Nonadditive Dispersion Research Articles

Low Temperature Growth of the Nanotextured Island and Solid 3C-SiC Layers on Si from Hydric Si, Ge and C Compounds

Different growth stages and surface morphology of the epitaxial 3C-SiC/Si(100) structures were studied. Heterocompositions were grown in vacuum from hydric compounds at a lower temperature. The composition, surface morphology and crystal structure of the 3C-SiC films were tested using X-ray diffraction, second ion mass spectrometry, scanning ion and electron microscopy, photo- and cathode luminescence. It was demonstrated that the fine crystal structure of the 3C-SiC islands was formed by the close-packed nanometer-size grains and precipitated on the underlying solid carbonized Si layer. Luminescence spectral lines of the solid carbonized Si layer, separated island and solid textured 3C-SiC layer were shifted toward the high ultraviolet range. The spectra measured by different methods were compared and the nature of the revealed lines was considered. This article discusses a quantum confinement effect observation in the 3C-SiC nanostructures and a perspective for the use of nanotextured island 3C-SiC layers as a two-dimensional surface quantum superlattice for high-frequency applications. The conductivity anisotropy and current-voltage characteristics of the two-dimensional superlattices with a non-additive electron dispersion law in the presence of a strong electric field were studied theoretically. Main efforts were focused on a search of the mechanisms allowing realization of the high-frequency negative dynamical conductivity for the structures having a positive static differential conductivity.

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.

A Simple Correction for Nonadditive Dispersion within Extended Symmetry-Adapted Perturbation Theory (XSAPT).

Extended symmetry-adapted perturbation theory (XSAPT), in conjunction with empirical "+ aiD" potentials fit to ab initio dispersion data, is a low-scaling approach to compute intermolecular interaction energies in noncovalent clusters. One shortcoming is that the aiD atom-atom dispersion potentials are independent of the chemical environment of the atoms in question and therefore neglect nonadditive dispersion effects. These can be significant in large systems, so to account for them we test a simple correction to XSAPT(KS)+ aiD, where "KS" indicates the use of Kohn-Sham orbitals. This correction, which can be evaluated at fourth-order cost using double-ζ basis sets, is based on comparing second-order SAPT dispersion with and without a self-consistent charge embedding for the monomer wave functions. The correction amounts to ∼1.4 kcal/mol in (H2O)6 but ∼5.5 kcal/mol in (H2O)20. With the nonadditive dispersion correction, XSAPT(KS)+ aiD affords errors of ∼1 kcal/mol for isomers of F-(H2O)10 and (H2O)20, where the benchmarks are complete-basis CCSD(T) energies, as well as for ion-water clusters X(H2O) n where n ≤ 6 and X = F-, Cl-, SO42-, Li+, Na+, or K+. We also test the MP2 method and a variety of density-functional methods that have been specifically recommended for noncovalent interactions. Among the latter, only ωB97X-V and ωB97M-V can be recommended for ion-water clusters, as mean errors for other popular approaches (including ωB97X-D3 and several Minnesota functionals) exceed 1 kcal/mol. Lastly, we examine clathrate-hydrate host/guest complexes whose mixture of hydrogen bonding and dispersion make them challenging tests for noncovalent quantum chemistry. Although the B97-D2 functional performs best for clathrate hydrates and has been previously recommended in other studies of these inclusion complexes, its performance for other systems examined here is quite poor. We are unable to find a functional whose accuracy is ≲1 kcal/mol accuracy for both clathrate hydrates and ion-water clusters. However, the XSAPT(KS)+ aiD method with the nonadditive dispersion correction can achieve this, with a mean error for the clathrate hydrates of 0.3 kcal/mol.

Nonadditive three-body potential and third to eighth virial coefficients of carbon dioxide.

