Two- and three-body interatomic dispersion energy contributions to binding in molecules and solids

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

Giant Correlated Gap and Possible Room-Temperature Correlated States in Twisted Bilayer MoS_{2}

Moiré superlattices have emerged as an exciting condensed-matter quantum simulator for exploring the exotic physics of strong electronic correlations. Notable progress has been witnessed, but such correlated states are achievable usually at low temperatures. Here, we report evidence of possible room-temperature correlated electronic states and layer-hybridized SU(4) model simulator in AB-stacked MoS_{2} homobilayer moiré superlattices. Correlated insulating states at moiré band filling factors v=1, 2, 3 are unambiguously established in twisted bilayer MoS_{2}. Remarkably, the correlated electronic state at v=1 shows a giant correlated gap of ∼126  meV and may persist up to a record-high critical temperature over 285 K. The realization of a possible room-temperature correlated state with a large correlated gap in twisted bilayer MoS_{2} can be understood as the cooperation effects of the stacking-specific atomic reconstruction and the resonantly enhanced interlayer hybridization, which largely amplify the moiré superlattice effects on electronic correlations. Furthermore, extreme large nonlinear Hall responses up to room temperature are uncovered near correlated electronic states, demonstrating the quantum geometry of moiré flat conduction band.

Accurate Calculation of Many-Body Energies in Water Clusters Using a Classical Geometry-Dependent Induction Model

We incorporate geometry-dependent distributed multipole and polarizability surfaces into an induction model that is used to describe the 3- and 4-body terms of the interaction between water molecules. The moment expansion is carried out up to the hexadecapole with the multipoles distributed on the atom sites. Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole distributed polarizabilities are used to represent the response of the multipoles to an electric field. We compare the model against two large databases consisting of 43,844 3-body terms and 3,603 4-body terms obtained from high level ab initio calculations previously used to fit the MB-pol and q-AQUA classical interaction potentials for water. The classical induction model with no adjustable parameters reproduces the ab initio 3-/4-body terms contained in these two databases with a root-mean-square error (RMSE) of 0.104/0.058 and a mean-absolute error (MAE) of 0.054/0.026 kcal/mol, respectively. These results are on par with the ones obtained by fitting the same data using over 14,000 (for the 3-body) and 200 (for the 4-body) parameters via Permutationally Invariant Polynomials (PIPs). This demonstrates the accuracy of this physically motivated model in describing the 3- and 4-body terms in the interactions between water molecules with no adjustable parameters. The triple-dipole-dispersion energy, included in the calculation of the 3-body energy, was found to be small but not quite negligible. The model represents a practical, efficient, and transferable approach for obtaining accurate nonadditive interactions for multicomponent systems without the need to perform tens of thousands of high level electronic structure calculations and fitting them with PIPs.

On the Intermolecular Interactions in Thiophene-Cored Single-Stacking Junctions

There have been attempts, both experimental and based on density-functional theory (DFT) modeling, at understanding the factors that govern the electronic conductance behavior of single-stacking junctions formed by pi-conjugated materials in nanogaps. Here, a reliable description of relevant stacked configurations of some thiophene-cored systems is provided by means of high-level quantum chemical approaches. The minimal structures of these configurations, which are found using the dispersion-corrected DFT approach, are employed in calculations that apply the coupled cluster method with singles, doubles and perturbative triples [CCSD(T)] and extrapolations to the complete basis set (CBS) limit in order to reliably quantify the strength of intermolecular binding, while their physical origin is investigated using the DFT-based symmetry-adapted perturbation theory (SAPT) of intermolecular interactions. In particular, for symmetrized S-Tn dimers (where "S" and "T" denote a thiomethyl-containing anchor group and a thiophene segment comprising "n" units, respectively), the CCSD(T)/CBS interaction energies are found to increase linearly with n ≤ 6, and significant conformational differences between the flanking 2-thiophene group in S-T1 and S-T2 are described by the CCSD(T)/CBS and SAPT/CBS computations. These results are put into the context of previous work on charge transport properties of S-Tn and other types of supramolecular junctions.

