A new expansion for dispersion forces and its application

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.

The hierarchy of ab initio and DFT methods for describing an intramolecular non-covalent SiN contact in the silicon compounds using electron diffraction geometries

In the series of silatranes XSi(OCH2CH2)3N, 1 (X = Me, 1a; H, 1b; F, 1c) with the known gas electron diffraction (GED) structures, the problematic geometry of 1-methylsilatrane 1a has been revised. In particular, the new value of the SiN distance (dSiN) in 1a turned out to be ∼0.06 Å longer than the generally accepted one. This dSiN resolves the long-standing contradiction between the data of the structural and spectral experiments regarding the sensitivity of 1 to the medium effect. We also performed the ab initio and DFT study of the combined series of silatranes 1a-c, silylalkylamines H3Si(CH2)3NMe2 (2a) and F3SiCH2NMe2 (2b), silylhydrazines F3SiN(Me)NMe2 (2c) and F3SiN(SiMe3)NMe2 (2d), and silyloxyamines ClH2SiONMe2 (2e,f), (F3C)F2SiONMe2 (2g,h) and F3SiONMe2 (2i), in which the GED dSiN values are in a wide range of 2-3 Å. None of the involved quantum chemical methods has succeeded in reproducing all the experimental gas-phase dSiN values in 1a-c, 2a-i with an acceptable accuracy (0.01-0.03 Å). The problems of the used methods, primarily CCSD with the Pople basis sets, are caused by four molecules with the geminal SiNN and SiON fragments (2d,f-i) and dSiN < 2.3 Å. A reasonable hierarchy of computationally accessible theory levels for studying the physicochemical manifestation of the non-covalent intramolecular SiN interactions can be constructed only at dSiN > 2.3 Å: MP2 < PBE0 ∼ B3PW91 ∼ SCS-MP2 < CCSD < CCSD(T).

van der Waals Function for Molecular Mechanics

van der Waals (vdW) interaction has been described with a Lennard-Jones potential for decades in molecular mechanics. Here, we report a new potential function Exp-PE from quantum mechanical derivation for vdW interactions for molecular mechanic simulation. High-order ab initio calculations and experimental atomic force microscopy measurements have been used to test its feasibility, and the results suggest that this formula is simple, accurate, and transferable. This new potential function is capable of upgrading the traditional force fields especially for the applications involving vdW interactions.

Faraday cage screening reveals intrinsic aspects of the van der Waals attraction

General properties of the recently observed screening of the van der Waals (vdW) attraction between a silica substrate and silica tip by insertion of graphene are predicted using basic theory and first-principles calculations. Results are then focused on possible practical applications, as well as an understanding of the nature of vdW attraction, considering recent discoveries showing it competing against covalent and ionic bonding. The traditional view of the vdW attraction as arising from pairwise-additive London dispersion forces is considered using Grimme's "D3" method, comparing results to those from Tkatchenko's more general many-body dispersion (MBD) approach, all interpreted in terms of Dobson's general dispersion framework. Encompassing the experimental results, MBD screening of the vdW force between two silica bilayers is shown to scale up to medium separations as 1.25 de/d, where d is the bilayer separation and de is its equilibrium value, depicting antiscreening approaching and inside de Means of unifying this correlation effect with those included in modern density functionals are urgently required.

Definitive thermochemistry and kinetics of the interconversions among conformers of n-butane and n-pentane

The focal-point analysis (FPA) technique is used for the definitive characterization of conformational interconversion parameters, including activation energy barriers, activation free energies, and kinetic rate coefficients at 298 K, of two n-alkanes, n-butane, and n-pentane, yielding the first complete analysis of their interconversion kinetics. The FPA implementation developed in this study is based on geometry optimizations and harmonic frequency computations carried out with density functional theory methods and single-point energy computations up to the CCSD(T) level of electronic structure theory using atom-centered Gaussian basis sets as large as cc-pV5Z. The anharmonic vibrational computations are carried out, at the MP2/6-31G* level of theory. Reflecting the convergence behavior of the Gibbs free-energy terms and the interconversion parameters, well-defined uncertainties, mostly neglected in previous theoretical studies, are provided. Finally, the effect of these uncertainties on the concentrations of the conformers of n-butane and n-pentane is examined via a global Monte-Carlo uncertainty analysis. © 2017 Wiley Periodicals, Inc.

Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem

Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.

A Density Functional with Spherical Atom Dispersion Terms

A new hybrid density functional, APF, is introduced, which avoids the spurious long-range attractive or repulsive interactions that are found in most density functional theory (DFT) models. It therefore provides a sound baseline for the addition of an empirical dispersion correction term, which is developed from a spherical atom model (SAM). The APF-D empirical dispersion model contains nine adjustable parameters that were selected based on a very small training set (15 noble gas dimers and 4 small hydrocarbon dimers), along with two computed atomic properties (ionization potential and effective atomic polarizability) for each element. APF-D accurately describes a large portion of the potential energy surfaces of complexes of noble gas atoms with various diatomic molecules involving a wide range of elements and of dimers of small hydrocarbons, and it reproduces the relative conformational energies of organic molecules. The accuracy for these weak interactions is comparable to that of CCSD(T)/aug-cc-pVTZ calculations. The accuracy in predicting the geometry of hydrogen bond complexes is competitive with other models involving DFT and empirical dispersion.

Natural polarizability and flexibility via explicit valency: the case of water

As the dominant physiological solvent, water drives the folding of biological macromolecules, influences conformational changes, determines the ionization states of surface groups, actively participates in catalytic events, and provides "wires" for long-range proton transfer. Elucidation of all these roles calls for atomistic simulations. However, currently available methods do not lend themselves to efficient simulation of proton transfer events, or even polarizability and flexibility. Here, we report that an explicit account of valency can provide a unified description for the polarizability, flexibility, and dissociability of water in one intuitive and efficient setting. We call this approach LEWIS, after the chemical theory that inspires the use of valence electron pairs. In this paper, we provide details of the method, the choice of the training set, and predictions for the neat ambient liquid, with emphasis on structure, dynamics, and polarization. LEWIS water provides a good description of bulk properties, and dipolar and quadrupolar responses.

Accurate and efficient method for many-body van der Waals interactions

An efficient method is developed for the microscopic description of the frequency-dependent polarizability of finite-gap molecules and solids. This is achieved by combining the Tkatchenko-Scheffler van der Waals (vdW) method [Phys. Rev. Lett. 102, 073005 (2009)] with the self-consistent screening equation of classical electrodynamics. This leads to a seamless description of polarization and depolarization for the polarizability tensor of molecules and solids. The screened long-range many-body vdW energy is obtained from the solution of the Schrödinger equation for a system of coupled oscillators. We show that the screening and the many-body vdW energy play a significant role even for rather small molecules, becoming crucial for an accurate treatment of conformational energies for biomolecules and binding of molecular crystals. The computational cost of the developed theory is negligible compared to the underlying electronic structure calculation.

Lewis-inspired representation of dissociable water in clusters and Grotthuss chains

Proton transfer to and from water is critical to the function of water in many settings. However, it has been challenging to model. Here, we present proof-of-principle for an efficient yet robust model based on Lewis-inspired submolecular particles with interactions that deviate from Coulombic at short distances to take quantum effects into account. This "LEWIS" model provides excellent correspondence with experimental structures for water molecules and water clusters in their neutral, protonated and deprotonated forms; reasonable values for the proton affinities of water and hydroxide; a good value for the strength of the hydrogen bond in the water dimer; the correct order of magnitude for the stretch and bend force constants of water; and the expected time course for Grotthuss transport in water chains.

Performance of the van der Waals Density Functional VV10 and (hybrid)GGA Variants for Thermochemistry and Noncovalent Interactions

The nonlocal van der Waals density functional VV10 (Vydrov, O. A.; Van Voorhis, T. J. Chem. Phys.2010, 133, 244103) is tested for the thermochemical properties of 1200+ atoms and molecules in the GMTKN30 database in order to assess its global accuracy. Five GGA and hybrid functionals in unmodified form are augmented by the nonlocal (NL) part of the VV10 functional (one parameter adjusted). The addition of the NL dispersion energy definitely improves the results of all tested functionals. On the basis of little empiricism and basic physical insight, DFT-NL can be recommended as a fully electronic, robust electronic structure method.

Nonlocal van der Waals density functional: the simpler the better

We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability.