Intermolecular Non-Bonded Interactions from Machine Learning Datasets.

Accurate determination of intermolecular non-covalent-bonded or non-bonded interactions is the key to potentially useful molecular dynamics simulations of polymer systems. However, it is challenging to balance both the accuracy and computational cost in force field modelling. One of the main difficulties is properly representing the calculated energy data as a continuous force function. In this paper, we employ well-developed machine learning techniques to construct a general purpose intermolecular non-bonded interaction force field for organic polymers. The original ab initio dataset SOFG-31 was calculated by us and has been well documented, and here we use it as our training set. The CLIFF kernel type machine learning scheme is used for predicting the interaction energies of heterodimers selected from the SOFG-31 dataset. Our test results show that the overall errors are well below the chemical accuracy of about 1 kcal/mol, thus demonstrating the promising feasibility of machine learning techniques in force field modelling.

Maximal occupation by bases of π-hole bands surrounding linear molecules.

Linear molecules such as CO2 contain a positive π-hole ring that surrounds C on the molecule's equator. Quantum calculations examine the question as to how many bases can simultaneously bind to this ring. Linear molecules examined are TO2 , where T = C, Si, Ge, Sn; bases are NCH and NH3 . CO2 engages in the weakest of the tetrel bonds, and can bind up to three NCH and two NH3 . Unlike σ-hole tetrel bonds, Si forms the strongest tetrel bonds, with interaction energies as high as 43 kcal/mol with NH3 . But like GeO2 , SiO2 can sustain only two bases in its equatorial ring. The π-hole ring of SnO2 can engage in up to four tetrel bonds with either NCH or NH3 , even though these bonds are weaker than those with GeO2 or SiO2 . As all of these complexes cast TO2 in the role of multiple electron acceptor, the resulting negative cooperativity makes each successive bond weaker than its predecessor as bases are added, as well as reducing the magnitude of the central molecule's π-hole.

London Dispersion Favors Sterically Hindered Diarylthiourea Conformers in Solution.

We present an experimental and computational study on the conformers of N,N'-diphenylthiourea substituted with different dispersion energy donor (DED) groups. While the unfolded anti-anti conformer is the most relevant for thiourea catalysis, intramolecular noncovalent interactions counterintuitively favor the folded syn-syn conformer, as evident from a combination of low-temperature nuclear magnetic resonance measurements and computations. In order to quantify the noncovalent interactions, we utilized local energy decomposition analysis and symmetry-adapted perturbation theory at the DLPNO-CCSD(T)/def2-TZVPP and sSAPT0/6-311G(d,p) levels of theory. Additionally, we applied a double-mutant cycle to experimentally study the effects of bulky substituents on the equilibria. We determined London dispersion as the key interaction that shifts the equilibria towards the syn-syn conformers. This preference is likely a factor why such thiourea derivatives can be poor catalysts.

Interaction Energy Analysis of Monovalent Inorganic Anions in Bulk Water Versus Air/Water Interface.

Soft anions exhibit surface activity at the air/water interface that can be probed using surface-sensitive vibrational spectroscopy, but the structural implications of this surface activity remain a matter of debate. Here, we examine the nature of anion-water interactions at the air/water interface using a combination of molecular dynamics simulations and quantum-mechanical energy decomposition analysis based on symmetry-adapted perturbation theory. Results are presented for a set of monovalent anions, including Cl-, Br-, I-, CN-, OCN-, SCN-, NO2-, NO3-, and ClOn- (n=1,2,3,4), several of which are archetypal examples of surface-active species. In all cases, we find that average anion-water interaction energies are systematically larger in bulk water although the difference (with respect to the same quantity computed in the interfacial environment) is well within the magnitude of the instantaneous fluctuations. Specifically for the surface-active species Br-(aq), I-(aq), ClO4-(aq), and SCN-(aq), and also for ClO-(aq), the charge-transfer (CT) energy is found to be larger at the interface than it is in bulk water, by an amount that is greater than the standard deviation of the fluctuations. The Cl-(aq) ion has a slightly larger CT energy at the interface, but NO3-(aq) does not; these two species are borderline cases where consensus is lacking regarding their surface activity. However, CT stabilization amounts to <20% of the total induction energy for each of the ions considered here, and CT-free polarization energies are systematically larger in bulk water in all cases. As such, the role of these effects in the surface activity of soft anions remains unclear. This analysis complements our recent work suggesting that the short-range solvation structure around these ions is scarcely different at the air/water interface from what it is in bulk water. Together, these observations suggest that changes in first-shell hydration structure around soft anions cannot explain observed surface activities.