Optimized Quantum Drude Oscillators for Atomic and Molecular Response Properties

The quantum Drude oscillator (QDO) is an efficient yet accurate coarse-grained approach that has been widely used to model electronic and optical response properties of atoms and molecules as well as polarization and dispersion interactions between them. Three effective parameters (frequency, mass, and charge) fully characterize the QDO Hamiltonian and are adjusted to reproduce response properties. However, the soaring success of coupled QDOs for many-atom systems remains fundamentally unexplained, and the optimal mapping between atoms/molecules and oscillators has not been established. Here we present an optimized parametrization (OQDO) where the parameters are fixed by using only dipolar properties. For the periodic table of elements as well as small molecules, our model accurately reproduces atomic (spatial) polarization potentials and multipolar dispersion coefficients, elucidating the high promise of the presented model in the development of next-generation quantum-mechanical force fields for (bio)molecular simulations.

Development and Implementation of Atomically Anisotropic First-Principles Force Fields: A Benzene Case Study

π-interactions are an important motif in chemical and biochemical systems. However, due to their anisotropic electron densities and complex balance of intermolecular interactions, aromatic molecules represent an ongoing challenge for accurate and transferable force field development. Historically, ab initio force fields for aromatics have not exhibited good accuracy with respect to bulk properties or have only been used to study gas-phase dimers. Using benzene as a proof of concept, herein we show how our own ab initio MASTIFF force field incorporates an atomically anisotropic description of intermolecular interactions to yield an accurate and robust model for aromatic interactions irrespective of phase. Compared to existing models, the MASTIFF benzene force field not only is accurate for liquid phase properties but also offers transferability to the gas and solid phases. Additionally, we introduce a computationally efficient OpenMM plugin which enables customizable anisotropic intermolecular functional forms and which can be generically used in any MD simulation where a model for nonspherical atomic features is required. Overall, our results demonstrate the importance of atomic-level anisotropy in enabling next-generation ab initio force field development.

Efficient Computation of the Interaction Energies of Very Large Non-covalently Bound Complexes

We present a new benchmark set consisting of 16 large non-covalently bound systems (LNCI16) ranging from 380 up to 1988 atoms and featuring diverse interaction motives. Gas-phase interaction energies are calculated with various composite DFT, semi-empirical quantum mechanical (SQM), and force field (FF) methods and are evaluated using accurate DFT reference values. Of the employed QM methods, PBEh-3c proves to be the most robust for large systems with a relative mean absolute deviation (relMAD) of 8.5% with respect to the reference interaction energies. r2SCAN-3c yields an even smaller relMAD, at least for the subset of complexes for which the calculation could be converged, but is less robust for systems with smaller HOMO–LUMO gaps. The inclusion of Fock-exchange is therefore important for the description of very large non-covalent interaction (NCI) complexes in the gas phase. GFN2-xTB was found to be the best performer of the SQM methods with an excellent result of only 11.1% deviation. From the assessed force fields, GFN-FF and GAFF achieve the best accuracy. Considering their low computational costs, both can be recommended for routine calculations of very large NCI complexes, with GFN-FF being clearly superior in terms of general applicability. Hence, GFN-FF may be routinely applied in supramolecular synthesis planning.

1 Introduction

2 The LNCI16 Benchmark Set

3 Computational Details

4 Generation of Reference Values

5 Results and Discussion

6 Conclusions

Assessing the Interplay between Functional-Driven and Density-Driven Errors in DFT Models of Water

We investigate the interplay between functional-driven and density-driven errors in different density functional approximations within density functional theory (DFT) and the implications of these errors for simulations of water with DFT-based data-driven potentials. Specifically, we quantify density-driven errors in two widely used dispersion-corrected functionals derived within the generalized gradient approximation (GGA), namely BLYP-D3 and revPBE-D3, and two modern meta-GGA functionals, namely strongly constrained and appropriately normed (SCAN) and B97M-rV. The effects of functional-driven and density-driven errors on the interaction energies are first assessed for the water clusters of the BEGDB dataset. Further insights into the nature of functional-driven errors are gained from applying the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) to the interaction energies, which demonstrates that functional-driven errors are strongly correlated with the nature of the interactions. We discuss cases where density-corrected DFT (DC-DFT) models display higher accuracy than the original DFT models and cases where reducing the density-driven errors leads to larger deviations from the reference energies due to the presence of large functional-driven errors. Finally, molecular dynamics simulations are performed with data-driven many-body potentials derived from DFT and DC-DFT data to determine the effect that minimizing density-driven errors has on the description of liquid water. Besides rationalizing the performance of widely used DFT models of water, we believe that our findings unveil fundamental relations between the shortcomings of some common DFT approximations and the requirements for accurate descriptions of molecular interactions, which will aid the development of a consistent, DFT-based framework for the development of data-driven and machine-learned potentials for simulations of condensed-phase systems.

