Second-Order Exchange-Dispersion Energy Based on a Multireference Description of Monomers

Abstract

We present a method for calculation of the second-order exchange-dispersion energy in the framework of the symmetry-adapted perturbation theory (SAPT) for weakly interacting monomers described with multiconfigurational wave functions. The proposed formalism is based on response properties obtained from extended random phase approximation (ERPA) equations and assumes the single-exchange (S 2 ) approximation. The approach is applicable to closed shell systems where static correlation cannot be neglected or to systems in nondegenerate excited states. We examine the new method in combination with either generalized valence bond perfect pairing (GVB) or complete active space self consistent field (CASSCF) description of the interacting monomers. For model multireference dimers in ground-states (H 2 · · · H 2 , Be· · · Be, He· · · H 2 ) exchange-dispersion energies are reproduced accurately. For the interaction between the excited hydrogen molecule and the helium atom we found unacceptably large errors which is attributed to the neglect of diagonal double excitations in the employed approximation to the linear response function.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers

“…This confirms that the CAS-based ERPA provides a better approximation for both transition density matrices and transition energies than when GVB density matrices are used. 46 , 47 Similar as in the first order, the polarization terms ( E ind (2) and E disp (2) ) from multiconfigurational SAPT compare favorably with SAPT(HF), but do not match the quality of SAPT(DFT) or SAPT2+(CCD) results. The discrepancy is more pronounced for the dispersion energy where the mean absolute errors from CCD+ST(CCD) and SAPT(DFT) calculations are equal to 2.2 and 2.9%, respectively, compared to 6.4% obtained with SAPT(CAS) and 9.9% at the SAPT(GVB) level of theory.…”

“…The 1-TRDM is defined as Note that for singlet states αα and ββ blocks are equal: γ p α q α ν = γ p β q β ν = γ pq ν . The general definition of 2-TRDM reads The 1-TRDM is expressed through the ERPA eigenvectors as 60 , 62 and the formula for the half of spin-summed 2-TRDM reads 47 …”

“…In ref ( 47 ), we have derived the density-matrix formula for the exchange–dispersion energy based on transition properties in the ERPA framework. The corresponding expression for the exchange–induction energy component takes the form The intermediates in eq 49 read and where the effective two-electron potential ( eq 45 ) in the matrix representation is (a φ p orbital may belong to either monomer X p = A or B ).…”

“…Recently, we have demonstrated that the uncoupled approximation in the ERPA framework combined with either CASSCF or GVB description of the monomers leads to a poor quality of the second-order dispersion energy. 46 , 47 A more accurate dispersion energy is obtained if the monomer response properties are expanded up to the first order in the coupling parameter, which we refer to as the semicoupled approximation. 46 The fully coupled ERPA scheme gives the best results for both dispersion and exchange–dispersion energies.…”

“…First steps in these directions have already been taken. Recently, we have devised multiconfigurational approaches for second-order dispersion 46 and exchange–dispersion 47 energy calculations. In this work, we use the same methodology to derive the second-order induction energy expressions and present formulas for the first-order electrostatic and exchange energies.…”