Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit?

Nitrosation mechanisms, kinetics, and dynamics of the guanine and 9-methylguanine radical cations by nitric oxide-Radical-radical combination at different electron configurations

As a precursor to various reactive nitrogen species formed in biological systems, nitric oxide (•NO) participates in numerous processes, including enhancing DNA radiosensitivity in ionizing radiation-based radiotherapy. Forming guanine radical cations is another common DNA lesion resulting from ionization and oxidation damage. As such, the interaction of •NO with guanine radical cations (G•+) may contribute to the radiosensitization of •NO. An intriguing aspect of this process is the participation of multiple spin configurations in the reaction, including open-shell singlet 1,OS[G•+(↑)⋯(↓)•NO], closed-shell singlet 1,CS[G(↑↓)⋯NO+], and triplet 3[G•+(↑)⋯(↑)•NO]. In this study, the reactions of •NO with both unsubstituted guanine radical cations (in the 9HG•+ conformation) and 9-methylguanine radical cations (9MG•+, a guanosine-mimicking model compound) were investigated in the absence and presence of monohydration of radical cations. Kinetic-energy dependent reaction product ions and cross sections were measured using an electrospray ionization guided-ion beam tandem mass spectrometer. The reaction mechanisms, kinetics, and dynamics were comprehended by interpreting the reaction potential energy surface using spin-projected density functional theory, coupled cluster theory, and multiconfiguration complete active space second-order perturbation theory, followed by RRKM kinetics modeling. The combined experimental and computational findings revealed closed-shell singlet 1,CS[7-NO-9MG]+ as the major, exothermic product and triplet 3[8-NO-9MG]+ as the minor, endothermic product. Singlet biradical products were not detected due to high reaction endothermicities, activation barriers, and inherent instability.

Kohn-Sham fragment energy decomposition analysis

We introduce the concept of Kohn-Sham fragment localized molecular orbitals (KS-FLMOs), which are Kohn-Sham molecular orbitals (MOs) localized in specific fragments constituting a generic molecular system. In detail, we minimize the local electronic energies of various fragments, while maximizing the repulsion between them, resulting in the effective localization of the MOs. We use the developed KS-FLMOs to propose a novel energy decomposition analysis, which we name Kohn-Sham fragment energy decomposition analysis, which allows for rationalizing the main non-covalent interactions occurring in interacting systems both in vacuo and in solution, providing physical insights into non-covalent interactions. The method is validated against state-of-the-art energy decomposition analysis techniques and with high-level calculations.

Orientational Disorder Drives Site Disorder in Plastic Ammonia Hemihydrate

In the 2-10 GPa pressure range, ammonia hemihydrate H_{2}O:(NH_{3})_{2} (AHH) is a molecular solid in which intermolecular interactions are ruled by distinct types of hydrogen bonds. Upon heating, the low-temperature ordered P2_{1}/c crystal (AHH-II) transits to a bcc phase (AHH-pbcc) where each site is randomly occupied by water or ammonia. In addition to the site disorder, experiments suggest that AHH-pbcc is a plastic solid, but the physical origin and mechanisms at play for the rotational and site disordering remain unknown. Using large-scale (∼10^{5}  atoms) and long-time (>10  ns) simulations, we show that, as temperature rises above the transition line, orientational disorder sets in, breaking the strongest hydrogen bonds that provide the largest contribution to the cohesion of the ordered AHH-II phase and enabling the molecules to migrate from a crystal site to a neighboring one. This generates a plastic molecular alloy with site disorder while the solid state is overall maintained until melting at a higher temperature. The case of high (P,T) plastic ammonia hemihydrate can be extended to other water-ammonia alloys where a similar interplay between distinct hydrogen bonds occurs.

Assessing the domain-based local pair natural orbital (DLPNO) approximation for non-covalent interactions in sizable supramolecular complexes

The titular domain-based local pair natural orbital (DLPNO) approximation is the most widely used method for extending correlated wave function models to large molecular systems, yet its fidelity for intermolecular interaction energies in large supramolecular complexes has not been thoroughly vetted. Non-covalent interactions are sensitive to tails of the electron density and involve nonlocal dispersion that is discarded or approximated if the screening of pair natural orbitals (PNOs) is too aggressive. Meanwhile, the accuracy of the DLPNO approximation is known to deteriorate as molecular size increases. Here, we test the DLPNO approximation at the level of second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)] for a variety of large supramolecular complexes. DLPNO-MP2 interaction energies are within 3% of canonical values for small dimers with ≲10 heavy atoms, but for larger systems, the DLPNO approximation is often quite poor unless the results are extrapolated to the canonical limit where the threshold for discarding PNOs is taken to zero. Counterpoise correction proves to be essential in reducing errors with respect to canonical results. For a sequence of nanoscale graphene dimers up to (C96H24)2, extrapolated DLPNO-MP2 interaction energies agree with canonical values to within 1%, independent of system size, provided that the basis set does not contain diffuse functions; these cause the DLPNO approximation to behave erratically, such that results cannot be extrapolated in a meaningful way. DLPNO-CCSD(T) calculations are typically performed using looser PNO thresholds as compared to DLPNO-MP2, but this significantly impacts accuracy for large supramolecular complexes. Standard DLPNO-CCSD(T) settings afford errors of 2-6 kcal/mol for dimers involving coronene (C24H12) and circumcoronene (C54H18), even at the DLPNO-CCSD(T1) level.