vdW-DF-ahcx: a range-separated van der Waals density functional hybrid

Hybrid density functionals replace a fraction of an underlying generalized-gradient approximation (GGA) exchange description with a Fock-exchange component. Range-separated hybrids (RSHs) also effectively screen the Fock-exchange component and thus open the door for characterizations of metals and adsorption at metal surfaces. The RSHs are traditionally based on a robust GGA, such as PBE (Perdew J Pet al1996Phys. Rev. Lett.773865), for example, as implemented in the HSE design (Heyd Jet al2003J. Chem. Phys.1188207). Here we define an analytical-hole (Henderson T Met al2008J. Chem. Phys.128194105) consistent-exchange RSH extension to the van der Waals density functional (vdW-DF) method (Berland Ket al2015Rep. Prog. Phys.78066501), launching vdW-DF-ahcx. We characterize the GGA-type exchange in the vdW-DF-cx version (Berland K and Hyldgaard P 2014Phys. Rev. B89035412), isolate the short-ranged exchange component, and define the new vdW-DF hybrid. We find that the performance vdW-DF-ahcx compares favorably to (dispersion-corrected) HSE for descriptions of bulk (broad molecular) properties. We also find that it provides accurate descriptions of noble-metal surface properties, including CO adsorption.

2D colloids in rotating electric fields: A laboratory of strong tunable three-body interactions

Many-body forces play a prominent role in structure and dynamics of matter, but their role is not well understood in many cases due to experimental challenges. Here, we demonstrate that a novel experimental system based on rotating electric fields can be utilised to deliver unprecedented degree of control over many-body interactions between colloidal silica particles in water. We further show that we can decompose interparticle interactions explicitly into the leading terms and study their specific effects on phase behaviour. We found that three-body interactions exert critical influence over the phase diagram domain boundaries, including liquid-gas binodal, critical and triple points. Phase transitions are shown to be reversible and fully controlled by the magnitude of external rotating electric field governing the tunable interactions. Our results demonstrate that colloidal systems in rotating electric fields are a unique laboratory to study the role of many-body interactions in physics of phase transitions and in applications, such as self-assembly, offering exciting opportunities for studying generic phenomena inherent to liquids and solids, from atomic to protein and colloidal systems.

New Approach for Correcting Noncovalent Interactions in Semiempirical Quantum Mechanical Methods: The Importance of Multiple-Orientation Sampling

A new approach is presented to improve the performance of semiempirical quantum mechanical (SQM) methods in the description of noncovalent interactions. To show the strategy, the PM6 Hamiltonian was selected, although, in general, the procedure can be applied to other semiempirical Hamiltonians and to different methodologies. A set of small molecules were selected as representative of various functional groups, and intermolecular potential energy curves (IPECs) were evaluated for the most relevant orientations of interacting molecular pairs. Then, analytical corrections to PM6 were derived from fits to B3LYP-D3/def2-TZVP reference–PM6 interaction energy differences. IPECs provided by the B3LYP-D3/def2-TZVP combination of the electronic structure method and basis set were chosen as the reference because they are in excellent agreement with CCSD(T)/aug-cc-pVTZ curves for the studied systems. The resulting method, called PM6-FGC (from functional group corrections), significantly improves the performance of PM6 and shows the importance of including a sufficient number of orientations of the interacting molecules in the reference data set in order to obtain well-balanced descriptions.