Interactions of CO2 with cluster models of metal-organic frameworks.

The interactions between carbon dioxide and cluster models of coordinatively unsaturated metal-organic frameworks (MOFs) were studied using a variety of ab initio methods. Three metal species and three organic linkers in four structures were considered in these models as a representation of the tunable nature of MOFs and the potential multireference character of such systems. Common single-reference methods, such as MP2 and CCSD(T), were compared with multireference methods based on complete active space self-consistent field theory, going as far as multireference configuration interaction with single and double excitations (MRCISD). Special consideration is taken to avoid issues of size inconsistency in the CI results, where an alternate reference is used in the interaction energy definition. The benchmark values are used to judge the adequacy of a selection of density functionals for the current systems. Symmetry-adapted perturbation theory (SAPT) decomposition was performed to elucidate the important effects that comprise the binding interactions. The systems proved to have very limited multireference character, and MP2 values were closer to the CCSD(T) benchmark than the more difficult MRCISD results. Though the SAPT total energies prove to be relatively poor approximations to the benchmark interaction energies, they reveal (in most cases) the correct trends with respect to the choice of the metal. The SAPT energy decompositions indicate that the CO2 binding is primarily driven by electrostatics, but induction and dispersion also provide sizable, and quite similar, attractive contributions. Importantly, the small diformate model provides a faithful representation of complexes with large aromatic linkers, both in terms of the total interaction energy and the SAPT decomposition.

Metastable Chiral Azobenzenes Stabilized in a Double Racemate.

The self-assembly of chiral organic chromophores is gaining huge significance due to the abundance of supramolecular chirality found in natural systems. We report an interdigitated molecular assembly involving axially chiral octabrominated perylenediimide (OBPDI) which transfers chiral information to achiral aromatic moieties. The crystalline two-component assemblies of OBPDI and electron-rich aromatic units were facilitated through π-hole⋅⋅⋅π donor-acceptor interactions, and the charge-transfer characteristics in the ground and excited states of the OBPDI cocrystals were established through spectroscopic and theoretical techniques. The OBPDI cocrystals entail a remarkable homochiral segregation of P and M enantiomers of both molecular entities in the same crystal system, leading to twisted double-racemic arrangements. Synergistically engendered cavities with the stored chiral information of the twisted OBPDI stabilize higher-energy P/M enantiomers of trans-azobenzene through non-covalent interactions.

Exploring Nature and Predicting Strength of Hydrogen Bonds: A Correlation Analysis Between Atoms-in-Molecules Descriptors, Binding Energies, and Energy Components of Symmetry-Adapted Perturbation Theory.