The interplay of covalency, cooperativity, and coupling strength in governing C-H bond activation in Ni2E2 (E = O, S, Se, Te) complexes

Dinickel dichalcogenide complexes hold vital multifaceted significance across catalysis, electron transfer, magnetism, materials science, and energy conversion. Understanding their structure, bonding, and reactivity is crucial for all aforementioned applications. These complexes are classified as dichalcogenide, subchalcogenide, or chalcogenide based on metal oxidation and coordinated chalcogen, and due to the associated complex electronic structure, ambiguity often lingers about their classification. In this work, using DFT, CASSCF/NEVPT2, and DLPNO-CCSD(T) methods, we have studied in detail [(NiL)2(E2)] (L = 1,4,7,10-tetramethyl-1,4,7,10-tetraazacyclododecane; E = O, S, Se and Te) complexes and explored their reactivity towards C-H bond activation for the first time. Through a comprehensive analysis of the structure, bonding, and reactivity of a series of [(NiL)2(E2)] complexes with E = O, S, Se, and Te, our computational findings suggest that {Ni2O2} and {Ni2S2} are best categorised as dichalcogenide-type complexes. In contrast, {Ni2Se2} and {Ni2Te2} display tendencies consistent with the subchalcogenide classification, and this aligns with the earlier structural correlation proposed (Berry and co-workers, J. Am. Chem. Soc. 2015, 137, 4993) reports on the importance of the E-E bond strength. Our study suggests the reactivity order of {Ni2O2} > {Ni2S2} > {Ni2Se2} > {Ni2Te2} for C-H bond activation, and the origin of the difference in reactivity was attributed to the difference in the Ni-E bond covalency, and electronic cooperativity between two Ni centres that switch among the classification during the reaction. Further non-adiabatic analysis at the C-H bond activation step demonstrates a decrease in coupling strength as we progress down the group, indicating a correlation with metal-ligand covalency. Notably, the reactivity trend is found to be correlated to the strength of the antiferromagnetic exchange coupling constant J via developing a magneto-structural-barrier map - offering a hitherto unknown route to fine-tune the reactivity of this important class of compound.

Self-Association and Microhydration of Phenol: Identification of Large-Amplitude Hydrogen Bond Librational Modes

The self-association mechanisms of phenol have represented long-standing challenges to quantum chemical methodologies owing to the competition between strongly directional intermolecular hydrogen bonding, weaker non-directional London dispersion forces and C-H⋯π interactions between the aromatic rings. The present work explores these subtle self-association mechanisms of relevance for biological molecular recognition processes via spectroscopic observations of large-amplitude hydrogen bond librational modes of phenol cluster molecules embedded in inert neon "quantum" matrices complemented by domain-based local pair natural orbital-coupled cluster DLPNO-CCSD(T) theory. The spectral signatures confirm a primarily intermolecular O-H⋯H hydrogen-bonded structure of the phenol dimer strengthened further by cooperative contributions from inter-ring London dispersion forces as supported by DLPNO-based local energy decomposition (LED) predictions. In the same way, the hydrogen bond librational bands observed for the trimeric cluster molecule confirm a pseudo-C3 symmetric cyclic cooperative hydrogen-bonded barrel-like potential energy minimum structure. This structure is vastly different from the sterically favored "chair" conformations observed for aliphatic alcohol cluster molecules of the same size owing to the additional stabilizing London dispersion forces and C-H⋯π interactions between the aromatic rings. The hydrogen bond librational transition observed for the phenol monohydrate finally confirms that phenol acts as a hydrogen bond donor to water in contrast to the hydrogen bond acceptor role observed for aliphatic alcohols.

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

Impact of Combination Rules, Level of Theory, and Potential Function on the Modeling of Gas- and Condensed-Phase Properties of Noble Gases

The systems of noble gases are particularly instructive for molecular modeling due to the elemental nature of their interactions. They do not normally form bonds nor possess a (permanent) dipole moment, and the only forces determining their bonding/clustering stems from van der Waals forces─dispersion and Pauli repulsion, which can be modeled by empirical potential functions. Combination rules, that is, formulas to derive parameters for pair potentials of heterodimers from parameters of corresponding homodimers, have been studied at length for the Lennard-Jones 12-6 potentials but not in great detail for other, more accurate, potentials. In this work, we examine the usefulness of nine empirical potentials in their ability to reproduce quantum mechanical (QM) benchmark dissociation curves of noble gas dimers (He, Ne, Ar, Kr, and Xe homo- and heterodimers), and we systematically study the efficacy of different permutations of combination relations for each parameter of the potentials. Our QM benchmark comprises dissociation curves computed by several different coupled cluster implementations as well as symmetry-adapted perturbation theory. The two-parameter Lennard-Jones potentials were decisively outperformed by more elaborate potentials that sport a 25-30 times lower root-mean-square error (RMSE) when fitted to QM dissociation curves. Very good fits to the QM dissociation curves can be achieved with relatively inexpensive four- or even three-parameter potentials, for instance, the damped 14-7 potential (Halgren, J. Am. Chem. Soc. 1992, 114, 7827-7843), a four-parameter Buckingham potential (Werhahn et al., Chem. Phys. Lett. 2015, 619, 133-138), or the three-parameter Morse potential (Morse, Phys. Rev. 1929, 34, 57-64). Potentials for heterodimers that are generated from combination rules have an RMSE that is up to 20 times higher than potentials that are directly fitted to the QM dissociation curves. This means that the RMSE, in particular, for light atoms, is comparable in magnitude to the well-depth of the potential. Based on a systematic permutation of combination rules, we present one or more combination rules for each potential tested that yield a relatively low RMSE. Two new combination rules are introduced that perform well, one for the van der Waals radius σij as ( 1 2 ( σ i 3 + σ j 3 ) ) 1 / 3 and one for the well-depth ϵij as ( 1 2 ( ϵ i - 2 + ϵ j - 2 ) ) - 1 / 2 . The QM data and the fitted potentials were evaluated in the gas phase against experimental second virial coefficients for homo- and heterodimers, the latter of which allowed evaluation of the combination rules. The fitted models were used to perform condensed phase molecular dynamics simulations to verify the melting points, liquid densities at the melting point, and the enthalpies of vaporization produced by the models for pure substances. Subtle differences in the benchmark potentials, in particular, the well-depth, due to the level of theory used were found here to have a profound effect on the macroscopic properties of noble gases: second virial coefficients or the bulk properties in simulations. By explicitly including three-body dispersion in molecular simulations employing the best pair potential, we were able to obtain accurate melting points as well as satisfactory densities and enthalpies of vaporization.