A comparison of three DFT exchange-correlation functionals and two basis sets for the prediction of the conformation distribution of hydrated polyglycine

The performance of three density functional theory (DFT) exchange-correlation functionals, namely, Perdew-Burke-Ernzerhof (PBE), BP86, and B3LYP, in predicting conformational distributions of a hydrated glycine peptide is tested with two different basis sets in the framework of adaptive force matching (AFM). The conformational distributions yielded the free energy profiles of the DFT functional and basis set combinations. Unlike traditional validations of potential energy and structural parameters, our approach allows the free energy of DFT to be validated. When compared to experimental distributions, the def2-TZVP basis set provides better agreement than a slightly trimmed aug-cc-pVDZ basis set. B3LYP is shown to be better than BP86 and PBE. The glycine model fitted against B3LYP-D3(BJ) with the def2-TZVP basis set is the most accurate and named the AFM2021 model for glycine. The AFM2021 glycine model provides better agreement with experimental J-coupling constants than C36m and ff14SB, although the margin is very small when compared to C36m. Our previously published alanine model is also refitted with the slightly simplified AFM2021 energy expression. This work shows good promise of AFM for developing force fields for a range of proteinogenic peptides using only DFT as reference.

DFT Functionals for Modeling of Polyethylene Chains Cross-Linked by Metal Atoms. DLPNO-CCSD(T) Benchmark Calculations

Density functional theory (DFT) functionals for calculations of binding energies (BEs) of the polyethylene (PE) chains cross-linked by selected metal atoms (M) are benchmarked against DLPNO-CCSD(T) and DLPNO-CCSD(T1) data. PEX-M-PEX complexes as compared with plain parallel PEX···PEX chains with X = 3-9 carbon atoms are model species characterized by a cooperative effect of covalent C-M-C bonds and interchain dispersion interactions. The accuracy of DLPNO-CC methods was assessed by a comparison of BEs with the canonical CCSD(T) results for small PE3-M-PE3 complexes. Functionals for PEX···PEX and closed-shell PEX-M-PEX complexes (M = Be, Mg, Zn) were benchmarked against DLPNO-CCSD(T) BEs; open-shell complexes (M = Li, Ag, Au) were benchmarked against the DLPNO-CCSD(T1) method with iterative triples. Three dispersion corrections were combined with 25 DFT functionals for calculations of BEs with respect to PEX-M and PEX fragments employing def2-TZVPP and def2-QZVPP basis sets. Accuracy to within 5% for the closed-shell PEX-M-PEX complexes was achieved with five functionals. Less accurate are functionals for the open-shell PEX-M-PEX complexes; only two functionals deviate by less than 15% from DLPNO-CCSD(T1). Particularly problematic were PEX-Li-PEX complexes. A reasonable overall performance across all complexes in terms of the mean absolute percentage error is found for the range-separated hybrid functionals ωB97X-D3 and CAM-B3LYP/D3(BJ)-ABC.

Performing Molecular Dynamics Simulations and Computing Hydration Free Energies on the B3LYP-D3(BJ) Potential Energy Surface with Adaptive Force Matching: A Benchmark Study with Seven Alcohols and One Amine

The potential energy surfaces at the B3LYP-D3(BJ) level for eight solutes in dilute aqueous solutions were mapped into simple pairwise additive force field expressions using the adaptive force matching (AFM) method. The quality of the fits was validated by computing the hydration free energy (HFE), enthalpy of hydration, and diffusion constant for each solute. By force matching B3LYP-D3(BJ), the predictions from the models agree with the closest experimental HFE and enthalpy of hydration within chemical accuracy. The diffusion constants from the models are also in good agreement with experimental references. The good agreement provides confidence on the quality of B3LYP-D3(BJ) in producing potential energy surfaces for thermodynamic property calculations through AFM for the molecules studied. Accurate computational predictions could potentially provide validations to experimental measurements in cases where experimental measurements from different sources do not agree.

Requirements for an accurate dispersion-corrected density functional

Post-self-consistent dispersion corrections are now the norm when applying density-functional theory to systems where non-covalent interactions play an important role. However, there is a wide range of base functionals and dispersion corrections available from which to choose. In this work, we opine on the most desirable requirements to ensure that both the base functional and dispersion correction, individually, are as accurate as possible for non-bonded repulsion and dispersion attraction. The base functional should be dispersionless, numerically stable, and involve minimal delocalization error. Simultaneously, the dispersion correction should include finite damping, higher-order pairwise dispersion terms, and electronic many-body effects. These criteria are essential for avoiding reliance on error cancellation and obtaining correct results from correct physics.

