Using Kohn−Sham Orbitals in Symmetry-Adapted Perturbation Theory to Investigate Intermolecular Interactions

Abstract

This is the first reported use of a hybrid method involving density functional theory (DFT) and symmetry-adapted perturbation theory (SAPT) to calculate intermolecular interactions. This work was stimulated by the reported failures of supermolecular DFT calculations to adequately predict intermolecular (and interatomic) interactions, particularly of the van der Waals type. The goals are to develop a hybrid scheme that will calculate intermolecular interaction energies accurately and in a computationally efficient fashion, while including the benefits of the energy decomposition provided by SAPT. The computational savings result from replacing the costly perturbation theory treatment with DFT, which should include the intramolecular correlation effects on the intermolecular interaction energies. The accuracy of this new hybrid approach (labeled SAPT(DFT)) is evaluated by comparisons with higher level calculations. The test cases include He2, Ar2, Ar−H2, (H2O)2, (HF)2, CO2−CH3CN, and CO2-dimethylnitramine. The new approach shows mixed results concerning the accuracy of interaction energies. SAPT(DFT) correctly predicts all the qualitative trends in binding energies for all test cases. This is particularly encouraging in dimer systems dominated by dispersive interactions where supermolecular DFT fails to predict binding. In addition, the method achieves a drastic reduction (a factor of at least 100) in computational time over the higher level calculations often used to predict these forces. With respect to quantitative accuracy, this initial hybrid scheme, using the very popular exchange-correlation functional B3LYP, overestimates the second-order energy components (e.g., induction and dispersion terms) for all of the test cases, and subsequently overestimates the total interaction energy for all dimer systems except those heavily dominated by the electrotstatic interactions. The SAPT energy decomposition points to the use of DFT virtual orbital eigenvalues in the second-order perturbation terms as the likely cause for this error. These results are consistent with earlier work suggesting that DFT canonical virtual orbital energies obtained from commonly used functionals are less than optimal for use in such a perturbative scheme. The first-order interaction energy terms from the SAPT(DFT) are found to be generally more accurate than the second-order terms, and agree well with the benchmark values for dimers containing molecules with a permanent electric dipole moment. These first-order terms depend only upon the occupied MO eigenvectors, and hence are not affected by the inaccuracies in the Kohn−Sham DFT virtual orbital eigenvalues. These observations encourage future studies utilizing newly reported functionals, some of which have been developed to directly address problems with DFT virtual orbital energies and the asymptotic region of the electron density.

Perspective: Found in translation: Quantum chemical tools for grasping non-covalent interactions

“…12,13,58,134,135 Moreover, the approach can be systematically improved owing to the double-perturbation nature of its standard formulation. Currently, the coupled-cluster variant of SAPT has been shown to be very accurate for many systems 84 (and the much more computationally efficient SAPT(DFT) is not far behind), 83,136 although the treatment of multi-reference systems remains problematic. 137,138 Fortunately, in recent years an open-shell variant of SAPT has been developed, 139,140 which is an important prerequisite for a version capable of treating systems with a multi-reference character, including molecules reacting with one another and metallic systems.…”

Communication: Resolving the three-body contribution to the lattice energy of crystalline benzene: Benchmark results from coupled-cluster theory

“…4 Further estimates of three-body lattice energy contributions using symmetry-adapted perturbation theory based on densityfunctional descriptions of the monomers [SAPT(DFT)] [5][6][7][8][9][10][11][12] for crystalline benzene indicated that three-body effects contribute around 1.6 kcal mol −1 (or about 14% of the total lattice energy). 13 More recent studies 14,15 suggest that the majority of the three-body effects in crystalline benzene are due to three-body dispersion interactions, estimated to contribute 1.1 or 1.7 kcal mol −1 using the Axilrod-Teller-Muto expression (below).…”

New CO–CO interaction potential tested by rovibrational calculations

“…21,22 As an alternative to treating intramonomer electron correlation through many-body perturbation theory it has been proposed to combine SAPT with a relatively inexpensive description of the monomers through density functional theory ͑DFT͒. 23,24 Such a combined DFT-SAPT scheme is well founded for the first-order Coulomb and the second-order induction and dispersion energy contributions, which are potentially exact if ͑time-dependent͒ coupled-perturbed KohnSham DFT is utilized to calculate the monomer response densities, and provided that the exact exchange-correlation potential ͑xc-potential͒ and the exact exchange-correlation kernel ͑xc-kernel͒ are known. 24 By contrast, the intermolecular exchange corrections to the first-and second-order contributions are not potentially exact and can only be approximated with DFT-SAPT.…”