Axial-equatorial equilibrium in substituted cyclohexanes: a DFT perspective on a small but complex problem

In Chemistry, complexity is not necessarily associated to large systems, as illustrated by the textbook example of axial-equatorial equilibrium in mono-substituted cyclohexanes. The difficulty in modelling such a simple isomerization is related to the need for reproducing the delicate balance between two forces, with opposite effects, namely the attractive London dispersion and the repulsive steric interactions. Such balance is a stimulating challenge for density-functional approximations and it is systematically explored here by considering 20 mono-substituted cyclohexanes. In comparison to highly accurate CCSD(T) reference calculations, their axial-equatorial equilibrium is studied with a large set of 48 exchange-correlation approximations, spanning from semilocal to hybrid to more recent double hybrid functionals. This dataset, called SAV20 (as Steric A-values for 20 molecules), allows to highlight the difficulties encountered by common and more original DFT approaches, including those corrected for dispersion with empirical potentials, the 6-31G*-ACP model, and our cost-effective PBE-QIDH/DH-SVPD protocol, in modeling these challenging interactions. Interestingly, the performance of the approaches considered in this contribution on the SAV20 dataset does not correlate with that obtained with other more standard datasets, such as S66, IDISP or NC15, thus indicating that SAV20 covers physicochemical features not already considered in previous noncovalent interaction benchmarks.

Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry

The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.

The Role of Bond Functions in Describing Intermolecular Electron Correlation for Van der Waals Dimers: A Study of (CH4)2 and Ne2

We present a study of the intermolecular interactions in van der Waals complexes of methane and neon dimers within the framework of the CCSD method. This approach was implemented and applied to calculate and examine the behavior of the contracted two-particle reduced density matrix (2-RDM). It was demonstrated that the region near the minimum of the two-particle density matrix correlation part, corresponding to the primary bulk of the Coulomb hole contribution, exerts a significant influence on the dispersion interaction energetics of the studied systems. As a result, the bond functions approach was applied to improve the convergence performance for the intermolecular correlation energy results with respect to the size of the atomic basis. For this, substantial acceleration was achieved by introducing an auxiliary basis of bond functions centered on the minima of the 2-RDM. For both methane and neon dimers, this general conclusion was confirmed with a series of CCSD calculations for the 2-RDM and the correlation energies.

Combined FTIR/Raman spectroscopic studies and ab initio electronic structure calculations of Dithiothreitol

A total of seven minimum energy geometries were obtained on exploring the conformational landscape of dithiothreitol (DTT) by varying the prominent dihedral angles in the molecule through a relaxed scan with a step size of 5° at B3LYP/cc-pVTZ with further geometry optimization at CCSD/cc-pVDZ level of theory. Single point energies were calculated for all the conformers at CCSD(T)/CBS limit with cc-pVNZ (N = T, Q) level of theory and revealed the similar energy pattern. The two conformers, namely G'TG'1 and G'TT, were found iso-energic even though they differed in their structure significantly and were of the lowest energy compared to others. Energies corresponding to the cyclic as well as other configurational counterpart of the global minimum were found much higher in energy compared to the global minimum structure. Intramolecular sulfur centered hydrogen bond was seen to stabilize the global minimum structure of DTT as revealed by AIM, NBO, FMO and ESP charge analysis. Computed NMR of DTT matched well with the experimental data gleaned from the literature. Vibrational spectra (Raman and IR) were measured and compared with computed normal modes of DTT, which were found in good agreement.

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.

Noncovalently bound excited-state dimers: a perspective on current time-dependent density functional theory approaches applied to aromatic excimer models

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for time-dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

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.

Basis Set Limit of CCSD(T) Energies: Explicit Correlation Versus Density-Based Basis-Set Correction

A thorough comparison is carried out for explicitly correlated and density-based basis-set correction approaches, which were primarily developed to mitigate the basis-set incompleteness error of wave function methods. An efficient implementation of the density-based scheme is also presented, utilizing the density-fitting approximation. The performance of these approaches is comprehensively tested for the second-order Møller-Plesset (MP2), coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] methods with respect to the corresponding complete basis set references. It is demonstrated that the density-based correction together with complementary auxiliary basis set (CABS)-corrected Hartree-Fock energies is highly robust and effectively reduces the error of the standard approaches; however, it does not outperform the corresponding explicitly correlated methods. Nevertheless, what still makes the density-corrected CCSD and CCSD(T) methods competitive is that their computational costs are roughly half of those of the corresponding explicitly correlated variants. Additionally, an incremental approach for standard CCSD and CCSD(T) is introduced. In this simple scheme, the total energies are corrected with the CABS correction and explicitly correlated MP2 contributions. As demonstrated, the resulting methods yield surprisingly good results, below 1 kcal/mol for thermochemical properties even with a double-ζ basis, while their computational expenses are practically identical to those of the density-based basis-set correction approaches.

Assessing Implicit and Explicit Polarizable Solvation Models for Nuclear-Electronic Orbital Systems: Quantum Proton Polarization and Solvation Energetics

Accurate simulations of many chemical processes require the inclusion of both nuclear quantum effects and a solvent environment. The nuclear-electronic orbital (NEO) approach, which treats electrons and select nuclei quantum mechanically on the same level, combined with a polarizable continuum model (PCM) for the solvent environment, addresses this challenge in a computationally practical manner. In this work, the NEO-PCM approach is extended beyond the IEF-PCM (integral equation formalism PCM) and C-PCM (conductor PCM) approaches to the SS(V)PE (surface and simulation of volume polarization for electrostatics) and ddCOSMO (domain decomposed conductor-like screening model) approaches. IEF-PCM, SS(V)PE, C-PCM, and ddCOSMO all exhibit similar solvation energies as well as comparable nuclear polarization within the NEO framework. The calculations show that the nuclear density does not leak out of the molecular cavity because it is much more localized than the electronic density. Finally, the polarization of quantized protons is analyzed in both continuum solvent and explicit solvent environments described by the polarizable MB-pol model, illustrating the impact of specific hydrogen-bonding interactions captured only by explicit solvation. These calculations highlight the relationship among solvation formalism, nuclear polarization, and energetics.