This work studies the underlying nature of H-bonds (HBs) of different types and strengths and tries to predict binding energies (BEs) based on the properties derived from wave function analysis. A total of 42 HB complexes constructed from 28 neutral and 14 charged monomers were considered. This set was designed to sample a wide range of HB strengths to obtain a complete view about HBs. BEs were derived with the accurate coupled cluster singles and doubles with perturbative triples correction (CCSD(T))(T) method and the physical components of the BE were investigated by symmetry-adapted perturbation theory (SAPT). Quantum theory of atoms-in-molecules (QTAIM) descriptors and other HB indices were calculated based on high-quality density functional theory wave functions. We propose a new and rigorous classification of H-bonds (HBs) based on the SAPT decomposition. Neutral complexes are either classified as "very weak" HBs with a BE ≥ -2.5 kcal/mol that are mainly dominated by both dispersion and electrostatic interactions or as "weak-to-medium" HBs with a BE varying between -2.5 and -14.0 kcal/mol that are only dominated by electrostatic interactions. On the other hand, charged complexes are divided into "medium" HBs with a BE in the range of -11.0 to -15.0 kcal/mol, which are mainly dominated by electrostatic interactions, or into "strong" HBs whose BE is more negative than -15.0 kcal/mol, which are mainly dominated by electrostatic together with induction interactions. Among various explored correlations between BEs and wave function-based HB descriptors, a fairly satisfactory correlation was found for the electron density at the bond critical point (BCP; ρBCP ) of HBs. The fitted equation for neutral complexes is BE/kcal/mol = - 223.08 × ρBCP /a. u. + 0.7423 with a mean absolute percentage error (MAPE) of 14.7%, while that for charged complexes is BE/kcal/mol = - 332.34 × ρBCP /a. u. - 1.0661 with a MAPE of 10.0%. In practice, these equations may be used for a quick estimation of HB BEs, for example, for intramolecular HBs or large HB networks in biomolecules. © 2019 Wiley Periodicals, Inc.

Trisulfide-Bond Acenes for Organic Batteries.

The molecular design of organic battery electrodes is a big challenge. Here, we synthesize two metal-free organosulfur acenes and shed insight into battery properties using first-principles calculations. A new zone-melting chemical-vapor-transport (ZM-CVT) apparatus was fabricated to provide a simple, solvent-free, and continuous synthetic protocol, and produce single crystals of tetrathiotetracene (TTT) and hexathiapentacene (HTP) at a large scale. Single crystals of HTP showed better Li-ion battery performance and higher cycling stability than those of TTT. A two-step, three-electron lithiation mechanism instead of the commonly depicted two-electron mechanism is proposed for the HTP Li-ion battery. The superior performance of HTP is linked to unique trisulfide bonding scenarios, which are also responsible for the formation of empty channels along the stacking direction. In-depth theoretical analysis suggests that organosulfur acenes are potential prototypes for organic battery materials with tunable properties, and that the tuning of sulfur bonds is critical in designing these new materials.

Intramolecular interactions in sterically crowded hydrocarbon molecules.

A molecular fragmentation method has been used to analyze the intramolecular interactions in the three molecules coupled diamantane, hexaphenylethane, and all-meta-tert-butyl substituted hexaphenylethane. The significance of these systems lies in the fact, that steric crowding effects enable a stabilization of the central carbon bond that possesses an extended length (1.6 to 1.7 Å) beyond conventional carbon-carbon bonds due to the steric repulsion of the attached hydrocarbon groups. The total stability of these molecules therefore depends on a delicate balance between attractive interaction forces on the one hand and on repulsive forces on the other hand. We have quantified the different interaction energy contributions using symmetry-adapted perturbation theory based on a density functional theory description of the monomers. It has been found that the attractive dispersion interactions increase more strongly with the level of crowding in the systems than the counteracting exchange interactions. This shows that steric crowding effects can have a significant impact on the structure and stability of large and branched molecules. © 2017 Wiley Periodicals, Inc.

Energy decomposition analysis of cation-π, metal ion-lone pair, hydrogen bonded, charge-assisted hydrogen bonded, and π-π interactions.

This study probes the nature of noncovalent interactions, such as cation-π, metal ion-lone pair (M-LP), hydrogen bonding (HB), charge-assisted hydrogen bonding (CAHB), and π-π interactions, using energy decomposition schemes-density functional theory (DFT)-symmetry-adapted perturbation theory and reduced variational space. Among cation-π complexes, the polarization and electrostatic components are the major contributors to the interaction energy (IE) for metal ion-π complexes, while for onium ion-π complexes (NH4+, PH4+, OH3+, and SH3+) the dispersion component is prominent. For M-LP complexes, the electrostatic component contributes more to the IE except the dicationic metal ion complexes with H2 S and PH3 where the polarization component dominates. Although electrostatic component dominates for the HB and CAHB complexes, dispersion is predominant in π-π complexes.

