The same number of optimized parameters scheme for determining intermolecular interaction energies

Abstract

We propose the Same Number Of Optimized Parameters (SNOOP) scheme as an alternative to the counterpoise method for treating basis set superposition errors in calculations of intermolecular interaction energies. The key point of the SNOOP scheme is to enforce that the number of optimized wave function parameters for the noninteracting system is the same as for the interacting system. This ensures a delicate balance between the quality of the monomer and dimer finite basis set calculations. We compare the SNOOP scheme to the uncorrected and counterpoise schemes theoretically as well as numerically. Numerical results for second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster with single, double, and approximate triple excitations (CCSD(T)) show that the SNOOP scheme in general outperforms the uncorrected and counterpoise approaches. Furthermore, we show that SNOOP interaction energies calculated using a given basis set are of similar quality as those determined by basis set extrapolation of counterpoise-corrected results obtained at a similar computational cost.

The explicitly correlated same number of optimized parameters (SNOOP-F12) scheme for calculating intermolecular interaction energies

“…In Section II A we summarize the UC, CP, and SNOOP approaches, noting that a more detailed description of the SNOOP scheme is given in Ref. 29. In Section II B we describe how the UC, CP, and SNOOP interaction energies may be augmented with an F12 correction.…”

“…(3) is satisfied if the HF optimization for monomer A is carried out using a basis containing both the orbital space for A (spanned by O A ∪ V A ) and the virtual orbitals for B obtained in the UC calculations (V B ), and vice versa for monomer B. 29 The SNOOP interaction energy may thus be written as…”

“…The number of non-redundant wave function parameters used to describe the interacting AB dimer is larger (smaller) than the corresponding number of parameters for the noninteracting A + B system described at the UC (CP) level. As an attempt to impose a balanced description, we have suggested the SNOOP scheme, 29 where the number of wave function parameters for the noninteracting A + B system is the same as for the AB dimer. Thus, if the number of parameters is denoted P, the following set of inequalities hold:…”

“…It turns out that the number of wave function parameters is smaller/larger for the noninteracting A + B system than for the interacting AB system when the UC/CP approaches are used. In acknowledgment of this observation, we have recently proposed the Same Number Of Optimized Parameters (SNOOP) approach, 29 where it is imposed that the number of non-redundant Hartree-Fock (HF) optimization parameters is the same for the noninteracting A + B system as for the interacting AB system to ensure a balanced description of the interaction. This, in turn, implies that the SNOOP interaction energy by construction is sandwiched between the UC and CP interaction energies.…”

“…In fact, the BSIE of the total dimer energy may easily be an order of magnitude larger than the interaction energy itself when typical basis sets of double-or triple-ζ quality are employed. 29 Consequently, the determination of the interaction energy as the difference between the dimer energy and the monomer energies relies on a remarkable error cancellation. The main reason for the sizable BSIE is the inability of the wave function to represent the Coulomb cusp, 30 because conventional wave functions expressed in terms of Slater determinants do not satisfy Kato's cusp condition.…”