A new nonadditive three-body interaction potential for carbon dioxide was determined from supermolecular ab initio calculations up to the coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] level of theory for 9401 configurations. A physically motivated analytical function with terms for describing nonadditive dispersion, induction, and exchange contributions was fitted to the calculated nonadditive three-body interaction energies. For the 7996 configurations with a total interaction energy of less than 3000 K, the mean absolute error of the analytical function is 0.32 K. The new nonadditive three-body potential was applied together with a previously published pair potential [R. Hellmann, Chem. Phys. Lett. 613, 133 (2014)] to calculate the third to seventh virial coefficients of CO2 at subcritical and supercritical temperatures up to 2000 K. The eighth virial coefficient was also calculated, but using only the pair potential and only at temperatures from 600 K to 2000 K because of the enormous computational costs. A simple analytical function was fitted individually to the calculated values of each virial coefficient, including previously determined values of the second virial coefficient, to obtain an analytical virial equation of state (VEOS). For densities at which the VEOS is converged, the agreement in pressure with the reference EOS of Span and Wagner [J. Phys. Chem. Ref. Data 25, 1509 (1996)] is mostly within ±0.5%. However, for temperatures above about 700 K, much larger deviations occur at higher densities, which we ascribe mainly to deficiencies of the reference EOS due to the lack of accurate data for these experimentally difficult conditions.

Calculations of long-range three-body interactions forLi(2S2)−Li(2S2)−Li(2P2)

General formulas for calculating the several leading long-range interactions among three identical atoms where two atoms are in identical $S$ states and the other atom is in a $P$ state are obtained using perturbation theory for the energies up to second order. The first order (dipolar) interactions depend on the geometrical configurations of the three atoms. In second order, additive and nonadditive dispersion interactions are obtained. The nonadditive interactions depend on the geometrical configurations in marked contrast to the case where all three atoms are in identical $S$ states, for which the nonadditive (also known as triple-dipole or as Axilrod-Muto-Teller) dispersion interactions appear at the third order. The formalism is demonstrated by the calculation of the coefficients for the Li($2\,^2S$)-Li($2\,^2S$)-Li($2\,^{2}P$) system using variationally-generated atomic lithium wave functions in Hylleraas coordinates. The present dipolar coefficients and additive and nonadditive dispersion coefficients may be useful in constructing precise potential energy surfaces for this three lithium atom system.

Density-functional approach to the three-body dispersion interaction based on the exchange dipole moment.

We implement and compute the density functional nonadditive three-body dispersion interaction using a combination of Tang-Karplus formalism and the exchange-dipole moment model of Becke and Johnson. The computation of the C9 dispersion coefficients is done in a non-empirical fashion. The obtained C9 values of a series of noble atom triplets agree well with highly accurate values in the literature. We also calculate the C9 values for a series of benzene trimers and find a good agreement with high-level ab initio values reported recently in the literature. For the question of damping of the three-body dispersion at short distances, we propose two damping schemes and optimize them based on the benzene trimers data, and the fitted analytic potentials of He3 and Ar3 trimers fitted to the results of high-level wavefunction theories available from the literature. Both damping schemes respond well to the optimization of two parameters.

First-Principles Many-Body Force Fields from the Gas Phase to Liquid: A “Universal” Approach

We extend our previously developed approach for generating "physically-motivated" force fields from symmetry-adapted perturbation theory by introducing explicit terms to account for nonadditive three-body exchange and dispersion interactions, yielding transferability from the gas- to condensed-phase. These Axilrod-Teller-Muto-type three-body terms require no additional parametrization and can be implemented with high computational efficiency. We demonstrate the accuracy of our force fields for a diverse set of six organic liquids/fluids, examining a wide variety of structural, thermodynamic, and dynamic properties. We find that three-body dispersion and exchange interactions make significant contributions to the internal pressure of condensed phase systems and cannot be neglected in truly ab initio force field development. These resulting force field parameters are extremely transferable over wide ranges in temperature and pressures and across chemical systems, and should be widely applicable in condensed phase simulation.

Anomalous nonadditive dispersion interactions in systems of three one-dimensional wires

The non-additive dispersion contribution to the binding energy of three one-dimensional (1D) wires is investigated using wires modelled by (i) chains of hydrogen atoms and (ii) homogeneous electron gases. We demonstrate that the non-additive dispersion contribution to the binding energy is significantly enhanced compared with that expected from Axilrod-Teller-Muto-type triple-dipole summations and follows a different power-law decay with separation. The triwire non-additive dispersion for 1D electron gases scales according to the power law $d^{-\beta}$, where $d$ is the wire separation, with exponents $\beta(r_s)$ smaller than 3 and slightly increasing with $r_s$ from 2.4 at $r_s = 1$ to 2.9 at $r_s=10$, where $r_s$ is the density parameter of the 1D electron gas. This is in good agreement with the exponent $\beta=3$ suggested by the leading-order charge-flow contribution to the triwire non-additivity, and is a significantly slower decay than the $\sim d^{-7}$ behaviour that would be expected from triple-dipole summations.