Assessment of hydrophobic interactions and their contributions through the analysis of the methane dimer.

Hydrophobic Interactions (HIs) are important in many phenomena of molecular recognition in chemistry and biology. Still, the relevance of HIs is sometimes difficult to evaluate particularly in large systems and intramolecular interactions. We put forward a method to estimate the magnitude and the different contributions of a given HI of the C···C, H-C···H, and H···H type through (i) the analysis of the electron density in the intermolecular region for eleven relative orientations of the methane dimer and (ii) the subsequent decomposition of the corresponding interaction energy in physically significant contributions using Symmetry Adapted Perturbation Theory (SAPT). Strong correlations were found between the topological properties of ρ(r) calculated at intermolecular bond critical points and Eint(SAPT) plus its different contributions with the C···C distance of the considered orientations of (CH4 )2 . These correlations were used to construct Mollier-like diagrams of Eint(SAPT) and its components as a function of the separation between two carbons and the orientation of the groups bonded to these atoms. The ethane dimer and tert-butylcyclohexane are used as representative examples of this new approach. Overall, we anticipate that this new method might prove useful in the study of both intramolecular and intermolecular HIs particularly of those within large systems wherein SAPT or electronic structure calculations are computationally expensive or even prohibitive.

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2 )2 and (PCCP)2.

This work characterizes eight stationary points of the P2 dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second-order Møller-Plesset (MP2) electronic structure method and six different basis sets: aug-cc-pVXZ, aug-cc-pV(X+d)Z, and aug-cc-pCVXZ where X = T, Q. A new L-shaped structure with C2 symmetry is the only minimum for the P2 dimer at the MP2 level of theory with these basis sets. The previously reported parallel-slipped structure with C2 h symmetry and a newly identified cross configuration with D2 symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2-F12 and CCSD(T)-F12 methods and the aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2-F12 significantly overbind the P2 and PCCP dimers relative to the CCSD(T) and CCSD(T)-F12 binding energies by as much as 1.5 kcal mol(-1) for the former and 5.0 kcal mol(-1) for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry-adapted perturbation theory analyses.

Interaction between ions and substituted buckybowls: a comprehensive computational study.

Complexes formed by substituted buckybowls derived from corannulene and sumanene with sodium cation or chloride anion have been computationally studied by using a variety of methods. Best results have been obtained with the SCS-MP2 method extrapolated to basis set limit, which reproduces the highest-level values obtained with the MP2.X method. All bowls form stable complexes with chloride anion, with stabilities ranging from -6 kcal/mol in the methylated corannulene derivative to -45 kcal/mol in the CN-substituted sumanene. The opposite trend is observed in sodium complexes, going from deeply attractive complexes with the methylated derivatives (-36 kcal/mol with sumanene derivative) to slightly repulsive ones in the CN-substituted bowls (2 kcal/mol in the corannulene derivative). Anion complexes are stabilized by large electrostatic interactions combined with smaller though significant dispersion and induction contributions. Conversely, cation complexes are stabilized by large induction contributions capable of holding together the bowl and the cation even in cases where the electrostatic interaction is repulsive. The effect of substitution is mainly reflected on changes in the molecular electrostatic potential of the bowl and, thus, in the electrostatic contribution to the interaction. Therefore, the variations in the stability of the complexes on substitution could be roughly predicted just considering the changes in the electrostatic interaction. However, other contributions also register changes mainly as a consequence of displacements on the position of the ion at the minimum, so the accurate prediction of the stability of this kind of complexes requires going further than the electrostatic approach.

Is electrostatics sufficient to describe hydrogen-bonding interactions?

The stability and geometry of a hydrogen-bonded dimer is traditionally attributed mainly to the central moiety A-H⋅⋅⋅B, and is often discussed only in terms of electrostatic interactions. The influence of substituents and of interactions other than electrostatic ones on the stability and geometry of hydrogen-bonded complexes has seldom been addressed. An analysis of the interaction energy in the water dimer and several alcohol dimers--performed in the present work by using symmetry-adapted perturbation theory--shows that the size and shape of substituents strongly influence the stabilization of hydrogen-bonded complexes. The larger and bulkier the substituents are, the more important the attractive dispersion interaction is, which eventually becomes of the same magnitude as the total stabilization energy. Electrostatics alone are a poor predictor of the hydrogen-bond stability trends in the sequence of dimers investigated, and in fact, dispersion interactions predict these trends better.

