Krzysztof Szalewicz

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.

Predictions of the Properties of Water from First Principles

A force field for water has been developed entirely from first principles, without any fitting to experimental data. It contains both pairwise and many-body interactions. This force field predicts the properties of the water dimer and of liquid water in excellent agreement with experiments, a previously elusive objective. Precise knowledge of the intermolecular interactions in water will facilitate a better understanding of this ubiquitous substance.

Many‐body symmetry‐adapted perturbation theory of intermolecular interactions. H2O and HF dimers

A many‐body version of the symmetry‐adapted perturbation theory is developed for a direct calculation of intermolecular potentials as a sum of the electrostatic, exchange, induction, and dispersion contributions. Since no multipole expansion is used, the obtained interaction energy components are properly dampened at short distance by the charge‐overlap (penetration) effects. The influence of the intramonomer correlation is accounted for by the perturbation expansion in terms of the Mo/ller–Plesset type fluctuation potentials WA and WB for the individual molecules. For the electrostatic and for the dispersion energy, the terms of the zeroth, first, and second order in WA+WB are considered. In this way, the leading three‐particle correlation contribution to the dispersion energy is taken into account. As a test of our method, we have performed calculations of the interaction energy for the water and hydrogen fluoride dimers. Both the geometry and the basis set dependence of the interaction energy component...

A theoretical study of the water dimer interaction

We have performed a study of the water dimer interaction using larger basis sets and higher levels of theory than have been previously applied to this system. For the minimum geometry we have used spdf basis sets containing up to 212 orbitals. Our most accurate SCF interaction energy for the minimum is −3.73±0.05 kcal/mol. We have shown that this energy can be reproduced to within 0.1 kcal/mol using much smaller basis sets containing proper (diffuse) exponents. Accounting for the basis set superposition error is shown to be essential. We computed the dispersion energy with neglect of the intramolecular correlation using basis sets of various sizes. The best value obtained in a large spdf basis set with exponents which optimize this quantity is −1.93 kcal/mol and it is expected to be accurate to 0.1 kcal/mol or better. Using some of these basis sets we have performed supermolecular many‐body perturbation theory (MBPT) and coupled‐cluster (CC) calculations including triple excitations. We have shown that if...

Intermolecular forces from asymptotically corrected density functional description of monomers

Abstract Symmetry-adapted perturbation theory based on Kohn–Sham determinants, SAPT(KS), was shown before to perform poorly for the electrostatic energy which is potentially exact in this approach. We demonstrate that some deficiencies of SAPT(KS) result from wrong asymptotics of exchange-correlation potentials. On applying an asymptotic correction, we were not only able to recover the electrostatics, but also the first-order exchange and second-order induction and exchange-induction energies fairly accurate. Dispersion is still reproduced poorly but can be computed reasonably accurately from the damped asymptotic expansion.

Helium dimer potential from symmetry-adapted perturbation theory calculations using large Gaussian geminal and orbital basis sets

The symmetry-adapted perturbation theory (SAPT) has been employed to calculate an accurate potential energy curve for the helium dimer. For major components of the interaction energy, saturated values have been obtained using extended Gaussian-type geminal bases. Some other, less significant components were computed using a large orbital basis and the standard set of SAPT codes. The remaining small fraction of the interaction energy has been obtained using a nonstandard SAPT program specific for two-electron monomers and the supermolecular full configuration interaction (FCI) calculations in a moderately large orbital basis. Accuracy of the interaction energy components has been carefully examined. The most accurate to date values of the electrostatic, exchange, induction, and dispersion energies are reported for distances from 3.0 to 7.0 bohr. After adding the retardation correction predicted by the Casimir theory, our new potential has been shown [A. R. Janzen and R. A. Aziz (submitted)] to recover the ...

Symmetry-adapted double-perturbation analysis of intramolecular correlation effects in weak intermolecular interactions

A general symmetry-adapted double-perturbation procedure for treating intramolecular or intra-atomic correlation in the theory of intermolecular forces is developed. The method was applied to the interaction of two helium atoms. The calculations were made employing the Moller-Plesset partition of atomic hamiltonians and using a large basis set of explicitly correlated gaussian wave functions. At the van der Waals minimum the total intra-atomic correlation contribution to the interaction energy amounts to -2·9 K and is mainly due to the change of the dispersion energy. The total interaction energy is equal to -10·3 K being in agreement with the latest experimental result of Burgmans, Farrar and Lee.

Symmetry‐adapted perturbation theory of intermolecular forces

Basic concepts and most recent developments of symmetry‐adapted perturbation theory (SAPT) are described. In particular, the methods that combine SAPT with density‐functional theory are discussed. It is explained how SAPT allows one to predict and understand the structure and properties of clusters and condensed phase. The broadest range of such predictions can be achieved by constructing potential energy surfaces from a set of SAPT interaction energies and using these surfaces in nuclear dynamics calculations.

New Born–Oppenheimer potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule

The Born–Oppenheimer potential energy curve for the electronic ground state of the hydrogen molecule has been computed for internuclear distances 0.2≤R≤12.0 bohr. At all R the energies are lower than any previously reported values. At the equilibrium distance the improvement is negligible; its largest value, 0.47 cm−1, has been obtained for R=2.4 bohr. Vibrational energies have been computed for all isotopic species using the new potential energy curve. For H2, HD, and D2 the recent nonadiabatic corrections of Wolniewicz have been included. The resulting dissociation energies of H2 and HD agree with the experimental values within the experimental error limits; for D2 the discrepancy amounts to 0.6±0.3 cm−1.

On the effectiveness of monomer‐, dimer‐, and bond‐centered basis functions in calculations of intermolecular interaction energies

A range of basis sets differing in the location of basis functions has been explored from the point of view of the effectiveness of calculating the electrostatic, induction, dispersion, and exchange components of intermolecular interaction energies. Possible location strategies range from monomer‐centered basis sets, through the dimer‐centered ones, to sets with functions centered at the intermolecular bond. It is shown that the most effective approach is to use the so‐called ‘‘monomer plus’’ basis sets containing, in addition to monomer‐centered functions and bond functions, a small number of functions centered on the interacting partner. Using such basis sets for He2 and (H2O)2 the best values to date have been obtained for several interaction energy components. The conclusions from this work are relevant also for supermolecular calculations of interaction energies.