Crystal Structure Prediction Methods for Organic Molecules: State of the Art

The prediction of the crystal structures that a given organic molecule is likely to form is an important theoretical problem of significant interest for the pharmaceutical and agrochemical industries, among others. As evidenced by a series of six blind tests organized over the past 2 decades, methodologies for crystal structure prediction (CSP) have witnessed substantial progress and have now reached a stage of development where they can begin to be applied to systems of practical significance. This article reviews the state of the art in general-purpose methodologies for CSP, placing them within a common framework that highlights both their similarities and their differences. The review discusses specific areas that constitute the main focus of current research efforts toward improving the reliability and widening applicability of these methodologies, and offers some perspectives for the evolution of this technology over the next decade.

Determining the hydration free energies of selected small molecules with MP2 and local MP2 through adaptive force matching

Force fields for seven small solute molecules, ethanol, 2-methyl-1-propanol, 2-butanol, cyclohexene, tetrahydropyran, 1,4-dioxane, and 1,4-butanediol, in dilute aqueous solutions were created with the adaptive force matching (AFM) method using MP2 or local MP2 as reference. The force fields provide a way to predict the hydration free energies (HFEs) of these molecules with only electronic structure calculations as reference. For six of the seven molecules, the predicted HFEs are in very good agreement with experiments. For 1,4-butanediol, the model created by force matching LMP2 provides a HFE that is too positive. Further investigation suggests that LMP2 may not be sufficiently accurate for computing HFEs for alcohols with AFM. Other properties, such as enthalpy of hydration, diffusion constants, and vibrational spectra, are also computed with the force field developed. The force fields developed by AFM provide a bridge for computing ensemble properties of the reference electronic structure method. With MP2 and LMP2 as reference methods, the computed properties of the small molecular solutes are found to be in good agreement with experiments.

Development and Validation of a DFT-Based Force Field for a Hydrated Homoalanine Polypeptide

A new force field has been created for simulating hydrated alanine polypeptides using the adaptive force matching (AFM) method. Only density functional theory calculations using the Perdew-Burke-Ernzerhof exchange-correlation functional and the D3 dispersion correction were used to fit the force field. The new force field, AFM2020, predicts NMR scalar coupling constants for hydrated homopolymeric alanine in better agreements with experimental data than several other models including those fitted directly to such data. For Ala₇, the new force field shows about 15% helical conformations, 20% conformation in the β basin, and 65% polyproline II. The predicted helical population of short hydrated alanine is higher than previous estimates based on the same experimental data. Gas-phase simulations indicate that the force field developed by AFM solution-phase data is likely to produce a reasonable conformation distribution when hydration water is no longer present, such as the interior of a protein.

Many-Body Dispersion

A broad range of approaches to many-body dispersion are discussed, including empirical approaches with multiple fitted parameters, augmented density functional-based approaches, symmetry adapted perturbation theory, and a supermolecule approach based on coupled cluster theory. Differing definitions of "body" are considered, specifically atom-based vs molecule-based approaches.

What is “many-body” dispersion and should I worry about it?

“Many-body” dispersion can refer to two distinct phenomena, here termed electronic and atomic many-body effects, both of which cause the dispersion energy to be non-additive.

Leveraging local MP2 to reduce basis set superposition errors: An efficient first-principles based force-field for carbon dioxide

Pairwise additive model potentials for CO₂ were developed by fitting to gradients computed with the local second order Møller Plesset Perturbation theory (LMP2) method, with and without consideration of 3-body dispersion using adaptive force matching. Without fitting to experiments, all models gave good predictions of properties of CO₂, such as the density-temperature diagram, diffusion constants, and radial distribution functions. For the prediction of vibrational spectra, the inclusion of a bond-bond coupling term has been shown to be important. The CO₂ models developed only have pairwise additive terms, thus allowing microsecond time scale simulations to be performed with practical computational cost. LMP2 performed significantly better than second order Møller Plesset Perturbation theory (MP2) for the development of the CO₂ model. This is attributed to the appreciable reduction in the basis set superposition error when the localized method was used. It is argued that LMP2 is a more appropriate method than MP2 for force matching for systems where the basis set superposition error is large.