Optimizing the regularization in size-consistent second-order Brillouin-Wigner perturbation theory

Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter (α) was set to recover the exact dissociation limit of H2 in a minimal basis set. Alternatively α can be viewed as a regularization parameter, where each value of α represents a valid variant of BW-s2, which we denote as BW-s2(α). In this work, we semi-empirically optimize α for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal α parameter (α = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2(α) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2(α) is iterative O(N5), this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.

Accurate Thermochemical and Kinetic Parameters at Affordable Cost by Means of the Pisa Composite Scheme (PCS)

A new strategy for the computation at an affordable cost of geometrical structures, thermochemical parameters, and rate constants for medium-sized molecules in the gas phase is proposed. The most distinctive features of the new model are the systematic use of cc-pVnZ-F12 basis sets, the addition of MP2 core-valence correlation in geometry optimizations by a double-hybrid functional, the separate extrapolation of MP2 and post-MP2 contributions, and the inclusion of anharmonic contributions in zero-point energies and thermodynamic functions. A thorough benchmark based on a wide range of prototypical systems shows that the new scheme outperforms the most well-known model chemistries without the need for any empirical parameter. Additional tests show that the computed zero-point energies and thermal contributions can be confidently used for obtaining accurate thermochemical and kinetic parameters. Since the whole computational workflow is translated in a black-box procedure, which can be followed with standard electronic structure codes, the way is paved for the accurate yet not prohibitively expensive study of medium- to large-sized molecules also by nonspecialists.

Comparison of Density-Functional Theory Dispersion Corrections for the DES15K Database

While density-functional theory (DFT) remains one of the most widely used tools in computational chemistry, most functionals fail to properly account for the effects of London dispersion. Hence, there are many popular post-self-consistent methods to add a dispersion correction to the DFT energy. Until now, the most popular methods have never been compared on equal footing due to not being implemented in the same electronic structure packages. In this work, we performed a large-scale benchmarking study, directly comparing the accuracy of the exchange-hole dipole moment (XDM), D3BJ, D4, TS, MBD, and MBD-NL dispersion models when applied to the recent DES15K database of nearly 15,000 molecular complexes at both expanded and compressed geometries. Our study showed similarly good performance for all dispersion methods (except TS) when applied to neutral complexes. However, they all performed worse for ionic complexes, particularly those involving dications of alkaline earth metals, due to systematic overbinding by the base PBE0 density functional. Investigation of the largest outliers also revealed that only the MBD and MBD-NL methods demonstrate surprising errors for complexes involving alkali metal cations at compressed geometries where they tended to significantly overbind. As we would expect minimal dispersion binding for such complexes, we further investigated the origins of these errors for the potential energy curve of a model cation-π complex. Overall, there is little choice between the XDM, D3BJ, D4, MBD, and MBD-NL dispersion methods for most systems. However, the MBD-based methods are not recommended for complexes involving organic species and alkali or alkaline earth metal cations, for example when modeling Li+ intercalation into graphite.

Accurate thermochemistry at affordable cost by means of an improved version of the JunChS-F12 model chemistry

The junChS-F12 composite method has been improved by means of the latest implementation of the CCSD(F12*)(T+) ansatz and validated for the thermochemistry of molecules containing atoms of the first three rows of the periodic table. A thorough benchmark showed that this model, in conjunction with cost-effective revDSD-PBEP86-D3(BJ) reference geometries, offers an optimal compromise between accuracy and computational cost. If improved geometries are sought, the most effective option is to add MP2-F12 core-valence correlation corrections to CCSD(T)-F12b/jun-cc-pVTZ geometries without the need of performing any extrapolation to the complete basis set limit. In the same vein, CCSD(T)-F12b/jun-cc-pVTZ harmonic frequencies are remarkably accurate without any additional contribution. Pilot applications to noncovalent intermolecular interactions, conformational landscapes, and tautomeric equilibria confirm the effectiveness and reliability of the model.

Sulfur Centered Hydrogen Bonding in Thioglycolic Acid and Its Clusters: A Computational Exploration

The conformational landscape of thioglycolic acid (TGA) was investigated by using the CCSD/cc-pVTZ level of theory. The GGC conformer was identified as the global minimum, followed by the GAC conformer. The calculated rotational constant for the GGC conformer exhibited good agreement with the previously reported experimental results. Subsequently, the study delved into the exploration of sulfur-centered hydrogen bonding in TGA's dimer and trimer clusters, employing the CCSD/cc-pVDZ level of theory. These clusters revealed the participation of both oxygen and sulfur atoms in noncovalent H-bonding, contributing to their stability. The presence of these noncovalent interactions in TGA clusters was elucidated through Atoms in Molecule (AIM), reduced density gradient (RDG), and natural bond order (NBO) analysis, while electrostatic potential (ESP) charge and vibrational mode analysis further supported these findings.

Probing pH-Dependent Dehydration Dynamics of Mg and Ca Cations in Aqueous Solutions with Multi-Level Quantum Mechanics/Molecular Dynamics Simulations

The dehydration of aqueous calcium and magnesium cations is the most fundamental process controlling their reactivity in chemical and biological phenomena, such as the formation of ionic solids or passing through ion channels. It holds particular relevance in light of recent advancements in the development of carbon capture techniques that rely on mineralization for long-term carbon storage. Specifically, dehydration of Ca2+ and Mg2+ is a key step in proposed carbon capture processes aiming to exploit the relatively high concentration of dissolved carbon dioxide in seawater via the formation of carbonate minerals from solvated Ca2+ and Mg2+ cations for sequestration and storage. Nevertheless, atomic-scale understanding of the dehydration of aqueous Ca2+ and Mg2+ cations remains limited. Here, we utilize rare event sampling via density functional theory molecular dynamics and embedded wavefunction theory calculations to elucidate the dehydration dynamics of aqueous Ca2+ and Mg2+. Emphasis is placed on the investigation of the effect pH has on the stability of the different coordination environments. Our results reveal significant differences in the dehydration dynamics of the two cations and provide insight into how they may be modulated by pH changes.

