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611cc248f5c7c37347dd1c61 | 31 | Next, we proceed to the optimised minimum of the S 1 state. The S 1 energy is found at an adiabatic energy of 2.37 and 2.36 eV using LR-PCM and SS-PCM, respectively. The obtained emission energy is 2.19 eV. We find that the S 1 state at the S 1 minimum geometry has significant local BDT character (blue, 56 % at SS-PCM level) and a small exciton size of 6.20 Å, which is slightly reduced when compared to the ground state geometry (6.52 Å). We can understand this in the sense that the planarisation of the Ph-BDT-Ph unit, as represented by the θ 2 /θ 2 values in Table , provides the basis for an extended locally excited state. The state retains the formal gerade symmetry present at the S 0 geometry and, therefore, has vanishing oscillator strength. |
611cc248f5c7c37347dd1c61 | 32 | A locally excited and optically dark S 1 minimum certainly runs counter to the initial design strategy of using a D-π-A-π-D system and may well explain the poor performance of Cz-BDT in TADF applications. To further test this hypothesis, we have spent some effort in searching for a different local minimum on the S 1 energy surface that might have enhanced CT character considering two strategies: (i) pre-optimisation with the PBE functional before starting the ωPBEh optimisation and (ii) optimisation of S 2 . Neither of these strategies led to the location of an S 1 minimum with enhanced CT character and we conclude that, indeed, the excitation localises on the Ph-BDT-Ph part upon excited-state relaxation. Furthermore, we find that inclusion of state-specific solvation using the toluene solvent only has a minor overall effect of the energies. All energy shifts are below 0.01 eV and the state characters and exciton sizes virtually unaffected suggesting that the conclusions made are robust with respect to the specifics of the solvation model used. |
611cc248f5c7c37347dd1c61 | 33 | Proceeding to T 1 , we compare data using three different methods: TDDFT/LR-PCM and TDDFT/SS-PCM at the TDDFT/LR-PCM geometry, as well as TDDFT/SS-PCM at the UKS/PCM T 1 geometry. In all cases we find that optimisation of T 1 leads to a slight stabilisation of T 1 obtaining an adiabatic T 1 energy of |
611cc248f5c7c37347dd1c61 | 34 | Results for geometry optimisiations of the individual states for Cz-AQ are presented in (Figure ). At the S 0 minimum, we find similar state characters as in vacuo (Figure , centre) only that, again, the ππ * states are somewhat reduced in energy altering the overall state ordering. Once again, we find excellent agreement between the bright S 2 state obtained at 2.97 eV using the ptSS scheme and the experimental absorption maximum of 2.91 eV. Unlike Cz-BDT, there are notable differences in the energies and state characters at the individual geometries, which also agrees well with the fact that the geometries obtained (see Table ) are quite different to each other. Crucially, we find for the TDDFT optimised S 1 geometry that the S 1 state becomes bright and has a significant amount of charge transfer character (red) along with an enhanced exciton size of 7.99 Å (SS-PCM). We propose to interpret this phenomenon in the context of excited-state symmetry breaking: The S 1 state is Laporte forbidden at the ground state geometry due to its approximate inversion symmetry but this restriction is lifted once the symmetry is broken in the excited state as one half of the molecule planarises (see Table ). To represent the symmetry breaking, we use the linear electron-hole separation (d he , Eq. ( )). This value vanishes for symmetric charge transfer systems but approaches the value of d exc in the idealised case where charge is transferred from one donor to one acceptor, both represented as point charges. As expected, d he is zero for the symmetric S 0 -optimised geometries. In the case of S 1 , by contrast, we find that for all the ππ * states d he differs strongly from zero reaching half of d exc or more. This highlights that symmetry breaking of the geometry does indeed also localise the excited states. |
611cc248f5c7c37347dd1c61 | 35 | The T 1 state at the T 1 geometry has enhanced local character (blue) and a clearly reduced exciton size (<6 Å) when compared to S 1 at the S 1 geometry considering all three levels of theory considered. Nonetheless, pronounced symmetry-breaking occurs, which is reflected by the brightness of the S 1 state and the nonvanishing d he values. |
611cc248f5c7c37347dd1c61 | 36 | Once again, we find that all solvation schemes afford similar descriptions of the state energies and characters, with the exception of the T 4 state at the S 1 geometry, which is swapped in order with the almost degenerate S 1 state. The small influence of the LR-and SS-solvation schemes can be understood by the fact that the influence of non-polar solvent like toluene on the excited state energies and characters is small; more polar solvents are expected to lower the energy of charge transfer states and reduce ∆E ST under the SS-PCM solvation scheme. |
611cc248f5c7c37347dd1c61 | 37 | Reviewing Figures and, we find that both molecules retain significant adiabatic singlet-triplet gaps, even when solvation effects are accounted for. Thus, the singlet-triplet gap does not serve as a suitable figure of merit to differentiate between the two molecules. On the other hand, a clear difference is observed in terms of excited-state character of the optimised S 1 state. This state becomes a dark locally excited state for Cz-BDT whereas it becomes a bright symmetry-broken CT state for Cz-AQ. The enhanced optical brightness is certainly beneficial for luminescence while also enhanced CT agrees with the underlying design strategy. Both phenomena explain the enhanced performance of Cz-AQ. The difference in state character is reflected by the more planar structure of Cz-BDT in its ground and excited states when compared to Cz-AQ. This planar structure along with shorter bond lengths is an indication of enhanced conjugation between BDT and Ph when compared to AQ and Ph. The difference can, in part, be understood by the reduced steric repulsion between BDT and Ph but electronic effects most probably also play a role as Cz-AQ is, indeed, able to planarise as seen for the T 1 minimum. |
611cc248f5c7c37347dd1c61 | 38 | Having provided a detailed analysis of Cz-BDT and Cz-AQ, we will now proceed to two additional molecules, alluded to briefly in the introduction and shown in Fig. (i) Cz-BDT-SO 2 containing an oxidised derivative of the BDT acceptor, with two oxygen atoms bound to each sulfur atom; and (ii) Cz-BDF, the benzodifuran derivative of BDT, where the sulfur atoms are replaced with oxygen atoms. As opposed to Cz-BDT and Cz-AQ, which have been synthesised and well-characterised, these two molecules have not yet been synthesised. |
611cc248f5c7c37347dd1c61 | 39 | The geometric parameters for Cz-BDT-SO 2 and Cz-BDF, obtained in analogy to Table , are listed in Table . Starting with the S 0 state of Cz-BDT-SO 2 , we find that its Cz/Ph torsion angles are almost unaltered when compared to the previous two molecules whereas the core/Ph torsion angles (θ 2 /θ 2 ) are significantly reduced indicating that the central Ph-core-Ph system is almost planar. Excitation into T 1 breaks the symmetry for Cz-BDT-SO 2 and one of the angles (θ 2 ) planarises even more whereas the other one remains largely unaltered. Interestingly, excitation into S 1 has the opposite effect and the θ 2 /θ 2 angles are slightly increased, which is the opposite trend to what was seen for Cz-BDT. Proceeding to Cz-BDF, we find that this molecule stays symmetric and fairly rigid in all states considered possessing a largely planar central Ph-core-Ph system. Finally, it is interesting to note that for all four molecules in this work, the bond distances change with the twisting angles. An increase/decrease in θ leads to an increase/decrease in d showing that the effect of enhanced conjugation produced by a smaller torsion angle also affects the bond distances. |
611cc248f5c7c37347dd1c61 | 40 | An analysis of the excited states of Cz-BDT-SO 2 and Cz-BDF at their S 0 , S 1 , and T 1 optimised geometries in solution is presented in Fig. . The data shown is analogous to Figs and with the exception that we only present results using the higher-level state-specific solvation models here. Starting with Cz-BDT-SO 2 shown on the left in Fig. , we find that the excitation energies are significantly reduced when compared to Cz-BDT with all seven calculated excited states at or below 2.0 eV in the ptSS scheme at S 0 geometry. The two low lying triplet states are predominantly locally excited, with only slightly enhanced CT character when compared to Cz-BDT. The S 1 is found to be a CT state with predominant Cz→core contributions located at 1.73 eV and, as opposed to Cz-BDT, S 1 is bright with an oscillator strength of Optimisation of Cz-BDT-SO 2 in the S 1 state only has a negligible effect on energies and characters of the first four excited states. Up to S 2 , the only notable change is some mixing and symmetry breaking between S 1 and S 2 meaning that both states obtain some non-vanishing oscillator strength, their amount of CT character is slightly altered, and their d he values deviate from zero. Importantly, the S 1 remains bright at the S 1 geometry meaning that emission from this state is favoured. For the higher excited states some reordering is observed, e.g., the nπ * -state disappears and all states obtain some partial CT character. Optimisation of T 1 further stabilises the T 1 energy to 1.06 eV, thus, yielding an adiabatic ∆E ST of 0.67 eV. Optimisation of T 1 also slightly re-duces the CT character of this state, as seen by the exciton size, which is reduced from 5.64 Å at the S 0 geometry to 5.35 Å. At the T 1 geometry, also the other states obtain reduced CT character as seen by reduced exciton sizes and red Cz→core bars. |
611cc248f5c7c37347dd1c61 | 41 | The excited states of Cz-BDF (Fig. , right) bear resemblance to those of Cz-BDT (Fig. ). At the S 0 geometry two locally excited triplet states are found before S 1 , which is also locally excited and dark similarly to Cz-BDT and Cz-AQ. S 2 is found to be a bright CT state at an excitation energy of 2.73 eV, which is almost equivalent to Cz-BDT. In addition, two triplet nπ * states (T 3 and T 4 ) and another singlet CT state (S 3 ) is found. Optimisation of S 1 slightly lowers its energy (from 2.47 eV to 2.30 eV) while retaining its local character. The other states remain largely unaffected when compared between the S 0 and S 1 geometries. However, it is noteworthy that the gap between S 1 and S 2 becomes 0.51 eV after optimisation. A dark S 1 state along with a large gap to S 2 indicates that any coupling between the states is expected to be small and Cz-BDF is expected to be at most weakly emissive, similarly to Cz-BDT. Optimisation of T 1 slightly stabilises the energy of this state inducing an adiabatic singlet-triplet gap of 0.63 eV. Otherwise, the states remain largely unaffected. |
611cc248f5c7c37347dd1c61 | 42 | Before concluding, we want to summarise and discuss the results, presented above, in the context of three specific issues: (i) the overall photophysics of the molecules studied, (ii) general differences in singlet and triplet state wavefunctions and their relevance in terms of photophysics and computational modelling, and (iii) further methodological aspects. |
611cc248f5c7c37347dd1c61 | 43 | A summary of the key photophysical data for the four molecules is presented in Table . Here, we consider our highest level results, i.e., absorption energies at the TDDFT/ptSS level and emission energies using TDDFT/SS-PCM all with the ωPBEh functional. Notably, all four molecules studied have adiabatic singlet-triplet above 0.5 eV, which, at first sight, does not seem to make them optimal TADF emitters. Reviewing Fig. , we can speculate that despite this energy gap Cz-AQ profits from a high density of states connecting the T 1 and S 1 states (see also Ref. 8). In addition, the presence of nπ * states in this area is expected to mediate SOC efficiently. Finally, symmetry breaking in the excited state produces a strongly emissive CT state (f em = 0.341) localised on one branch. The presence of a number of different excited states with varying properties, as found here, is consistent with the rich photophysics measured experimentally for a related D-AQ-D molecules. Viewing Tab. 5, we find the main difference between Cz-AQ and Cz-BDT to be in the oscillator strength for emission (f em ), which vanishes for Cz-BDT. We attribute this difference to the absence of a symmetry breaking CT state for Cz-BDT, which, in turn, is caused by a localisation of the excited state on the central Ph-BDT-Ph part mediated by enhanced planarisation. |
611cc248f5c7c37347dd1c61 | 44 | Considering Tab. 5, we find that Cz-BDT-SO 2 shows similar characteristics to Cz-AQ only that the absorption and emission energies are strongly red-shifted and that the singlet-triplet gap is slightly raised. Cz-BDT-SO 2 may, therefore, be considered a TADF candidate assuming that its ∆E ST is still sufficiently low. Cz-BDF, on the other hand, has very similar characteristics to Cz-BDT in all of the values considered in Tab. 5. It is, thus, expected to exhibit a low photoluminescence quantum yield similarly to Cz-BDT. |
611cc248f5c7c37347dd1c61 | 45 | A striking observation made in the above plots relates to the differences in excited state character found between singlet and triplet states. It is tempting to think of singlet and triplet excited states as involving the same orbital transitions, only differing in their spin coupling. However, the above results show that this picture is oversimplified for realistic push-pull systems. Specifically, we find that low energy triplet states have enhanced local character whereas CT is enhanced for the singlets. This is reflected in all the bar graphs shown in the centre panels of Figs 8 to 10 with enhanced blue and orange bars for the triplets and more red/green for the triplets. The difference is even more apparent in terms of the exciton sizes (bottom panels of Figs 8 to 10) showing that the triplet states (red dots) are mostly below ≈ 6 Å whereas, except for nπ * states, the singlets (black dots) are well above this value. |