CrystaLattE: Automated computation of lattice energies of organic crystals exploiting the many-body expansion to achieve dual-level parallelism

We present an algorithm to compute the lattice energies of molecular crystals based on the many-body cluster expansion. The required computations on dimers, trimers, etc., within the crystal are independent of each other, leading to a naturally parallel approach. The algorithm exploits the long-range three-dimensional periodic order of crystals to automatically detect and avoid redundant or unnecessary computations. For this purpose, Coulomb-matrix descriptors from machine learning applications are found to be efficient in determining whether two N-mers are identical. The algorithm is implemented as an open-source Python program, CrystaLattE, that uses some of the features of the Quantum Chemistry Common Driver and Databases library. CrystaLattE is initially interfaced with the quantum chemistry package Psi4. With CrystaLattE, we have applied the fast, dispersion-corrected Hartree-Fock method HF-3c to the lattice energy of crystalline benzene. Including all 73 symmetry-unique dimers and 7130 symmetry-unique trimers that can be formed from molecules within a 15 Å cutoff from a central reference monomer, HF-3c plus an Axilrod-Teller-Muto estimate of three-body dispersion exhibits an error of only -1.0 kJ mol^-1 vs the estimated 0 K experimental lattice energy of -55.3 ± 2.2 kJ mol^-1. The convergence of the HF-3c two- and three-body contributions to the lattice energy as a function of intermonomer distance is examined.

Assessing Electronic Structure Methods for Long-Range Three-Body Dispersion Interactions: Analysis and Calculations on Well-Separated Metal Atom Trimers

Three-body dispersion interactions are much weaker than their two-body counterpart. However, their importance grows quickly as the number of interacting monomers rises. To explore the numerical performance of correlation methods for long-range three-body dispersion, we performed calculations on eight very simple dispersion-dominated model metal trimers: Na₃, Mg₃, Zn₃, Cd₃, Hg₃, Cu₃, Ag₃, and Au₃. One encouraging aspect is that relatively small basis sets of augmented triple-ζ size appear to be adequate for three-body dispersion in the long-range. Coupled cluster calculations were performed at high levels to assess MP3, CCSD, CCSD(T), empirical density functional theory dispersion (D3), and the many-body dispersion (MBD) approach. We found that the accuracy of CCSD(T) was generally significantly lower than for two-body interactions, with errors sometimes reaching 20% in the investigated systems, while CCSD and particularly MP3 were generally more erratic. MBD is found to perform better than D3 at large distances, whereas the opposite is true at shorter distances. When computing reference numbers for three-body dispersion, care should be taken to appropriately represent the effect of the connected triple excitations, which are significant in most cases and incompletely approximated by CCSD(T).

Accurate and Efficient ab Initio Calculations for Supramolecular Complexes: Symmetry-Adapted Perturbation Theory with Many-Body Dispersion

Symmetry-adapted perturbation theory (SAPT) provides a chemically meaningful energy decomposition scheme for nonbonded interactions that is useful for interpretive purposes. Although formally a dimer theory, we have previously introduced an "extended" version (XSAPT) that incorporates many-body polarization via self-consistent charge embedding. Here, we extend the XSAPT methodology to include nonadditive dispersion, using a modified form of the many-body dispersion (MBD) method of Tkatchenko and co-workers. Dispersion interactions beyond the pairwise atom-atom approximation improve total interaction energies even in small systems, and for large π-stacked complexes these corrections can amount to several kilocalories per mole. The XSAPT+MBD method introduced here achieves errors of ≲1 kcal/mol (as compared to high-level ab initio benchmarks) for the L7 data set of large dispersion-bound complexes and ≲4 kcal/mol (as compared to experiment) for the S30L data set of host-guest complexes. This is superior to the best contemporary density functional methods for noncovalent interactions, at comparable or lower cost. XSAPT+MBD represents a promising method for application to supramolecular assemblies, including protein-ligand binding.

