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We have obtained a series of isomorphous crystals that exhibit various complex morphologies with first-row metal salts, M(NO3)2 with M = Cu 2+ , Ni 2+ , Co 2+ , and Mn 2+ , as well as an organic ligand. The growth of the crystals is controlled by coordination chemistry. During the solvothermal reactions, the rearrangements of the assemblies is probably affected by the different M-N bond strengths. The relative M-N bond strength is expressed by the Irving-Williams series: Mn 2+ < Co 2+ < Ni 2+ < Cu 2+ . Regardless of the metal used, the crystals show a high level of uniformity, in both their dimensions and shapes.
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Molecular modulators have been used by others to control crystal morphology and dimensions. In this system, the components themselves act as modulators by shaping the appearance and dimensions of their architecture at the microscale while keeping their molecular arrangement nearly identical. These morphologies depend not only on the metal cations used, but also on the metal salt-to-ligand ratio. Decreasing the Cu 2+ concentration resulted in a series of different structures resembling flower-like morphologies. The fascinating double-decker flower-like morphology has a sixfold (C6) and twofold (C2) axis of symmetry perpendicular to each other. The high level of symmetry indicates that the growth rate for each sub-unit of the double-decker crystals is very similar. This study revealed that the nature of the first-row metal salts controls the crystal growth with our tetrahedral polypyridyl ligand, and hence the morphology, while maintaining a similar crystallographic packing with hexagonal space group P622. We have previously reported on stellate and chiral crystals grown from related ligand systems. Interestingly, Cheul Cho et al. recently reported the co-crystals of C60 and C70, which have similarly shaped double-decker flowers. The observation that completely different types of materials may crystallize in highly unusual double-decker flower morphologies indicates that this crystal shape may be a general phenomenon, with the expectation that additional examples remain to be discovered.
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India's population is expected to increase by 10% between 2030 and 2050 to 1.66 billion (United Nations, 2022). This surge in population increases the demand for freshwater, which in turn increases the wastewater (WW) generation in the country. As of 2021, 72,368 MLD (Million L/d) of sewage is generated in the country, of which only 30% is treated (Downtoearth.org, 2021). Most of the WW treatment facilities are operated at Tier-I and Tier-II cities, while rural regions are ignored. The non-availability of treatment facilities and lack of advanced resource recovery mechanisms has led to the discharge of 52,133 MLD of untreated WW into the water bodies . This untreated discharge of WW not only contaminates the freshwater resources, but also harms the ecology of waterbodies by causing eutrophication due to the presence of nutrients suspended in them. Thus, reducing the level of dissolved oxygen (DO) in water bodies . WW contains Nitrogen (N) and phosphorus (P) which are usually lost during WW treatment as sludge or discharged after treatment. Recovering and reusing them helps in achieving self-reliance and sustainability. Since N and P are critical components for plant growth, they are used as raw materials in fertilizer production. P is used as an energy source (ADP -adenosine triphosphate), while N is used for building DNA and RNA in plants . Ammonia (NH3) is a nitrogen-based fertilizer produced through the Haber-Bosch process from atmospheric N. Meanwhile, P is produced from phosphate rock, which is a non-renewable and limited resource. Moreover, the increasing demand for fertilizer might lead to exhaustion of the global P resources in the upcoming years. Thus, treatment and nutrient recovery from WW not only aids in preventing the contamination of freshwater resources but also abets recovering P thereby achieving sustainable development goal (SDG) 6 before 2030. Nutrient recovery from WW directly relates to the sustainability in four ways; i) reducing the production of synthetic fertilizers which makes the fertilizers industry enroute towards sustainability (SDG 2,12,13, and 15) ; ii) reduces the nutrient pollution in waterbodies thereby maintaining the sustainable ecology in aquatic systems (SDG 6) ; iii) efficient treatment of WW directly helps in reducing the over usage of freshwater resources (SDG 6); iv) mitigates CO2 emissions caused by WW treatment by production of value-added products (SDG 11) .
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Typical urban sewage contains N of 75-125 mg/L, while P ranges between 20-40 mg/L . Earlier nutrient recovery studies show that between 80% and 90% of N and P is recoverable from WW using different treatment methods namely, chemical precipitation, microbial fuel cells, ion-exchange, and microalgae production . Several challenges exist in transitioning these technologies to field-level including robustness, material and energy efficiency, economics, design and optimization, and sustainability analysis.
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Nutrient recovery from WW results in liquid fertilizers, struvite, biomass, and sludge as products. worked on duckweed wastewater treatment with biorefinery options and identified that the pond construction had the highest share for global warming potential (GWP). Meanwhile, it was also reported that the GWP varied between 0.27 -0.47 kg CO2 Eq./m 3 of WW treated based on the treatment system employed. In addition, microalgae-based treatment system had a reduction in GWP by about 40%. Similar estimates were reported for struvite crystallization with a GWP of 27 kg CO2 Eq./kg P (Rodriguez-Garcia et al., 2014). Industrial data suggests that GWP can be negative, while precipitating struvite at -1.4 kg CO2 Eq./PE/Year (AirPrex, 2022). Microalgae based nutrient recovery options had a wide range of GWP based on the choice of technology between -0.180 and 2.1 kg CO2 Eq./m 3 of WW . This can be attributed to the variation in the energy consumption between different methods employed and end use of algae.
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In this work, five scenarios were compared from a LCA perspective for sewage generated from a mid-sized city in India. The scenarios compared include conventional treatment and four-nutrient recovery systems (chemical precipitation, microbial fuel cell, ion-exchange, microalgae cultivation). No previous studies had compared the LCA of nutrient recovery systems that has been mentioned above. In addition, the present study, attempts to conduct attributional LCA for all 5 scenarios and aids in identifying the best performing alternative for conventional treatment method in terms of its environmental performance. Furthermore, this is the first work to report the LCA of nutrient recovery in Indian context. The objective of this work comprises of 1. Estimate the N and P balance of different nutrient recovery systems; 2.
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The goal and scope of this study is to assess the environmental impacts of sewage treatment plant (STP) and four different nutrient recovery systems. The International Organization for Standardization (ISO) had established a standardized methodology for conducting LCAs that involves four steps: the definition of a goal and scope, inventory analysis, impact assessment, and interpretation of result . All four steps have been considered in this study, where cradle-to-gate approach was used to carry out LCA. The functional unit used to assess the environmental impacts was 1-m 3 of WW treated/day for 365days operating period.
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The system boundary considered for this study begins with WW entering the treatment plant, wherein different methods are compared. Post to WW treatment and nutrient recovery, the treated water, respective products, and sludge leaves out of the system (Figure ). Scenario I (Base Case) comprise of the conventional WW treatment with unit operations including primary settling tank, clarifier, sludge thickener, anaerobic digester, decanter, and pump for dewatering and sludge drying. The base case was compared with microbial fuel cell (MFC) (Scenario II), while scenario III, IV and V corresponds to chemical precipitation, ion-exchange, and microalgae based nutrient recovery systems respectively. Scenario III-V used the STP of scenario I followed by nutrient recovery. The information related to mass and energy balance were obtained based on our previous study .
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A life cycle inventory (LCI) of energy (e.g., electricity, diesel), chemicals (e.g., coagulation/flocculation, precipitant, adsorbents, and absorbents), direct emissions (e.g., CH4 and N2O), nutrients emissions (e.g., discharged to surface water and soil via reclaimed water and biosolids), and avoided products was compiled into the process based on Ecoinvent 3 and Agri-footprint databases. Table represents the operational parameters of the wastewater treatment plant.
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The standard procedure of ISO 14040:2006 was used to assess the environmental impact of the process known as life cycle assessment (LCA). There are two different LCA methods namely attributional LCA and consequential LCA. Among these, attributional LCA was used in this study as the system boundary was limited until the production stage The impact assessment was conducted using SimaPro v9.3.0.3 and Ecoinvent 3 database for background information in mapping the LCI. Impact assessment was carried out using ReCiPe 2016 Midpoint (v1.03) method. A total of 18 impact categories were considered including: global warming potential (GWP), stratospheric ozone depletion, ionizing radiation, ozone formation-human health, ozone formation-terrestrial ecosystems, terrestrial acidification, freshwater eutrophication, marine eutrophication, terrestrial ecotoxicity, marine ecotoxicity, freshwater ecotoxicity, carcinogenic toxicity, non-carcinogenic toxicity, land use, mineral resource scarcity, fossil resource scarcity, and water consumption.
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STP process was developed by adding up the individual unit processes such as primary settling, secondary treatment, secondary clarifier, sludge thickening, anaerobic digestion, sludge dewatering, and return sludge . Mechanical equipment such as pumps, thickener, aeration unit, and dewatering unit with energy consumptions were taken from the energy consumption calculations (Table ). The total energy consumption of STP was 303 kWh/1000 m 3 , after deducting the electricity generated from the biogas produced from anaerobic digestion (AD) process.
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When it comes to nutrient recovery systems, the entire process of microbial fuel cell happens in a single chamber. Hence, a separate scenario is considered to evaluate its life cycle assessment. Pumping, aeration, and discharging are the major unit operations carried out in microbial fuel cell (MFC) process. On the other hand, chemical precipitation happens in a reactor equipped with agitator to ensure homogeneous mixing of the added chemical in the wastewater. Magnesium oxide or magnesium chloride was used in this process, wherein MgO reacts with N and P to form struvite . Producing struvite consumes energy for pumping, mixing, magnesium dosing, discharging, and drying unit operations.
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The ion-exchange process recovers the nutrients in the form of crude fertilizer by using adsorbents like zeolites, which can recover about 100 mg of nutrients per gram of zeolite . To regenerate the zeolites after recovering crude fertilizer, a brine solution was used. The key ingredients of this process include zeolites and regeneration solution, at the same time, majority of energy was consumed in pumping the zeolite bed and for regeneration activities. Microalgae, the third-generation feedstock, was considered as the future of biorefineries as diverse bioproducts and biofuels can be produced from it. The WW after secondary treatment was used for microalgae cultivation. The growth rate of microalgae used in this study was 1 g/d/L of wastewater treated, which was based on .
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In each scenario, all the necessary material and energy consumption, and allocation were considered (Table ). The electrical energy used in the STP was assumed to be derived from coal power plant in the base case scenario. The effect of reduced global warming potential was studied for an incremental renewable share was considered at 25%, 50%, 75% and 100% respectively.