611cc248f5c7c37347dd1c61 | 46 | Differences between singlet and triplet states can be understood by considering the different contributing energy terms. Singlet and triplet states are both affected by an attractive Coulomb interaction favouring locally excited states while singlets are also affected by a repulsive exchange interaction favouring CT states. The discussion for triplet energies is a bit more ambiguous and depends on the reference chosen. If one considers the Kohn-Sham orbital energies as reference, then one finds that triplets are independent of any exchange contribution. However, if one further considers that the LUMO energy is lowered by the exchange interaction between HOMO and LUMO, then one finds that triplet energies are indeed stabilised by this exchange interaction. Independently of this discussion one finds that low-energy triplets should be more localised, which is well represented by the data shown. Furthermore, the above plots highlight the differences between singlet and triplet states, which cannot be explained by simply reordering the states without also mixing them. Clearly, there is no one-to-one correspondence between the singlet and triplet states. These differences are important for at least three reasons. First, it should be understood that the photophysics of these molecules cannot be understood in terms of a simplified picture containing only two or three MOs but that a number of terms ultimately influence the final energies of the states. In this context, it has been pointed out, before, that the idealised picture where singlets and triplets differ by twice the exchange energy would only hold if their wavefunctions were the same except for the spin coupling. Discussions of how to go beyond this and understand singlet-triplet gaps within and beyond the orbital picture are provided in Refs 7,28. Second, the discussion shows that the available space for molecular design is larger than one would anticipate viewing only two or three MOs. Indeed, there are a large number of terms that can potentially be fine-tuned to optimise the overall photophysics. Third, differences in the wavefunctions of singlet and triplet states explain why singlets and triplets differ strongly in their computational description using, e.g., TDDFT or the Bethe-Salpeter equation. Being aware of these differences may help in the development of computational methods that provide a balanced and accurate description of singlets and triplets. |
611cc248f5c7c37347dd1c61 | 47 | Reviewing the computations within this manuscript we found that the density functional used, and in particular the amount of nonlocal HFX, plays a critical role. As shown in Fig. increasing the amount of HFX has four critical consequences: (i) raising the overall excitation energies, (ii) widening ∆E ST , (iii) reducing CT character, and (iv) increasing oscillator strengths. This illustrates how a change in density functional does not only shift excitation energies but potentially affects many different aspects of the predicted photophysics. Furthermore, we found that geometry optimisation in the excited state was critical for two individual effects. First, it allowed for adjustments in the torsion angles altering delocalisation and CT for the individual states. Second, it was seen as the basis for excited state symmetry breaking yielding a strongly emissive state for Cz-AQ whereas for Cz-BDT the S 1 state remained dark at its symmetric minimum. Solvation effects were considered using three different approaches: the LR-PCM and SS-PCM methods in connection with TDDFT as well as ground-state PCM in connection with UKS. It was found that solvation produced a slight energetic stabilisation of CT states. However, differences between these solvation models were comparatively small suggesting that the choice of solvation model is not as critical as the choice of density functional and an appropriate treatment of geometry relaxation, at least for weakly polar solvents. |
611cc248f5c7c37347dd1c61 | 48 | Within this work, we have presented a detailed study of four closely related D-π-A-π-D molecules: the effective TADF chromophore Cz-AQ, its close analogue Cz-BDT, which undergoes red-shifted TADF albeit with a much lower quantum yield, and two molecules not yet synthesised Cz-BDT-SO 2 and Cz-BDF. After presenting the main structural parameters, we have presented a detailed evaluation of computational methods benchmarking five density functionals to experimental absorption data and the high-level ab initio computational reference ri-ADC(2). This highlighted that not only the energies but also the overall wavefunctions depend heavily on the functional used and particularly the amount of Hartree-Fock exchange. |
611cc248f5c7c37347dd1c61 | 49 | Using the ωPBEh functional, which was shown to represent energies and wavefunctions accurately, we have studied excitedstate minima in solution highlighting the importance of planarisation and excited-state symmetry breaking leading to markedly different photophysics between the molecules despite their similar molecular structures. The adiabatic singlet-triplet gaps of Cz-AQ and Cz-BDT were found to be very similar not providing a suitable figure of merit to differentiate between the two molecules. Conversely, we have related the strong TADF activity of Cz-AQ to the existence of a strongly emissive symmetry broken S 1 minimum with CT character whereas Cz-BDT formed a dark locally excited S 1 minimum. Moreover, Cz-AQ was characterised by a dense set of states of different character connecting the T 1 and S 1 states providing a pathway between them despite their comparatively large gap. |
611cc248f5c7c37347dd1c61 | 50 | In a more general sense, we show that a detailed analysis of excited-state wavefunctions can provide detailed insight into the photophysics of push-pull systems compared to a simple analysis of energies and frontier orbitals. General differences between singlet and triplet states have been outlined with triplets being more compact and local whereas enhanced CT was found for singlets. We believe that the presented protocol will be valuable for studying various push-pull systems in the future providing detailed insight into the properties of existing chromophores and providing new design ideas for the future. |
6493424724989702c2baf2e5 | 0 | Per-and polyfluoroalkyl substances (PFAS) are a group of substances of high environmental and toxicological concern gaining increasing attention due to bioaccumulation and a growing reputation as "forever chemicals" -so much so that there is now a drive to treat PFAS as a class for environmental regulation . The 2011 definition of PFAS by Buck et al. included substances as PFAS if they contained two (or more) connected saturated CF 2 groups. In 2021, the Organisation for Economic Co-operation and Development (OECD) revised the definition of PFAS in ENV/CBC/MONO(2021)25 as follows: "PFAS are defined as fluorinated substances that contain at least one fully fluorinated methyl or methylene carbon atom (without any H/Cl/Br/I atom attached to it), i.e. with a few noted exceptions, any chemical with at least a perfluorinated methyl group (-CF 3 ) or a perfluorinated methylene group (-CF 2 -) is a PFAS." |
6493424724989702c2baf2e5 | 1 | While early research efforts focused mainly on a very limited list of PFAS, the number of documented PFAS are increasing. With the emergence of high resolution mass spectrometry (HRMS) and the potential for so-called "suspect screening" for contaminants of interest using non-target analytical techniques , more extensive lists of PFAS became available. The first PFAS list hosted by the NORMAN Suspect List Exchange (hereafter NORMAN-SLE) was the 2015 list contributed by Trier et al. , which became the basis for the OECD list of ~4700 PFAS released in 2017 . The NORMAN-SLE currently (June 2023) contains twelve PFAS lists . The United States Environmental Protection Agency (US EPA) CompTox Chemistry Dashboard 11 also hosts chemical lists and presently (June 2023) hosts 424 lists, including 51 lists matching the PFAS search term , of which 41 contain exclusively fluorinated content. The National Institute of Standards and Technology (NIST) recently coordinated a list (hereafter the "NIST PFAS Suspect List") of 4,948 entries, including expanded homologues and expert contributions . Several other research efforts describe PFAS lists, with various degrees of availability. The OECD PFAS collection of ~4700 PFAS and the US EPA PFASMASTER list (~10,000 PFAS in 2020, currently 12,034 entries in June 2023) are two of the most frequently used PFAS lists in suspect screening. Both lists also contain entries that are not discrete chemicals, i.e., they also include polymer and substances of Unknown or Variable Composition, Complex Reaction Products, or Biological Materials (UVCBs) . A recent effort with Google and OntoChem investigated the influence of PFAS definition on the number of PFAS extracted from literature (CORE repository) and patents (Google Patent set), resulting in PFAS lists of between 3,457 (CORE, Buck et al. definition) and 1,783,651 (Patent set, 2021 OECD PFAS 3 definition) discrete chemicals . At the time, over 200,000 of these PFAS were not in PubChem , one of the largest open chemistry databases, but were deposited soon thereafter . |
6493424724989702c2baf2e5 | 2 | There have been several attempts to classify and group PFAS to help answer different questions. The comprehensive OECD efforts 9,10 contained detailed classifications. The "splitPFAS" method for automated classification was developed and tested on five of these categories . Recently, overviews of PFAS uses have emerged , while others have looked at strategies for grouping PFAS for the protection of human and environmental health , or narrowed the OECD PFAS list down to those of commercial relevance, estimated to be ~6 % of the total list . Most, if not all, of these approaches are still largely manual. |
6493424724989702c2baf2e5 | 3 | While integrating the NORMAN-SLE content into PubChem 6 , it became clear that the number of chemicals within PubChem (115 million chemicals, June 2023) that could satisfy the 2021 OECD PFAS definition dwarfed the several thousand entries in the common PFAS suspect lists. A simple substructure search for "CF 2 " revealed millions of potential matches in PubChem. Since new PFAS are emerging very rapidly, the need for a manageable, relevant, rapidly updateable open collection of PFAS for the community is increasingly obvious. This article describes efforts to develop an interactive, open, dynamic, browsable collection of PFAS content in PubChem to serve this purpose. |
6493424724989702c2baf2e5 | 4 | The "PFAS and Fluorinated Compounds in PubChem" collection (hereafter "PubChem PFAS Tree") is openly available and integrated into the Classification Browser of PubChem. It is designed to support the exploration and exchange of information on PFAS and fluorinated compounds within the community. This information is compiled and assembled using several different approaches, described further in the following sections. The online collection (shown with the first two layers of nodes in Figure ) is updated frequently and is available at . |
6493424724989702c2baf2e5 | 5 | Four sections of the PubChem PFAS Tree are collated by running custom-designed PERL scripts (available on GitLab ) over the entirety of PubChem on a weekly basis, since the chemical content of PubChem updates daily, and annotation content weekly. The "OECD PFAS definition" section contains all discrete chemicals (excluding salts and mixtures) fulfilling the 2021 OECD PFAS definition 3 quoted above (hereafter termed an "OECD PFAS"), while the "PFAS breakdowns by chemistry" section contains all discrete chemicals, including salts and mixtures, that are an "OECD PFAS" . Figure of the OECD Monograph ENV/CBC/MONO(2021)25 3 also included a breakdown of organofluorine content into several aliphatic and aromatic categories; this structure is reflected in the "Organofluorine compounds" section of the PubChem PFAS Tree (see Figure ). Over 100,000 fluorinated compounds in PubChem did not fit into the categories set out in the OECD Monograph, either because fluorine was connected to non-carbon atoms or due to the presence of non-organic elements (or both). These cases were separated into the "Other diverse fluorinated compounds" section, which was broken down into these two subsections (see Figure ). A more detailed description of the contents of each section and how this is constructed is contained in the PubChem PFAS Tree documentation . |
6493424724989702c2baf2e5 | 6 | The scripts that construct the PubChem PFAS Tree run over content that is publicly available. This data is found on the PubChem FTP site and via openly available active programming interfaces (APIs) such as PUG REST . The processing takes approximately two hours to complete (processing each of the 337 structure data files, as of June 2023, in parallel) via the PubChem compute environment. |
6493424724989702c2baf2e5 | 7 | The remaining two major sections of the PubChem PFAS Tree are compiled in a semi-automated manner using scripts in R and are integrated into construction of the entire PubChem PFAS Tree via mapping files. All code, mapping files and associated supporting files are on the Environmental Cheminformatics (ECI) GitLab pages . These sections and code build likewise on publicly available PubChem functionality, some of which was custom designed to enable the work described here, including adding new classification browser functionality to PUG REST. The final integration of this content into the PubChem PFAS Tree is programmed and run in PERL, as part of the routine described in the previous section . |