A Machine Learning Force Field for Bio-Macromolecular Modeling Based on Quantum Chemistry-Calculated Interaction Energy Datasets.

Accurate energy data from noncovalent interactions are essential for constructing force fields for molecular dynamics simulations of bio-macromolecular systems. There are two important practical issues in the construction of a reliable force field with the hope of balancing the desired chemical accuracy and working efficiency. One is to determine a suitable quantum chemistry level of theory for calculating interaction energies. The other is to use a suitable continuous energy function to model the quantum chemical energy data. For the first issue, we have recently calculated the intermolecular interaction energies using the SAPT0 level of theory, and we have systematically organized these energies into the ab initio SOFG-31 (homodimer) and SOFG-31-heterodimer datasets. In this work, we re-calculate these interaction energies by using the more advanced SAPT2 level of theory with a wider series of basis sets. Our purpose is to determine the SAPT level of theory proper for interaction energies with respect to the CCSD(T)/CBS benchmark chemical accuracy. Next, to utilize these energy datasets, we employ one of the well-developed machine learning techniques, called the CLIFF scheme, to construct a general-purpose force field for biomolecular dynamics simulations. Here we use the SOFG-31 dataset and the SOFG-31-heterodimer dataset as the training and test sets, respectively. Our results demonstrate that using the CLIFF scheme can reproduce a diverse range of dimeric interaction energy patterns with only a small training set. The overall errors for each SAPT energy component, as well as the SAPT total energy, are all well below the desired chemical accuracy of ~1 kcal/mol.

Hole interactions of aerogen oxides with Lewis bases: an insight into σ-hole and lone-pair-hole interactions.

σ-Hole and lone-pair (lp)-hole interactions of aerogen oxides with Lewis bases (LB) were comparatively inspected in terms of quantum mechanics calculations. The ZOn ⋯ LB complexes (where Z = Kr and Xe, n = 1, 2, 3 and 4, and LB = NH3 and NCH) showed favourable negative interaction energies. The complexation features were explained in light of σ-hole and lp-hole interactions within optimum distances lower than the sum of the respective van der Waals radii. The emerging findings outlined that σ-hole interaction energies generally enhanced according to the following order: KrO4 ⋯ < KrO⋯ < KrO3⋯ < KrO2⋯LB and XeO4⋯ < XeO⋯ < XeO2⋯ < XeO3⋯LB complexes with values ranging from -2.23 to -12.84 kcal mol-1. Lp-hole interactions with values up to -5.91 kcal mol-1 were shown. Symmetry-adapted perturbation theory findings revealed the significant contributions of electrostatic forces accounting for 50-65% of the total attractive forces within most of the ZOn⋯LB complexes. The obtained observations would be useful for the understanding of hole interactions, particularly for the aerogen oxides, with application in supramolecular chemistry and crystal engineering.

Physical mechanisms of intermolecular interactions from symmetry-adapted perturbation theory.

Symmetry-adapted perturbation theory (SAPT) is a method for computational studies of noncovalent interactions between molecules. This method will be discussed here from the perspective of establishing the paradigm for understanding mechanisms of intermolecular interactions. SAPT interaction energies are obtained as sums of several contributions. Each contribution possesses a clear physical interpretation as it results from some specific physical process. It also exhibits a specific dependence on the intermolecular separation R. The four major contributions are the electrostatic, induction, dispersion, and exchange energies, each due to a different mechanism, valid at any R. In addition, at large R, SAPT interaction energies are seamlessly connected with the corresponding terms in the asymptotic multipole expansion of interaction energy in inverse powers of R. Since such expansion explicitly depends on monomers' multipole moments and polarizabilities, this connection provides additional insights by rigorously relating interaction energies to monomers' properties.

