z (see Computational Details). |
6331ea3fe665bd2ec8139e52 | 23 | As the spectroscopic quantities of interest, we choose the vibrational fundamental and the first five harmonics, i.e., the intervals πΈ with 1 π£ 6. Experimental values have been reported by Douay et al. We restrict attention to the range of distances that correspond to the classical turning points on g2(R) for v = 8, which allows a margin for disagreement between g2(R) and our final high-level potential. Those turning points (R = 1.07637 and 1.52955 Γ
) are the two initial points computed at the CCSDT(Q) level. Using a linear function as fM(R), eq. ( ) yields continuous potential-energy functions E1(R) (from the CASSCF guiding potential) and E2(R) (from MRCI+Q). The spectroscopic quantities are computed using E1(R) and using E2(R); the root-mean-square difference (RMSD) of the results is evaluated as 150.96 cm -1 , which is very large, indicating that another point is needed. The difference E2(R) -E1(R) is computed over a grid of distances covering the range of attention. The difference of largest magnitude is at R = 1.31952 Γ
, which is then computed at the high level. With three high-level points in hand, a quadratic function is used as fM and the process repeated. The RMSD drops below 1 cm -1 with only seven points, terminating the algorithm. The numerical results are summarized in Table and the resulting potential-energy functions are shown in Figure . The location of points in Figure may not match intuitive expectations. For example, there is no point near Re and the points do not occur as pairs of turning points. Moreover, seven points is fewer than might be selected merely from intuition. For example, one might choose the two turning points for each vibrational level of interest. That would be 14 points for 0 π£ 6. This suggests an improvement in computational efficiency from guided point-selection: fewer expensive calculations are needed. |
6331ea3fe665bd2ec8139e52 | 24 | As a second test, we return to the data presented above for F2, with the target quantities of Table . Using guided point selection converges the RMSD to 0.01 cm -1 with seven high-level points, fewer than the nine that were chosen by hand. Detailed results are shown in the Supporting Information. All the target quantities have errors less than 0.01 cm -1 . As the highlevel points are accumulated, the RMSD decreases. In this case, we have access to "correct" values and see that the RMS errors also decrease. The RMS errors of direct fitting, using eq. ( ), also decrease, although they are larger than the errors from guided fitting. |
6331ea3fe665bd2ec8139e52 | 25 | Besides the procedure presented here, other methods can also be effective for selecting points. For example, Dawes et al. compared two different orders of interpolation for the same high-level data. One could also use the same interpolative method with and without a coordinate transformation such as π
exp π
. The common idea is to generate points that minimize the dependence upon the method of interpolation. |
6331ea3fe665bd2ec8139e52 | 26 | For a given family of parametric fitting functions, such as polynomials or splines of different order, computed spectroscopic quantities are more consistent, i.e., have smaller uncertainties, when a physics-based guiding function is used as a reference, instead of directly fitting highlevel ab initio data. The best results appear to be obtained when the difference between the highlevel data and the guiding function is a linear function of bond length. The technique may be especially advantageous for noisy data, as from stochastic electronic-structure methods, because a low-order polynomial can more easily fit the data while averaging the noise. The same strategy may be useful for encoding experimental data or for describing dipole moment surfaces. Meaningful spectroscopic predictions can be obtained from as few as two high-level data points. Comparing the results from two guiding potentials provides a systematic and efficient way to select geometries for high-level calculation. |
670435d751558a15ef66d508 | 0 | Obtaining accurate electronic energies of molecules is essential for the quantitative analysis of their chemical properties. Due to its affordability and accuracy for even moderately sized systems, coupled cluster theory with single and double excitations and a quasiperturbative inclusion of connected triple excitations (CCSD(T)) is sometimes called the gold standard for quantum chemistry calculations, and is often employed for the study of thermochemistry and chemical reactions. However, although Gaussian basis sets are in principle complete so that convergence to a solution of the SchrΓΆdinger equation is guaranteed if enough Gaussians are used, the convergence of the dynamic correlation energy to the complete basis set (CBS) limit is achingly slow and can be the limiting factor in the accuracy of electronic structure calculations. This is the reason why various schemes that extrapolate the finite basis set results to the CBS limit have been developed and applied in the calculation of molecular properties. Extrapolation can greatly reduce the finite-basis-set error with no additional computational cost. |