6493424724989702c2baf2e5 | 8 | The "PFAS and fluorinated compound collections" contains five major sources of suspect lists (see top right inset of Figure ), including NORMAN-SLE , CompTox 11 , OntoChem , PubChem and NIST . The CompTox chemical list content is retrieved programmatically from the PubChem EPA DSSTox Classification Browser () and curated manually to retain only PFAS lists, which are included in the mapping file to retrieve the respective CIDs in each list via their classification hierarchy node identifier (HNID). The files containing the CIDs for the remaining four sources are hosted on the ECI GitLab pages; the URLs for each file are contained within the mapping file used for retrieval during the PubChem PFAS Tree construction. The NORMAN-SLE subsection contains all PFAS lists within the NORMAN-SLE (currently 12); one CID list was manually adjusted to remove non-PFAS entries such as counterions. The OntoChem CID lists are broken down by the three PFAS definitions and two data sources to form 6 categories. The NIST PFAS Suspect List was downloaded and deposited to PubChem (resulting in 1,232 new CIDs, i.e., new compound record entries in PubChem) and updated once all new CIDs were registered. Finally, the PubChem content was compiled by identifying several fluorinated compound sections in other classification browsers, including the MeSH, Cameo and ChEBI browsers. Since the NIDs were not always stable (especially for ChEBI), these were also added by providing fixed files via the GitLab pages. These lists and mapping files are updated as necessary under full version control in GitLab ; all updates appear with the next PubChem PFAS Tree update. |
6493424724989702c2baf2e5 | 9 | The final section, "Regulatory PFAS collections" was added upon interactions with Andreas Buser from the Federal Office of the Environment (FOEN), Switzerland (see acknowledgements) to support regulatory PFAS efforts. As shown in Figure , inset bottom right, regulation surrounding four cases are covered: long-chain perfluorocarboxylic acids (LC-PFCAs), perfluorohexane sulfonic acid (PFHxS), perfluorooctanoic acid (PFOA), perfluorooctane sulfonic acid (PFOS) and the related substances for all cases. The fifth section deals with exclusions from the PFOA cases, which are separated to avoid "exclusions" being added to the PFOA category totals. Each section is constructed according to definitions from regulatory efforts such as the Stockholm Convention 32 , European Union (EU) Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH) and EU Environmental Chemicals Agency (ECHA) . The sections include several lists published with these definitions, as well as various PubChem queries to find matching content in PubChem according to the definitions. Exact details of the PubChem queries are in the respective tool tips (obtained by clicking the "?" next to each heading) and in the documentation . For the LC-PFCAs, the definitions came from reports UNEP/POPS/POPRC.17/7 and UNEP/POPS/POPRC.18/6/Add.1 as well as EU Regulation 2021/1297 , with an indicative list from report UNEP/POPS/POPRC.18/INF/14 . For PFHxS the definitions came from UNEP/POPS/COP.10/CRP.10 39 and a draft ECHA report , while the initial indicative list came from UNEP/POPS/POPRC.15/INF/9 . The definition for PFOA came from Annex A of the Stockholm Convention (2019 revision) , while the initial, updated and exclusions from the PFOA lists were taken from UNEP/POPS/POPRC.17/INF/14/Rev.1 . Finally, the PFOS definition and PFOS listing was taken from Annex B of the Stockholm Convention . The motivation and methods behind these efforts are described further in the documentation , as well as in a presentation at POPRC.18 and a webinar . |
6493424724989702c2baf2e5 | 10 | As shown in Figure , the number of fluorinated compounds (>21 million) and PFAS (7.4 million with salts and mixtures, 6.5 million without) in PubChem is much higher than the common PFAS screening lists of four to ten thousand entries. Of the 20 million organofluorine compounds classified according to the OECD 3 (see Figure ), ~900,000 are fluorinated aliphatic substances and 19.4 million are fluorinated aromatic substances; just under 100,000 fall into the "other" category which contain fluorine connected to non-carbon organic elements (a more detailed breakdown can be obtained by expanding the respective node in the PubChem PFAS Tree). Note that compounds can fall into more than one of these categories; the node totals always indicate the total number of CIDs under the entire node. For instance, there is no overlap between the fluorinated aliphatic and fluorinated aromatic substances, while 17,044 of the "other fluorinated substances" are also "fluorinated aromatic substances" and 7,633 are also "fluorinated aliphatic substances" (queries performed via PubChem "saved search" functionality on 17 June 2023). Approximated 120,000 fluorinated compounds fall outside the OECD organofluorine classification , contained within the "Other diverse fluorinated compounds" node. |
6493424724989702c2baf2e5 | 11 | A more detailed breakdown of the PFAS sections according to the updated OECD definition 3 is shown in Figure . Figure reveals that 6.5 million PFAS fit this new definition (excluding salts and mixtures), of which 5.7 million contain an isolated CF 3 group, ~670,000 an isolated CF 2 group and ~230,000 a PFAS moiety larger than CF 2 /CF 3 -in other words, ~230,000 PFAS also satisfy the 2011 Buck et al. PFAS definition of substances containing at least CF 2 -CF 2 . As shown in Figure , this can be broken down further to determine e.g., how many molecules with an isolated CF 3 also contain larger PFAS parts (~27,000) and whether the parts are linear, branched, cyclic, and so on. As shown in the bottom of Figure , the breakdown will eventually reveal the formulas of the PFAS part (here C 2 F 4 -note the leading zeros are added to maintain a logical sorting order), should a given chain length be of interest. The total number of nodes in the tree is very high (currently 9890 nodes, June 2023). The nodes below the major sections are created dynamically depending on the data to maintain performance and functionality. As a result, formulas and other nodes appear once certain conditions are met -more details are given in the documentation . Suspect lists and/or databases can be created for workflows by clicking on the nodes of interest (i.e., the blue numbers), which will open a search window to either browse or download the entries. The download file contains several fields of interest; details on how to perform searches and downloads are given in the documentation . Figure shows the breakdown of PFAS including salts and mixtures, with ~1 million additional entries due to salts and mixtures. The difference in numbers on the "OECD PFAS definition" total (6.51 million) versus the "Neutral" category (6.44 million, 3 rd row of Figure ) is due to differences in the processing as well as ambiguities in the wording of the PFAS definition. Currently, this difference is being maintained to enable an easier comparison of these "edge cases" (cyclic PFAS and PFAS-ether cases) and thus to stimulate discussion with experts within the PFAS community to help develop/refine PFAS definitions in a way that is both easy to understand and implement consistently with automated cheminformatics approaches (discussed further below). Figure also reveals additional ways of browsing the PFAS content in a complementary manner to Figure , including by functional groups (with the PFAS part connected to C, N, O, P, S or other elements), by connectivity (with only one connection, i.e., where the PFAS is a terminal part of the molecule, or with two or more connections to the PFAS part) and by formulas, so that it is possible to search by the length of the PFAS part if a particular chain length is of interest. Again, leading zeros are present in formulas to enable a logical sort order of the formulas since the classification browser nodes appear alphabetically. The section shown in Figure can be broken down by each of the respective categories, such that it is possible to exclude salts and mixtures, or only search for PFAS formulas connected to S, and so on. The dynamic "PFAS breakdowns by chemistry" section (Figure ) contains 24,600 nodes, over double the number of nodes in the "OECD PFAS definition" section (Figure ). Further details and examples are again given in the documentation and explained in the webinar . |
6493424724989702c2baf2e5 | 12 | The suspect list section was entitled "PFAS and fluorinated compound collections" rather than "PFAS suspect lists" since the content of various suspect lists were not always PFAS and extremely large lists such as the OntoChem Patent collection (> 1 million entries) are too big for suspect screening. Fluorinated compounds that are not necessarily PFAS are also gaining attention as potentially harmful. For instance, there is great interest in fluorine containing pesticides and pharmaceuticals, but not all entries in the published lists (e.g., lists S92 and S94 of the NORMAN-SLE, containing fluorinated pharmaceuticals and pesticides 49 respectively) are PFAS. By sending these nodes to PubChem Search and subsequently Entrez, it is possible to subset the entire PubChem PFAS Tree by a given suspect list (or combination thereof) and determine which entries are PFAS, organofluorine, etc., as shown in Figure . The steps required to perform this query are explained in greater detail elsewhere . The OntoChem lists, which are too big for efficient suspect screening, are already available elsewhere as database files . Note that the numbers in the suspect lists in the PubChem PFAS Tree may deviate from the original lists, since only discrete chemicals are included, such that polymers and/or UVCBs will be missing (and the numbers consequently smaller) for lists containing polymer/UVCB entries in addition to discrete chemicals. Only one CompTox PFAS list (PFASMARKUSH) contained exclusively polymer/UVCB entries by design and is not displayed. While the OntoChem lists contained only discrete chemicals, these numbers also differ slightly from the published article due to edge cases encountered during PubChem deposition. As discussed in Barnabas et al. , different cheminformatics toolkits perceive the structures differently: PubChem use internal code as well as the OEChem and CACTVS 52 toolkits for standardization and deposition to create chemical records, while OntoChem used OpenChemLib 54 to produce their final lists. This "PFAS and fluorinated compound collections" section is also designed to enable the addition of new PFAS or fluorinated content into PubChem as they are documented, to fill gaps in the database and ensure rapid discovery of new and relevant entries by the community. The necessity for a rapid discovery of new PFAS of concern is one motivation for the regular updates of the entire PubChem PFAS Tree. As mentioned above, the integration of these collections has resulted in the addition of >200,000 new PFAS entries to PubChem, including >200,000 from OntoChem, 1,232 from the NIST PFAS Suspect List and several entries from both the CompTox and NORMAN-SLE contributions, which have been deposited progressively over several years. Almost 25% of the NIST PFAS list was new content to PubChem, showing the importance of hand curated expert knowledge from researchers to fill knowledge and database gaps. The NORMAN-SLE 6,7 hosts several lists, developed using templates designed together with PubChem , which can be used to add new PFAS or other compounds as soon as a reference information is available, thus providing a channel for the scientific community to add new data to the public domain. Contact details are given in the documentation . Several examples of community contributions were provided in the webinar . The information should be available under an appropriate license (e.g., CC-BY ) to enable inclusion. |
6493424724989702c2baf2e5 | 13 | The final node in the PubChem PFAS Tree, "Regulatory PFAS collections" allows users to investigate several aspects of PFAS regulation, including the impact of different wording in definitions under consideration on the number of compounds potentially covered by the regulation. The following paragraphs cover the different cases one by one. Further details on how to perform the search queries, overlaps, downloads and other functions mentioned below can be found in the tooltips, documentation and webinar . |
6493424724989702c2baf2e5 | 14 | The "PFOS and related substances" section is the simplest. It contains the original eight entries for "PFOS plus salts, isomers and PFOSF" listed in the Stockholm Convention Annex B and an extended listing of all content in PubChem matching the "PFOS plus salts, isomers and PFOSF" definition, currently 1,304 entries in total (first node appearing in this section, which can be expanded to see the contributing subsections/categories). This 1,304 comprises PFOS and branched isomers (18), PFOS, PFOSF and salts (239) and a merged PFOS and PFOSF substructure query to find all matching mixtures (1,291 CIDs). An additional section outlines compounds that transform to PFOS (under normal conditions, i.e., excluding advanced treatment transformations) that are in PubChem for information purposes, but these four entries are not included in the extended listing of "PFOS and related substances". |
6493424724989702c2baf2e5 | 15 | The "PFHxS and related substances" section contains a lot more detail than the PFOS section, as two different definitions are currently being explored for the Stockholm Convention and EU REACH. This is an interesting example where a slight change in the wording of the definition results in a difference of over 100 CIDs (chemicals) in the resulting lists. The Stockholm Convention PFHxS definition defines related compounds as compounds with a C 6 F 13 S(=O)(=O) moiety (596 CIDs in total), whereas the EU REACH definition defines this as C 6 F 13 S (710 CIDs total). Both definitions appear at the top of the PFHxS section, with content breakdowns (indicated by blue arrows, Figure ) to show how these have been compiled. |
6493424724989702c2baf2e5 | 16 | For each PFHxS definition, a breakdown by major categories of annotation content has also been provided (see inset of Figure for the example of EU REACH), including whether literature, use and manufacturing, safety and hazards, toxicity or patent information is available in PubChem, or whether the chemical was added only recently (CID date 2022 or 2023). In total, 598 CIDs are covered under the Stockholm Convention PFHxS definition , 303 with patent, 108 with use, 43 with safety or toxicity, 15 with literature information and 76 recent entries (from 2022 or 2023). The EU REACH definition contains 710 CIDs total, 346 with patent, 113 with use, 44 with safety/toxicity, 25 with literature information and 80 recent CIDs (see Figure ). The section exploring the difference between the definitions contains 112 CIDs in total, of which relatively few have either use, literature or safety/toxicity information (only 14 CIDs total). |
