Effective valence shell Hamiltonian and potential curves of the oxygen molecule from quasidegenerate many‐body perturbation theory

Accurate calculations on the 22 electronic states and 54 spin-orbit states of the O2 molecule: potential energy curves, spectroscopic parameters and spin-orbit coupling

The potential energy curves (PECs) of 54 spin-orbit states generated from the 22 electronic states of O2 molecule are investigated for the first time for internuclear separations from about 0.1 to 1.0nm. Of the 22 electronic states, the X(3)Σg(-), A(')(3)Δu, A(3)Σu(+), B(3)Σu(-), C(3)Πg, a(1)Δg, b(1)Σg(+), c(1)Σu(-), d(1)Πg, f(1)Σu(+), 1(5)Πg, 1(3)Πu, 2(3)Σg(-), 1(5)Σu(-), 2(1)Σu(-) and 2(1)Δg are found to be bound, whereas the 1(5)Σg(+), 2(5)Σg(+), 1(1)Πu, 1(5)Δg, 1(5)Πu and 2(1)Πu are found to be repulsive ones. The B(3)Σu(-) and d(1)Πg states possess the double well. And the 1(3)Πu, C(3)Πg, A'(3)Δu, 1(5)Δg and 2(5)Σg(+) states are the inverted ones when the spin-orbit coupling is included. The PEC calculations are done by the complete active space self-consistent field (CASSCF) method, which is followed by the internally contracted multireference configuration interaction (icMRCI) approach with the Davidson correction. Core-valence correlation and scalar relativistic corrections are taken into account. The convergence of present calculations is evaluated with respect to the basis set and level of theory. The vibrational properties are discussed for the 1(5)Πg, 1(3)Πu, d(1)Πg and 1(5)Σu(-) states and for the second well of the B(3)Σu(-) state. The spin-orbit coupling effect is accounted for by the state interaction method with the Breit-Pauli Hamiltonian. The PECs of all the electronic states and spin-orbit states are extrapolated to the complete basis set limit. The spectroscopic parameters are obtained, and compared with available experimental and other theoretical results. Analyses demonstrate that the spectroscopic parameters reported here can be expected to be reliably predicted ones. The conclusion is obtained that the effect of spin-orbit coupling on the spectroscopic parameters are small almost for all the electronic states involved in this paper except for the 1(5)Σu(-), 1(5)Πg and 1(3)Πu.

Simplified diagrammatic expansion for effective operators

For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams, and evaluation rules from effective transition operators that give exact transition matrix elements between effective eigenvectors in reduced model space. By modifying these diagrams slightly and considering the linked diagrams for all the terms of the same order, we find that the evaluation rules can be made the same for both effective Hamiltonian and effective transition operator diagrams, and in many cases it is possible to combine many diagrams into one modified diagram. We give the rules to evaluate these modified diagrams and show their validity.