Andreas Heßelmann

Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting: A new efficient method to study intermolecular interaction energies

The previously developed DFT-SAPT approach, which combines symmetry-adapted intermolecular perturbation theory (SAPT) with a density-functional theory (DFT) representation of the monomers, has been implemented by using density fitting of two-electron objects. This approach, termed DF-DFT-SAPT, scales with the fifth power of the molecular size and with the third power upon increase of the basis set size for a given dimer, thus drastically reducing the cost of the conventional DFT-SAPT method. The accuracy of the density fitting approximation has been tested for the ethyne dimer. It has been found that the errors in the interaction energies due to density fitting are below 10(-3) kcal/mol with suitable auxiliary basis sets and thus one or two orders of magnitude smaller than the errors due to the use of a limited atomic orbital basis set. An investigation of three prominent structures of the benzene dimer, namely, the T shaped, parallel displaced, and sandwich geometries, employing basis sets of up to augmented quadruple-zeta quality shows that DF-DFT-SAPT outperforms second-order Moller-Plesset theory (MP2) and gives total interaction energies which are close to the best estimates inferred from combining the results of MP2 and coupled-cluster theory with single, double, and perturbative triple excitations.

Intermolecular dispersion energies from time-dependent density functional theory

Abstract Non-expanded dispersion energies are calculated from time-dependent coupled-perturbed density functional theory (DFT) employing various non-hybrid and hybrid exchange-correlation potentials and suitable adiabatic local density approximations for the exchange-correlation kernel. Considering the dimer systems He 2 , Ne 2 , Ar 2 , NeAr, NeHF, ArHF, (H 2 ) 2 , (HF) 2 , and (H 2 O) 2 it is shown that the effects of intramonomer electron correlation on the dispersion energy are accurately reproduced with the PBE0AC exchange-correlation potential. In contrast, the uncoupled sum-over-states approximation yields inacceptable errors. These are mainly due to neglect of the Coulomb and exchange-correlation kernels and therefore, not substantially improved through an asymptotic correction of the exchange-correlation potential.

Intermolecular induction and exchange-induction energies from coupled-perturbed Kohn-Sham density functional theory

Abstract Coupled-perturbed Kohn–Sham theory has been used to calculate intermolecular induction and exchange-induction energies for the systems He 2 , Ne 2 , Ar 2 , NeAr, NeHF, ArHF, (H 2 ) 2 , (HF) 2 , and (H 2 O) 2 . The approach is potentially exact for the induction energy. For a systematic choice of exchange-correlation potentials the results of the coupled approach were compared with an uncoupled sum-over-states approximation and with many-body symmetry-adapted perturbation theory. The asymptotically corrected PBE0AC exchange-correlation potential is found to yield very accurate induction and fairly accurate exchange-induction energies.

The helium dimer potential from a combined density functional theory and symmetry-adapted perturbation theory approach using an exact exchange–correlation potential

Starting with an analytic representation of the electron density from a Hylleraas wavefunction we have obtained an analytic representation of the exchange–correlation potential of the helium atom. This, essentially exact, exchange–correlation potential has been employed to test a recently developed approach, named DFT-SAPT, which combines symmetry-adapted perturbation theory of intermolecular interaction energies with a density functional theory description of the interacting monomers. In DFT-SAPT all of the second-order contributions including the exchange corrections are determined from coupled-perturbed density functional theory. Comparison of the results for the helium dimer to previous high-quality supermolecular and intermolecular perturbation theory results demonstrates the success of the new approach.

Accurate Intermolecular Interaction Energies from a Combination of MP2 and TDDFT Response Theory

A new method is presented that improves the supermolecular second-order Møller-Plesset (MP2) method for dimer systems with strong dispersion interactions while preserving the generally good performance of MP2 for other types of intermolecular interactions, e.g., hydrogen-bonded systems. This is achieved by adding a correction term to the supermolecular MP2 energy that is determined using time-dependent density functional (TDDFT) response theory and that accounts for the error of the dispersion energy contained in the supermolecular MP2 method. It is shown for the S22 database set of noncovalent complexes and some potential energy curves of noncovalent bound aromatic dimers that the approach gives strong improvements over MP2 if compared to coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) reference energies. An efficient computer implementation of the method is presented that is shown to scale only with the fourth power of the system size and thus leads only to a slightly higher computational cost than that of the supermolecular MP2 itself.

