Rafał Podeszwa

Intermolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations

Recently, three of us have proposed a method [Phys. Rev. Lett. 91, 33201 (2003)] for an accurate calculation of the dispersion energy utilizing frequency-dependent density susceptibilities of monomers obtained from time-dependent density-functional theory (DFT). In the present paper, we report numerical calculations for the helium, neon, water, and carbon dioxide dimers and show that for a wide range of intermonomer separations, including the van der Waals and short-range repulsion regions, the method provides dispersion energies with accuracies comparable to those that can be achieved using the current most sophisticated wave-function methods. If the dispersion energy is combined with (i) the electrostatic and first-order exchange interaction energies as defined in symmetry-adapted perturbation theory (SAPT) but computed using monomer Kohn-Sham (KS) determinants, and (ii) the induction energy computed using the coupled KS static response theory, (iii) the exchange-induction and exchange-dispersion energies computed using KS orbitals and orbital energies, the resulting method, denoted by SAPT(DFT), produces very accurate total interaction potentials. For the helium dimer, the only system with nearly exact benchmark values, SAPT(DFT) reproduces the interaction energy to within about 2% at the minimum and to a similar accuracy for all other distances ranging from the strongly repulsive to the asymptotic region. For the remaining systems investigated by us, the quality of the SAPT(DFT) interaction energies is so high that these energies may actually be more accurate than the best available results obtained with wave-function techniques. At the same time, SAPT(DFT) is much more computationally efficient than any method previously used for calculating the dispersion and other interaction energy components at this level of accuracy.

Density-Fitting Method in Symmetry-Adapted Perturbation Theory Based on Kohn-Sham Description of Monomers.

With the DF-SAPT(DFT) approach, RDX dimer can be calculated within a reasonable CPU time. This system is beyond the reach of correlated ab initio methods such as CCSD(T). SAPT(DFT) also provides an insight into physical picture of the interactions by decomposing the interaction energy into physical contributions. The analysis of the interaction energy components suggests that the dispersion interaction is very important, at least for some of the geometrical configurations of the RDX dimer and, therefore, methods that are unable to properly account for the dispersion interaction (such as the supermolecular DFT method with standard density functionals) cannot be expected to yield correct results. With the full potential energy surface of the RDX dimer which is under development, we are able to model the properties of this important energetic material

Report on the sixth blind test of organic crystal structure prediction methods

The results of the sixth blind test of organic crystal structure prediction methods are presented and discussed, highlighting progress for salts, hydrates and bulky flexible molecules, as well as on-going challenges.

Physical origins of interactions in dimers of polycyclic aromatic hydrocarbons

Dimers of several polycyclic aromatic hydrocarbons (PAHs): naphthalene, anthracene and pyrene have been investigated by symmetry-adapted perturbation theory based on the density functional description of the monomers [SAPT(DFT)]. Calculations have been performed for a number of radial cross-sections of selected stacked and T-shaped configurations. The interaction energies at the minima of stacked configurations of the benzene, naphthalene, anthracene and pyrene dimers increase with the number of rings, but -- in contrast to literature findings -- the rate of increase is somewhat irregular. In particular, the anthracene molecules interact slightly stronger than indicated by the number of rings and the pyrene molecules interact significantly weaker (although the latter do interact stronger than the former). These trends can be partly rationalized by the physical decomposition of the interaction energies given by SAPT. We find the stacked structures to be significantly more stable than the T-shaped ones, with the relative stability of the former structures increasing as the size of the system increases. This observation extends to the benzene dimer where the two structures are nearly isoenergetic and a tilted T-shaped structure actually becomes the global minimum. For the naphthalene dimer, the greater stability of the stacked configuration than of the T-shaped one is in disagreement with recent experiments observing only the latter structure. For the anthracene dimer, theory is in agreement with experiments.