Estimating Strengths of Individual Hydrogen Bonds in RNA Base Pairs: Toward a Consensus between Different Computational Approaches

Noncoding RNA molecules are composed of a large variety of noncanonical base pairs that shape up their functionally competent folded structures. Each base pair is composed of at least two interbase hydrogen bonds (H-bonds). It is expected that the characteristic geometry and stability of different noncanonical base pairs are determined collectively by the properties of these interbase H-bonds. We have studied the ground-state electronic properties [using density functional theory (DFT) and DFT-D3-based methods] of all the 118 normal base pairs and 36 modified base pairs, belonging to 12 different geometric families (cis and trans of WW, WH, HH, WS, HS, and SS) that occur in a nonredundant set of high-resolution RNA crystal structures. Having addressed some of the limitations of the earlier approaches, we provide here a comprehensive compilation of the average energies of different types of interbase H-bonds (E _HB). We have also characterized each interbase H-bond using 13 different parameters that describe its geometry, charge distribution at its bond critical point (BCP), and n → σ*-type charge transfer from filled π orbitals of the H-bond acceptor to the empty antibonding orbital of the H-bond donor. On the basis of the extent of their linear correlation with the H-bonding energy, we have shortlisted five parameters to model linear equations for predicting E _HB values. They are (i) electron density at the BCP: ρ, (ii) its Laplacian: ∇²ρ, (iii) stabilization energy due to n → σ*-type charge transfer: E(2), (iv) donor-hydrogen distance, and (v) hydrogen-acceptor distance. We have performed single variable and multivariable linear regression analysis over the normal base pairs and have modeled sets of linear relationships between these five parameters and E _HB. Performance testing of our model over the set of modified base pairs shows promising results, at least for the moderately strong H-bonds.

Semiempirical Quantum-Chemical Methods with Orthogonalization and Dispersion Corrections

We present two new semiempirical quantum-chemical methods with orthogonalization and dispersion corrections: ODM2 and ODM3 (ODM x). They employ the same electronic structure model as the OM2 and OM3 (OM x) methods, respectively. In addition, they include Grimme's dispersion correction D3 with Becke-Johnson damping and three-body corrections E ABC for Axilrod-Teller-Muto dispersion interactions as integral parts. Heats of formation are determined by adding explicitly computed zero-point vibrational energy and thermal corrections, in contrast to standard MNDO-type and OM x methods. We report ODM x parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine that are optimized with regard to a wide range of carefully chosen state-of-the-art reference data. Extensive benchmarks show that the ODM x methods generally perform better than the available MNDO-type and OM x methods for ground-state and excited-state properties, while they describe noncovalent interactions with similar accuracy as OM x methods with a posteriori dispersion corrections.

Interrogation of fractional crystallization behavior of a newly exploited chiral resolution method for racemic 1-(pyridin-2-yl)ethylamine via DFT-D3 calculations of cohesive energy

A novel chiral separation method for 1-(pyridin-2-yl)ethylamine is developed and the underlying energetics is investigated by DFT-D3.

Theory and practice of modeling van der Waals interactions in electronic-structure calculations

The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of molecules and materials. vdW forces arise from the interaction of quantum-mechanical fluctuations in the electronic charge density. Within (semi-)local density functional approximations or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calculations. These methods include vdW-inclusive Density Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of Density Functional Theory, including non-local van der Waals density functionals, interatomic dispersion models within many-body and pairwise formulation, and random phase approximation-based approaches. This review aims to guide the reader through the theoretical foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addition, we give an overview of complementary experimental approaches, and discuss tools for the qualitative understanding of non-covalent interactions as well as energy decomposition techniques. Besides representing a reference for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calculations for a general and broad audience.

Tuning the balance between dispersion and entropy to design temperature-responsive flexible metal-organic frameworks

Temperature-responsive flexibility in metal-organic frameworks (MOFs) appeals to the imagination. The ability to transform upon thermal stimuli while retaining a given crystalline topology is desired for specialized sensors and actuators. However, rational design of such shape-memory nanopores is hampered by a lack of knowledge on the nanoscopic interactions governing the observed behavior. Using the prototypical MIL-53(Al) as a starting point, we show that the phase transformation between a narrow-pore and large-pore phase is determined by a delicate balance between dispersion stabilization at low temperatures and entropic effects at higher ones. We present an accurate theoretical framework that allows designing breathing thermo-responsive MOFs, based on many-electron data for the dispersion interactions and density-functional theory entropy contributions. Within an isoreticular series of materials, MIL-53(Al), MIL-53(Al)-FA, DUT-4, DUT-5 and MIL-53(Ga), only MIL-53(Al) and MIL-53(Ga) are proven to switch phases within a realistic temperature range.

Rational design of metal organic frameworks (MOFs) with shape-memory nanopores is a formidable challenge. Here the authors use an accurate theoretical approach to design thermo-responsive MOFs based on a balance of van der Waals and entropy contributions.