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Understanding the mass and energy balance provides the LCI for carrying out LCA. In our previous work, detailed mass and energy balance of various nutrient recovery systems were carried out, hence, those data were used for LCI. As this work deals with WW post to secondary treatment, wherein most of carbon (C) was degraded already and only a negligible level exists. Hence, C was not considered for mass balancing.
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Post-secondary treated WW was considered towards nutrient recovery for all scenarios except Scenario-II (MFC). The activated sludge process uptakes 62.3% of N and 37.4% of P, respectively. Sludge cake processing, post to anaerobic digestion has 15.4% N and 19.2% P. Thus, leaving behind 22.3% N and 43.4% P in the effluent (Figure ). This N and P after activated sludge process was considered for nutrient recovery using chemical precipitation, ion-exchange, and micro-algae systems. On the other hand, MFC works as a single-pot system to treat raw WW and recover nutrients at the same time (recovery rate = 80%) (Figure ). From MFC, N & P were recovered as nutrient-rich solution, which can be used as a raw material for fertilizer production. Scenarios III -V recovers N & P in the form of struvite, fertilizer crude, and microalgae biomass, respectively. Based on the type of nutrient recovery systems, the recovery rate of N & P varied between 11.3 -17.8% and 35.4 -36.4%, respectively (Figure ). This mass balance information of different nutrient recovery systems was used as LCI.
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Based on the LCI, life cycle assessment was performed using SimaPro. About 18 impact categories were analysed using ReCiPe 2016 Midpoint indicator to study the LCA. Among the impact categories, global warming potential (GWP), freshwater eutrophication, marine eutrophication, and stratospheric ozone depletion are the major environmentally impacting categories in all the scenarios. Conventional STP in Scenario I yielded a net GWP of 411 g CO2 Eq./m 3 (Figure ), which was mainly attributed to the energy consumption in aeration tanks, sludge thickening etc. (401 kWh/m 3 WW). Meanwhile, the GWP of STP was also influenced by factors such as type of wastewater, technology used, and materials usage . Conventional STPs using activated sludge process reported a similar GWP ranged between 240 -700 g CO2 Eq./m 3 (Campos et al., 2016; Chen et al., 2018) (Figure ). The increase in GWP was attributed towards modifying conventional processes by extended aeration and denitrification etc. When two treatment systems were combined, GHG emissions increase up to 4 times than the conventional systems .
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In contrast, Scenario-II (MFC) acts as a single-pot system to treat WW, recovering energy and nutrients simultaneously. Because of this multimodal approach, the energy consumption on the overall treatment and recovery could be reduced substantially, which reduced the overall GWP as well. The GWP of recovered fertilizer in Scenario II corresponds to -538 gCO2 Eq./m 3 , while the MFC part consumes a GWP of 304 gCO2 Eq./m 3 , thus, the net GWP of MFC is -234 g CO2 Eq./m 3 (Figure ). Though MFC has a negative GWP, the key issue was towards the scaling up of this technology. MFC lacks proof of concept in scale, wherein till date 10 m 3 /d operating capacity was reported to be the highest capacity .
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Subsequent scenarios (III-V) used WW after secondary treatment for nutrient recovery (Chemical precipitation, ion-exchange, and microalgae). The net GWP of Scenarios III-V were 329, 262, and 1154 g CO2 Eq./m 3 . When compared with conventional WW treatment (Scenario-I), chemical precipitation and ion-exchange offers 20 and 36% reduction in GWP respectively. However, microalgae consumed energy in its race-way pond (550 kWh/m 3 ) and subsequent unit operations (pumping, aeration, recirculation and harvesting) resulted in higher GWP (85% higher than Scenario-I). Other literature reported similar GWP of 1100 -2160 gCO2 Eq./m 3 using microalgae as a nutrient recovery option post to WW treatment (Arashiro et al., 2022; Schneider et al., 2018) (Figure ). However, when compared with Schneider et al, this work reports a 53% reduction in GWP.
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Eq./m 3 , when WW was treated with advanced treatment systems such as SBR and combined with microalgae systems. The above comparison clarifies that microalgae, when combined with other WW treatment might not reduce GWP and hence, the question arises was whether it could be considered for nutrient recovery. The answer to this question lies as when or if microalgae can be standalone WW treatment and nutrient recovery, a single-pot system like MFC. As MFC had a negative emission, only single-pot solutions can solve the environmental issues of nutrient recovery.
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Freshwater eutrophication corresponds to the direct impact of excess N and P in WW, when let out leads to algal blooms and growth of aquatic plants. This results in decrease of dissolved oxygen questioning the life in aquatic ecosystems. The N and P balance after secondary WW treatment corresponds to 22.3% and 43.4% respectively, which was let out into waterbodies causing eutrophication. The conventional WW treatment corresponds to a eutrophication levels of 277 g P Eq./m 3 , while Rodriguez-Garcia et al., (2014) reported 320 g P Eq./m 3 for similar conditions. The same work reported a reduction of 81% for a struvite precipitation based nutrient recovery from conventional treatment, while in this work 91% reduction was achieved in MFC (10% excess).
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Terrestrial ecotoxicity corresponds to the release of effluent and toxic gases in air, land, and waterbodies. Higher energy consumption results in the release of higher concentration of Arsenic and Chromium into the environment due to its presence in coal. These pollutants when enter the food web results in bioaccumulation. Conventional WW treatment (Scenario-I) corresponds to a terrestrial ecotoxicity levels of 386 g 1,4-DCB. When compared with conventional WW treatment, MFC (Scenario-II) reported a 580% reduction (Figure ). Other pilot-level studies on nutrient recovery reported a terrestrial ecotoxicity levels of 1000 -5000 g 1,4-DCB for treating 1 m 3 of WW (Rufí-Salís et al., 2020).
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Fossil resource scarcity corresponds to the amount of fossil energy used for various operations during the process. Net fossil oil scarcity was reported in a unit of g oil Eq. The fossil oil scarcity ranged between -36 to 313 g oil Eq. based on the scenario adopted. Bisinella de Faria et al., (2015) reported a fossil oil depletion in the range of 120-130 g oil Eq., when urine from WW was separated and used for nutrient recovery as struvite. Figure represents the characterization of the major impact categories such as a) ozone formation-human health, b) fine particulate matter formation, c) ozone formation-terrestrial ecosystems, d) terrestrial acidification, e) freshwater ecotoxicity, f) marine ecotoxicity, g) human carcinogenic toxicity, and h) human non carcinogenic toxicity for the five scenarios.
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Overall, the environmental performance of MFC was reported to outperform other scenarios including microalgae based nutrient recovery systems. The main attribution of MFC was that it was a single-pot system, where in it recovers nutrients as well as treat the WW simultaneously. Whereas, for microalgae systems, treated WW after secondary treatment was used. Hence, further studies on microalgae are necessary to understand its effect on a combined solution as a nutrient recovery and a raw WW treatment system.
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One of the objectives of this work was to esimate and compare the impact of bio-based fertilizer produced out of WW treatment with the petro-chemical based fertilizers. In India, three fertilizers were commonly used namely, urea, diammonium phosphate (DAP), mono ammonium phosphate (MAP) . The GWP of a fertilizer varies based on a factors such as production process and raw material usage. The GWP of conventional fertilisers varied between 6760 and 8980 g CO2 Eq./kg of fertilizer .
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Nutrient recovery to a WW treatment was an add-on process and hence, the GWP of WW treatment was ignored in this comparison. The GWP of fertlizer recovered from various nutrient recovery systems varied between 190 and 3000 g CO2 Eq./kg. When compared with conventional fertlizers, nutrient recovery options had shown a reduced GWP between 56 and 98% (Figure ). In addition, recovering nutrients reduces the import burden on the economy .
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The global nations have pledged to achieve 17 sustainable goals by 2030 to ensure equality, good health, and prosperity of people living across the world. SDG is a qualitative approach that requires quantitative validation for better understanding the effects of any industrial process . In this regard the LCA is used to evaluate the environmental performance of given industrial process. This LCA study reveal that the nutrient recovery from WW directly aids in production of biofertilizer which can act as substitute for fossilbased fertilizers thereby enabling to achieve SDG 2, 11, 12, and 15. Meanwhile production of organic fertilizer by recovering nutrients from WW helps to inhibit the water pollution (SDG 6). Detailed mapping of SDGs with nutrient recovery has represented in figure .
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The source of energy or electricity have a greater impact on the overall environmental performance of a WW treatment as well as the nutrient recovery system. The energy source must have a significantly reduced carbon footprint to have a less impact on the environment . Replacing fossil fuels with renewable energy can have a significant impact towards the reduction of GHGs. In this regard, a stepwise (25%) incremental share of renewable energy was used to analyse the effect of reduction in GWP.
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Table shows the reduction in GWP based on incremental renewable energy share. It was found that on incrementing the renewable energy share by 25%, 50%, 75%, 100% for all the five scenarios, the GWP reduced by 23%, 47%, 71%, and 94 -95%, respectively. Usage of renewable energy not only aids in enhancing the environmental performance of the nutrient recovery, but also helps in achieving self-sustainability in agriculture sector. The conventional STP process energized by 75% renewable energy could reduce 71% in GWP. The highest reduction in GWP (96%) was seen for MFC when 100% renewable energy was used to drive it.
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Nutrient recovery has the potential to avoid emissions compared with conventional fertilizers. However, the technology has different limitations based on location and adaptation of it. For instance, in developing countries like India, WW collection and treatment has not reached 100%, while advanced nutrient recovery systems are far from reaching reality. Nutrient recovery process has complex stages and substages that must be appropriately evaluated for the technology to be used on an industrial scale. Nutrient recovery systems have reached the demonstration level, which is indicated as TRL 4 -6.
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The life cycle inventory data taken for the nutrient recovery rate is 80% that needs experimental validation for different wastewater. As the WW has high load of bacterial content which might inhibit the nutrient recovery especially in algae growth. In addition, the applications and market value for the recovered products plays a vital role in achieving the feasibility of the system. The energy, water, and land footprint of these systems needs to be analysed to validate its sustainability.
