Theoretical spectroscopy of the calcium dimer in the A 1Sigma(u)+, c3Pi(u), and a3Sigma(u)+ manifolds: an ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca(2) spectrum in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states.