Higher-order electric multipole contributions to retarded non-additive three-body dispersion interaction energies between atoms: Equilateral triangle and collinear configurations

The theory of molecular quantum electrodynamics (QED) is used to calculate higher electric multipole contributions to the dispersion energy shift between three atoms or molecules arranged in a straight line or in an equilateral triangle configuration. As in two-body potentials, three-body dispersion interactions are viewed in the QED formalism to arise from exchange of virtual photons between coupled pairs of particles. By employing an interaction Hamiltonian that is quadratic in the electric displacement field means that third-order perturbation theory can be used to yield the energy shift for a particular combination of electric multipole polarizable species, with only six time-ordered diagrams needing to be summed over. Specific potentials evaluated include dipole-dipole-quadrupole (DDQ), dipole-quadrupole-quadrupole (DQQ), and dipole-dipole-octupole (DDO) terms. For the geometries of interest, near-zone limiting forms are found to exhibit an R(-11) dependence on separation distance for the DDQ interaction, and an R(-13) behaviour for DQQ and DDO shifts, agreeing with an earlier semi-classical computation. Retardation weakens the potential in each case by R(-1) in the far-zone. It is found that by decomposing the octupole moment into its irreducible components of weights-1 and -3 that the former contribution to the DDO potential may be taken to be a higher-order correction to the leading triple dipole energy shift.

Energy benchmarks for water clusters and ice structures from an embedded many-body expansion

We show how an embedded many-body expansion (EMBE) can be used to calculate accurate ab initio energies of water clusters and ice structures using wavefunction-based methods. We use the EMBE described recently by Bygrave et al. [J. Chem. Phys. 137, 164102 (2012)], in which the terms in the expansion are obtained from calculations on monomers, dimers, etc., acted on by an approximate representation of the embedding field due to all other molecules in the system, this field being a sum of Coulomb and exchange-repulsion fields. Our strategy is to separate the total energy of the system into Hartree-Fock and correlation parts, using the EMBE only for the correlation energy, with the Hartree-Fock energy calculated using standard molecular quantum chemistry for clusters and plane-wave methods for crystals. Our tests on a range of different water clusters up to the 16-mer show that for the second-order Møller-Plesset (MP2) method the EMBE truncated at 2-body level reproduces to better than 0.1 mE(h)/monomer the correlation energy from standard methods. The use of EMBE for computing coupled-cluster energies of clusters is also discussed. For the ice structures Ih, II, and VIII, we find that MP2 energies near the complete basis-set limit reproduce very well the experimental values of the absolute and relative binding energies, but that the use of coupled-cluster methods for many-body correlation (non-additive dispersion) is essential for a full description. Possible future applications of the EMBE approach are suggested.