6493424724989702c2baf2e5 | 17 | Although PFOA, like PFOS, has been regulated already for several years, the PFOA section was much trickier to construct than the PFOS section, and remains incomplete due to the wording of the definition in Annex A of the Stockholm Convention . The entire node currently contains 25,472 CIDs, but only 789 of these have been included in the "PFOA plus its salts and PFOA-related compounds as defined in Annex A of the Stockholm Convention" section, since the exclusions to the definition are almost impossible to define or automate cheminformatically with existing PubChem functionality. Thus, at this stage, entries that (to the best of our knowledge) meet the definition have been included, and several other sections are included under this node for users to explore other content further. The entries that are included are the selected and updated lists from the Stockholm Convention (80 and 299 CIDs, respectively) plus three PubChem queries covering PFOA and branched isomers (47 CIDs), PFOA, branched isomers and salts (162 CIDs) and the PFOA plus branched isomer substructure query to capture mixtures (546 CIDs). An additional section breaks down the 789 matching PFOA content by annotation categories, such as found in literature (81), use information available (228), safety or toxicity information (41), patent information (401) or recent addition (in 2022 or 2023, 60 entries). This helps find potentially relevant entries among the hundreds of potentially regulated matches. The PFOA exclusions have been included in the node below, with placeholder nodes for content that cannot currently be created with reasonable effort. The halide exclusions have been implemented (currently 26 entries), and the updated indicative list of exclusions (35 CIDs). Polymers are inherently excluded from the tree as it currently covers compound space only, with additional functionality to enable polymer/UVCB inclusion still under active development at PubChem (and thus a potential future extension). The automatic detection of the remaining two exclusion categories, perfluoroalkyl carboxylic and phosphonic acids (including their salts, esters, halides and anhydrides) with ≥8 perfluorinated carbons, plus the perfluoroalkane sulfonic acids (including their salts, esters, halides and anhydrides) with ≥9 perfluorinated carbons has proven tricky. Although it may theoretically be possible to implement these exclusions programmatically, the current wording would require the creation of thousands of lines of custom code or several hundred very inefficient queries which, given the potentially thousands of possible matching entries, would be likewise difficult to check for accuracy and curate accordingly (several attempts at implementing this have been made already and sidelined as currently unviable). This remains an area of development for the PubChem PFAS Tree and a conversation topic with regulators, highlighting the challenges in implementing the current definition into an automated cheminformatics workflow, which will be necessary to update these regulatory lists in a manner scalable to the current numbers of PFAS (millions). |
6493424724989702c2baf2e5 | 18 | Like PFOA, the LC-PFCAs section remains difficult to complete due to the sheer number of chemicals involved. This is primarily due to the wording choice in the definition for the "related chemicals". As for PFHxS, two definitions are being explored for LC-PFCAs, the Stockholm Convention nomination of C 9 -C 21 LC-PFCAs and the EU REACH definition of C 9 -C 14 LC-PFCAs . The CIDs contained within these sections currently fulfil the LC-PFCAs, branched isomers, salts and mixture requirements of the regulation, but have not been extended to the related substances which, even in the current incomplete state, covers an additional 18,275 entries (the "related substances" sub-section remains as work in progress as the functionality required to perform these queries efficiently and automatically is still being developed). The C 9 -C 14 LC-PFCAs section is constructed using the "PFAS breakdowns by chemistry" section of the PubChem PFAS Tree and contains 230 CIDs. The C 9 -C 21 LC-PFCAs section contains 745 CIDs, which includes the draft indicative listing (83 CIDs), compounds that transform to LC-PFCAs (3 CIDs), plus queries for C 9 -C 21 LC-PFCAs, their branched isomers, salts, and mixtures. In total 584 of these have some form of annotation content, including 129 with use, 34 with safety or toxicity, 47 with literature, 490 with patent information, and finally 38 CIDs created recently (from 2022 or 2023). Again, these categories help determine which of the C 9 -C 21 LC-PFCAs may be relevant for different use cases. |
6493424724989702c2baf2e5 | 19 | The number of PFAS contained within the PubChem PFAS Tree, let alone the number of fluorinated compounds, is overwhelming. As mentioned in previous sections, there is a large amount of data present to add context to these numbers, as well as a variety of search functions and workflows available to browse and explore the contents further to help find the most relevant PFAS or fluorinated compounds for given use cases. This section gives a brief overview of some possibilities, with further information available in the PubChem documentation 58 , PubChem PFAS Tree documentation and the webinars . |
6493424724989702c2baf2e5 | 20 | Every node in the PubChem PFAS Tree (i.e., the blue numbers besides each category name in Figures ) or any classification browser in PubChem can be sent to PubChem Search by clicking on the numbers. A separate search window will open, which allows browsing and sorting of the results, the ability to interact with individual compound records, as well as the ability to save and combine searches (see Figure ) or send the content to Entrez for advanced search building and/or to browse in the classification browser (see Figure for example outputs). Each search query can then be downloaded in a variety of formats (see Figure ). It is also possible to upload custom lists to search via the PubChem landing page 20 (either pasting into the search bar, or via the "Upload ID list" option) or the PubChem Identifier Exchange . The download file contains a number of useful fields, a selection of which will be described here (for more information see the PubChem documentation 58 ). Several chemical identifier and structural information fields are included, such as names, synonyms (including CAS numbers where provided), the PubChem CID, the International Chemical Identifier (InChI) and the hashed form InChIKey , plus the Simplified Molecular Input Line Entry System (SMILES) . Several property fields are also given, including molecular formula, exact mass, molecular weight and octanol-water partitioning prediction (XlogP 66 ). Several additional fields help add context to the chemicals, including (at the time of writing; column header in brackets) the consolidated literature count (pclidcnt), patent count (gpidcnt), annotation categories (annothits), the count of annotation (annothitcnt), the date the CID was added (cidcdate), the names of the sources who deposited this structure (sidsrcname) and the deposition categories of the sources (depcatg). The annotation categories will be discussed more in the next paragraph; note that the columns, headers, and content are potentially subject to change. The patent and literature counts have been used for many years to help prioritise chemicals in non-target identification efforts , but as demonstrated in Figure and D, the distribution of the counts shown by the Chemical Stripes per chemical can also reveal interesting patterns, with the patent data often increasing earlier than the literature. This means that patent data could potentially be useful to find chemicals that are being used increasingly in industry (above the trend of other chemicals) before they are discovered through problematic emissions. It is possible to find recently added CIDs using the CID date (cidcdate). Since PubChem originated in 2004, this CID date will not always be an accurate reflection of the origin date of older chemicals. For older chemicals, the literature and patent dates can help build a more accurate history, as shown in Figure and D for PFOS, which was first added to PubChem in 2005, but was first mentioned in patents in 1913 and in the literature (within the collection available to PubChem) in 1981. The name of the depositors and the deposition category can help distinguish whether these chemicals come exclusively from patent literature or combinatorial libraries used for drug discovery, or whether these have been deposited by researchers, or the US EPA and so on. While these lists can be extremely long for well-known PFAS, these also tend to have substantial quantities of annotation, literature, and patent counts; the source information can help distinguish interesting entries among the long tail of matching chemicals with very little other data that potentially includes chemicals of high concern that have only just been discovered and documented. |
6493424724989702c2baf2e5 | 21 | Then annotation content of PubChem is very rich, coming from a wide variety of sources (currently over 920 data sources contribute to PubChem). The download file contains information on several major categories. The most relevant ones for environmental applications include, for example: drug and medication information; food additives and ingredients; literature; patents; pharmacology and biochemistry; safety and hazards; toxicity; use and manufacturing. The presence of these categories in the download file makes it easy to filter results by the categories of interest. Further annotation content can be browsed using the PubChem Table of Contents (TOC) Classification Browser (the "landing page" of the classification browser at ), which provides an overview of all annotation content in PubChem -currently 598 categories (20 June 2023). The overlap of PFAS and annotation content can be explored using the PubChem saved search and Entrez functionality. Figure demonstrates how the "saved search" feature can be used to calculate how many OECD PFAS (7,448,354 CIDs, bottom row) are also agrochemicals (from the TOC heading, 3086 CIDs, of which 305 are also OECD PFAS, third row) with mass spectral data in MassBank Europe (second row: 71 CIDs that are OECD PFAS agrochemicals in MassBank Europe) or measured collision cross section (CCS) data (top row: 27 CIDs that are OECD PFAS and agrochemicals with experimental CCS values in PubChem). Each of these overlap queries can also be browsed/downloaded. Further information on how to perform these queries is available in the PubChem documentation 58 , PubChem PFAS Tree documentation and in the webinars . |
6493424724989702c2baf2e5 | 22 | Creating a dynamic, user-friendly, browsable, and intuitive resource to explore >21 million fluorinated compounds in PubChem has been an incredibly challenging exercise in informatics and design, with several draft approaches attempted and revised before settling on the current version presented here. The functionality remains under development; automation of the regulatory and suspect list sections will be improved as the required functionality is developed. The handling of PFAS ethers (CF 2 -O connections) and cyclic PFAS structures has been particularly challenging, along with the implementation of automated queries for the PFOA exemptions and the related compounds for the LC-PFCAs (as described above). While salts and mixtures have been added to the OECD PFAS section (resulting in an extra million CIDs included in the PubChem PFAS Tree), these are still missing in the "Organofluorine compounds" and "Other diverse fluorinated compounds" sections. With rising awareness of fluorinated counterions increasing in concentrations in wastewater and potentially becoming problematic for treatment and thus drinking water production , adding this is a shorter term future development, which may add a few million more CIDs to the PubChem PFAS Tree. Polymers and UVCBs will be added to the PubChem PFAS Tree once PubChem functionality is available to do so -and will likewise increase numbers further. |
6493424724989702c2baf2e5 | 23 | Community feedback has been and will continue to be valuable to help improve the design and features of future versions, potentially including the addition of new sections or substantial revision to existing sections where this is justified. The addition of the annotation content breakdowns to the regulatory collection was based on many questions from users about how to find the most relevant PFAS entries. As this annotation content is also available in the download files, it is possible to retrieve this information for any subset of the PubChem PFAS Tree. However, since the annotation data in PubChem is compiled from publicly available data and user contributions, it is not completely exhaustive. In other words, the presence of "Use and Manufacturing" information for a PFAS implies that this information is available in PubChem for that chemical with a suitable reference, but this does not imply that the entire "Use and Manufacturing" section covers all known uses. The PubChem PFAS Tree has been available for over a year (since March 2022), was the subject of several presentations and webinars and has already been used in published research . Contributions of new PFAS or fluorinated chemicals and/or related annotation content, as well as feedback and suggestions about how the PubChem PFAS Tree can help the PFAS community answer their pressing questions are very welcome. |