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The life cycle assessment of four different nutrient recovery systems and traditional wastewater treatment were compared in this study. Form the results, it was identified that about 80% of the P present in the effluent can be recovered by employing single-pot system (Microbial fuel cell). Meanwhile, the maximum reduction in global warming potential of 36% was achieved when nutrient recovery system is combined with conventional wastewater treatment. The nutrients recovered from wastewater have significantly decreased the carbon footprint (56-98%) when compared to conventional fertilizer such as diammonium phosphate and urea. The results of this study demonstrate the necessity of single-pot treatment and recovery systems for improved environmental and economic performance. It is necessary to conduct more research on microalgae as a combined technique for nutrient recovery and wastewater treatment.
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The properties of a solid-state material are intimately coupled with its crystalline structure, pushing polymorphism, the ability of a molecule to self assemble into multiple solid-state crystalline forms, to the forefront of advanced material discovery. In the pharmaceutical industry alone, 90% of all drugs are sold in the solid state, making the solid-state form selection process of the utmost importance, as key material properties, such as bioavailability, shelf life, compactability, nucleation and growth kinetics, all depend on the polymorphic form employed . Although a molecule can assemble in 230 space groups, only a small fraction of these solid-state structures are ever obtained experimentally as current methods of crystallization, which rely on agitation rate, flow rate, solvent, temperature, and pressure as external control variables, only render a handful of the lowest energy metastable forms kinetically accessible. Thus, only a small fraction of the solid-state properties a molecule can exhibit are ever observed. The current inability to extend the landscape of obtainable crystal structures leads to issues such as the bioavailability crisis in pharma, where 60% of all newly discovered active pharmaceutical ingredients (API) possess poor aqueous solubility in the crystallized solid-state structures , thereby limiting the absorption of these drugs in vivo. Novel material synthesis methods are required to provide experimentalist with the tools to extend the landscape of accessible crystals to encompass all of the possible crystal lattices for a given molecule, and therefore unlock all potential solid-state material properties a molecule can exhibit. With initiatives such as the Materials Genome Initiative , and the growing field of assembly engineering , it is now recognized ubiquitously across government, industry, and academia, that computer simulation produced predictions are required to accelerate the discovery of these synthesis methods and materials at reduced cost. We attribute the importance of this work to its capacity to guide experimentalists towards manipulating crystal structures with electric fields constructed from atomic level insights provided by computer simulations.
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By manipulating a laser light field in space and time, electromagnetic radiation can be used to control the spatial positions and orientations of molecules, therefore potentially allowing the extension of the crystal landscape to encompass previously unobtainable, but now electric field stabilized, crystal lattices. Specifically, electric field controlled crystallization presents the tantalizing possibility of allowing dynamic and spatial manipulation of the underlying potential energy surface upon which the crystallization process is taking place. Formally, this amounts to adding a perturbation term to the molecular Hamiltonian that seeks to align the dipole moment of a molecule with the applied electric field . This is shown in equation (1):
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increased its region of stability, the melting temperatures of ice III and IV increased by 15 K, and the melting temperature of ice Ih was not impacted, in the presence of a 0.3 V/nm static electric field applied along the principal axis of the dielectric tensor, further illustrating the impact of the perturbation term in equation ( ) . MD simulations of sixsite and tip4p/ICE water models demonstrated that heterogenous nucleation rates increased in the presence of 1.5-3.5 V/nm and a 5 V/nm intensity electric field .
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Homogeneous nucleation simulations with the six-site water model demonstrated that the metastable ice Ic polymorph crystallized exclusively when subjected to 1-2 V/nm intensity electric fields, and that the ice Ic nanocrystal melting temperatures were 40 K higher in the presence of the field than in the no field scenario . This was attributed to the near perfect alignment between the ice Ic molecules and the applied electric field vector . However, ice nucleation kinetics were not demonstrated to change when subjected to a field strength 10 4 times weaker in experiments . Even for the large electric field intensities studied in molecules dynamics (~ 1 V/nm), the electric field induced forces are still a moderate fraction of the intrinsic forces, where the linear response regime is maintained for electric field intensities up to 0.7 V/nm . This potentially rationalizes why fields of much weaker strength are not successful in impacting crystallization kinetics of water, as the weak electric field induced forces are not of sufficient magnitude to compete with intrinsic forces. This demonstrates how the electric field induced forces may not impact the crystallization process without a sufficiently strong electric field intensity, and hence electric field induced forces. Outside the field of electrofreezing, MD simulations demonstrated that static field strengths between 0.5 V/nm and 3 V/nm induced dissociation of methane hydrate crystallites, as a result of the aligned water molecules facilitating transport of methane molecules out of the water cages . Similar dissociation of methane hydrate crystals were also observed in the work in work of English and MacElroy, where dissolution was facilitated by field strengths greater than 1 V/nm, and by frequencies between 50-100 GHz . Work recently performed by our groups demonstrated the ability of 1.5 V/nm electric fields to induce a solid-state transition of paracetamol, one of the most widely used antipyretic (fever suppressant) and analgesic (pain suppressant) drugs in the world, from the globally stable form I polymorph to a previously unknown, but electric field stabilized, polymorph , during the crystal growth process, posing the prediction that strong electric fields allow for the formation of novel polymorphic forms.
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What molecular dynamics can ultimately provide is a low cost computational screening tool for the selection of a well-defined spatial (or polarization state) and temporal distribution of an electric field vector that is consistent with Maxwell's equations, and which maximizes the formation of a desired material. Here, key properties of nucleation, growth, and dissolution rates, along with the polymorphic form produced, would be mapped as a function of the state of the applied field, allowing the question of "what is the optimal field for the formation of the desired material" to be addressed. To this end, we show that MD computer simulations predict that the dynamics and final solid-state form of a seeded glycine crystallization process can be controlled through the application of a static electric field. It is demonstrated how 𝛼-, 𝛽-, and 𝛾-glycine nanocrystals can be made to dissolve or grow at a rate unique to the applied electric field from a glycine aqueous solution. This is performed through an exhaustive screening of the applied electric field intensity. Furthermore, it is shown that the growth of the nanocrystals in the presence of strong electric fields takes place due to a solid-state transformation to a never before made polymorph of glycine. The resulting crystal morphology is also shown to be a function of the applied electric field strength. This new form is subsequently stabilized after the removal of the electric field through a temperature quench, but demonstrates electric field memory loss on longer time scales, yielding the prediction that the electric field vector would need to be applied throughout the crystallization trajectory to maintain the newly produced polymorphic form.
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2a. MD computational details. As done in our previous works , all MD simulations were performed with an MD code parallelized to fit the embarrassingly parallel nature of the crystallization trajectories . The details of the code can be found in the literature , and can either be obtained on github or through contacting the authors. Short-range non-bonded forces were truncated at 1.2 nm. Reciprocal space electrostatic forces were computed using a particle mesh Ewald (PME) solver with a 1 x 10 -6 error tolerance. 100 grid points were used in each direction for the PME solver. The electric field augmented equations of motion, equation (2), were solved using a velocity Verlet algorithm with a 2 fs timestep to generate atomic trajectories. The temperature was controlled using a Langevin thermostat with a relaxation time of 2000 fs. The isotropic Berendsen barostat was used with a 1000 fs relaxation time and a set point of 1 atm. A value of 21454.85 atm was used for the bulk modulus of water to determine the relaxation time constant in the Berendsen barostat. The shake algorithm was employed to constrain the motion of all bonds containing hydrogen. A shake tolerance of 1 x 10 -4 was employed for all simulations, and a maximum number of 25 shake iterations were allowed. Periodic boundary conditions were employed in all directions. All production simulations were performed at 330 K. 10 trajectories were simulated for each polymorph and electric field intensity to provide average growth and dissolution system dynamics.
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This force field combination is motivated by the work of Cheong and Boon, where the ability of MD to simulate 𝛼glycine crystallization was studied with four different force fields (CHARMM, GAFF, OPLS, and Gromos), two water models (tip3p and SPC/e), and five charge sets (CNDO, DZP, DNP, LCAO, and 6-31G * ) . Of all the force fields, charges, and water model combinations studied, only the GAFF/CNDO + SPC/e water combination produced the correct sign of the enthalpy of solvation, and hence was the only single force field set capable of simulation glycine crystallization . The sensitivity of the enthalpy of solvation to the molecular force field is well illustrated by previous glycine crystal growth simulations of Banerjee and Briesen, where bulk glycine crystal dissolution in aqueous solution was only observed, despite the high supersaturations and low temperatures employed, using the Gromos53a6 force field with SPC water .
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Although, issues may arise from the use of non-polarizable molecular force fields in the presence of time dependent electric field vectors. Here, previous studies of the microwave heating of water subjected to time-dependent electric fields demonstrated the ability of a polarizable water model (tip4p-FQ) to display better agreement with a macroscopic energy balance than a nonpolarizable water model (F-SPC) . However, given the sensitivity of the enthalpy of solvation to the force field/charges/water model employed, we elected to use the SPC/e water model, as it was the only force field combination that allows glycine crystallization to occur of all the combinations studied by Cheong and Boon, and is the force field used in our previous studies of glycine growth, dissolution, and nucleation in the absence of an electric field , allowing us to make rigorous comparisons to prior MD simulations of glycine and water crystallization.
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The specific number of glycine and water molecules in the simulation box for each polymorph can be found in supplementary table 1 in the supplementary material. To create an initial fluid, 2700 glycine molecules were solvated with SPC/E water using the gromacs/5.0 36 solvate command at a concentration of 0.34 g/ml. The fluid was then equilibrated by first performing NVT MD for 6 ns, and then NPT MD for an additional 6 ns at 380 K to prevent any crystallization from occurring. The box length of the equilibrated fluid was 9.8 nm. A single a-, b-, or 𝛾-glycine spherical nanonanocrystal, with a 2.3 nm radius, was then embedded in the equilibrated fluid using the gromacs/5.0 solvate command. Nanocrystals were sliced out of their respective bulk crystal structures obtained from the Cambridge Structural Database . The nanocrystals had an initial net zero dipole-alignment with the x-axis, as discussed below in section 3c. The number of solid molecules in the nanocrystals cut from their respective bulk structures can be obtained in supplementary table . The energy of the nanocrystal embedded in fluid system was then minimized in gromacs/5.0, using steepest descent minimization, with an energy minimization tolerance of 100.0 kJ/mol/nm. Production runs were then launched from this energy minimized configuration. Production simulations were performed for 4.2 ns.