Many‐Body Dispersion Interactions in Molecular Crystal Polymorphism

Polymorphs of molecular crystals are often very close in energy, yet they may possess very different physical and chemical properties. The understanding of polymorphism is therefore of great importance for a variety of applications, ranging from drug design to nonlinear optics and hydrogen storage. While the crystal structure prediction blind tests conducted by the Cambridge Crystallographic Data Centre have shown steady progress toward reliable structure prediction for molecular crystals, several challenges remain, including molecular salts, hydrates, and flexible molecules with several stable conformers. The ability to identify and rank all of the relevant polymorphs of a given molecular crystal hinges on an accurate description of their relative energetic stability. Hence, a first-principles quantum mechanical method that can attain the required accuracy of around 0.1–0.2 kcalmol 1 would clearly be an indispensable tool for polymorph prediction. In this work, we show that accounting for the nonadditive many-body dispersion (MBD) energy beyond the standard pairwise approximation is crucial for the correct qualitative and quantitative description of polymorphism in molecular crystals. We demonstrate this through three fundamental and stringent benchmark examples: glycine, oxalic acid, and tetrolic acid. These systems represent a broad class of molecular crystals, comprising hydrogenbonded (H-bonded) networks of amino acids and carboxylic acids. Among the first-principles methods, density functional theory (DFT) is the most widely used approach in the study of polymorphism in molecular crystals. However, most common exchange-correlation functionals (including hybrid functionals) are based on semi-local electron correlation, and thereby fail to capture the contribution of dispersion interactions to the stability of molecular crystals. These ubiquitous noncovalent interactions are quantum mechanical in nature and correspond to the multipole moments induced in response to instantaneous fluctuations in the electron density. To incorporate these long-range electron correlation effects within DFT, significant progress has been made by using the standard C6/R 6 pairwise additive expression for the dispersion energy. Indeed, DFT with pairwise dispersion terms can yield accurate results when the energy differences between molecular crystal polymorphs are sufficiently large. Notably, Neumann et al. have achieved the highest success rate in the last two blind tests using such methods. However, these pairwise dispersion approaches, even when used in conjunction with state-of-the-art functionals, are still unable to reach the level of accuracy required to describe polymorphism in many relevant molecular crystals, including glycine and oxalic acid. Recently, a novel and efficient method for describing the many-body dispersion (MBD) energy has been developed, building upon the Tkatchenko–Scheffler (TS) pairwise method. Within the TS approach, the effective dispersion coefficients (C6) are calculated from the DFTelectron density, hence the effect of the local environment of an atom in a molecule is accurately accounted for by construction. The MBD method presents a two-fold improvement over the TS approach by including: 1) the long-range electrodynamic screening through the self-consistent solution of the dipole– dipole electric-field coupling equations for the effective polarizability, and 2) the non-pairwise-additive many-body dispersion energy to infinite order through diagonalization of the Hamiltonian corresponding to a system of coupled fluctuating dipoles. The inclusion of the MBD energy in DFT leads to a significant improvement in the binding energies between organic molecules, and for the cohesion of the benzene and oligoacene molecular crystals. The MBD energy, like the TS energy, can be added to any DFT functional, requiring only the adjustment of a single rangeseparation parameter per functional. [*] N. Marom, J. R. Chelikowsky Center for Computational Materials Institute for Computational Engineering and Sciences The University of Texas at Austin Austin, TX 78712 (USA) E-mail: noa@ices.utexas.edu

Can nonadditive dispersion forces explain chain formation of nanoparticles?

We study to what extent dielectric nanoparticles prefer to self-assemble into linear chains or into more compact structures. To calculate the Van der Waals (VdW) attraction between the clusters we use the Coupled Dipole Method (CDM), which treats each atom in the nanoparticle as an inducible oscillating point dipole. The VdW attraction then results from the full many-body interactions between the dipoles. For non-capped nanoparticles, we calculate in which configuration the VdW attraction is maximal. We find that in virtually all cases we studied, many-body effects only result in local potential minima at the linear configuration, as opposed to global ones, and that these metastable minima are in most cases rather shallow compared to the thermal energy. In this work, we also compare the CDM results with those from Hamaker-de Boer and Axilrod-Teller theory to investigate the influence of the many-body effects and the accuracy of these two approximate methods.

The long-range non-additive three-body dispersion interactions for the rare gases, alkali, and alkaline-earth atoms

The long-range non-additive three-body dispersion interaction coefficients Z(111), Z(112), Z(113), and Z(122) are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term Z(111) arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms Z(112), Z(113), and Z(122) arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four Z coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.

First principles predictions of thermophysical properties of refrigerant mixtures

We present pair potentials for fluorinated methanes and their dimers with CO(2) based on ab initio potential energy surfaces. These potentials reproduce the experimental second virial coefficients of the pure fluorinated methanes and their mixtures with CO(2) without adjustment. Ab initio calculations on trimers are used to model the effects of nonadditive dispersion and induction. Simulations using these potentials reproduce the experimental phase-coexistence properties of CH(3)F within 10% over a wide range of temperatures. The phase coexistence curve of the mixture of CH(2)F(2) and CO(2) is reproduced with an error in the mole fractions of both phases of less than 0.1. The potentials described here are based entirely on ab initio calculations, with no empirical fits to improve the agreement with experiment.