670435d751558a15ef66d508 | 1 | Several two-point and three-point extrapolation schemes have been formulated in past years. The two-point extrapolation schemes are especially convenient. The best general extrapolation schemes can be obtained by optimizing one or more empirical parameters against a dataset. The accuracy of such an extrapolation scheme depends in part on the quality and appropriateness of the datasets on which the extrapolation schemes are trained. A recent paper by Xi et al. revisited the problem of inadequate data sets and trained several two-point extrapolation schemes against a new expansive data set with 183 species that includes several closed-shell, open-shell, ionic, and neutral species extending well-beyond the second period of the periodic table with reference energies calculated at CCSD(T)/aug-cc-pV6Z level. They employed aug-cc-pV{X,Y}Z basis sets pairs with {X,Y} = {D,T}, {T,Q}, or {Q,5} for the twopoint extrapolation schemes. A key aspect of their work is the optimization of separate parameters for each pair of basis sets. The results of the work were very promising, and their results provide a great improvement on the existing extrapolation schemes. The objective of the present paper is to show that using jun-cc-pVXZ basis sets or jul-cc-pVXZ basis sets instead of aug-cc-pVXZ basis sets provides comparable accuracy at greatly reduced costs. |
670435d751558a15ef66d508 | 2 | In their paper, Xi et al. used aug-cc-pVXZ (where X = 2, 3, β¦) basis sets. However, it has been shown that for many calculations of thermochemistry and thermochemical kinetics, these basis sets contain many diffuse functions that have a relatively small effect on the calculation of several chemical properties. For efficient calculations, one wants to eliminate the least useful diffuse functions in a systematic way, and the calendar basis sets jul-cc-pVXZ and jun-cc-pVXZ were designed to do this. The jul-cc-pVXZ basis sets are constructed from their aug counterparts by removing all diffuse functions from hydrogen and helium. The jun-cc-pVXZ basis sets 32,33 remove these diffuse functions and also remove the the highest-angular-momentum diffuse function from atoms heavier than He. For example, an aug-pVTZ basis set for a hydrocarbon contains diffuse s, p, and d functions on each H and diffuse s, p, d, and f functions on each C. The jul-pVTZ basis set removes all the diffuse functions on H atoms, and the jun-cc-pVTZ basis set also removes the diffuse f functions on each carbon. The jul and jun basis sets are thus significantly smaller than their aug counterparts, the difference being more pronounced with the increase in system size. |
670435d751558a15ef66d508 | 3 | and that strategy is adopted in both the Xi et al. study and the present one. One parameter is involved in two-point extrapolation of πΈ !" , and another parameter is involved in two-point extrapolation of πΈ #$%% ; the former is called a, and the latter is called b. Xi et al. examined five formulas for two-point extrapolation of πΈ !" , and five formulas for two-point extrapolation of πΈ #$% , they found that, as long as a and b were separately optimized for each formula and each pair of basis sets [D,T or T,Q or Q,5], the results showed similar high accuracy all five formulas for HF extrapolation and similar high accuracy all five formulas for correlation-energy extrapolation. We therefore chose to use only one formula in each case, and we chose the model that they named Truhlar-1998 Error! Bookmark not defined. for both cases. |
670435d751558a15ef66d508 | 4 | They found Ξ = 1.36, 0.44, and 0.04 kcal/mol, for the X pairs (D,T), (T,Q), and (Q,5), respectively. Note that the reference values are supposed to represent CCSD(T)/CBS, not the exact answer (which would be all-electron configuration interaction at the CBS limit). A previous study of 48 reaction energies and barrier heights gave a mean absolute deviation of CCSD(T)/CBS energies from more accurate benchmarks (with beyond-CCSD(T) contributions) of 0.44 kcal/mol. We conclude that that including beyond-CCSD(T) correlation effects is often more important than improving the CCSD(T) extrapolation from (T,Q) to (Q,5). For this reason and because (Q,5) extrapolation is often unaffordable, the present study is limited to (D,T) and (T,Q). |
670435d751558a15ef66d508 | 5 | The original aug-cc-pVXZ paper 36 emphasized electron affinities, but the paper has been cited 13,783 times, and the great majority of these papers are not devoted to electron affinities. It is well known that diffuse functions are useful for accurate calculations of bond energies and barrier heights. For example, a paper 37 on barrier heights showed that the mean unsigned errors in a set of hydrogen-atom transfer reactions involving only neutral species is 1.41 kcal/mol with CCSD(T)/cc-pVTZ and 0.70 kcal/mol with aug-cc-PVTZ. Similarly, the mean unsigned errors in a set of nonhydrogenic-atom transfer reactions involving only neutral species are 1.90 kcal/mol with CCSD(T)/cc-pVTZ and 0.95 kcal/mol with aug-cc-PVTZ. We conclude that augmentation is very useful for neutral species as well as anions. |