65b154a166c13817292fad82 | 0 | In recent years, artificial intelligence in the form of deep learning has permeated the molecular sciences. Deep learning -based on artificial neural networks with multiple processing layers -has demonstrated remarkable potential in numerous applications, such as protein structure prediction and organic reaction planning . Deep learning has three main advantages: (a) it can learn complex and highly non-linear patterns from data , (b) it can be trained on a wide range of molecular representations (e.g., SMILES strings and graphs, Fig. ), and (c) it can be adapted to various types of training regimes, facilitating the development of tailored models for diverse applications. These aspects open novel modeling avenues compared to using human-engineered features only . Yet, its transformative potential has primarily been harnessed in data-rich settings where extensive datasets are readily available (e.g., , ). This relates to the fact that deep learning approaches optimize millions (or even billions) of neural-network parameters, which is made more robust by training on large datasets. Drug discovery, on the contrary, is often a low-data endeavor. |
65b154a166c13817292fad82 | 1 | Due to costs and time limitations, typical drug discovery datasets are comprised of only several hundreds of molecules -a number drastically smaller compared to other deep learning applications. Moreover, drug discovery datasets are often characterized by limited structural diversity, and insufficient 'negative data' (e.g., inactive molecules) , which restricts the information accessible for learning. Finally, the need to represent molecules as 'computerreadable' formats inevitably leads to information loss (e.g., about molecular systems dynamics), which might hamper the performance, for instance, with highly nonlinear structure-activity landscapes , , , . |
65b154a166c13817292fad82 | 2 | Despite these limitations, neural networks shine for their 'adaptable' nature; e.g., to different types of inputs and modeling tasks , and to manipulation of internal model representations -which unlocks novel avenues compared to traditional methods. Hence, deep learning for drug discovery bears incredible potential to extract relevant information from complex molecular systems and perform tasks that are not accessible via traditional computational approaches. Its application in low-data regimes faces unique challenges that demand innovative approaches. |
65b154a166c13817292fad82 | 3 | Stemming from these observations, this minireview delves into existing deep learning approaches for drug discovery with limited data availability, with a focus on bioactivity prediction (i.e., how to predict if and how a ligand will interact with one or more macromolecular targets) and de novo design (i.e., how to design novel bioactive molecules from scratch, Fig. ). While extensive reviews on how machine learning is employed for drug discovery exist , , this minireview provides a structured overview of deep learning for lowdata drug discovery, with special emphasis on recent approaches, their advantages and limitations, and the opportunities ahead. |
65b154a166c13817292fad82 | 4 | The term 'data augmentation' refers to approaches that artificially inflate the data available for training. This is usually done by generating multiple (and different) instances of the same molecule to be used as input for a deep learning model (Fig. ). Data augmentation can be applied to the entire training set, or selectively to mitigate the presence of imbalanced classes, e.g., lack of negative data. |
65b154a166c13817292fad82 | 5 | The most common data augmentation strategy has been applied to Simplified Input Molecular Line System (SMILES ) strings. SMILES strings are one of the most common ways to represent a molecular structure for deep learning. They encode two-dimensional aspects of the molecular structure (i.e., atom connectivity and type, and bond type) and, optionally, stereochemistry in the form of a string, by traversing the molecular graph and annotating the encountered atoms and bonds with predefined characters (Fig. ). Any heavy (nonhydrogen) atom can be used as a starting point, and, therefore, one molecule can have multiple valid and different SMILES strings. where two-dimensional molecular information is converted into a string format) and molecular graphs (where nodes and edges represent atoms and bonds, respectively). c. Two key tasks in drug discovery are molecular property prediction (whereby a property like bioactivity is predicted from the molecular structure) and de novo design (whereby structures with desirable properties are generated from scratch). |
65b154a166c13817292fad82 | 6 | This characteristic of SMILES strings can be used for data augmentation, by representing the same molecule in the training set with n different SMILES strings, usually generated at random. SMILES augmentation has been shown beneficial to improve the performance of quantitative structure-activity relationship (QSAR) models , as well as to improve the quality of de novo design models , with the magnitude depending on the structural complexity of the training molecules . The performance improvement of SMILES augmentation plateaus with increasing the number of SMILES per molecule , leading to progressively smaller performance gains with increasing computational cost. |
65b154a166c13817292fad82 | 7 | Other molecular representations often used for deep learning, like molecular graphs or molecular descriptors are less suited to data augmentation. Molecular graphs, for instance, encode molecular topology (atoms and bonds) and properties (atom properties and/or coordinates, and bond properties) in a permutation-invariant manner. In other words, every molecule (given a set of atom and bond properties to capture) maps to a unique molecular graph, rendering a 'SMILES-like' augmentation impossible. Similarly, molecular descriptors map one-to-one with the molecular representation they are computed from, rendering permutation-based augmentation unfeasible. A useful, albeit less explored, approach to circumvent this limitation is by considering 3D conformations and performing 'conformer-based augmentation'. Here, the same molecule is described by several, different 3D conformations, which enables data augmentation with molecular graphs and/or molecular descriptors that capture 3D information . How to aggregate information on different conformations is, however, still far from trivial, and several approaches can be explored . To date, the benefits of using multiple conformations are not fully evident , , and the performance might be affected by the chosen conformer generator . Finally, 3D-based approaches do not necessarily outperform more well-established ones that consider only 2D molecular information (e.g., ). |
65b154a166c13817292fad82 | 8 | Other molecule augmentation strategies exist, e.g., by calculating molecular descriptors on molecular fragments obtained by pre-defined decomposition rules , or by adding noise (mask, swap, deletion, and fusion) to existing SMILES strings . These strategies have, however, found limited application to date. Advances from the deep learning domain might help further boosting the performance in low data scenarios, e.g., for SMILES augmentation . |
65b154a166c13817292fad82 | 9 | While 'conventional' deep learning approaches rely on extensively labeled datasets to learn a given task in 'onego', other training paradigms have been developed to address the challenges posed by limited data scenarios. These strategies will herein be referred to as 'multistage', since they iteratively adapt to the information contained in multiple datasets or tasks (usually utilized in a stepwise manner for training) to improve model performance. The three most common multi-staged strategies are (Fig. ): |
65b154a166c13817292fad82 | 10 | • Transfer Learning, which leverages knowledge gained from one task to improve the model performance on a different, but related, task (e.g., , ) (Fig. ). In drug discovery, transfer learning is achieved by 'pre-training' a model on a large dataset (e.g., ChEMBL or ZINC ), and then 'fine-tuning' it (by additional training) on a smaller, and task-focused dataset (e.g., bioactivity on a given macromolecular target ). The pre-training approach depends on the task to be performed and on the chosen molecular representation . Pre-training enables bypassing the need of numerous labeled training data and leveraging large corpora of unlabeled molecules; this is particularly suited for molecular properties with little experimental annotations available. Transfer learning can improve model performance in smalldata regimes, especially for de novo drug design (e.g., ). However, undesired biases incurred during pre-training may persist after fine-tuning and affect the quality of the de novo designs . Overall, the efficacy of transfer learning can depend on how related the pre-training and fine-tuning datasets are (e.g., , , ), and on the chosen molecular representation and related training strategies (e.g., ). • Reinforcement Learning, whereby the actions taken by a model are steered towards promising solutions via a reward function (Fig. ). Reinforcement learning waives the need for a labeled starting dataset entirely, at the cost of requiring an 'oracle' (e.g., a machine learning model predicting a specific property) that can accurately reward specific choices. |
65b154a166c13817292fad82 | 11 | In drug discovery, reinforcement learning has been used mostly for de novo design , where it consists of the following phases: (1) de novo molecule design using a molecule generator (e.g., trained on ChEMBL or ZINC ), ( ) ranking of the designs via a scoring function (e.g., docking , and structural similarity ), and (3) use of the top designs as new input to the model, to bias future generations towards desirable properties. However, reinforcement learning is faced with several challenges , , e.g., related to (a) the difficulty of condensing (multiple) complex chemical properties into single scoring functions, or, (b) possible model shortcuts, where a 'loophole' in the scoring function is exploitatively capitalized upon (e.g., learning to append a single carbon atom to trivially fulfill a novelty criterion). To avoid these failure modes, caution with the used data and reward functions becomes essential . • Active learning, which selects molecules for screening over multiple iterations to expand the current dataset and, correspondingly, improves the model for the next screening round . While many factors can be tuned when performing active learning, how molecules are selected for screening is a key aspect in hit discovery . In low-data bioactivity prediction, active learning can remarkably outperform traditional machine learning approaches, leading to several fold improvement in hit retrieval . In de novo design, active learning has (to the best of our knowledge) not been extensively explored yet. Nevertheless, active learning requires both experimental and computational resources and expertise, which might increase the barriers for its adoption. |
65b154a166c13817292fad82 | 12 | In this minireview, we define context-enriched training as an umbrella term encompassing approaches that provide additional knowledge to the model ('context') to improve its performance on a given task. Unlike multistage learning, in context-enriched training all available information is provided to the model simultaneously. Context-enrichment can be performed in several different ways, such as: • Multimodal training. Multimodal training leverages multiple input types (e.g., different molecular representations) to enhance the model performance on a given task . Combining molecular information from different modalities might allow the model to learn more informative representations for the task at hand, potentially improving performance compared to models that rely on a single representation. In several application domains (e.g., medical image analysis and computer vision ) multimodal learning has shown promise to alleviate the limitations of scarce data. In the molecular sciences, it has been applied to several tasks (for instance, to combine molecular graphs and textual data , and ligand and proteins graphs ), showing promise for zero-and few-shot prediction . Since each molecular representation captures only part of the underlying 'molecular reality', multimodal deep learning is particularly relevant in the molecular sciences. However, it also carries several limitations, e.g., choosing how to effectively combine modalities, and 'modality competition' , whereby only a subset of the input modalities is leveraged by the model to make a prediction. • Multi-task learning. In multi-task learning, a model is trained to predict multiple outputs in parallel (e.g., multiple molecular properties ). The underlying idea is that the model error is optimized across all tasks (with the possibility to include missing values, if necessary), encouraging learning a shared representation that is beneficial for all tasks . Although multi-task learning does not seem to systematically outperform single-task approaches for bioactivity prediction, it seems beneficial on tasks that have fewer labelled molecules . Multi-task learning also comes with some caveats, for instance: (a) Its effectiveness relies on the assumption that the tasks are related, leading to failure when tasks that are too different from each other ; (b) the unavailability of all labels for each datapoint might affect the overall performance; and (c) an 'easy' tasks to model may become dominant during the training process, to the detriment of the more difficult ones. Hence, the complexity-performance trade-off of multi-task learning should be evaluated on a case-bycase basis. Additional approaches have been used to provide additional context at training time, e.g., by learning associations between a small set of molecules of interest with a larger set of (contextual) molecules , . A particularly interesting strategy is meta-learning whereby the outputs of multiple machine learning algorithms are combined to predict a novel task, which is finding increasing application in drug discovery , , , e.g., to predict bioactivity on novel binding assays and protein targets . |
65b154a166c13817292fad82 | 13 | Deep learning has enabled exciting new avenues in drug discovery. Despite the need for large training datasets being the 'Achilles heel' of deep learning in drug discovery, several advances allow neural networks to be, paradoxically, powerful tools in low-data scenarios. An increasing body of literature shows how strategies like the ones discussed in this minireview can lead to highperforming deep learning models, even with little data. However, many challenges are still lurking in the data shallows. |