Molecular aniline clusters. I. The electronic ground state

The aniline dimer and trimer are investigated in their electronic ground state. The potential energy surface was thoroughly searched for low lying minima by applying global optimizations on a model potential, which is recalibrated on-the-fly by ab initio calculations (spin-component-scaled LMP2) at relevant configurations. The most stable structure of the dimer corresponds to a head-to-tail arrangement with both aniline monomers being nearly equivalent. DFT-SAPT calculations reveal that the interaction energy is dominated by van der Waals dispersion, which is of comparable size as for the benzene dimer, but with a much larger total interaction energy than for the latter. The global minimum of the aniline trimer corresponds to a hydrogen bonding arrangement involving three directional NH-N hydrogen bonds, with the individual monomers being clearly distinguishable. Nonadditive three-body dispersion contributions appear to play a minor role for the trimer.

First principles models of the interactions of methane and carbon dioxide

We present ab initio calculations on the CH 4–CH 4 and CH 4–CO 2 dimer potential energy surfaces. We show that the fit to these surfaces is improved over the Lennard–Jones potential by changing the form of the repulsive wall. Ab initio calculations are also performed on trimers to evaluate the strength of nonadditive interactions. The experimental CH 4 phase properties are reproduced in simulations that include correction for nonadditive dispersion. The phase-coexistence curve of mixtures of CH 4 and CO 2 is also improved by including this nonadditive dispersion term.

Additive and nonadditive models of vapor-liquid equilibrium in CO2 from first principles

We describe quantum-chemical calculations on dimers of CO(2) and use the results to develop first-principles models for Gibbs ensemble Monte Carlo simulations of the phase coexistence curve. Isotropic pairwise potentials are insufficient to model the phase behavior and overestimate the binding in liquid CO(2) by 4 kJ mol(-1). An anisotropic treatment of the atoms in the pairwise potential reduces the strength of the binding by approximately 0.5 kJ mol(-1). We use ab initio calculations on trimers of CO(2) to assess the strength of nonadditive interactions. Including nonadditive dispersion in Gibbs ensemble simulations gives an enthalpy of vaporization within 1.5 kJ mol(-1) of the experimental value over a wide range of temperatures.

Dynamic localization and self-induced transparency in a two-dimensional superlattice with a nonadditive dispersion law

Electron dynamics and the nonlinear effects of electric conduction in a two-dimensional semiconductor superlattice with nonadditive miniband dispersion relations have been studied in the case of strong high-frequency electric fields applied to the superlattice. The conditions for dynamic electron localization and electromagnetic transparency in such superlattices have been revealed.

Three-body symmetry-adapted perturbation theory based on Kohn-Sham description of the monomers

An implementation of three-body symmetry-adapted perturbation theory (SAPT) of intermolecular interactions based on Kohn-Sham (KS) description of monomers with dispersion and induction nonadditive energies obtained from KS frequency-dependent density susceptibilities [SAPT(DFT)] is presented. Using the density-fitting approach, the nonadditive dispersion energy can be obtained with O(N(5)) scaling with respect to the system size, the best scaling among all available methods of evaluating this quantity. Numerical results are reported for the helium, argon, water, and benzene trimers. The nonadditive energy computed for these systems is in a good agreement with benchmarks. Some hybrid perturbational-supermolecular approaches are proposed that can provide--with only O(N(5)) scaling--nonadditive energies with accuracy comparable to more expensive supermolecular methods, such as the third-order Moller-Plesset perturbation theory. Such approaches can be used for studying nonadditive effects in systems larger than it is currently possible with supermolecular methods at a level high enough to capture all essential components of the three-body interaction energy.

Anisotropy of the conductivity and high-frequency characteristics of two-dimensional quantum superlattices in a strong electric field

The conductivity anisotropy and high-frequency properties of a two-dimensional superlattice (SL) with a non-additive electron dispersion law in the presence of a strong static electric field are studied theoretically. The main effort was a search for mechanisms allowing realization of the high-frequency negative differential conductivity in the range with positive static differential conductivity.