670435d751558a15ef66d508 | 6 | Therefore, the study of quantities other than electron affinities is very relevant. Nevertheless, our test set includes 3 cations and 12 anions along with 106 neutral species, so we made an analysis where we calculated separate errors for cations, neutrals, and anions. Our goal is to see if we can obtain equally as accurate results with jun-and jul-basis sets as with the more expensive aug-basis sets. |
670435d751558a15ef66d508 | 7 | where π is the cardinal number (called X in the introduction) of the basis set used, πΈ(π) is the energy calculated with the basis set of cardinal number π, πΈ &-' is the CBS limit, and π(π) is a function of π with a coefficient, π΄. The function π(π) approaches zero as π approaches infinity. The coefficient π΄ can be eliminated by substituting two consecutive values of π and π in eq 3 and subtracting the two equations. This also gives the formula for the linear extrapolation to the CBS limit. |
670435d751558a15ef66d508 | 8 | The database for this study is taken from the supporting information of ref. Frozen-core single-point energy calculations were carried out for each of the 121 species at the CCSD(T)/jul-cc-pVXZ and CCSD(T)/jun-cc-pVXZ levels with X = D, T, and Q. All calculations were carried out using the Gaussian 16 program. Table gives the mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum absolute deviation (MaxAD), of the CCSD(T) energies calculated with jun-, jul-, and aug-cc-pVXZ basis sets. In the present context, we can also label these deviations as "errors." These are the results before extrapolation to the CBS limit. The errors are quite large for the VDZ basis sets, and the numbers get better as one goes from VDZ to VTZ to VQZ. In all cases, the jul basis sets perform just as well as the aug basis sets, and he jun basis sets are slightly worse. However, all the errors are still quite large, and even the more expensive QZ calculations don't reach chemical accuracy making them inadequate for accurate quantitative analysis of chemical properties. Next, we consider how two-point extrapolation to the CBS limit improves the calculated energies. Table shows that for the {D,T} extrapolations, the jul basis sets perform just as well as the aug basis sets, and the smallest basis sets, jun, perform the best among the three. As expected, the {T,Q} extrapolation performs better than {D,T} extrapolation for cases. Both jun and jul basis sets perform as well as aug basis sets in the {T,Q} extrapolation (the small differences are not significant). It is also interesting that we obtain similar values of Ξ± with jun and jul basis sets as compared to aug basis sets. |
670435d751558a15ef66d508 | 9 | Table shows the optimized parameters, MAD, RMSD, and MaxAD for extrapolation of CCSD(T) correlation energy to the CBS limit. The trends for {D,T}are similar to the trends in HF extrapolation; we see that the results get better as one goes from aug to jul to jun basis sets. For the {T,Q} calculations, the jul basis sets match the results of aug basis sets, whereas jun performs slightly worse compared to the other two. The final column of Table shows the overall figure of demerit defined by eq 2. The values are comparable to those mentioned above from Xi et al. gives the most important results, the total energy extrapolation. Since the total energy is the sum of HF and CCSD(T) correlation energies, the trends are the same as the HF and CCSD(T) correlation energy extrapolation. For {T,Q} extrapolation, the jul and aug results are almost the same, and jun is lightly worse. For {D,T} extrapolation, jul is slightly better than aug, and jun is much better. Comparing the results in Table and It is interesting to also look at the separate results for cations, neutrals, and anions. |
670435d751558a15ef66d508 | 10 | The test set consists of 3 cations, 106 neutrals, and 12 anions, and Table presents the extrapolated total energies for each charge state separately. In the {D,T} extrapolation, the jul basis set outperforms both jun and aug, while the jun basis set performs slightly worse than both jul and aug for cations and anions. However, in the {T,Q} extrapolation for cations and anions, both jun and jul perform just as well as the aug basis set. The results for neutrals follow the same trends as observed in Table , where all three basis sets perform equally well. Since the above results show that the jun and jul basis sets perform just as well as aug basis sets, the next objective of this study was to compare the computational load associated with the jun, jul, and aug calculations. Table shows the number of contracted basis functions used in the calculations for several molecules with aug, jul, and jun-cc-pVXZ basis sets. The number of contracted basis functions is important because of the scaling of the computational effort of CCSD(T) with the size of the basis. It is often stated that in the limit of large n, where π is the number of contracted functions, the computational effort of CCSD(T) calculations scales ππ ; , where b is a constant. It is more informative to look at the costs of two leading terms, that is the iterative CCSD part and that of the noniterative (T) |