65b154a166c13817292fad82 | 14 | One of the central trials models face in a low-data setting is out-of-domain generalization. Since deep learning models are typically trained on a specific set of molecules (and the corresponding structure-activity relationships), they might be challenged in generalizing to new, unseen molecules that may come from a different distribution (e.g., novel molecular scaffolds, structural motifs, or binding modes). Although this aspect is relevant for deep learning in general, low-data regimes intrinsically put additional strains on the model's ability to generalize out of the (limited) training distribution. Awareness of prediction uncertainty and out-ofdistribution performance are expected to become crucial guides in the future for prospective decision making, especially in low-data scenarios. We also expect causal and explainable deep learning to become instrumental tools in low-data scenarios and for out-ofdomain generalization, by shedding light on causal relationships, spurious correlations, and potential model shortcuts. |
65b154a166c13817292fad82 | 15 | Geometric deep learning -which incorporates and processes symmetry information -is also getting increasing attention in the molecular sciences, especially in the context of complex, three-dimensional molecular systems . Incorporating symmetry information, such as invariance or equivariance to rototranslations into neural network architectures, bears promise to learn sophisticated molecular information, which might be especially relevant when little training data is available. However, little is currently known on the performance of geometric deep learning in low-data scenarios, and the incorporation of molecular symmetry might not necessarily lead to better performing approaches . |
65b154a166c13817292fad82 | 16 | Structure-based drug discovery also bears a great potential in the low-data setting . These approaches, in fact, can leverage large corpora of protein-ligand affinity annotations, and can apply them to targets for which little (or no) ligand affinity information is available. Current structure-based approaches do not necessarily outperform approaches based on ligand information only , and hence we encourage the cheminformatics community to explore novel strategies to combine protein structure and ligand information with deep learning. Finally, multimodal learning , , and meta-learning , , strategies are getting increasing traction, and we expect them to become commonplace in drug discovery with low-data. |
65b154a166c13817292fad82 | 17 | A current 'known unknown' in the field is the minimal data requirement for deep learning in drug discovery. Only a limited number of studies systematically examine the effect of dataset size and diversity on the model performance and out-of-domain generalization , , . The same holds for knowledge on what deep learning strategy to choose based on the task and data at hand. In this context, FSmol -which provides the first-in-kind benchmark and set of baselines for low-data training -is a notable effort to further propel deep learning approaches in drug discovery. We expect the development of metrics and datasets tailored to low-data training to be key to harmonize the evaluation, choice, and development of novel approaches with an increased potential for drug discovery. |
66092d619138d23161ce8175 | 0 | Plane waves (PW) represent the standard basis-set choice in solid-state chemistry, implying periodicity by construction and enabling the efficient computation of electrostatic interactions by fast Fourier transformation (FFT) techniques. Linked to intrinsic periodicity is however the major disadvantage of non-locality, representing a challenge when it comes to describing local fluctuations of the electronic density at the core or when tackling systemspecific local features like defects or local charges. Mixed or augmented approaches, that combine plane waves with local basis sets, have therefore been developed extensively, enabling to exploit the advantages of both representations. Mixed schemes expand the global density using both intrinsically periodic plane waves and atom-centered local basis functions, such as Gaussian 1 or numerical orbitals. Doing so, the Gaussian and plane wave (GPW) method enables to still evaluate Coulomb and exchange correlation (XC) contributions efficiently using FFT, while sparsity of the density matrix can be exploited for contributions of kinetic energy and electron-nuclei interaction. In consequence, Kohn-Sham matrix build up in GPW scales linearly with system size, which has to be compared with the typical quadratic scaling of PW codes. However, relying on global densities only, GPW has to replace core electrons with pseudo potentials: The plane wave representation is sufficiently accurate for feasibly small energy cutoffs when dealing with smooth electron densities in interatomic regions. The description of the heavily oscillating density at the atomic cores would require impracticably high thresholds if not relying on pseudo potentials. The latter however hinder all-electron computations and thus the modeling of core excitations in e.g. X-ray, nuclear magnetic or electron paramagnetic resonance (NMR or EPR) spectroscopy. Furthermore, in the case of second-row transition metals, it might be necessary to consider localized semi-core states in the explicitly treated valence region, requiring high cutoffs for state-of-the-art norm-conserving pseudo potentials. Augmented plane wave (APW) approaches therefore combine a dual basis-set representation with the standard strategy to divide the system into two regions, an interatomic region, which is still relying on plane waves, and core regions, which are in contrast represented by localized basis sets. Within the extensive research field of APW methods, the projector augmented wave (PAW) method by introduced the general idea to rely on a linear transformation between pseudo and all-electron wave functions based on projection operators, ensuring that the relevant ground-state or excited-state equations can be reformulated within the auxiliary basis sets, while still expanding integrals over all space. Using projection operators enables to separate the hard local atomic densities from the soft smoothly decaying global density. |
66092d619138d23161ce8175 | 1 | While the separation of densities can be easily transferred to a separation of local potentials and energies, the treatment of non-local Coulomb contributions furthermore requires to introduce screening charges, constructed such that the corresponding multipoles sum to zero, cancelling spurious interactions between core and interatomic regions. PAW is closely related to ultrasoft pseudo potentials and is state-of-the-art in leading program packages of solid-state material science. The PAW scheme was also used to extend GPW to the all-electron Gaussian and augmented plane wave (GAPW) approach. Starting from an initial implementation for groundstate properties, GAPW was extended to time-dependent linear response perturbation theory and it was shown, that convergence of the plane-wave energy cutoff is accelerated in comparison to GPW, enabling efficiency due to smaller cutoffs while still keeping the GPW scaling for the Kohn-Sham (KS) matrix construction at O(N logN ) with system size N . More precisely, a threshold of 200 Ry was shown to be sufficient to ensure converged energies within ≈ 1µE h and bond lengths fluctuations of less then 20 µÅ. Furthermore, GAPW implementations were generalized for the treatment of core electrons, replacing pseudo potential contributions by corresponding full nuclear potential expressions, and extended to describe X-ray absorption as well as NMR and EPR spectroscopy. Regarding the computation of hyperfine parameters for the latter spectroscopies, Van Speybroeck and Waroquier et al. furthermore suggested a hybrid scheme, which implies an all-electron treatment only for selected nuclei while keeping pseudo potentials for the remaining atoms of the system. Within this contribution, we present the implementation of GAPW excited-state nuclear gradients based on a variational Lagrangian, circumventing the outlined restrictions of the recently published related GPW implementation 38 (section 2.1). Based on the fundamental ideas of Blöchl to separate the hard and soft densities (section 2.2) implying screening charges for non-local energies (section 2.3), the required working equations (section 2.4) involve a discrimination of the GAPW representation for ground-and excited-state densities. |
66092d619138d23161ce8175 | 2 | Only the former include core compensation charges and thus imply adjusted multipoles for screening. Accuracy of GAPW is assessed for a test set of 35 molecules, investigating both singlet and triplet vertical excitation energies as well as corresponding excited-state geometries (section 3.1). Enabling the description of excited-state properties, the GAPW excited-state gradient code is finally applied to compute the zero-phonon line of defective hBN (section 3.2). |
66092d619138d23161ce8175 | 3 | relying on the density matrix D for the description of one-electron and exact exchange contributions, h and E EX , while the plane-wave density n(G) is used to compute electrostatic and XC contributions, E es and E XC . Ω UC is the unit cell volume. Relying on Ewald summation, a core charge compensation potential has been removed from the external potential contribution to h and added to the electronic electrostatic terms. These are divided into Coulomb, self and overlap energy contributions, thus including core compensation charges n c (G) with the total charge distribution being given as |
66092d619138d23161ce8175 | 4 | representing the reciprocal space vectors. More explicit expressions for E ovlp and E self and their derivatives are summarized in the supplementary information. The number of plane waves needed for an all-electron description would increase with the square of the nuclear charge and is therefore not feasible in routine applications. In order to avoid this bottleneck the external potential contributions of h uses pseudo potential for core electron contributions |
66092d619138d23161ce8175 | 5 | To circumvent high energy cutoffs for the plane wave basis without being dependent on pseudo potentials, the GAPW method divides the system into core and interatomic regions, U A and U I , with the former being characterized by heavily fluctuating densities requiring high plane wave cutoffs while the latter represent smoothly decaying densities sufficiently described within a small plane wave basis. To describe the core regions within GAPW, the conventional plane wave and Gaussian orbital basis sets of the underlying GPW method are therefore augmented with adjusted basis sets, that are either mimicking a fluctuating "hard" density using a manifold of atomic orbitals generated from primitive Gaussians with large exponents, {ϕ µ (r)}, or a smoothly decaying "soft" density with, in contrast, diffuse primitive Gaussians with small exponents, { φµ (r)}. Furthermore, corresponding hard and soft localized atom-centered atomic orbitals, {χ µ (r)} and { χµ (r)}, enable to construct related atomic one-center densities within the core regions, ñ1 A (r) and n 1 A (r). A description of any arbitrary total density n(r) in terms of a respective global soft density ñ(r) is then possible if the smooth atomic densities within the core regions, ñ1 A (r), are corrected by their hard counterparts, n 1 A (r), |
66092d619138d23161ce8175 | 6 | the fixed contraction coefficients P and P of the primitive Gaussians g l are chosen to fulfill P = P for small exponents to imply ñ = n within the interatomic region and the highest exponents of P are set to zero according to a given threshold so that ñ is smoothened within the atomic region. The construction of hard and soft atomic densities, |
66092d619138d23161ce8175 | 7 | The first term is calculated on a global grid using FFT techniques and the remaining two contributions are computed numerically using atomic grids. Due to the non-local character of the Coulomb operator, the decomposition is however more complex for the electrostatic energy, requiring to introduce atom-dependent screening densities n 0 A , |
66092d619138d23161ce8175 | 8 | where q L mn is the multipole moment of the local basis product g m (r)g n (r). Soft contributions can analogously to Eq. ( ) be computed using FFT, while remaining terms are evaluated, in contrast to Eq. ( ), analytically using spherical harmonics. The current formulation is restricted to choosing one screening charge n 0 , not discriminating between hard n 0 and soft ñ0 variants, since the gain in computational cost provided by the latter variant is negligibly small. |
66092d619138d23161ce8175 | 9 | When implying periodic boundary conditions as outlined in section 2.1, the total groundstate density n tot thus includes core charges (in contrast to n X and n Z ), so that the so far discussed equations for the separation of the density, the multipole moments, GAPW energy and potential have to be adjusted in this case as |
66092d619138d23161ce8175 | 10 | The special form of the GAPW energy functional involves several approximations: The accuracy of the local expansion of the density is controlled by the flexibility of the product basis of primitive Gaussians. As already mentioned, the highest exponents of the soft contraction coefficients are hereby defined by a given threshold. Atomic basis sets are constructed choosing the primitives of the orbital basis, with the option to add further primitives. Core compensation charges are built from one primitive with kind-dependent exponent proportional to the square root of the core charge. The exponent of the screening charge n 0 can be defined on input, otherwise it is computed so that the radius of the primitive Gaussian is smaller than 0.8 a.u. (or 1.2 a.u. in the special case of hydrogen) for a chosen threshold. The definition of the atomic radius R at and to what extend the strict conditions on the density are fulfilled in an actual calculation will further determine the accuracy that can be reached. |