Efficient Calculation of the Dispersion Energy for Multireference Systems with Cholesky Decomposition: Application to Excited-State Interactions

Accurate and efficient prediction of dispersion interactions in excited-state complexes poses a challenge due to the complex nature of electron correlation effects that need to be simultaneously considered. We propose an algorithm for computing the dispersion energy in nondegenerate ground- or excited-state complexes with arbitrary spin. The algorithm scales with the fifth power of the system size due to employing Cholesky decomposition of Coulomb integrals and a recently developed recursive formula for density response functions of the monomers. As a numerical illustration, we apply the new algorithm in the framework of multiconfigurational symmetry adapted perturbation theory, SAPT(MC), to study interactions in dimers with localized excitons. The SAPT(MC) analysis reveals that the dispersion energy may be the main force stabilizing excited-state dimers.

Repartitioned Brillouin-Wigner perturbation theory with a size-consistent second-order correlation energy

Second-order Møller-Plesset perturbation theory (MP2) often breaks down catastrophically in small-gap systems, leaving much to be desired in its performance for myriad chemical applications such as noncovalent interactions, thermochemistry, and dative bonding in transition metal complexes. This divergence problem has reignited interest in Brillouin-Wigner perturbation theory (BWPT), which is regular at all orders but lacks size consistency and extensivity, severely limiting its application to chemistry. In this work, we propose an alternative partitioning of the Hamiltonian that leads to a regular BWPT perturbation series that, through the second order, is size-extensive, size-consistent (provided its Hartree-Fock reference is also), and orbital invariant. Our second-order size-consistent Brillouin-Wigner (BW-s2) approach can describe the exact dissociation limit of H2 in a minimal basis set, regardless of the spin polarization of the reference orbitals. More broadly, we find that BW-s2 offers improvements relative to MP2 for covalent bond breaking, noncovalent interaction energies, and metal/organic reaction energies, although rivaling coupled-cluster with single and double substitutions for thermochemical properties.

Realistic phase diagram of water from "first principles" data-driven quantum simulations

Since the experimental characterization of the low-pressure region of water's phase diagram in the early 1900s, scientists have been on a quest to understand the thermodynamic stability of ice polymorphs on the molecular level. In this study, we demonstrate that combining the MB-pol data-driven many-body potential for water, which was rigorously derived from "first principles" and exhibits chemical accuracy, with advanced enhanced-sampling algorithms, which correctly describe the quantum nature of molecular motion and thermodynamic equilibria, enables computer simulations of water's phase diagram with an unprecedented level of realism. Besides providing fundamental insights into how enthalpic, entropic, and nuclear quantum effects shape the free-energy landscape of water, we demonstrate that recent progress in "first principles" data-driven simulations, which rigorously encode many-body molecular interactions, has opened the door to realistic computational studies of complex molecular systems, bridging the gap between experiments and simulations.

Modeling coarse-grained van der Waals interactions using dipole-coupled anisotropic quantum Drude oscillators

The Quantum Drude Oscillator (QDO) model is a promising candidate for accurately calculating the van der Waals (vdW) interaction. Anisotropic QDO models have recently been used to represent quantum fluctuations of molecular fragments rather than that of single atoms. While this model promises accurate calculation of vdW energy, there is significant room for improvements, such as incorporating a proper fragmentation method, higher-order dispersion corrections, and so forth. The present work attempts to gauge dipole-dipole interactions' ability without fragmentation. A suitable anisotropic damping function is also introduced to work with anisotropic QDO. This revised model accurately predicts the binding energies of vdW complexes for most of the systems considered. This work indicates the limit of dipole approximation for an anisotropic QDO-based model.

Solvent Induced Proton Polarization within the Nuclear-Electronic Orbital Framework

To explicitly account for nuclear quantum effects and solvent environments in simulations of chemical processes, the nuclear-electronic orbital approach is coupled with a polarizable continuum model (PCM). This NEO-PCM approach is used to explore the influence of solvation on nuclear polarization through applications to a water dimer and a set of protonated water tetramers. Nuclear polarization in these species is analyzed in terms of changes in proton density and oxygen-hydrogen bond length. Solvation is shown to enhance nuclear polarization with increasing dielectric constant. For the water dimer, the internal, hydrogen-bonded proton is shown to polarize more than the external, free proton. Moreover, proton quantization leads to greater solvent polarization through their mutual polarization. These calculations highlight the complex interplay among electronic, nuclear, and solvent polarization in chemical systems.

Accurate Prediction of Three-Body Intermolecular Interactions via Electron Deformation Density-Based Machine Learning

This work extends the electron deformation density-based descriptor, originally developed in the electron deformation density-based interaction energy machine learning (EDDIE-ML) algorithm to predict dimer interaction energies, to the prediction of three-body interactions in trimers. Using a sequential learning process to select the training data, the resulting Gaussian process regression (GPR) model predicts the three-body interaction energy within 0.2 kcal mol^-1 of the SRS-MP2/cc-pVTZ reference values for the 3B69 and S22-3 trimer data sets. A hybrid kernel function is introduced, which combines contributions from the average and individual atomic environments, allowing the total trimer interaction energy to be predicted in addition to the three-body contribution using the same descriptor. To extend the range and diversity of trimer interaction energies available in the literature, a new data set based on a protein-ligand crystal structure is introduced, consisting of 509 structures of a central ligand with two protein fragments. Benchmark calculations are provided for the new data set, which contains significantly larger molecular interactions than current databases in the literature in addition to charged fragments. Compared to density funtional theory (DFT)- and wavefunction-based methods for calculating the three-body interaction energy, our model makes predictions in a significantly shorter time frame by reducing the number of required SCF calculations from 7 to 4 performed at the PBE0 level of theory, showcasing the utility and efficiency of our Δ-ML method particularly when applied to larger systems.

Counterintuitive Oxidation of Alcohols at Air-Water Interfaces

This study shows that the oxidation of alcohols can rapidly occur at air-water interfaces. It was found that methanediols (HOCH₂OH) orient at air-water interfaces with a H atom of the -CH₂- group pointing toward the gaseous phase. Counterintuitively, gaseous hydroxyl radicals do not prefer to attack the exposed -CH₂- group but the -OH group that forms hydrogen bonds with water molecules at the surface via a water-promoted mechanism, leading to the formation of formic acids. Compared with gaseous oxidation, the water-promoted mechanism at the air-water interface significantly lowers free-energy barriers from ∼10.7 to ∼4.3 kcal·mol^-1 and therefore accelerates the formation of formic acids. The study unveils a previously overlooked source of environmental organic acids that are bound up with aerosol formation and water acidity.

A "gold standard" computational proof for the existence of gold(III) aurophilicity

The existence of aurophilic gold(III)⋯gold(III) interactions has for a long time been neglected due to structural arguments and comparison with the aurophilicity of gold(I) compounds. We show with calculations at the CCSD(T) level of theory that the [Au^III(CH₃)₃(NH₃)]₂ dimer has a metallophilic dispersion interaction between the gold(III) atoms of 10.5 kJ mol^-1. The aurophilic interaction is illustrated by topological QTAIM calculations and IRI analysis.

Exploring alkali metal cation⋯hydrogen interaction in the formation half sandwich complexes with cycloalkanes: a DFT approach

Gas and solvent phase stability of half sandwich complexes between cycloalkanes viz. cyclopropane, cyclobutane, cyclopentane, cyclohexane, bicyclo[2.2.2]octane and adamantane with alkali metal cations (Li+, Na+ and K+) are analysed using density functional theory (DFT). M06-2X/6-31++G(d,p) level is primarily used for the study. The studied half sandwich complexes are stable in gas phase (stabilization energy upto 26.55 kcal mol−1). Presence of solvent phase irrespective of its dielectric, imparts negative impact on the stability of the chosen complexes. The formation of the complexes is exothermic in nature. The process of complexation is both enthalpy (ΔH) and free energy (ΔG) driven. Variation in HOMO (highest occupied molecular orbital) energy also indicates towards the chemical stability of complexes. The interaction is non-covalent with primary contribution from induction component. NBO analysis indicates that C–H bond is the donor and antibonding metal orbital is the acceptor site in the process of complexation. Stability of the complexes depends on the size of the interacting monomers.

TFRegNCI: Interpretable Noncovalent Interaction Correction Multimodal Based on Transformer Encoder Fusion

The interpretability is an important issue for end-to-end learning models. Motivated by computer vision algorithms, an interpretable noncovalent interaction (NCI) correction multimodal (TFRegNCI) is proposed for NCI prediction. TFRegNCI is based on RegNet feature extraction and a transformer encoder fusion strategy. RegNet is a network design paradigm that mainly focuses on local features. Meanwhile, the Vision Transformer is also leveraged for feature extraction, because it can capture global features better than RegNet while lowering the computational cost. Using a transformer encoder as the fusion strategy rather than multilayer perceptron can enhance model performance, due to its emphasis on important features with less parameters. Therefore, the proposed TFRegNCI achieved high accurate prediction (mean absolute error of ∼0.1 kcal/mol) comparing with the coupled cluster single double (triple) (CCSD(T)) benchmark. To further improve the model efficiency, TFRegNCI applies two-dimensional (2D) inputs transformed from three-dimensional (3D) electron density cubes, which saves time (30%), while the model accuracy remains. To improve model interpretability, a visualization module, Gradient-weighted Regression Activation Mapping (Grad-RAM) has been embedded. Grad-RAM is promoted from the classification algorithm, Gradient-weighted Class Activation Mapping, to perform feature visualization for the regression task. With Grad-RAM, the visual location map for features in deep learning models can be displayed. The feature map visualizations suggest that the 2D model has the similar performance as the 3D model, because of equally effective feature extractions from electron density. Moreover, the valid feature region on the location map by the 3D model is consistent with the NCIPLOT NCI isosurface. It is confirmed that the model does extract significant features related to the NCI interaction. The interpretable analyses are carried out through molecular orbital contribution on effective features. Thereby, the proposed model is likely to be a promising tool to reveal some essential information on NCIs, with regard to the level of electronic theory.

An explicitly correlated six-dimensional potential energy surface for the SiCSi + H2 complex

The first six-dimensional potential energy surface (PES) for the SiCSi + H₂ complex is presented in this work. This surface is developed from a large number of ab initio energies computed at the explicitly correlated coupled-cluster level of theory together with the augmented correlation-consistent polarized valence triple zeta basis set (CCSD(T)-F12/aug-cc-pVTZ). These energies are fitted to an analytical function through a procedure that combines spline, least-squares, and kernel-based methods. Two minimums of similar depths were found at the equilibrium geometry of the SiCSi molecule. The dependence of the PES on the bending angle is analyzed. Furthermore, a reduced four-dimensional PES averaged over the H₂ orientation is presented. Finally, the six-dimensional PES is used for computing the second virial coefficient of the SiCSi + H₂ pair using classical and semi-classical methods.