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2b. Electric Field Implementation and Selection. At the beginning of production runs, a static electric field was applied in the x direction with no component in the y and z direction. A static field was chosen as the interaction between the molecule and the electric field would be mainly due to its classically defined permanent dipole such that higher order dipole terms, which are quantum mechanical in nature, and hence not captured in the GAFF /CNDO 33 + SPC/E molecular force field used in this work, can be neglected , allowing classical MD to be performed. Furthermore, the large permanent dipole moment of the glycine zwitterion (9.98 D with CNDO charges) and SPC/E water molecule (2.35 D), suggests that the effect of the electric field is accurately determined by classical mechanics where the electric field interaction with the permanent dipole is far greater than its induced dipole and other higher-order polarization counterparts. In the case of water, recent molecular simulation investigating into the polarizability of water under static fields have demonstrated that overall dipole moment of liquid water will only vary by 1% when subjected to a static field intensity of 5 V/nm . In this work, an exhaustive electric field screening was performed by simulating static electric field strengths of 0 V/nm (no field), 0.1 V/nm, 0.2 V/nm, 0.3 V/nm, 0.4 V/nm, 0.5 V/nm, 0.6
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V/nm for each nanocrystal. These field intensities are lower than the 5 V/nm field intensity necessary for a 1% change in the total dipole moment of liquid water, rendering induced polarization immaterial to the results stated herein. Future work towards incorporating polarizability into molecular mechanics force fields, that reproduce the enthalpy of solvation of organic molecules in various solvents, will allow for the accurate simulation of crystallization under time-dependent, and not only static, electric field vectors .
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To date, the static field intensities simulated in this work are larger than what has been experimentally applied to glycine crystallization systems, where glycine crystallization from solution has been studied under a 0.005 V/nm static electric field intensity from a 4500 V battery source . However, these intensities are in line with electric field intensities implemented in MD studies, which are on the order of 1 V/nm, as outlined in the introduction. Despite these large field strengths, the system remains in the linear response regime, where electric field induced forces are no more than a few percent of the intrinsic forces , and the energy of the electric field molecule interaction is only a few multiples of the thermal energy.
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2c. Solid Molecule Identification. Solid and liquid particles were differentiated based on the local density of a molecule, a method previously employed for solid-molecule detection in glycine , NaCl , and paracetamol , along with the rest of the source code used to perform the simulations herein. For all production runs, 𝑛 was calculated at a 2 ps interval.
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2d. Water Analysis. The impact of the applied electric field on water is first investigated through radial distribution function (RDF) analysis to determine if the applied electric field intensity is sufficiently high to induce ice crystallization. The OW-OW and HW-HW RDFs calculated from the no field and 0.6 V/nm electric field intensity simulations are compared to discern any structural changes indicative of freezing. Snapshots of atomic coordinates for RDF calculations were gathered at 25 ps intervals from a single production run trajectory for RDF calculation.
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In addition to RDF analysis, the locally averaged Steinhardt order parameters, 〈𝑞 @ 〉 and 〈𝑞 B 〉, are calculated for each water molecule, to further address the possibility of ice crystallization . The Steinhardt order parameters are local bond order parameters based on spherical harmonics that have been frequently used in the literature to monitor ice formation . In the locally averaged form, 𝑞 @ and 𝑞 B of a given molecule is averaged over all neighbors within the first RDF shell, to yield 〈𝑞 @ 〉 and 〈𝑞 B 〉. These order parameters have been demonstrated to yield good separation between ice Ic, ice Ih, and water 〈𝑞 @ 〉 vs. 〈𝑞 B 〉 distributions at lower temperatures, allowing for the identification of ice molecules based on the 〈𝑞 @ 〉 and 〈𝑞 B 〉 values of an individual molecule . In this work, the locally averaged Steinhardt order parameters were calculated using the position of oxygen atoms from all 10 simulation trajectories at the conclusion of the simulations.
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2e. Morphological Analysis. The morphology can be analyzed through the sphericity (𝑆) of the nanoparticle in question . 𝑆 can be calculated at any instant in time through quantitative analysis of the moment of inertia tensor. Diagonalizing this tensor yields the principal moments and axes of inertia through the eigenvalues and eigenvectors respectively. Specifically, 𝑆 is given by the ratio of the minimum and maximum eigenvalues of the moment of inertia tensor as shown in equation ( ):
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2f. Temperature Screening Procedure. To study the stability of nanocrystals grown in the presence of the electric field, temperature-screening simulations were performed. The electric field was instantaneously switched off after 4.2 ns of simulation, and the set point temperature for all 10 trajectories, from the crystal grown from the initially 𝛼-glycine seed, was reset to a new temperature. The velocities were reinitialized according to the new set point temperature. The resulting 𝑛 and solid glycine dipole alignment were then monitored with time in the absence of the electric field. The initially 𝛼-glycine seed system was selected for temperature screening analysis, as the crystal size produced from this system was smaller at the end of the 4.2 ns of 0.6 V/nm electric field simulation than the crystal produced by either 𝛽-, or 𝛾-glycine. As the stability of a nanocrystal decreases with decreasing size due to an increased surface area to volume ratio, the crystal produced from 𝛼-glycine provided the hardest test case to prevent solid-state conversion of the new form to 𝛼-, 𝛽-, or 𝛾-glycine.
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3a. Dissolution and Growth Rate Analysis. The dissolution and growth results for all electric field intensities and polymorphs are shown in figure . As displayed in figure plot D, the application of electric field intensities less than 0.3 V/nm accelerates the dissolution of the 𝛼and 𝛽-glycine nanoparticles. Both 𝛼and 𝛽-glycine dissolve at a rate 3 times faster at 0.2 V/nm (~ -150 molecules/ns) than in the case of no field (~ -50 molecules/ns), allowing for a wide window of control over the dissolution rate. Unlike its counterparts, 𝛾 -glycine is only stabilized by the electric field, and dissolves at a decreasing rate with increasing field intensity. Remarkably, 𝛼 -, 𝛽 -, and 𝛾 -glycine nanocrystals can be forced to grow at rates upwards of 140 molecules/ns from an initially undersaturated solution for electric field intensities greater than 0.4 V/nm. This shows that the dissolution and growth rates of glycine nanocrystals in solution can be manipulated over two orders of magnitude through the application of the electric field, providing a significant control variable over the crystallization process dynamics. As such, crystal size distributions, which impact critical downstream processes such as milling and drying, are predicted to be controllable through manipulating the electric field intensity.
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The strong impact of the electric field intensity observed in this work is analogous to the observation made by Knot et al. in which the effects of different pulse durations and intensity were tested and the latter, but not the former, has a significant effect of the success of nucleation . Furthermore, the manipulation of growth and dissolution dynamics through varying electric field intensity in MD simulations has previously been demonstrated in our work with paracetamol nanocrystals in aqueous solution. However in the case of paracetamol, the electric field was found to only impede the crystallization growth rate at 300 K . The paracetamol aquesous solution system at 370 K, however, demonstrated that dissolution rate could be increased or decreased by a factor of two, depending on the magnitude of the applied electric field . This shows that MD predicts that the magnitude of the variation in the crystallization kinetics, in response to the applied electric field vector, will be both material, and temperature, dependent, yet provides reaffirming evidence that the crystallization growth and dissolutions dynamics will be impacted by the application of an externally applied electric field vector.
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3b. Water Analysis. The electrofreezing of water has been reported previously in the literature using the tip4p and six site water model, as outlined in the introduction. In the work of Yan et al. for example, it was observed that electric field intensities between 1-2 V/nm could induce the electrofreezing of the six-site water model within 50 ns at 270 K . The electrofreezing of water was attributed to the near 40 K elevated melting temperatures of ice Ic crystals, relative to the no field 289 K melting temperature, due to near perfect alignment with the applied electric field vector . In this work however, the SPC/E water model is employed to accurately reproduce the enthalpy of solvation of glycine in water , as outlined in section 2a. In contrast to the 289 K melting temperature of the six-site water model, the melting temperature of SPC/E water is only 215 K in the absence of any dissolved solute . Previous observations by Svishchev and Kusalik demonstrated that pure SPC/e water did not undergo electrofreezing, even with electric field strengths as large a 5 V/nm . These facts make it highly unlikely that the lower electric field intensities (0.6 V/nm), higher temperatures (330 K), and dissolved solute (glycine), used in this work could facilitate electrofreezing. However, this must be confirmed quantitatively.
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As mentioned in the computational details section, the OW-OW and HW-HW RDFs were calculated using both the no field and the 0.6 V/nm intensity electric field data from the 𝛼-, 𝛽-, and 𝛾glycine simulations. This is done to observe whether any structural differences corresponding to ice Ic peaks , the form of ice observed to crystallize during electrofreezing , were observed. Although the growth and dissolution of nanocrystals in the presence of the electric field is a nonequilibrium process, any structural differences between the calculated distributions can be used to analyze the impact of the electric field vector on the water molecules. The resulting OW-OW and HW-HW RDFs are plotted below in figure . In all cases, the no field and 0.6 V/nm intensity electric field RDFs are nearly identical, implying that the structure of water is at most only weakly impacted by the applied electric field intensity. This is consistent with the analysis of Yan, Overduin, and Patey who found that the structure of six-site liquid water remains qualitatively unchanged by polarization due to the electric field . Furthermore, the structural and quantitative similarities between the RDFs show that electrofreezing did not occur to an observable extent, as the RDFs would show similarity with the ice Ic RDF , and not that of liquid water.
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〈𝑞 B 〉 plot will be indicative of electrofreezing. The 〈𝑞 @ 〉 vs. 〈𝑞 B 〉 results for the no field case, and the 0.6 V/nm electric field intensity, are plotted in figure . The distributions are broad and diffuse due to the high temperature at which the simulations were performed in this work. This would render the labeling of individual particles as ice or liquid based off 〈𝑞 @ 〉 or 〈𝑞 B 〉 alone impossible at these temperatures, as the 〈𝑞 @ 〉 vs. 〈𝑞 B 〉 distributions will likely overlap for ice and water molecules. However, the location and density of data points can still be compared between the no field and electric field simulations through visual inspection to glean whether any change due to ice formation is present. Similar to the RDF results, figure shows the electric field results in no discernable variation in the 〈𝑞 @ 〉 vs. 〈𝑞 B 〉 plot for any of the glycine polymorph systems.
