Quantum Nuclear Dynamics: Application to Spin-Forbidden Transitions and Lifetime of Vibrational States
AuthorFedorov, Dmitry Fedorov
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The first part of this work is motivated by the field of ultracold physics, where the alkali and alkaline-earth diatomic molecules cooled down to ultralow temperatures (μK – nK range) can be prepared in specific quantum states and used for a variety of applications, such as quantum computing and ultracold chemistry. Theoretical predictions of the spectroscopic constants and the lifetimes of the vibrational quantum states of these molecules are needed for selecting the suitable molecules for novel ultracold experiments and applications. We investigate the spectroscopic properties and the vibrational state lifetimes of the following molecules XY (X, Y = Li, Na, K, Rb, Cs) and cations LiBe+, LiMg+, NaBe+, NaMg+. The spectroscopic constants, and the potential energy and dipole moment curves for the ground electronic states of these molecules and ions are computed with the coupled cluster with single, double, and triple excitations (CCSDT) and multireference configuration interaction (MRCI) electronic structure methods. The vibrational energies and wave functions are obtained from the numerical solution of the time-dependent nuclear Schrödinger equation using the B-spline method. The lifetimes of the ground and excited vibrational states are estimated from the Einstein coefficients describing the rates of the following processes: spontaneous emission, and absorption and emission stimulated by the black body radiation. We demonstrate that the ground vibrational states of the diatomic alkali molecules have much longer lifetimes than the excited states. In contrast, the lifetimes of the highly excited vibrational states of the alkali-alkaline-earth ions are similar, or even larger, than the ground state lifetimes. In the second part of this work, we introduce a new direct molecular dynamics method to study nonadiabatic dynamics of spin-forbidden reactions in which nonradiative transitions between the electronic states of different spin multiplicities occur due to the relativistic effect of spin-orbit coupling. In this molecular dynamics method based on the propagation of the Gaussian wave packets, the time-dependent Schrödinger equation for nuclear motion on multiple electronic states is solved using the ab initio multiple spawning (AIMS) technique. This new nonadiabatic molecular dynamics method is used to study the spin-forbidden transitions between the 1A1 and 3B1 electronic states of GeH2. The rate constants for the 3B1→1A1 and 1A1→3B1 transitions and the lifetime of the excited 3B1 state are calculated by fitting the excited state population decay with the first-order kinetic equation for a reversible unimolecular reaction. The performance of new AIMS direct molecular dynamics with different electronic structure methods, including the complete active space self-consistent field (CASSCF) and density functional theory (DFT) methods is analyzed. The rate constants and the excited state lifetime obtained with the AIMS molecular dynamics and the nonadiabatic transition state theory are compared.