Geometries and vibrational frequencies with Kohn-Sham methods using σ-functionals for the correlation energy

Recently, Kohn-Sham (KS) methods with new correlation functionals, called σ-functionals, have been introduced. Technically, σ-functionals are closely related to the well-known random phase approximation (RPA); formally, σ-functionals are rooted in perturbation theory along the adiabatic connection. If employed in a post-self-consistent field manner in a Gaussian basis set framework, then, σ-functional methods are computationally very efficient. Moreover, for main group chemistry, σ-functionals are highly accurate and can compete with high-level wave-function methods. For reaction and transition state energies, e.g., chemical accuracy of 1 kcal/mol is reached. Here, we show how to calculate first derivatives of the total energy with respect to nuclear coordinates for methods using σ-functionals and then carry out geometry optimizations for test sets of main group molecules, transition metal compounds, and non-covalently bonded systems. For main group molecules, we additionally calculate vibrational frequencies. σ-Functional methods are found to yield very accurate geometries and vibrational frequencies for main group molecules superior not only to those from conventional KS methods but also to those from RPA methods. For geometries of transition metal compounds, not surprisingly, best geometries are found for RPA methods, while σ-functional methods yield somewhat less good results. This is attributed to the fact that in the optimization of σ-functionals, transition metal compounds could not be represented well due to the lack of reliable reference data. For non-covalently bonded systems, σ-functionals yield geometries of the same quality as the RPA or as conventional KS schemes combined with dispersion corrections.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Toward Accurate yet Effective Computations of Rotational Spectroscopy Parameters for Biomolecule Building Blocks

The interplay of high-resolution rotational spectroscopy and quantum-chemical computations plays an invaluable role in the investigation of biomolecule building blocks in the gas phase. However, quantum-chemical methods suffer from unfavorable scaling with the dimension of the system under consideration. While a complete characterization of flexible systems requires an elaborate multi-step strategy, in this work, we demonstrate that the accuracy obtained by quantum-chemical composite approaches in the prediction of rotational spectroscopy parameters can be approached by a model based on density functional theory. Glycine and serine are employed to demonstrate that, despite its limited cost, such a model is able to predict rotational constants with an accuracy of 0.3% or better, thus paving the way toward the accurate characterization of larger flexible building blocks of biomolecules.

A Tug of War between the Self- and Cross-associating Hydrogen Bonds in Neutral Ammonia-Water Clusters: Energetic Insights by Molecular Tailoring Approach

In the present work, the energies of various types of individual HBs observed in neutral (NH₃ )_m (H₂ O)_n , (m+n=2 to 7) clusters were estimated using the molecular tailoring approach (MTA)-based method. The calculated individual HB energies suggest that the O-H…N HBs are the strongest (1.21 to 12.49 kcal mol^-1 ). The next ones are the O-H…O (3.97 to 9.30 kcal mol^-1 ) HBs. The strengths of N-H…N (1.09 to 5.29 kcal mol^-1 ) and N-H…O (2.85 to 5.56 kcal mol^-1 ) HBs are the weakest. The HB energies in dimers also follow this rank ordering. However, the HB energies in dimers are much smaller than those obtained by the MTA-based method due to the loss in cooperativity contribution in the dimers. Thus, the calculated cooperativity contributions, for different types of HBs, fall in the range 0.64 to 5.73 kcal mol^-1 . We wish to emphasize based on the energetic rank ordering obtained by the MTA-based method that the O-H of water is a better HB donor than the N-H of ammonia. The reasons for the observed energetic rank ordering are two folds: (i) intrinsically stronger O-H…N HBs than the O-H…O ones as revealed by dimer energies and (ii) the higher cooperativity contribution in the former than the later ones. Indeed, the MTA-based method is useful in providing the missing energetic rank ordering of various type of HBs in neutral (NH₃ )_m (H₂ O)_n clusters, in the literature.

Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking

In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) approach from a computational quantum chemistry perspective and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single-determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multireference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.

Anisotropy, segmental dynamics and polymorphism of crystalline biogenic carboxylic acids

Carboxylic acids of the Krebs cycle possess invaluable biochemical significance. Still, there are severe gaps in the availability of thermodynamic and crystallographic data, as well as ambiguities prevailing in the literature on the thermodynamic characterization and polymorph ranking. Providing an unambiguous description of the structure, thermodynamics and polymorphism of their neat crystalline phases requires a complex multidisciplinary approach. This work presents results of an extensive investigation of the structural anisotropy of the thermal expansion and local dynamics within these crystals, obtained from a beneficial cooperation of NMR crystallography and ab initio calculations of non-covalent interactions. The observed structural anisotropy and spin-lattice relaxation times are traced to large spatial variations in the strength of molecular interactions in the crystal lattice, especially in the orientation of the hydrogen bonds. A completely resolved crystal structure for oxaloacetic acid is reported for the first time. Thanks to multi-instrumental calorimetric effort, this work clarifies phase behavior, determines third-law entropies of the crystals, and states definitive polymorph ranking for succinic and fumaric acids. These thermodynamic observations are then interpreted in terms of first-principles quasi-harmonic calculations of cohesive properties. A sophisticated model capturing electronic, thermal, and configurational-entropic effects on the crystal structure approaches captures the subtle Gibbs energy differences governing polymorph ranking for succinic and fumaric acids, representing another success story of computational chemistry.

Accurate Quantum-Mechanically Derived Force-Fields through a Fragment-Based Approach: Balancing Specificity and Transferability in the Prediction of Self-Assembly in Soft Matter

The wide range of time/length scales covered by self-assembly in soft matter makes molecular dynamics (MD) the ideal candidate for simulating such a supramolecular phenomenon at an atomistic level. However, the reliability of MD outcomes heavily relies on the accuracy of the adopted force-field (FF). The spontaneous re-ordering in liquid crystalline materials stands as a clear example of such collective self-assembling processes, driven by a subtle and delicate balance between supramolecular interactions and single-molecule flexibility. General-purpose transferable FFs often dramatically fail to reproduce such complex phenomena, for example, the error on the transition temperatures being larger than 100 K. Conversely, quantum-mechanically derived force-fields (QMD-FFs), specifically tailored for the target system, were recently shown (J. Phys. Chem. Lett.2022,13, 243) to allow for the required accuracy as they not only well reproduced transition temperatures but also yielded a quantitative agreement with the experiment on a wealth of structural, dynamic, and thermodynamic properties. The main drawback of this strategy stands in the computational burden connected to the numerous quantum mechanical (QM) calculations usually required for a target-specific parameterization, which has undoubtedly hampered the routine application of QMD-FFs. In this work, we propose a fragment-based strategy to extend the applicability of QMD-FFs, in which the amount of QM calculations is significantly reduced, being a single-molecule-optimized geometry and its Hessian matrix the only QM information required. To validate this route, a new FF is assembled for a large mesogen, exploiting the parameters obtained for two smaller liquid crystalline molecules, in this and previous work. Lengthy MD simulations are carried out with the new transferred QMD-FF, observing again a spontaneous re-orientation in the correct range of temperatures, with good agreement with the available experimental measures. The present results strongly suggest that a partial transfer of QMD-FF parameters can be invoked without a significant loss of accuracy, thus paving the way to exploit the method's intrinsic predictive capabilities in the simulation of novel soft materials.