Interactions of graphene sheets deduced from properties of polycyclic aromatic hydrocarbons

Intermolecular interactions of coronene dimer were studied with symmetry-adapted perturbation theory based on the density functional theory description of the monomers [SAPT(DFT)]. The most stable stacked structure was found to have the interaction energy of -17.45 kcal/mol, slightly lower than the structure analogous to graphite (-17.36 kcal/mol). The latter energy was extrapolated to the interaction energy of two graphene sheets. The effects of interactions of multiple layers were also estimated leading to the exfoliation energy of graphite equal to 45.3 meV per carbon atom. The SAPT(DFT)-based decomposition into physical quantities of the interaction energies shows the dominant effect of the dispersion interactions with a weaker electrostatic contribution due to penetration effects. The extrapolated physical picture of the graphene-graphene interaction is very similar to that of smaller stacked polycyclic aromatic hydrocarbons.

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.

Communication: Density functional theory overcomes the failure of predicting intermolecular interaction energies

Density-functional theory (DFT) revolutionized the ability of computational quantum mechanics to describe properties of matter and is by far the most often used method. However, all the standard variants of DFT fail to predict intermolecular interaction energies. In recent years, a number of ways to go around this problem has been proposed. We show that some of these approaches can reproduce interaction energies with median errors of only about 5% in the complete range of intermolecular configurations. Such errors are comparable to typical uncertainties of wave-function-based methods in practical applications. Thus, these DFT methods are expected to find broad applications in modelling of condensed phases and of biomolecules.

Crystal structure prediction for cyclotrimethylene trinitramine (RDX) from first principles

Crystal structure prediction and molecular dynamics methods were applied to the cyclotrimethylene trinitramine (RDX) crystal to explore the stability rankings of various polymorphs using a recently developed nonempirical potential energy function that describes the RDX dimer interactions. The energies of 500 high-density structures resulting from molecular packing were minimized and the 14 lowest-energy structures were subjected to isothermal-isostress molecular dynamics (NsT-MD) simulations. For both crystal structure prediction methods and molecular dynamics simulations, the lowest-energy polymorph corresponded to the experimental structure; furthermore, the lattice energy of this polymorph was lower than that of the other polymorphs by at least 1.1 kcal mol(-1). Crystal parameters and densities of the low-energy crystal produced by the NsT-MD simulations matched those of the experimental crystal to within 1% of density and cell edge lengths and 0.01 degrees of the cell angle. The arrangement of the molecules within the time-averaged unit cell were in equally outstanding agreement with experiment, with the largest deviation of the location of the molecular mass centers being less than 0.07 A and the largest deviation in molecular orientation being less than 2.8 degrees . NsT-MD simulations were also used to calculate crystallographic parameters as functions of temperature and pressure and the results were in a reasonable agreement with experiment.

Symmetry-adapted perturbation theory utilizing density functional description of monomers for high-spin open-shell complexes

We present an implementation of symmetry-adapted perturbation theory (SAPT) to interactions of high-spin open-shell monomers forming high-spin dimers. The monomer spin-orbitals used in the expressions for the electrostatic and exchange contributions to the interaction energy are obtained from density functional theory using a spin-restricted formulation of the open-shell Kohn-Sham (ROKS) method. The dispersion and induction energies are expressed through the density-density response functions predicted by the time-dependent ROKS theory. The method was applied to several systems: NH...He, CN...Ne, H2O...HO2, and NH...NH. It provides accuracy comparable to that of the best previously available methods such as the open-shell coupled-cluster method with single, double, and noniterative triple excitations, RCCSD(T), with a significantly reduced computational cost.

Potential energy surface for cyclotrimethylene trinitramine dimer from symmetry-adapted perturbation theory

We present a potential energy surface (PES) for the cyclotrimethylene trinitramine (RDX) dimer obtained using symmetry-adapted perturbation theory based on the Kohn-Sham density functional theory (DFT) description of the monomers [SAPT(DFT)]. More than a thousand dimer configurations were computed using an augmented double-zeta-quality basis set supplemented by bond functions. The ab initio interaction energies were used to obtain a six-dimensional analytic fit of the interaction PES. The geometries and energies of the minima on the PES have been found from the fit. The decomposition of the PES into physical components provided by the SAPT(DFT) method has been analyzed. The PES was then used in molecular dynamics simulations of the RDX crystal. The predicted crystal density is in an excellent agreement with experiment.