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In total, neither the RDFs nor Steinhardt order parameters provide any evidence to suggest that electrofreezing of SPC/e water occurred or contributed to the results stated herein. These results are in agreement with the previous observations of Svishchev and Kusalik, who also did not observe the electrofreezing of SPC/e water in their MD simulations .
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3c. Alignment Analysis. As evidenced by equation ( ), the electric field induces a potential that seeks to align the glycine dipole moment with the applied electric field vector. Hence, the electric field will stabilize the phase, either liquid or solid, that can align with the electric field (larger < cos(𝜃) >) on the fastest timescale. As such, the average alignment of both solid and liquid glycine, as well as water molecules, with the applied electric field was calculated as a function of time.
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The alignment results are shown in figure . For solid glycine, liquid glycine, and water molecules, the alignment with the electric field vector is found to be a monotonically increasing function of increasing electric field intensity. This is equivalent to previous observations of the alignment response from both water molecules , and paracetamol molecules , to increasing static electric field intensity. For all electric field intensities, the alignment of solid-state and liquid glycine is larger than that of liquid water molecules after 4.2 ns of simulation. This is agreement with the ranking of glycine > water ranking of dipole moments, where the 9.98 D dipole moment of the glycine zwitterion (estimating using CNDO charges) is nearly four times larger than the 2.35 D dipole moment of SPC/E water molecules. As such, the electric field induced forces seeking to align glycine molecules are larger, favoring a higher degree of alignment for glycine. However there is a transient associated with obtaining preferable alignment of solid-glycine molecules relative to water. Here, the time needed for solid glycine molecules to reorient preferably to liquid water molecules is a decreasing function with increasing electric field intensity. The electric field intensity dependent, time delayed, alignment of solid-state glycine molecules suggests that the reorientation to an electric field aligned glycine orientation is kinetically hindered due to an energy barrier. The increasing electric field strengths provide the necessary force to push the glycine molecules over the barrier, hence increasing the rate at which solid glycine molecules align.
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In the absence of the electric field vector, the system is undersaturated, evidenced by the dissolution of the nanocrystals in the no field case in figure . Furthermore, in the case of 𝛼and 𝛽glycine, it is observed that the solid-state glycine molecules are not able to reorient sufficiently to adopt an orientation more favorable (larger < cos(𝜃) >) than the liquid glycine molecules for electric field intensities less than 0.3 V/nm over the course of the simulation. The more favorable alignment of liquid phase glycine molecules enhances the stability of the liquid relative the solid, as conveyed by equation ( ), thereby increasing the rate of dissolution for electric field intensities less than 0.3 V/nm relative to the no field case. For the 0.2 V/nm case, the differences in alignment between solid and liquid molecules at the start of the simulation is largest, rationalizing the maximization of the dissolution rate observed for 𝛼and 𝛽-glycine at this electric field intensity. For electric field intensities above 0.5 V/nm, there is a reversal in the phase stability ranking, as crystal growth is observed. Here, solid glycine molecules reorient on a timescale similar to the liquid glycine molecules, and adopt a more favorable orientation, making the solid-state increasingly the preferred phase with increasing electric field intensity, hence facilitating crystal growth. In all cases, initially 𝛾-glycine molecules are able to reorient to a more favorable orientation than the liquid glycine molecules, rationalizing how the 𝛾 -glycine nanocrystal was only stabilized by the application of the electric field, and the dissolution kinetics did not increase with increasing field intensity. These results provide the prediction that the observed crystallization behavior of glycine as a function of applied electric field intensity is a result of a solid-state and liquid phase glycine competition over preferential alignment with the electric field vector on the fastest timescale. This finding, namely the competition between solid-state and liquid phase alignment driving electric field dependent growth or dissolution, is equivalent to our previous findings in the case of paracetamol from aqueous solution , suggesting that this may be a general finding displayed in seeded electric field crystallization MD simulations.
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3d. Polymorph Analysis. The reorientation of solid-state molecules to aligned configurations suggests a solid-state transformation, as the no field case in figure definitively shows 𝛼-, 𝛽-, and 𝛾-glycine possess no alignment in the x direction on average. Figure shows representative snapshots of the final state of the crystal structure from the 0.6 V/nm simulations for each initial nanocrystal. It is immediately apparent that there is no longer any indication of the initially present 𝛼-, 𝛽-, or 𝛾-glycine, and each nanocrystal has undergone a solid-state transformation to a previously unknown polymorph of glycine. In the newly discovered form, the glycine molecules pack in layers with hydrogen bonding between the positively charged amino group and negatively charged carboxyl group in separate layers. The new polymorphic form arranges glycine molecules such that C-N and C-O bonds are parallel respectively both within and between layers. This allows the dipole moment of the solid glycine molecules to point directly down the electric field vector, making it the most stable polymorphic form in the presence of the strong static field. This demonstrates how the field vector directed the assembly of an otherwise unseen polymorphic form, which only becomes accessible through electric field stabilization. Furthermore, the molecular motif of the unit cell could have simply been guessed through dipole alignment maximization, in agreement with the optical Kerr mechanism, which posits that the form produced will be the one which optimally aligns with the applied field . From figure , a characteristic induction time for the completion of the solid-state transformation can be inferred from the elapsed time between the application of the field, and the time at which the dynamics display growth.
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Of the three polymorphs, 𝛾-glycine shows the fastest solid-state transition rate, where the growth of the initially 𝛾-glycine nanocrystals takes places 0.25 ns after the application of the 0.6 V/nm field. This is in contrast to the case of 𝛼and 𝛽glycine, where growth occurs 0.5 ns after the application of the 0.6 V/nm field in the case of 𝛽-, or 1 ns after the application of the 0.6 V/nm field in the case of 𝛼-glycine.
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The crystallization of a material whose dipole moment displays maximal alignment with an applied static electric field has also been observed in the case of paracetamol 28 and ice . In the case of paracetamol, it was observed that 1.5 V/nm static electric fields applied during nanocrystal growth from aqueous solution induced the formation of a new polymorph of paracetamol, where the dipole vectors of paracetamol molecules in the new solid-state form displayed maximal alignment with the applied electric field vector , which is an equivalent finding to the results stated herein. In the case of ice, it was found that the application of an electric field resulted in the exclusive formation of ice Ic, a well-known metastable form of ice predicted to be kinetically competitive during nucleation by MD in the absence of field effects . This phenomenon is consistent with the observations in this work as well, as the chair conformation in cubic ice allowed for near perfect alignment with the applied field. Furthermore, ice crystals were grown from solution, allowing the cubic ice crystal to grow at a maximally aligned orientation with the field along the nucleation pathway. This shows that one of the already known low energy metastable ice structures is able to optimally align with a static field such that the formation of a new material is unnecessary. For the polymorphs of glycine however, as well as the polymorphs of paracetamol, the embedded 𝛼-, 𝛽-, and 𝛾-glycine nanocrystals show near zero alignment on average (figure shown for the case of the initially 𝛼-, 𝛽-, and 𝛾-glycine nanocrystals in figure . As the nanocrystals obtained from the bulk structures were speherical, the initial value of 𝑆 was above 0.95 for all initial nanocrystals (data not shown). The 𝑆 at the conclusion of simulations is observed to be a decreasing function with increasing electric field intensity for all initial polymorphic forms, showing that the electric field vector can control the morphology of nanocrystals in addition to the polymorphic form and crystallization kinetics. However, 𝑆 appears to be impacted little by increasing the electric field intensity past 0.4 V/nm. In the absence of the applied electric field, 𝛼and 𝛽-glycine nanocrystals dissolve along a spherical dissolution mechanism, where with the final 𝑆 after 4.2 ns of simulation is 𝑆=0.78 and 𝑆=0.76 respectively. To the contrary, 𝛾-glycine dissolves along a non spherical dissolution mechanism, in the absence of the field, with the final value being only 𝑆=0.48, a 38% decrease in sphericity relative to the no field 𝛼and 𝛽-glycine nanocrystals. For all systems, 𝑆 obtains a final value of approximately 0.4 during the 0.6
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The initially spherical 𝛼-, 𝛽-, and 𝛾-glycine nanocrystals, as well as representative final nanocrystals resulting from crystal growth in the presence of the 0.6 V/nm intensity electric field vector, are shown in figure . The effect of the applied electric field on the crystal morphology is to compress the crystal along the z-axis and to elongate the crystal along the x-axis, the principal axis, in the direction of the electric field vector. This result is akin to the observations of English and MacElroy who observed the elongation of methane hydrate crystals along the electric field vector, further demonstrating the potential of electric fields to aid in crystal habit control in pharmaceutical applications .
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3f. Temperature Quench Analysis. To test whether the new polymorphic form can be stabilized in the absence of the applied electric field, we performed temperaturescreening simulations to find the temperature at which the newly made nanocrystal neither grows nor dissolves on average (i.e. melting temperature) with no electric field applied. In these simulations, the electric field was removed, and the temperature set point was instantaneously changed to the new set point value. The temperature screening results are shown in figure . The estimated melting temperature of the new form nanocrystal is approximately 285 K. As displayed, by temperature quenching to 270 K, the newly discovered form can be stabilized from dissolution, and to the contrary, exhibits crystal growth. To determine if a solid-state conversion had taken place to the previous 𝛼-, 𝛽-, or 𝛾-glycine form, < cos(𝜃) > was calculated as a function of time after the temperature quench to 270 K. As shown in figure , the alignment shows a slow decay in time, but remains significantly above < cos(𝜃) > = 0 implying no transition to 𝛼-, 𝛽-, or 𝛾-glycine has completed, and thus demonstrating that the new form can be stabilized at short times. Similar decays in alignment have been observed in the case of liquid SPC water and the electric field induced polymorph of paracetamol . This demonstrates that frequent laser pulses may be required to preserve the newly produced polymorphic form, as the nanocrystals grow in size.
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A comparison with recently calculated nanocrystal glycine melting temperatures of 𝛼-, 𝛽, and 𝛾-glycine nanocrystals of comparable size show the melting temperature of the new form to be approximately 30 to 40 K lower than the 𝛼or 𝛽-glycine 30 , the two kinetically competitive forms during crystallization in water, clearly demonstrating thermodynamic instability of the new form, and explaining why it is not formed at either the nanoscale or micron scale , in the absence of the electric field. In comparison to 𝛾-glycine nanocrystal melting temperatures, the newly produced form is found to be competitive in stability at the nanoscale. Once formed, nanocrystals of the new polymorph are predicted to possess a large increase in the solubility relative to 𝛼and 𝛽-glycine, resulting from the reduced melting temperature. This presents a new method to combat low bioavailability API crystals, as the reduced melting temperature, and increased solubility, of electric field produced metastable forms may translate directly to enhanced dissolution kinetics in vivo .
