Bogumil Jeziorski

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.

Variation-perturbation treatment of the hydrogen bond between water molecules

The hydrogen-bond energy of two water molecules has been calculated as a sum of the electrostatic, exchange, induction and dispersion contributions, neglecting the electron correlation within the free monomers. The last two contributions have been evaluated by applying a variation-perturbation procedure and making use of an extensive basis set of contracted gaussian functions. It has been shown that the sum of the electrostatic, exchange and induction energies is very close to the binding energy obtained within the SCF scheme. The dispersion contribution to the hydrogen-bond energy amounts to about 2 kcal/mole and causes substantial reduction of the equilibrium distance of the oxygen atoms. The minimum of the total energy is attained at 2·86 A and its depth is equal to 5·8 kcal/mole. These values are consistent with the experimental results.

Spin‐adapted multireference coupled‐cluster approach: Linear approximation for two closed‐shell‐type reference configurations

An explicit form of the spin‐adapted multireference coupled‐cluster formalism in the linear approximation is developed for the special case of a two‐dimensional model space involving only closed‐shell‐type configurations. The formalism is applicable to a number of quasidegenerate systems with two valence orbitals of distinct spatial symmetry and should serve as a convenient testing ground for the suitability of the multireference coupled‐cluster theory. General problems of the multireference coupled‐cluster approach and its relationship with the corresponding configuration interaction formalism are discussed as well as the problems pertaining to a practical implementation of this formalism.

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.

Valence universal exponential ansatz and the cluster structure of multireference configuration interaction wave function

A rigorous algebraic formulation of open‐shell coupled‐cluster theory is presented. This formulation yields explicit formulas exhibiting the relationship between open‐shell cluster amplitudes and linear coefficients of multireference CI wave functions. When the valence‐universal exponential ansatz is used, the CI coefficients of states with n valence electrons contribute to the n‐body and higher‐order cluster operators. The implications of cluster conditions, requiring that the four‐body cluster amplitudes be small, are investigated. It is shown that for valence‐universal theories these conditions lead to approximate relations involving CI coefficients for states of systems differing in the number of electrons. For Lindgren’s ansatz these relations are linear in the CI coefficients corresponding to states with the largest electron number. For the valence‐nonuniversal exponential ansatz of Jeziorski and Monkhorst, the cluster conditions do not mix wave functions for systems which differ in the number of el...

Symmetry‐adapted perturbation theory calculation of the Ar–H2 intermolecular potential energy surface

The many‐body symmetry adapted perturbation theory has been applied to compute the Ar–H2 potential energy surface. Large basis sets containing spdfgh‐symmetry orbitals optimized for intermolecular interactions have been used to achieve converged results. For a broad range of the configuration space the theoretical potential energy surface agrees to almost two significant digits with the empirical potential extracted from scattering and infrared spectroscopy data by Le Roy and Hutson. The minimum of our theoretical potential is em=−164.7 cal/mol and is reached at the linear geometry for the Ar–H2 distance Rm=6.79 bohr. These values agree very well with corresponding empirical results em=−161.9 cal/mol and Rm=6.82 bohr. For the first time such a quantitative agreement has been reached between theory and experiment for a van der Waals system that large. Despite such excellent agreement in the overall potential, the exponential and the inverse R components of it agree to only about 20%.

Symmetry-adapted perturbation theory for the calculation of Hartree-Fock interaction energies

A symmetry-adapted perturbation theory is formulated for the calculation of Hartree-Fock interaction energies of closed-shell dimers. The proposed scheme leads to a basis-set-independent interpretation of the Hartree-Fock interaction energy in terms of basic concepts of the theory of intermolecular forces: electrostatics, exchange and induction. Numerical results for different geometries of HE2, Ne2, He-C2H2, He-CO, Ar-HF, (HF)2 and (H2O)2 complexes show that in the region of the van der Waals minimum the proposed perturbation theory reproduces accurately the Hartree-Fock interaction energy. This fast convergence and relatively small computational cost of the proposed perturbation scheme suggest that this method is a practical alternative for the standard supermolecular approach.

Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium

The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound state, but is important for the thermophysical properties of helium. Such properties computed from our potential have uncertainties that are generally significantly smaller (sometimes by nearly two orders of magnitude) than those of the most accurate measurements and can be used to establish new metrology standards based on properties of low-density helium.

Many‐body theory of exchange effects in intermolecular interactions. Density matrix approach and applications to He–F−, He–HF, H2–HF, and Ar–H2 dimers

The first‐order exchange energy for the interactions of closed‐shell many‐electron systems is expanded as a perturbation series with respect to the Mo/ller–Plesset correlation potentials of the monomers. Explicit orbital formulas for the leading perturbation corrections are derived applying a suitable density matrix formalism. The numerical results obtained using the Mo/ller–Plesset perturbation expansion, as well as nonperturbative, coupled‐cluster type procedure, are presented for the interactions of He–F−, He–HF, H2–HF, and Ar–H2. It is shown that the correlation part of the first‐order exchange energy increases the uncorrelated results by 10% to 30% for the investigated range of configurations. The analysis of the total interaction energies for selected geometries of these systems shows that at the present level of theory the symmetry‐adapted perturbation approach correctly accounts for major intramonomer correlation effects and is capable to accurately reproduce the empirical potential energy surfaces.