66092d619138d23161ce8175 | 11 | They refer to the ground-state KS orbitals Φ iσ (r), the solutions to the Coupled-Perturbed Kohn-Sham (CPKS) equations Φ Z iσ (r), and the response orbitals Φ X iσ (r) stemming from the TDA eigenvalue problem. Their corresponding basis-set expansion coefficients are denoted C µiσ , Z µiσ , and X µiσ , respectively. S represents the atomic overlap matrix, |
66092d619138d23161ce8175 | 12 | a EX is the global parameter to scale the exact exchange contribution. Within GAPW and GPW, the one-electron contributions h are computed either referring to Eq. (3) including kinetic energy and pseudo potential contributions or by replacing pseudo potentials with the all-electron nuclear potential operator, relying for both formulations on the conventional density matrix D. As mentioned before, GAPW ground-state electrostatic contributions take into account core compensation charges, thus referring to Eqs. (22, 23, 24, 25). |
66092d619138d23161ce8175 | 13 | In contrast to the ground-state KS matrix contributions, GAPW excited-state electrostatic contributions stemming from the kernel do not take into account core compensation charges, thus referring to Eqs. (4, 14, 15, 17). The corresponding derivative furthermore comprises mixed formulations including core charges in the potential while not in the density or vice versa, |
66092d619138d23161ce8175 | 14 | Even though n Z is not including core compensation charges, the KS matrix contributions of Eq. ( ) are based on the total ground-state density n tot , thus leading to the mixed core compensation gradient terms of Eq. ( ). The right-hand side of the CPKS equations, R, is determined by the TDA eigenvalue equations and included GAPW expressions therefore do not include core compensation charges. |
66092d619138d23161ce8175 | 15 | The GAPW force implementation is assessed with respect to, first, the conventional allelectron molecular quantum chemistry code Gaussian, and, second, the underlying pseudo potential based GPW implementation in CP2K. Both comparisons elucidate how the GAPW ansatz impacts the overall accuracy of the method, with the first comparison pointing out the error in choosing an additional plane wave basis for the interatomic domains and the second benchmark determining the introduced error by augmenting the basis set with local Gaussians for the atomic regions. For both assessments, we examined ground-state energies and forces, the first three singlet and triplet vertical energies as well as the forces associated with the first singlet and triplet excited states. The former two properties were already benchmarked in Refs. ) and are considered here additionally to enable a comparison of ground-state and excited-state forces and to emphasize consistency. As benchmark systems, we have chosen the molecular test set of Budzak et al., comprising 35 small molecules containing main-group elements from the first and second rows of the periodic table, as well as sulfur, selenium, chlorine, and bromine. The initial molecular geometries were adopted from our prior work, wherein we optimized ground-state geometries using the PBE0 functional and the def2-QZVPP basis set 41 within the Turbomole program package. For the sake of convenience, our examination of vertical excitation energies is throughout confined to a direct comparison of the first three vertical excitation energies, with states solely identified based on the corresponding electronic structure energy. Furthermore, only non-zero x, y and z components of the ground-state or excited-state forces were considered for statistical analysis. |
66092d619138d23161ce8175 | 16 | Regarding the overall computational settings, all benchmark computations were performed using the PBE0 density functional. Tight convergence criteria were implied throughout all computations, setting the Schwarz screening threshold for two-electron integrals to 10 -10 a.u. for both electron repulsion and corresponding derivative integrals. Excited states were converged up to an accuracy of 1.0×10 -7 eV. |
66092d619138d23161ce8175 | 17 | For the first comparison with the all-electron Gaussian reference results, one-electron contributions were computed using all-electron full nuclear potentials in combination with a def2-TZVPP basis set. The plane wave grid cutoff was set to 400 Ry. Twice as large radial and Lebedev grids were chosen for selenium and bromine and the atomic radius R at was adjusted specifically for each element (see supplementary information). Atomic basis sets were constructed by relying on the orbital basis adding a small number of additional primitive Gaussians. |
66092d619138d23161ce8175 | 18 | Maximum errors (MAX) and mean absolute errors (MAEs) for ground-state total energies and forces as well as corresponding excited-state analogues are given in Table . For groundstate energies, the maximum error is not exceeding 7.10×10 -5 Hartree/atom, and the MAE of 1.75×10 -5 Hartree/atom is negligibly small, emphasizing the agreement of both methods. |
66092d619138d23161ce8175 | 19 | Deviations for ground-state forces amount up to 0.0293 eV/Å and 0.0026 eV/Å, respectively, with the most significant deviations for the forces being observed for the C-C triple bonds in acetylene, cyanoacetylene, and diacetylene. The comparison of the first three singlet and triplet excitation energies gives a maximum error for singlet excitations of 0.0102 eV and a MAE of 0.0017 eV. The maximum error and MAE for triplet excitations is of only 0.0015 eV and 0.0005 eV, respectively. Most importantly, the accuracy of GAPW excited-state forces is comparable to the one of GAPW ground-state forces: The largest errors for the excited-state forces of the first singlet and triplet states are smaller than 0.0303 eV/Å and 0.0472 eV/Å, respectively, with the most substantial deviations originating again from C-C triple bonds. |
66092d619138d23161ce8175 | 20 | Table : Maximum errors (Max) and mean absolute errors (MAEs) of ground-state (GS) energies (in Hartree/atom) and forces (in eV/Å), vertical excitation energies of the first three singlet and triplet excited states (in eV) and of corresponding forces associated with the first singlet or triplet excited state (ES) (in eV/Å), comparing the GAPW implementation in CP2K with the all-electron Gaussian-orbital based TDA implementation in Gaussian. |
66092d619138d23161ce8175 | 21 | To compare the GAPW and GPW implementations, the plane wave grid cutoff was adjusted to 800 Ry. Computations were performed relying on Goedecker-Teter-Hutter (GTH) pseudo potentials that were optimized for PBE0 density functional computations and using ccGRB-T orbital basis sets. The augmented basis sets for GAPW were constructed as before by relying on the orbital basis, now of ccGRB-type, adding a small number of primitive Gaussians. A comparative analysis of maximum errors (Max) and mean absolute errors (MAEs) for both ground-state and excited-state computations is provided in Table . Even though maximum errors are slightly increased and MAEs slightly improved in comparison to the assessment with respect to Gaussian, the overall trend and magnitudes of errors are comparable, emphasizing that sufficient accuracy can be reached with GAPW. More explicitly, errors in ground-state and excited-state forces are again comparable with a maximum error of 0.0932 eV/Å and 0.0931 eV/Å, respectively. To highlight the overall retained accuracy of the GAPW ansatz, the agreement in GPW and GAPW excitation energies is visualized in the correlation plot of Figure . |
66092d619138d23161ce8175 | 22 | Table : Maximum errors (Max) and mean absolute errors (MAEs) of ground-state (GS) energies (in Hartree/atom) and forces (in eV/Å), vertical excitation energies of first three singlet and triplet excited states (in eV) and of corresponding forces associated with the first singlet or triplet excited state (ES) (in eV/Å), comparing GAPW with GPW. |
66092d619138d23161ce8175 | 23 | Hexagonal boron nitride (hBN) is a broadly-studied two-dimensional material characterized by its thermal and chemical stability. Consisting of boron and nitrogen atoms arranged in a hexagonal lattice, hBN belongs to the family of van der Waals materials, sharing similarities with graphene. One of its distinguishing features is its status as a wide bandgap semiconductor, with a band gap typically ranging from 5 to 6 eV. Due to these exceptional properties, hBN has attracted significant attention and found applications in diverse fields such as photonic devices, 50 fuel cells 51 and biomedicine. Techniques such as chemical vapor deposition, high-temperature annealing of boron nitride precursors, hydrothermal synthesis, and mechanical exfoliation enable the production of hBN in its pure and unaltered form. On the other hand, the controlled insertion of defects into hBN, such as vacancies or substitutions, can significantly alter its electronic and optical properties. The nitrogen or boron vacancies can introduce electronic states within the band gap of hBN, leading to absorption and emission of light in the visible or near-visible range of the electromagnetic spectrum. |
66092d619138d23161ce8175 | 24 | The unique capabilities of hBN's color centers have found application in quantum information processing. The zero-phonon line (ZPL), a distinct feature characterizing electronic transitions without concurrent involvement of vibrational modes or phonons, plays a pivotal role in understanding the luminescent behavior of defects. The ZPL represents a sharp and well-defined emission peak, indicative of a purely electronic transition within the defect. The purity of this electronic transition is particularly significant for applications in quantum optics, where the optically active V N N B defect's ZPL not only provides a clear signature of its luminescent behavior but also serves as a reliable and controllable source of single-photon emission, advancing applications in quantum optics and information processing. |
66092d619138d23161ce8175 | 25 | To showcase the effectiveness of the GAPW implementation for extended systems, we investigated the V N N B defect in hBN, in which a nitrogen occupies a boron site and a neighboring nitrogen site is missing, as visualized in Figure . Tran et al. show that the weak interaction between hBN sheets has minimal impact on the properties of the defect, therefore we opted for a single-layer hBN. The monolayer hBN unit cell was replicated to a multiple cell of 7 × 4 × 1 and the monolayer was padded with vacuum in z-direction to obtain a simulation box of volume 17.60 × 17.42 × 30 Å 3 . Computations were performed using the HSE06 functional, which is broadly used in studies of semiconductor defects providing bandgaps in agreement with experimental observations. An open-shell electronic configuration was implied to describe the vacancy appropriately. Shifting from highest-accuracy assessments of molecules to a large-scale application, the computational setup was furthermore adjusted: A MOLOPT basis of triple-ζ quality was used as primary orbital basis set. Exact exchange contributions are accelerated using ADMM, requiring an additional auxiliary basis of double-zeta quality. The plane-wave grid cutoff was set to 320 Ry. |
66092d619138d23161ce8175 | 26 | The accuracy of our GAPW implementation is compared first, to an all-electron quantum chemistry code and second, to the well-established pseudo potential GPW code with max errors not exceeding 3.40×10 -5 Hartrees/atom for ground-state energies and 0.09 eV/Å for ground-state forces, 0.01 eV for vertical excitation energies and 0.09 eV/Å for forces associ-ated with first singlet or triplet excited states, for both comparisons. Local features such as the V N N B defect in hexagonal boron nitride are accurately reproduced with errors of 0.2 or 0.4 eV in comparison to highly accurate GW-BSE reference computations or experimental data. The presented method developments pave the way for further advancements in the description of localized features and excited core states in solid-state materials, as required e.g. for time-resolved X-ray spectroscopy. |
6409fdf7cc600523a3ecb75c | 0 | Quantum embedding methods are promising for accurately describing electron correlation in molecules and materials, especially when correlated wave-function methods become prohibitively expensive due to their poor scaling with system size. These methods involve dividing a system into important regions (called impurities or fragments) that are treated with a highly correlated theory, while the rest of the system is described using a more approximate level of theory, such as Hartree-Fock (HF) or Kohn-Sham density functional theory. One particular type of quantum embedding method is density matrix embedding theory (DMET), which uses a wave function-in-wave function approach and models the environment of the impurity or fragment using a bath constructed from the Schmidt decomposition of a mean-field wave function. |