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In this work it is shown how the kinetics of a seeded crystallization process can be controlled through the application of an electric field. Not only were crystals made to dissolve at rates unique to the applied field, but also were forced to grow from an undersaturated solution, providing an additional control variable over crystal size distributions and crystallization dynamics. Analysis of the resulting crystal structure from the growth process reveals the formation of a previously unknown polymorph of glycine that maximizes the alignment of glycine molecules in the solid-state with the applied electric field, in agreement with the optical Kerr mechanism. In the newly discovered form, the glycine molecules pack with hydrogen bonding between the positively charged amino group and negatively charged carboxyl group in separate layers, with parallel C-N and C-O bonds within and between layers, making the dipole moment of each glycine molecule point directly down the applied electric field vector. This shows how applied fields can be used to stabilize and form hitherto unknown materials. Furthermore, the electric field is shown to direct the creation of needle like morphologies. Here, the glycine nanocrystals are observed to elongate and grow down the applied electric field vector. Through a temperature quench, the new form was stabilized from solid-state reversion to 𝛼-, 𝛽-, or 𝛾-glycine over a 5 ns simulation. These simulations present not only a novel control mechanism for growth and dissolution, but also novel polymorphic form production, showing how electric fields are predicted to be able to extend the landscape of accessible crystal structures, and unlock new solid-state material properties.
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Chemical and biochemical structures and processes are of great interest to machine learning with graph neural networks, as they are supposedly well-represented by undirected and directed graphs, respectively . Conversely, machine learning plays an ever-increasing role in the life sciences, where new methods have been adopted and adapted for a wide range of tasks such as the prediction of physico-and quantum-chemical properties in material science, the prediction of pharmacokinetic properties in drug development, the prediction of binding affinities between small-molecule ligands and proteins in drug discovery, or the prediction of chemical reaction yields in synthetic and process chemistry .
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With the introduction of graph neural networks (GNN), graph representation learning for molecules attracted a growing interest, as these neural network architectures allowed representation learning directly on the molecular graphs rather than first extracting features or precalculating descriptors from a given chemical structure , with newly proposed methods continuously escalating the architectures' complexity or amount of precomputed or, less likely, experimentally measured molecular properties, such as 3D coordinates or structural motifs, that are added to the graph . However, even though the published literature often touts the benefits of introducing new features based on molecular composition and topology, it is generally ignored that these features are also implicitly encoded by lower-order representations.
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For example, the most-used text representation of molecules, SMILES, are a string-encoding of the depth-first tree traversal of the molecular graph retaining all topological information and, in the case of isomeric SMILES, geometrical information pertaining to stereochemistry . The same applies to molecular fingerprints, which often even explicitly encode topological features . Meanwhile, the molecular graph introduces implicit constraints on the molecular 3D geometry, as topology and atom types induce structure. Conversely, representing a molecule as a graph often only encapsulates an approximation of molecular topology and geometry, as only a subset of chemical bonds, the covalent Molecular Set Representation Learning bonds, can be represented in this static data structure. However, in addition to covalent bonds, molecules and substances used as drugs or materials also contain ionic and metallic bonds generally not well represented in molecular graphs.
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In addition, dynamic intermolecular interactions such as hydrogen bonds and π-stacking are common occurrences in ligand-protein binding, which is of high interest in medicinal chemistry . Furthermore, specific bonds are not well defined in conjugated systems such as aromatic rings, as electrons are delocalised over multiple atoms and bonds. Atomic number: {0,1} 101 Formal charge:{0,1} Hybridization: {0,1} Chiral tag: {0,1} In ring: {0,1} Total hyrogens:{0,1} Bond Type: {0,1} Stereo: {0,1} Is Aromatic: {0,1} Is Conjugated: {0,1} Given this often somewhat fuzzy notion of bonds in molecules, we hypothesize that representing a molecule as a set of atoms rather than a graph may capture the true nature of molecules better than explicit graph representations while preserving implicit information about molecular structure. In this set-based approach, each atom is represented as a vector of one-hot encoded atom invariants as defined by Rogers & Hahn [12] (see details in Section 4.2). While this representation may encode the local topology of a molecular graph through these invariants, e.g. the degree of an atom, it does not encode any explicit connectivity of the molecular graph. In the context of set representation learning, a molecule is therefore defined as a set of k-dimensional vectors ⃗ a where the set's cardinality is the number of non-hydrogen atoms in the molecule. However, this set-based representation introduces two properties that are not supported by typical neural network-based machine learning architectures: (i) The cardinality of the molecular sets differs depending on the number of non-hydrogen atoms in a molecule, and (ii) the molecular sets are unordered.
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In addition, the architecture must support multiset input, as the number of identical vector representations of atoms matters in the context of molecular sets. Given these requirements, specifically the need for permutation invariance, it is insufficient to simply pad the sets. Therefore, performing machine learning tasks on such molecular sets requires a Molecular Set Representation Learning neural network architecture capable of permutation invariant representation of variable-sized sets. Over the past five years, multiple architectures, including DeepSets, Set-Transformer, or RepSet, have become available that fulfil these requirements .
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Here, we introduce several of what we denote molecular set representation learning architectures based on the scheme described above and in Figure , and evaluate them against widely used GNN methods on a wide array of tasks, including physico-and quantum-chemical property prediction for material science, pharmacokinetic property prediction for drug design, protein-ligand affinity prediction for drug discovery and biochemistry, and reaction yield prediction for synthetic and process chemistry. We show that using the concept of molecular set representation learning and combining it with GNN architectures, we can not only simplify current approaches but also improve on commonly used GNN implementations such as D-MPNN, GAT, or DimeNet . Furthermore, we uncover that compared to more modern benchmark data sets, extensively used older benchmark data sets may not be well-suited to evaluate the advantages of GNNs, as they perform worse than the most simple of our models. Finally, we introduce an easy-to-use, extensible collection of molecular set representation architectures ready to be used in various fields, including materials science, drug discovery and development, biochemistry, and synthetic and process chemistry.
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the formal charge, (4) the hybridization state, (5) the chiral tag as defined by RDKit, (6) whether the atom is in a ring, and (7) the number of hydrogens covalently bound to the atom. MRS2 expands on this concept and implements a neural network architecture with two parallel set representation layers, where the first takes the same input as the single layer in MSR1. In contrast, the second takes a set of vectors encoding bond invariants as an input. We include the following bond invariants: (1) the bond type, (2) whether the bond is aromatic, (3) whether the bond is conjugated, (4) the degree of the two atoms forming the bond, and (5) the atomic numbers of the two atoms forming the bond. Therefore, with MSR2, we introduce more information about molecular topology while avoiding explicit definitions of topology beyond bonded atom pairs. In addition to the purely set-representation architectures, we introduce SR-GINE, a graph invariant network with edge attributes (GINE) and a set RepSet representation pooling layer instead of global mean pooling in the vanilla GINE implementation. In all our architectures, the output of the set representation layer is read by an MLP with a single hidden layer for regression or classification. In the case of dual-set architectures, such as MSR2, the two sets' outputs are first concatenated. Finally, we chose the combination of RepSet and GINE based on their respective reported performances and the inert interpretability of RepSet . Further reasoning and data substantiating our choice can be found in Section 4.3. To benchmark our proposed architectures, we rely on well-known and recently published data sets to compare our method to widely used graph-based methods as a baseline. Initially, we focused on evaluating our methods on data sets commonly known as the MoleculeNet benchmark. We selected the relatively small data set BBBP (n = 2039), with Molecular Set Representation Learning the task of classifying small molecules on whether they penetrate the blood-brain barrier, to tune the hyperparameters, namely the number of hidden sets, the number of elements in the hidden sets, the number of epochs, as well as the number of hidden channels in the MLPs of all our models. Unless otherwise indicated, the established hyperparameters were used for all the benchmarks discussed in this study. We then compared our model to the performance achieved by MGCN (multiscale graph convolutional network), SchNet (quantum chemical deep tensor neural network), GCN (graph convolutional network), GIN (graph isomorphism network), and D-MPNN (directed message-passing neural network), as reported by Wang et al. [20]. In addition, we compare our approach to the current state of the art outside graph neural network-based approaches, namely MolFormer, a chemical large language model trained on approximately 100 million molecules extracted from the ZINC and PubChem databases . As a control, we benchmark an implementation of GINE with the standard global mean-pooling layer and the same one-hot encoded vectors as atom and bond attributes that were used for MSR1 and MSR2 . For all data sets, Murcko scaffold splits in accordance with Yang et al. [17] and
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As shown in Table , MSR1, the simplest of our models, exhibits a performance close to existing GNN approaches, namely GIN and D-MPNN, without any explicit topological information about the molecular graph. Indeed, it performed better than D-MPNN in 5 out of 11 benchmark data sets and better than GIN in 8 out of 11. This may suggest that up to now, too much value has been assigned to representing a molecule as a graph rather than a loose set of atoms.
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did not improve upon the performance of MSR1 as expected but performed generally worse. Finally, replacing the global mean-pooling layer of GINE with RepSet improved its performance in 8 out of 11 benchmarks. Overall, these results are promising in light of our hypothesis, which stipulates that a more relaxed definition of molecules than the one provided by graph encoding may be beneficial. However, as discussed previously, the performance of our simplistic models, especially MSR1, may be due to limitations of the data sets. Hence, we benchmarked our architectures on two recent and well-received data sets, the results of which are discussed in sections 2.1 and 2.2. In addition to these more generalized architectures, we introduce two architectures based on the dual-set approach of MSR2 tailored towards binding affinity prediction in protein-ligand complexes and reaction yield prediction in sections 2.3 and 2.4, respectively.
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The prediction of physicochemical properties is a common task in machine learning for chemistry, as the elucidation of these properties through either laboratory high-throughput screening or simulation-based computation is expensive and time-consuming at best and intractable at worst . Hence, multiple approaches have been proposed to enable data-driven approximation of properties such as frontier molecular orbital energies, the molecular dipole moment, rotational constants, or ionisation potentials. During our exploratory study of our proposed architectures on the quantum chemical benchmark data sets QM7 and QM8 (Table ), we found that our simplest model (MSR1) exhibited better performance than both GIN(E) and D-MPNN on QM7 and better performance than GIN(E) on QM8. In this section, we further investigate the performance of our models on additional physico-and quantum-chemical prediction tasks using the OCELOT chromophore data set .