Accurate Noncovalent Interactions via Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory

Noncovalent interactions govern many important areas of chemistry, ranging from biomolecules to molecular crystals. Here, an accurate and computationally inexpensive dispersion-corrected second-order Møller-Plesset perturbation theory model (MP2D) is presented. MP2D recasts the highly successful dispersion-corrected MP2C model in a framework based on Grimme's D3 dispersion correction, combining Grimme's D3 dispersion coefficients with new analogous uncoupled Hartree-Fock ones and five global empirical parameters. MP2D is faster than MP2C, and unlike MP2C, it is suitable for geometry optimizations and can describe both intra- and intermolecular noncovalent interactions with high accuracy. MP2D approaches the accuracy of higher-level ab initio wave function techniques and out-performs a widely used hybrid dispersion-corrected density functional on a range of intermolecular, intramolecular, and thermochemical benchmarks.

Communication: Accurate description of interaction energies and three-body effects in weakly bound molecular complexes by PBE-QIDH models

We apply a recently developed parameter-free double-hybrid density functional belonging to the quadratic-integrand double-hybrid model to calculate association energies (ΔE) and three-body effects (Δ³E) arising from intermolecular interactions in weakly bound supramolecular complexes (i.e., the dataset 3B-69). The model behaves very accurately for trimer association energies and is found to outperform widely used density functional approximations while approaching the accuracy of more costly ab initio methods for three-body effects. The results are further improved when we add some specific corrections for the remaining dispersion interactions, D3(BJ) or VV10 for two-body effects and Axilrod-Teller-Muto for three-body effects, leading to marginal deviations (less than 1 kcal/mol for ΔE and around 0.03-0.04 kcal/mol for Δ³E) with respect to benchmark results.

Modeling Nonreactive Molecule-Surface Systems on Experimentally Relevant Time and Length Scales: Dynamics and Conductance of Polyfluorene on Au(111)

We propose a computationally efficient strategy to accurately model nonreactive molecule-surface interactions that adapts density functional theory calculations with the Tkatchenko-Scheffler scheme for van der Waals interactions into a simple classical force field. The resulting force field requires just two adjustable parameters per atom type that are needed to capture short-range and polarization interactions. The developed strategy allows for classical molecular dynamics simulation of molecules on surfaces with the accuracy of high-level electronic structure methods but for system sizes (10³ to 10⁷ atoms) and timescales (picoseconds to microseconds) that go well beyond what can be achieved with first-principles methods. Parameters for H, sp² C, and O on Au(111) are developed and employed to atomistically model experiments that measure the conductance of a single polyfluorene on Au(111) as a continuous function of its length. The simulations qualitatively capture both the gross and fine features of the observed conductance decay during initial junction elongation and lead to a revised atomistic understanding of the experiment.

Origin of the size-dependence of the equilibrium van der Waals binding between nanostructures

Nanostructures can be bound together at equilibrium by the van der Waals (vdW) effect, a small but ubiquitous many-body attraction that presents challenges to density functional theory. How does the binding energy depend upon the size or number of atoms in one of a pair of identical nanostructures? To answer this question, we treat each nanostructure as a whole object, not as a collection of atoms. Our calculations start from an accurate static dipole polarizability for each considered nanostructure, and an accurate equilibrium center-to-center distance for the pair (the latter from experiment or from the vdW-DF-cx functional). We consider the competition in each term -C_2k/d^2k (k = 3, 4, 5) of the long-range vdW series for the interaction energy, between the size dependence of the vdW coefficient C_2k and that of the 2kth power of the center-to-center distance d. The damping of these vdW terms can be negligible, but in any case, it does not affect the size dependence for a given term in the absence of non-vdW binding. To our surprise, the vdW energy can be size-independent for quasi-spherical nanoclusters bound to one another by vdW interaction, even with strong nonadditivity of the vdW coefficient, as demonstrated for fullerenes. We also show that, for low-dimensional systems, the vdW interaction yields the strongest size-dependence, in stark contrast to that of fullerenes. We illustrate this with parallel planar polycyclic aromatic hydrocarbons. The size dependences of other morphologies or bonding types lie between, as shown by sodium clusters.