Improved supermolecular second order Møller–Plesset intermolecular interaction energies using time-dependent density functional response theory

The supermolecular second order Moller-Plesset (MP2) intermolecular interaction energy is corrected by employing time-dependent density functional (TDDFT) response theory. This is done by replacing the uncoupled second order dispersion contribution contained in the supermolecular MP2 energy with the coupled dispersion energy obtained from the TDDFT approach. Preliminary results for the rare gas dimers He2, Ne2, and Ar2 and a few structures of the (HF)2 and (H2O)2 dimers show that the conventional MP2 interaction energies are considerably improved by this procedure if compared to coupled cluster singles doubles with perturbative triples [CCSD(T)] interaction energies. However, the quality of the interaction energies obtained in this way strongly depends on the exchange-correlation potential employed in the monomer calculations: It is shown that an exact exchange-only potential surprisingly often performs better than an asymptotically corrected hybrid exchange-correlation potential. Therefore the method proposed in this work is similar to the method by Cybulski and Lytle [J. Chem. Phys., 127, 141102 (2007)] which corrects the supermolecular MP2 energies with a scaled dispersion energy from time-dependent Hartree-Fock. The results in this work are also compared to the combination of density functional theory and intermolecular perturbation theory.

Numerically stable optimized effective potential method with balanced Gaussian basis sets

A solution to the long-standing problem of developing numerically stable optimized effective potential (OEP) methods based on Gaussian basis sets is presented by introducing an approach consisting of an exact exchange OEP method with an accompanying construction and balancing scheme for the involved auxiliary and orbital Gaussian basis sets that is numerically stable and that properly represents an exact exchange Kohn-Sham method. The method is a purely analytical method that does not require any numerical grid, scales like Hartree-Fock or B3LYP procedures, is straightforward to implement, and is easily generalized to take into account orbital-dependent density functionals other than the exact exchange considered in this work. Thus, the presented OEP approach opens the way to the development and application of novel orbital-dependent exchange-correlation functionals. It is shown that adequately taking into account the continuum part of the Kohn-Sham orbital spectrum is crucial for numerically stable Gaussian basis set OEP methods. Moreover, it is mandatory to employ orbital basis sets that are converged with respect to the used auxiliary basis representing the exchange potential. OEP calculations in the past often did not meet the latter requirement and therefore may have led to erroneously low total energies.

Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn–Sham density-functional theory and Hartree–Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn–Sham framework while for Hartree–Fock reference states this is not the case. This shows that Kohn–Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree–Fock reference states. Both, Kohn–Sham and Hartree–Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.

Random phase approximation correlation energies with exact Kohn–Sham exchange

The random phase approximation (RPA) correlation energy is expressed in terms of the exact local Kohn–Sham (KS) exchange potential and corresponding adiabatic and nonadiabatic exchange kernels for density-functional reference determinants. The approach naturally extends the RPA method in which, conventionally, only the Coulomb kernel is included. By comparison with the coupled cluster singles doubles with perturbative triples method it is shown for a set of small molecules that the new RPA method based on KS exchange yields correlation energies more accurate than RPA on the basis of Hartree–Fock exchange.

Intermolecular symmetry-adapted perturbation theory study of large organic complexes.

Binding energies for the complexes of the S12L database by Grimme [Chem. Eur. J. 18, 9955 (2012)] were calculated using intermolecular symmetry-adapted perturbation theory combined with a density-functional theory description of the interacting molecules. The individual interaction energy decompositions revealed no particular change in the stabilisation pattern as compared to smaller dimer systems at equilibrium structures. This demonstrates that, to some extent, the qualitative description of the interaction of small dimer systems may be extrapolated to larger systems, a method that is widely used in force-fields in which the total interaction energy is decomposed into atom-atom contributions. A comparison of the binding energies with accurate experimental reference values from Grimme, the latter including thermodynamic corrections from semiempirical calculations, has shown a fairly good agreement to within the error range of the reference binding energies.