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The OCELOT chromophore data set contains chemically diverse π-conjugated molecules, meaning that our set-based architectures should, according to our hypothesis, perform better than graph-based architectures as they put less emphasis on specific bonds . For this data set, we changed our hyperparameters to reduce the size of all our models to less than 100K parameters, as the relatively high number of samples and tasks, combined with the 5-fold cross-validation, requires non-trivial computational resources. The original study used the data set to train a hierarchy of models that follow increasingly complex architectures, peaking with a message-passing neural network for quantum chemistry .
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In addition, the output of the MPNN was concatenated with precomputed molecular descriptors before the FFN. We denote this model MPNN+ in Table . Furthermore, a method based on a fingerprint-descriptor combination, which we donate ECFP2+, showed exceptional performance in the original study. ECFP2+ is a feed-forward neural network that takes ECFP fingerprints with radius r = 2 concatenated with precomputed molecular descriptors as an input.
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Our most straightforward model, MSR1, performs as well as MPNN over all predicted properties (paired t-test, p = 0.529), as MPNN performs remarkably poorly on the HOMO and H-L tasks. On the other hand, both setbased models, MSR1 and MSR2, perform significantly worse than MPNN+ (paired t-test p < 0.001 and p < 0.002, respectively). These results suggest that adding explicit bonds and introducing message-passing does not significantly improve the predictive accuracy on the OCELOT data set, and in order to improve performance, additional molecular precomputed descriptors are needed; however, in practice, the choice of model may be influenced by the property of interest given the poor performance of MPNN on specific tasks, namely, HOMO and H-L. Over all properties, the set-enhanced model SR-GINE performs significantly better than GINE (paired t-test, p < 0.0001), yet not significantly different from the MPNNs (paired t-test, p < 0.138), although without the significant outliers observed when predicting To compare our set-based approach to a current state-of-the-art chemical large language model we finetuned the publicly available pretrained variant of MolFormer on OCELOT (see Section 4.6). Interestingly, the finetuned MolFormer performed below expectations compared to the MoleculeNet benchmark. A reason for the comparatively lower performance could be a lack of relevant samples in the original training set of the publicly available variant of MolFormer .
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Together with the results on QM7 and QM8 (Table ), the results of the OCELOT chromophore benchmark suggest that set representation learning can perform as well as graph representation learning on physico-and quantum-chemical prediction tasks. Furthermore, combining graph and set representation learning, as is done with SR-GINE, exhibits synergistic effects that result in overall enhanced performance. Specifically, the significant performance increase of SR-GINE over GINE indicates that a set representation layer in lieu of a global pooling function can improve existing GNN architectures.
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A molecule's pharmacokinetic properties play an essential role in designing and developing new therapeutics . However, experimental pharmacokinetic data from in vitro and vivo experiments is scarce, as it is expensive to generate, making its approximation a priority for machine learning research . To evaluate our models' performance on pharmacokinetic tasks, we use the data set recently published by Fang et al. [31]. The data set contains 3,521 commercially available compounds that were tested against the following endpoints in Biogen ADME in vitro assays: Human liver microsomal stability (HLM, clearance in mL/min/kg), MDR1-MDCK efflux ratio (MDR1-MDCK ER, permeability with Madin Darby Canine Kidney cells transfected with MDR1), solubility at a pH of 6.8 (Solubility, ug/mL), rat liver microsomal stability (RLM, clearance in mL/min/kg), human plasma protein binding (hPPB, percent unbound), and rat plasma protein binding (rPPB, percent unbound). Fang et al. [31] provide baselines trained on the data set for random forests (RF), gradient boosting (LightGBM), a hyperparameter-tuned directed message-passing neural network (D-MPNN), and a hyperparameter-tuned directed message-passing neural network plus precomputed RDKit 2D descriptors (D-MPNN+) . Values for additional models can be found in the original publication. As input for RF and LightGBM, Fang et al. [31] concatenated 1024-bit binary functional connectivity fingerprint with radius 4 (FCFP4) concatenated with 316 2D descriptors that were precomputed using the RDKit package . In addition, we finetuned the publicly available pretrained variant of MolFormer on the Biogen ADME data set (see Section 4.6).
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Over all pharmacokinetic endpoints, SR-GINE performs significantly better than the control GINE (paired t-test, p = 1.98 • 10 -5 ), which uses the standard mean pooling instead of a set layer. Furthermore, the SR-GINE model ). As the benchmarks found in MoleculeNet remain the most used and cited when benchmarking new graph neural network architectures, our results may show a need to adopt a different practice or update MoleculeNet with more recent data sets when assessing possible advantages of graph representation-based approaches. In addition, the difference in performance between graph-and set-based methods with that of the chemical large language model (MolFormer) is not as stark on the Biogen ADME data set as it was in the MoleculeNet benchmarks. Indeed, MolFormer does not perform significantly better than SR-GINE (paired t-test, p = 0.158).
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Binding affinity is an important metric in biology and medicinal chemistry that measures the strength of a reversible association between biological macromolecules, such as proteins or DNA, and small-molecule ligands, such as drugs. It is, therefore, a central concept of rational drug design, where the potential efficacy of a drug is measured by its binding affinity to a known biological target implicated in a pathology the drug should treat . Traditionally, simulation-based molecular docking techniques, such as scoring functions, overfit to use-cases that adhere to rigid modelling assumptions, do not fully represent protein flexibility, and do not directly account for solvent effects . Non-parametric machine learning has been proposed as an alternative to infer complex binding effects that are difficult to explicitly represent directly from experimental data . Therefore, a wide array of neural network architectures combined with a multitude of scoring functions have been proposed . approaches that make use of engineered features and precomputed molecular descriptors such as the ECFP-inspired extended connectivity interaction features (ECIF) .
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The encoding of the ligand-protein complex consists of creating a multiset of atoms for the ligand and one for the protein, respectively. The set L representing the ligand is constructed by iterating over the atoms of the ligand, and adding those that are within a radius of r from any atom in the protein to the set. The set M representing the protein is constructed in the same way, however, with the roles of the ligand and protein reversed. The optimal value of r = 5.5
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We evaluated our method based on PDBbind splits and metrics of basic GNN methods architectures reported by Li et al. [39]. SR-BIND compares well to all GraphDTA and GNN-based methods (Table ) . This result suggests that, compared to the distance between specific protein and ligand atoms, the molecular topology of the ligand plays a relatively minor role. It must noted that the various GraphDTA Methods do not use geometric information but rely on the more readily available amino acid sequence information for representing the protein.
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Predicting outcomes of chemical reactions, such as their yield based on data gathered in high throughput screening, is an important task in machine learning for chemistry. Previously, we were able to show that relatively simple fingerprintbased gradient boosting models can perform at least as well as computationally expensive DFT and transformer-based methods . In cheminformatics, chemical reactions are often defined as two sets of molecules, reactants and products, where the reactants are fully or partially transformed into the products during the reaction process. This set-based definition of chemical reactions hints at a potential use for set representation learning. Again, we focused on the most straightforward implementation by creating a dual-set neural network, where the inputs are binary ECFP (with r = 3 and including stereochemistry) vectors of reactant and product molecules, respectively. We evaluated this architecture, denoted MSR2-RXN, against the state-of-the-art using a high throughput data set of Buchwald-Hartwig cross-coupling reactions with the task of predicting reaction yields, that is, the percentage of input material (reactants) that is transformed to output materials (product). The baseline models include our previously introduced gradient boosting and fingerprint-based method (DRFP), a DFT-based random forests model (DFT), as well as the transformer-based models Yield-BERT and its augmented variant (Yield-BERT and Yield-BERT (aug.)) .
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MSR2-RXN performs similarly to the SOTA methods on the ablation study (Rand x/y) using random splits and on the out-of-distribution splits (Test n), as shown in Table . Indeed, MSR2-RXN does not perform significantly different compared to Yield-BERT, Yield-BERT (aug.), and DRFP (paired t-test, p = 0.283, p = 1.000, and p = 0.307, respectively) and significantly better than the DFT-based method (paired t-test, p = 0.008). In addition, while it also performs below a usable threshold on the Buchwald-Hartwig ELN (electronic lab notebook) data set, it does perform better than both the BERT-and GNN-based models, coming closer in performance to DRFP.
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The results illustrate the power and flexibility of molecular set representation learning. While the other methods rely on DFT calculations, pretrained large language models, or a custom molecular fingerprint in the case of DRFP, MSR2-RXN uses the known simple and well-established ECFP embedding to represent the molecules participating in the reaction.
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We empirically investigated the SR-GINE approach's scalability by comparing its training time and performance to the non-extended GINE architecture. The average runtime for training GINE-SR on the OCELOT chromophore data set (N train = 20201) is 9m44s±44s, which is an increase of 6.2% compared to GINE (9m10s±42s). On the larger QM9 data set (N train = 107108), the training time increases to 50m25s±0m47s for GINE and 62m25s±3m27s for GINE-SR, an increase of 23.8%. In the case of QM9, this increase in training time is close to the average increase in performance, which is 24.4% (Table ). Although these numbers suggest that SR-GINE can scale well in terms of a performance-training time trade-off, it is not guaranteed that this is the case for all data sets. However, our experiments throughout this study showed a substantial increase of performance of SR-GINE over GINE on small to medium-sized data sets where the increase in training time was marginal as shown with the example of OCELOT. Overall, these observations agree with the evaluation of RepSet by Skianis et al. [16]. The timing data was taken form training runs on a Nvidia RTX 4090Ti GPU with 12 GB RAM for GINE and SR-GINE.