An account of noncovalent interactions in homoleptic palladium(II) and platinum(II) complexes within the DFT framework: A correlation between geometries, energy components of symmetry-adapted perturbation theory and NCI descriptors.

The present work addresses the underlying nature of weak noncovalent interactions (NCIs) in the self-assembled dimers of two square planar palladium(II) and platinum(II) complexes trans-[Pd(Hida)2] (1) and trans-[Pt(Hida)2] (2) (Hida = monoprotonated iminodiacetate) within the framework of density functional theory (DFT) in gas phase. Initial geometries of the dimers in different spatial orientations were extracted from the X-ray crystal structures, reported earlier, and optimized with three dispersion-corrected functionals that are frequently used to explore NCIs. The BP86-D3, M062X-D3 and ωB97X-D3 functionals have been used to test their performances over the present systems. The SARC-ZORA-TZVP and ZORA-def2-TZVP basis sets were applied for the metals and the remaining elements, respectively. The optimizations resulted in equilibrium geometries where the monomers are self-assembled through NCIs to form dimers in a cyclic fashion. This type of structural pattern is absent in the crystal structures of both 1 and 2. Physical components of interaction energies were investigated by symmetry-adapted perturbation theory (SAPT). The UV-Vis absorption spectra of the dimers are described by time-dependent density functional theory (TD-DFT). Global reactivity parameters for the dimers have been computed within the framework of conceptual density functional theory (CDFT). Detailed investigations on NCIs were performed for all dimer geometries. Simulated IR and 1H NMR spectra, charge transfer, QTAIM, NCI-RGD, IGM, ETS-NOCV and ELF studies confirmed the presence of intermolecular hydrogen bonds (HBs) and weak van der Waals interactions. Energies of the hydrogen bonds and associated orbital interaction energies were computed by QTAIM and ETS-NOCV methods, respectively.

Assessment of SAPT(DFT) with meta-GGA functionals.

This work examines the suitability of meta-GGA functionals for symmetry-adapted perturbation theory (SAPT) calculations. The assessment is based on the term-by-term comparison with the benchmark SAPT variant based on coupled-cluster singles and doubles description of monomers, SAPT(CCSD). Testing systems include molecular complexes ranging from strong to weak and the He dimer. The following nonempirical meta-GGAs are examined: TPSS, revTPSS, MVS, SCAN, and SCAN0 with and without the asymptotic correction (AC) of the exchange-correlation potential. One range-separated meta-GGA functional, LC-PBETPSS, is also included. The AC-corrected pure meta-GGAs (with the exception of MVS) represent a definite progress in SAPT(DFT) compared to pure GGA, such as PBEAC, with their more consistent predictions of energy components. However, none of the meta-GGAs is better than the hybrid GGA approach SAPT(PBE0AC). The SAPT(DFT) electrostatic energy offers the most sensitive probe of the quality of the underlying DFT density. Both SCAN- and TPSS-based electrostatic energies agree with reference to within 5% or better which is an excellent result. We find that SCAN0 can be used in SAPT without the AC correction. The long-range corrected LC-PBETPSS is a reliable performer both for the components and total interaction energies.

Spherical harmonics representation of the potential energy surface for the H2⋯H2 van der Waals complex.

We perform a study of the molecular anisotropy for the H2⋯H2 van der Waals system using a spherical harmonics expansion. We use six leading stable configurations to construct our analytical potential energy surface (PES) from ab initio calculations guided qualitatively by the symmetry-adapted perturbation theory (SAPT) analyses. We extrapolate the energies of the PES performed at the CCSD(T)/aug-cc-pVnZ (n = 2 and 3) levels to the complete basis set (CBS) limit. To best fit the shallow potential energy surface of each leading configuration with the intermolecular distance, it was employed an extended version of the Rydberg potential. To assess the quality of our extrapolated analytical PES, we calculate the second virial coefficients, which are in relatively good agreement with the experimental data. As a result, the spherical harmonics coefficients obtained might be of considerable relevance in spectroscopy and dynamics applications.