670435d751558a15ef66d508 | 11 | step. Then the leading terms in the computational effort maybe written as ππ <:2% π = + ππ ; , where π <:2% is the number of CCSD iterations, and a is a constant. These scalings apply to increasing the size of homonuclear systems, where the number of contracted basis functions is proportional to the number of atoms. When one considers the effect of increasing the basis set size for a given molecule, it is useful to recognize that π is the sum of the number of occupied orbitals π $ and the number π > of virtual orbitals, because changing the number of contracted functions changes π > but not π $ . Using π > and π $ rather than n, the leading terms in the cost are ππ <:2% π $ , π > ? + ππ $ @ π > ? , where c and d are constants. The dependence on the number of contracted functions for a given molecule is thus less steep (asymptotically π ~ π > , so the scaling becomes π ? rather than π ; ); nevertheless, it is still very significant. As the size of the molecule increases, the difference in the number of basis functions between the jun and aug basis sets, as well as between the jul and aug basis sets, becomes more pronounced. For DZ, Table shows that the number of contracted basis functions in the aug basis set is 18-46% more than in jun and 8-24% more than in jul, where in the comparison to jul we omit molecules that have no hydrogens. For TZ, these numbers change to 14-37% for jun, and they remain 8-24% for jul. For QZ, the increases become 10-31% for jun and 8-23% for jul. |
670435d751558a15ef66d508 | 12 | As the number of basis functions increase, so does the computational cost. Table lists the relative CPU time for each CCSD(T) single-point energy calculation for three example molecules. C4H4 is one of the most expensive systems in the current study, whereas C6H12 and C6H12O6 are included as examples of larger, more challenging systems on which to perform a CCSD(T) calculation, and we note that C6H12O6 was too big for us to perform CCSD(T) calculations with jun/jul/aug-cc-pVQZ basis sets. For DZ, the jun calculations reduce the cost as compared to aug calculations by a factor of 3 to 5. The other comparisons show smaller but still significant ratios. To put things into perspective, it takes two and a half days for a CCSD(T)/jun-cc-pVQZ calculation on C6H12, and a CCSD(T)/aug-cc-pVQZ calculation would take well over 6 days for completion. A CCSD(T)/aug-cc-pVTZ on C6H12O6 takes almost 11 days of CPU time, as compared to less than five days for jun-cc-pVTZ. The new science that can be explored with this procedure includes any problem where such cost savings make the calculations more practical. calculations in Table . This is because TZ calculations, being more resource-intensive than DZ calculations, dominate the total computation time for both DZ and TZ calculations. |
670435d751558a15ef66d508 | 13 | Similarly, the combined relative CPU time for TZ and QZ calculations resembles the time taken for QZ calculations in Table due to the higher computational demand of QZ calculations. There is a significant reduction in computational cost with smaller jun and jul basis sets without a loss of accuracy in the calculation of absolute energies. |
670435d751558a15ef66d508 | 14 | Our realization that diffuse functions are hardly ever needed on hydrogen atoms dates back a number of years when we noticed that diffuse functions on hydrogen raise the cost but do not usually increase the accuracy. To provide a hard test, we did calculations on a metal hydride, LiH, and found no significant improvement when diffuse functions were added on H. We concluded, "Since metal hydrides are seemingly a "worst case" for omitting diffuse functions on H, it appears to be confirmed that diffuse functions on hydrogen have little importance for most thermochemical calculations." We later reconfirmed this during very extensive studies performed when proposing the calendar basis sets. At that time, we also suggested that the augmented basis sets of Dunning bring in high-angular-momentum diffuse functions at an earlier zeta level than is necessary. For example, for C, N, O, and F, aug-cc-pVXZ brings in diffuse f functions already at X = T, whereas jun-cc-pVXZ brings them at X = Q; this is particularly important since adding a diffuse f subshell adds seven additional basis functions to the basis set. We have since found that jun-cc-pVXZ calculations are usually comparable in accuracy to aug-cc-pVXZ calculations but at a lower cost. Here we illustrate this in the context of two-point extrapolations. |
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