Asymptotics of the exchange-splitting energy for a diatomic molecular ion from a volume-integral formula of symmetry-adapted perturbation theory

Abstract

The exchange-splitting energy J of the lowest gerade and ungerade states of the H 2 + molecular ion was calculated using a volume integral expression of symmetry-adapted perturbation theory and standard basis set techniques of quantum chemistry. The performance of the proposed expression was compared to the well-known surface-integral formula. Both formulas involve the primitive function, which we calculated employing either the Hirschfelder-Silbey perturbation theory or the conventional Rayleigh-Schrödinger perturbation theory (the polarization expansion). Our calculations show that very accurate values of J can be obtained using the proposed volume-integral formula. When the Hirschfelder-Silbey primitive function is used in both formulas the volume formula gives much more accurate results than the surface-integral expression. We also show that using the volume-integral formula with the primitive function approximated by Rayleigh-Schrödinger perturbation theory, one correctly obtains only the first four terms in the asymptotic expansion of the exchange-splitting energy.

Three states global fittings with improved long range: singlet and triplet states of H+3

“…where J = À(2/e)Re ÀR and is positive for the gerade state and negative fo the ungerade. This term takes into account the exchange splitting of the interaction energy at large interatomic distances, due to the approximation of this energy as a series of the inverse powers of R. [31][32][33][34] The second term of eqn (1) is the sum of the three body terms and the long range contributions. Each element of the V ABC matrix is expressed as…”

Long-range asymptotics of exchange energy in the hydrogen molecule

“…[4]. In comparison to analytic approaches for H + 2 [19][20][21][22], examination of asymptotic energy splitting in H 2 is substantially more challenging due to electron-electron correlation, and it is prone to mistakes, as made evident by the presence of conflicting results in the literature [14,15,17,18], compare Eqs. ( 6) and (7).…”

First-order symmetry-adapted perturbation theory for multiplet splittings

“…In the past few years, the exchange splitting of interaction energy has been studied for the H + 2 system by Gniewek and Jeziorski [40][41][42]. Although this is a single-electron system, its two lowest states are asymptotically degenerate and correspond to symmetric (g) and antisymmetric (u) combinations of atomic orbitals.…”