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With this initial foray into molecular set representation methodology, we were able to show competitive results of the technique across a wide range of use cases, including the prediction of quantum-chemical properties, pharmacokinetic properties, binding affinities, and reaction yields with minimal hyperparameter adjustments and consistently straightforward architectures. Our most straightforward model, MSR1, which is essentially a set of ECFP fingerprints with a radius of zero, performs as well or better than D-MPNN on 5 out of 11 and better than GIN(E) on 9 out of 11 of the tested MoleculeNet benchmark data sets. With the poorer performance of the purely set representation-based methods MSR1 and MSR2 compared to SR-GINE, GINE, and (D-)MPNN on more recent data sets, we have shown that the commonly used benchmarks provided by MoleculeNet and other cheminformatics and machine learning libraries may not be well-suited to benchmark GNN architectures, as including explicit molecular topology does not seem to provide a significant advantage. Given the past and current reliance on these data sets of researchers when benchmarking new molecular deep learning architectures, we conclude and suggest that future architectures should be evaluated on other data sets, including those made available by Bhat et al. [24] and Fang et al. [31].
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Furthermore, we showed that introducing a set representation layer in place of a global pooling function in a GNN (specifically a GINE) improves its performance in virtually all benchmarks and, in more recently released data sets, performs equal or better than MPNN and D-MPNN without the need to introduce additional precomputed molecular descriptors. This insight may be used to extend and improve the performance of all currently used GNN-based molecular representation approaches. In addition, we introduced a set-based model for protein-ligand binding affinity prediction, which allows for the introduction of implicit geometric information through a radius near neighbour search between the protein and the bound ligand, allowing the model to perform better than existing graph-based approaches, which often cannot integrate such information easily. Finally, our conceptually naïve set-based reaction yield prediction model more than doubles the performance (R 2 ) of YieldGNN on the electronic lab notebook-extracted (ELN) data set of Buchwald-Hartwig cross-coupling reactions and matches the performance of established methods on the high-throughput experiment (HTE) data.
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Overall, we present results that introduce and back the value of considering molecular set representation learning as an additional important branch of machine learning in computational chemistry and cheminformatics, as it provides a relaxation of the explicit molecular graph topology used in graph representation learning, which we showed to improve and extend capabilities across a wide range of tasks. The results of our set-based and -enhanced methods on the OCELOT chromophore and PDBbind data sets also support our initial hypothesis that a more relaxed definition of molecular topologies enables the neural network to learn a more meaningful representation of molecules involving conjugated or transient bonds.
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Initially, we evaluated our general approach against the well-known MoleculeNet data sets, excluding data sets that would require significant training time due to their size or number of tasks (ToxCast, MUV, PCBA). QM9 is used to evaluate the scalability of SR-GINE. Furthermore, we excluded PDBbind from our initial evaluation as our base-models do not support protein-ligand complexes.
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After the initial experiments, we chose more modern and specific benchmark data sets, namely the OCELOT chromophore data set and a set of compounds evaluated against Biogen ADME in vitro assays. Furthermore, we introduced two additional set-based models to handle protein-ligand complexes from the PDBbind data set and reactions from the Buchwald-Hartwig HTE (high-throughput experiment) and ELN (electronic laboratory journal) data sets.
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In all models, the atom and bond invariants were chosen based on the choices by Rogers & Hahn [12] and Yang et al. [17]. As shown in Figure , the atom invariants are: (1) The degree (total number of bonds) of the atom, (2) the atomic number limited to 100-elements above Fermium are assigned the one-hot-encoded position 101, (3) the formal charge, (4) the hybridization state, (5) the chiral tag representing, if applicable, the chiral type such as tetrahedral or octahedral, (6) whether the atom is part of a ring, and (7) the total number of hydrogens bonded to the atom. Figure shows the bond invariants, namely: (a) The bond type, (b) the stereochemistry of the bond, (c) whether the bond is part of an aromatic system, (d) whether the bond is part of a conjugated system, (e) the type of the first atom connected by the bond, and (f) the type of the second atom connected by the bond.
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Initially we chose the set representation layer for MRS1 (which consists only of the set representation layer after a non-learned embedding based on atom invariants) by comparing the three architectures DeepSets, Set-Transformer, and RepSet . The hyperparameters were chosen based on defaults and findings from the initial publications of each method. Based on the performance of the three different implementations of MSR1 (Table ) on the four data sets BACE, BBBP, ClinTox, ESOL, FreeSolv, and Lipo, which were chosen for their relatively small size resulting in fast learning, we selected RepSet as our set representation layer of choice.
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For the GNN layer, we implemented and evaluated Graph Isomorphism Network (GIN), Graph Attention Network (GAT), and Graph Convolutional Network (GCN) as graph embedding layers for our set representation extended graph neural network . Again, we used default hyperparameters based on the original publications and, pairing each set representation layer with each GNN layer, evaluated different versions of our set representation-enhanced graph neural network. Using the same selection of benchmark data sets as with the set-representation layer selection, we evaluated the nine combinations of GNN and set representation layers (Tables and). Overall, the results point towards a need for hyperparameter optimization depending on the combination of models. We therefore picked the combination not on the performance shown in Tables and but the fact that we use RepSet in MSR1 and 2, and that GIN(E) is generally reported as a well performing baseline architecture in chemistry tasks .
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For the graph-based models (the GINE baseline and SR-GINE), we ran an initial simple search using the BBBP data set over both models while keeping the set representation parameters for SR-GINE fixed at 8 hidden sets with 8 elements each. For each set of hyperparameters, 6 models were trained on random seeds and their performance averaged. The best models were selected for lowest cross entropy loss during validation. During this search, SR-GINE performed consistently better than the baseline (GINE). In a next step, we conducted a further simple grid search on the number of hidden sets and elements, as the authors of the original publication have shown the performance to be influenced by these parameters . We chose 128 hidden sets with 64 elements each based on tests on the BBBP data set.
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MoleculeNet data sets The data sets that are often collected under the name MoleculeNet data sets, namely HIV, BACE, BBBP, Tox21, SIDER, ClinTox, ESOL, FreeSolv, Lipo, QM7, and QM8, were split into train, validation, and test sets based on Murcko scaffolds in accordance with Yang et al. [17] and Wang et al. [20]. Four other data sets from the MoleculeNet collection that are often used (ToxCast, MUV, PCBA, QM9) were ommited from the benchmarks, as they are either too large or have too many tasks to be processed with limited compute.
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62348e88d6d3edc4ae960358
| 0 |
Conventional luminescent materials normally contain large π-aromatic building blocks. In recent decades, intrinsic photoluminescence (PL) from unconventional luminophores in absence of any traditional conjugated luminophores nor aromatic motifs has been demonstrated. In general, these unconventional luminophors involve certain subgroups, such as alkene (C=C), cyano (C≡N), carbonyl (C=O), hydroxyl (-OH), acylamino (-NH-CO-). Although the corresponding emission mechanism remains an open question, it is generally accepted that the emission of these unconventional luminophores is attributed to the aggregation of non-conjugated chromophores (clustering-triggered emission, CTE). In particular, among the emerging luminescent materials, non-conjugated luminescent polymers (NCLPs) synthesized from non-luminescent monomers have aroused increasing interest because of their significant fundamental importance and promising technical applications. Taking advantage of non-conjugated polymeric materials, such as ease of synthesis, high processability, good biocompatibility, and environmental degradation, NCLPs have great potential for applications in bioimaging, anti-counterfeiting, and biosensors, etc. Based on the CTE mechanism, to achieve NCLPs from non-luminescent monomers, several factors need to be fulfilled. These include: (1) the presence of electron-rich heteroatoms, such as O, N, S, P, etc. ; (2) intra-and intermolecular interactions, e.g., dipole-dipole interactions, n-π interactions, that can afford through space electronic communications (3) rigid microenvironment that can inhibit the non-radiative relaxation of the chromophore and promote the photoluminescence efficiency of the chromophore. Therefore, as one intends to design and prepare a new NCLP, it is challenging to simultaneously fulfill all these requirements with a single species of monomer. As the first two issues can be realized by selecting proper monomers with certain pendants, the rigidity of non-conjugated polymers is usually limited due to the relatively high flexibility of main chains, especially for vinyl-based polymers with C-C backbones. In fact, the rigidity of polymer is reflected by the glass transition temperature (Tg), which can be enhanced through introducing conformational restriction around single bonds. Usually, the presence of bulky ring-like side groups can give rise to a high Tg due to the steric restriction of chain mobility. Indeed, copolymerization of two or more species of monomers can be a facile and effective approach to fabricate novel NCLPs with tunable photophysical properties from a wide range.
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| 1 |
So far, a few non-conjugated luminescent copolymers are reported. PL of maleic anhydride (MAh)-containing copolymers have been demonstrated by several groups. The copolymers of MAh and various comonomers, to name a few, vinyl acetate, acetoxy styrene, vinyl carbazole, N-vinyl-2-pyrrolidone, etc., exhibited remarkable intrinsic PL. You and coworkers synthesized copolymers with intrinsic PL via reversible addition-fragmentation chain transfer (RAFT). Ma and coworkers reported the room-temperature phosphorescence (RTP) of acrylamide and brominated olefins copolymers. The generation of RTP is attributed to the rigidified conformation that facilitates luminescence due to the space electronic connections supplied by the NH2 and C=O units. Zhang and coworkers demonstrated emission of perfluorosulfonate ionomers (PFSIs), a commercially available copolymer of tetrafluoroethylene and perfluorosulfonic acid, at solid state. Very recently, Zhang and coworkers reported color-tunable aliphatic polyesters with quantum yield (ΦF) as high as 38 %. Besides vinyl-based polymers, some nonaromatic polyurethanes (PUs) synthesized via condensation polymerization also possess intrinsic PL. Yuan and coworkers synthesized PUs by the addition reaction between diisocyanates and short-chain glycols, and bright blue light can be observed in the concentrated solutions, as-prepared solids, and cast films of the PUs, indicating the features of concentration-enhanced emission and aggregation-induced emission (AIE). As mentioned above, the key point to approach emission of non-luminescent polymers is to introduce electron-rich heteroatoms and intense interactions and to increase the rigidity of backbones. Methylenelactide (MLA) is a radically polymerizable vinyl-lactide derivative. Due to the presence of bulky lactone rings, the chain mobility of poly(methylenelactide) (PMLA) is heavily restricted, resulting in a high Tg of 244 ℃. Therefore, it is expected that copolymerization with MLA as the secondary monomer could effectively improve the rigidity of chains. Vinyl pyridine is a typical polar vinyl monomer that is important in many applications due to the ability of their polymers to form complexes of the electron-rich pyridine ring. Although vinyl pyridine monomers and their polymers are almost non-luminescent at a neutral state, the aromatic heterocyclic ring of pyridine makes it a potential luminophore.
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