Efficient and Accurate Description of Diels-Alder Reactions Using Density Functional Theory

Modeling chemical reactions using Quantum Chemistry is a widely used predictive strategy capable to complement experiments in order to understand the intrinsic mechanisms guiding the chemicals towards the most favorable reaction products. However, at this purpose, it is mandatory to use reliable and computationally tractable theoretical methods. In this work, we focus on six Diels-Alder reactions of increasing complexity and perform an extensive benchmark of middle- to low-cost computational approaches to predict the characteristic reactions energy barriers. We found that Density Functional Theory, using the ωB97XD, LC-ωPBE, CAM-B3LYP, M11 and MN12SX functionals, with empirical dispersion corrections coupled to an affordable 6-31G basis set, provides quality results for this class of reactions, at a small computational effort. Such efficient and reliable simulation protocol opens perspectives for hybrid QM/MM molecular dynamics simulations of Diels-Alder reactions including explicit solvation.

Uniting Nonempirical and Empirical Density Functional Approximation Strategies Using Constraint-Based Regularization

In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): nonempirical (NE) constraint satisfaction and empirical (E) data-driven optimization. The proposed method employs B-splines, bell-shaped spline functions with compact support, to construct each inhomogeneity correction factor (ICF). This choice offers several distinct advantages over traditional polynomial expansions by enabling explicit enforcement of linear and nonlinear constraints as well as ICF smoothness using Tikhonov and penalized B-splines (P-splines) regularization. As proof-of-concept, we use the so-called CASE (constrained and smoothed empirical) framework to construct a constraint-satisfying and data-driven global hybrid that exhibits enhanced performance across a diverse set of chemical properties. We argue that the CASE approach can be used to generate DFAs that maintain the physical rigor and transferability of NE-DFAs while leveraging high-quality quantum-mechanical data to remove the arbitrariness of ansatz selection and improve performance.

Analytic Gradients for the Long-Range-Corrected XYG3 Type of Doubly Hybrid Density Functionals: Theory, Implementation, and Assessment

An analytic gradient algorithm for the long-range-corrected (lrc-) XYG3 type of doubly hybrid functionals has been derived and implemented. Due to the introduction of a long-range second-order perturbation (lrPT2) as the correction, the Z-vector equations need to be modified, where the construction of a unique total Lagrangian of the method is required. Geometry optimizations using lrc-XYG3 and lrc-XYGJ-OS have then been applied to the A21 data set that consists of 21 noncovalently interacting systems with CCSD(T) reference data for structures, in order to testify the idea of introducing lrPT2 for a better description of intermolecular interactions. While lrc-XYG3 was observed to offer a better description in dispersion-dominant systems as compared to the XYG3 functional, lrc-XYGJ-OS stands out with an overall better balanced performance in reproducing intermolecular geometries.

A Minimum Quantum Chemistry CCSD(T)/CBS Data Set of Dimeric Interaction Energies for Small Organic Functional Groups: Heterodimers

We extend our previous quantum chemistry calculations of interaction energies for 31 homodimers of small organic functional groups (the SOFG-31 data set) by including 239 heterodimers with monomers selected within the SOFG-31 data set, thus resulting in the SOFG-31+239 data set. The minimum-level theoretical scheme contains (1) the basis set superposition error corrected supermolecule (BSSE-SM) approach for intermolecular interactions; (2) the second-order Møller-Plesset perturbation theory (MP2) with the Dunning's aug-cc-pVXZ (X = D, T, Q) basis sets for the geometry optimization and correlation energy calculations; and (3) the single-point energy calculations with the coupled cluster with single, double, and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS] using the well-tested extrapolation methods for the MP2 energy calibrations. In addition, we have performed a parallel series of energy decomposition calculations based on the symmetry adapted perturbation theory (SAPT) in order to gain chemical insights. That the above procedure cannot be further reduced has been proven to be very crucial for constructing reliable data sets of interaction energies. The calculated CCSD(T)/CBS interaction energy data can serve as a benchmark for testing or training less accurate but more efficient calculation methods, such as the electronic density functional theory. As an application, we employ a segmental SAPT model previously developed for the SOFG-31 data set to predict binding energies of large heterodimer complexes. These model energy "quanta" can be used in coarse-grained molecular dynamics simulations by avoiding large-scale calculations.

A Single Solvating Benzene Molecule Decouples the Mixed-valence Complex through Intermolecular Orbital Interactions

Characterization of covalency of intermolecular interactions in the van der Waals distance limit remains challenging because the interactions between molecules are weak, dynamic, and not measurable. Herein, we approach this issue in a series of supramolecular mixed-valence (MV) donor(D)-bridge(B)-acceptor(A) systems consisting of two bridged Mo₂ units with a C₆H₆ molecule encapsulated, as characterized by the X-ray crystal structures. Comparative analysis of the intervalence charge transfer spectra in benzene and dichloromethane substantiates the strong electronic decoupling effect of the solvating C₆H₆ molecule that breaks down the dielectric solvation theory. Ab initio and DFT calculations unravel that the intermolecular orbital overlaps between the complex bridge and the C₆H₆ molecule alter the electronic states of the D-B-A molecule through intermolecular nuclear dynamics. This work exemplifies that site-specific intermolecular interaction can be exploited to control the chemical property of supramolecular systems and to elucidate the functionalities of side-chains in biological systems.

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Decoupling mixed-valence complexes by an encapsulated benzene molecule

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Demonstrating intermolecular orbital interactions in the van der Waals distances

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Illustrating interplay between intermolecular electronic and nuclear degrees of freedom