6409fdf7cc600523a3ecb75c | 1 | For systems with significant static (strong) correlation, multiconfiguration methods are often used to describe the ground and excited states of molecular systems. The complete active space self-consistent field (CASSCF) method expresses the wave function as a linear combination of all possible configuration state functions that can be generated within a defined "active space" of n active electrons occupying N active orbitals. To get accurate electronic excitation energies and reaction energies, post-SCF methods such as the complete active space second-order perturbation theory (CASPT2) or n-electron valence state second-order perturbation theory (NEVPT2) can be used, as well as multiconfiguration pair-density functional theory (MC-PDFT). Multiconfiguration methods are desired as high-level (impurity) solvers in DMET because they can handle extended systems with multiple electronic configurations. Recently nelectron valence state second-order perturbation theory (NEVPT2) was implemented as a high-level quantum chemical solver within periodic DMET (pDMET) to capture dynamic correlation as a post-CAS-DMET procedure. However, even though NEVPT2-DMET is cheaper than NEVPT2, it scales poorly with the active space size and the parameter space (i.e. the number of orbitals in the impurity). A more affordable alternative for capturing electron correlation at the post-SCF level is multiconfiguration pair-density functional theory (MC-PDFT) and its hybrid version (HMC-PDFT). In a recent benchmark study of 373 vertical excitation energies from the QUESTDB dataset, HMC-PDFT was found to be as accurate or even more accurate than NEVPT2 for excitation energies. Here, we present a way to calculate the correlation energy starting from a CAS-DMET wave function using PDFT and hybrid PDFT. Our implementation is designed for systems with periodic boundary conditions (extended systems), specifically inspired by the class of problems we are tackling, such as point defects in crystals. It can be easily adapted to molecular systems with open boundary conditions. Here onwards, we refer to this approach as pDME-PDFT and we employ it to calculate singlet-singlet and singlet-triplet excitation energies in the F and M centers on the (100) surface of magnesium oxide. F centers play an important role in catalysis, energy storage, 37 photoelectrochemical applications and are responsible for several physical and chemical properties of MgO. M centers are an aggregate of two adjacent F centers, which also affect the physical and chemical properties of MgO, such as its electrical conductivity, magnetic behavior, and optical properties. 2 Theory |
6409fdf7cc600523a3ecb75c | 2 | Here, V NN is the nuclear-nuclear repulsion energy, p, q, r, and s denote molecular orbitals, h pq and g pqrs are one-and two-electron integrals, D pq are the elements of the one-electron reduced density matrices (1-RDMs) and E ot is a functional of the density (ρ) and the on-top pair-density (Π). The hybrid MC-PDFT energy 34 is expressed as: |
6409fdf7cc600523a3ecb75c | 3 | Our calculations were performed using a λ value of 0.25, referred to as tPBE0, in analogy with the PBE0 hybrid density functional theory (DFT) functional. DMET and its periodic implementation have been discussed in detail previously. DMET involves a low-level (usually Hartree-Fock) calculation on a whole system followed by a high-level (in our case, CASSCF or NEVPT2) calculation in an unentangled "embedding" subspace consisting of the union of user-specified fragment orbitals and corresponding bath (i.e. entangled environment) orbitals identified using the Schmidt decomposition. The 1-RDM and two-body reduced density matrix (2-RDM) of the whole system consist of the 1-and 2-RDMs, respectively, from the high-level calculation in the embedding subspace combined with those from the low-level calculation in the orthogonal "core" subspace. If (as in this work) only one embedded fragment is considered in each calculation and the low-level wave function (here, restricted open-shell HF or ROHF) is spin-symmetry-adapted and closed-shell in the core subspace, then the expressions for the DMET whole-system 1-and 2-RDMs assume the simple forms: |
6409fdf7cc600523a3ecb75c | 4 | Note that the implementation of pDME-PDFT differs from the one of NEVPT2-DMET in the following way: while pDME-PDFT evaluates the total energy using the density and on-top pair-density of the whole system (see eqs. 4 and 5), NEVPT2-DMET applies the NEVPT2 method only to the embedding space. Since pDME-PDFT is agnostic to the way in which the embedding calculation has been performed, it is designed to recover in part the effects of dynamic electron correlation even for inactive electrons, which are not correlated in the underlying trial wave function. In contrast, NEVPT2-DMET can not describe electron correlation beyond the embedding space. Moreover, pDME-PDFT has a lower cost scaling with respect to embedding space size compared to NEVPT2-DMET, making it potentially more advantageous both in terms of accuracy and cost reduction. |
6409fdf7cc600523a3ecb75c | 5 | All the DMET calculations were performed using our in-house pDMET and mrh codes which utilizes the electron integrals and quantum chemical solvers from PySCF. Wannierization was done using the wannier90 53 code via the pyWannier90 interface. The Goedecker-Teter-Hutter pseudopotentials were used for all the calculations. The geometry optimizations were performed at the spin-unrestricted PBEsol level 57 using the Vienna Ab initio Simulation Package (VASP). The convergence criteria of 10 -6 eV and 10 -3 eV/ Å were used for the energy and force, respectively. We represent a MgO(100) surface using a single layer of Mg and O with the chemical formula Mg 18 O 18 . We performed benchmark calculations on two point defects, namely the oxygen mono-vacancy (OV) and a oxygen di-vacancy (OOV). For these systems, we computed singlet-singlet and singlettriplet excitation energies using CAS-DMET, NEVPT2-DMET and pDME-PDFT. We used the translated PBE functional for both PDFT and hybrid PDFT which are referred to as pDME-tPBE and pDME-tPBE0 respectively. The oxygen mono-vacancy defect is created by removing one neutral oxygen atom at the center of the unit cell. The di-vacancy is created by removing an additional neutral oxygen atom nearest to the mono-vacant oxygen atom. |
6409fdf7cc600523a3ecb75c | 6 | To separate the layer and its periodic images, we used a vacuum of 23.518 Å along the [100] direction. In the DMET calculations, we place a dummy oxygen atom at the vacancy to provide basis functions to span the electron density of the defect. For the mono-vacancy, the dummy oxygen and four nearest atoms Mg atoms are treated using the polarized triplezeta basis set (GTH-TZVP) whereas the rest of the atoms are treated with the polarized double-zeta basis set (GTH-DZVP). For the di-vacancy, the dummy oxygens and six nearest Mg atoms are treated using the polarized triple-zeta basis set (GTH-TZVP) whereas the rest of the atoms are treated with the polarized double-zeta basis set (GTH-DZVP). The two and three layered models are constructed by placing non-defective one and two layers of Mg 18 O 18 below the first layer respectively. For these models the GTH-TZVP is used for the dummy oxygen and nine nearest atoms (4 O and 5 Mg) while GTH-DZVP is used for all other atoms. |
6409fdf7cc600523a3ecb75c | 7 | First, we investigate the performance of pDME-PDFT in calculating the S 0 → S 1 and S 0 → T 1 excitations of the F-center which is a neutral oxygen mono-vacancy (OV) on the (100) monolayer of MgO. Experimentally, detecting F centers on MgO surfaces presents a challenge due to its surface sensitivity, resulting in a range of S 0 → S 1 transitions observed between 1-5 eV as reported in Table . A quantum mechanics/molecular mechanics (QM/MM) approach, utilizing the multireference configuration interaction method, for a cluster model of the oxygen mono-vacancy predicted excitation energies of 3.24 eV for the S 0 → S 1 transition and 1.93 eV for the S 0 → T 1 transition. The MgO lattice is composed of Mg 2+ and O 2- ions, and when an oxygen atom is removed, it leaves behind two electrons in the defect site that occupy two defect-localized states between the valence band maximum (VBM) and the conduction band minimum (CBM). The computational model is illustrated in Figure . To examine how the excitation energies vary with the embedding space, we consider three impurity clusters of increasing size, as depicted in Figure . Figure shows the two active natural orbitals used for the minimal (2,2) active space in all calculations presented in Figures and. This active space has been used previously for the F-center. The two active orbitals have a 1g and a 2u symmetry in the D 4h point group. In Figures and, we show the vertical excitation energies of the S 0 → T 1 and S 0 → S 1 transitions in the OV system, respectively, as a function of the inverse of the number of embedding orbitals, using the minimal (2,2) active space. Specifically, the plot of excitation energies is shown as a function of N AO /N emb where N AO represents the total number of basis functions in the system considered (here Mg 18 O 18 ) and N emb is the number of embedding orbitals in the impurity clusters considered. We compare them to the corresponding nonembedded results represented by hollow markers. The values are reported in Table . The excitation energies computed using pDME-tPBE and pDME-tPBE0 agree to within 0.06 eV of the non-embedded reference values for all impurity clusters considered. NEVPT2-DMET, on the other hand, shows a higher sensitivity to the impurity cluster . This is expected since NEVPT2-DMET cannot describe electron correlation outside the embedding space. Considering the S 0 → T 1 gap, for example, the NEVPT2-DMET difference with respect to the non-embedding reference ranges from 0.17 eV to 0.05 eV. As previously done for NEVPT2-DMET, the linear dependence of the excitation energies with respect to the inverse of the number of embedding orbitals was utilized to extrapolate the non-embedding limit. Here, the non-embedding limit corresponds to the point where N AO /N emb =1, i.e. |
6409fdf7cc600523a3ecb75c | 8 | In Figure and Figure , we plot the vertical excitation energies using a (2,8) active space as was used in reference 32. The corresponding numbers are reported in Table . The active orbitals are reported in the SI. The excitation energies obtained from various non-embedding correlated theories exhibit closer agreement with one another in the larger (2,8) active space, providing a means of evaluating the performance of DME-PDFT for both smaller (2,2) and larger (2,8) active spaces. For the (2,8) active space, all pDME-tPBE and tPBE0 excitation energies agree to within 0.05 eV of the non-embedding references, whereas NEVPT2-DMET shows a higher (although not very significant) sensitivity to the impurity cluster. To quantify the sensitivity of the excitation energies to the embedding space we report the slopes for all the linear extrapolations in Tables and of the SI. Next, we investigate the S 0 → S 1 and S 0 → T 1 excitations of the M-center, which is a neutral oxygen di-vacancy (OOV) on the (100) monolayer of MgO. This defect is also known as the M centre. Here, the removal of two neutral oxygen atoms leaves four electrons in the cavity created by the two missing oxygens. In the singlet ground state these electrons occupy the two defect-localized states present between the VBM and the CBM. Experimentally, Kramer et al. tentatively assigned the 1.0 eV and 1.3 eV adsorption peaks to the M center on thin films of MgO. The computational model is shown in Figure . We consider four impurity clusters as shown in Figure . We show the five active natural orbitals forming the minimal (4,5) active space in Figure . In Figure , we present the vertical excitation energies for the OOV system. The corresponding numbers are reported in Table . Although the excitation energies calculated using pDME-tPBE0 for the three larger fragments OOV+Mg 6 O 2 , OOV+Mg 6 O 6 and OOV+Mg 6 O 10 are within 0.07 eV of the corresponding non-embedded calculations, the smallest fragment OOV+Mg 6 deviates by 0.14 eV for the S 0 → T 1 gap. This highlights the inadequacy of the smallest impurity cluster (OOV+Mg 6 ) in providing an accurate approximation of the overall system densities. Therefore, when extrapolating to the non-embedding limit, only the three larger fragments are taken into account. The excitation energies for the OOV+Mg 6 impurity cluster clearly fall outside the range of the linear extrapolation, as indicated by the detailed analysis presented in Section S01 of the Supporting Information, which includes R 2 values for the linear fits. The results for the OOV system appear to be slightly more sensitive, as indicated by the slopes of the linear extrapolations in Table of the SI, compared to Table : Vertical excitation energies (in eV) of the oxygen divacancy on the MgO(100) surface obtained using CAS-DMET, NEVPT2-DMET, pDME-tPBE and pDME-tPBE0, with an active space of 4 electrons in 5 orbitals. The extrapolated energies from linear regression of the last three points are labeled as "Extrap". "Reference" here indicates the non-embedded Γ-point CASSCF, NEVPT2, tPBE and tPBE0 calculations. Next, we explore electronic excitations in the oxygen mono-vacancy on MgO surfaces con- In the three-layer case, like in the example above, the non-embedding calculations are pro- |
6409fdf7cc600523a3ecb75c | 9 | We developed a new electronic stucture method, called pDME-PDFT, based on density matrix embedding theory and multiconfiguration pair-density functional theory, able to treat extended systems with periodic boundary conditions. Initial applications on oxygen vacancies in magnesium oxide showed that produces results that are comparable to the more expensive non-embedded MC-PDFT method. We then used pDME-PDFT to study larger models, namely the Mg 36 O 36 and Mg 54 O 54 surfaces, which are impractical to investigate with non-embedded MC-PDFT. Finally, pDME-PDFT gives results comparable with the more expensive and in many cases non-affordable NEVPT2-DMET method. We envision that pDME-PDFT will be used to investigate the electronic properties of defects in materials, as well as reactions on surfaces involving multireference systems. |
675f0698085116a1337f1a3a | 0 | Human respiratory viruses pose devastating threats on public health and the economy as demonstrated by the SARS-CoV-2 virus responsible for the COVID-19 pandemic. SARS-CoV-2 encodes two cysteine proteases, main protease (M Pro ) and papain-like protease (PL Pro ), which are responsible for cleaving 11 and 3 sites respectively along the viral polyprotein and enable infection. Considerable research efforts have been made to establish inhibitors for these viral proteases, resulting in several clinically available therapeutics including nirmatrelvir . Despite these important medicines providing therapeutic benefit, there is a concern for the development of antiviral resistance as well as the emergence of other pandemic threat respiratory viruses . Accordingly, respiratory antiviral agents (prophylactics and/or therapeutics) targeting human enzymes which mediate viral infection pathways and are less prone to resistance could serve as a first line of defense and mitigate the spread and/or severity of viral respiratory diseases. |
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