Quantum Dynamics of Nonadiabatic Renner-Teller Effects in Atom + Diatom Collisions

Representation and conservation of angular momentum in the Born-Oppenheimer theory of polyatomic molecules

This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born-Oppenheimer parameter κ = (m/M)^1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born-Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born-Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space.

Neglected Importance of Anharmonicity in Quantifying the Renner-Teller Effect

Linear molecules in degenerate electronic states are influenced by the Renner-Teller (RT) effect. Currently the formula to quantify this vibronic interaction only considers the harmonic term. However, such a harmonic formula cannot well describe molecules that have double-well potential along the bending coordinate. In this work, we propose a new formula to quantify the RT effect by explicitly including the anharmonic term. A sign function and a delta function are additionally included to distinguish different scenarios. It is mathematically proved that the new formula is capable of differentiating different degrees of RT splitting. Representative molecules of different types are calculated. According to the new formula, molecules experiencing a weak RT effect have a positive parameter smaller than 1. For those experiencing a medium RT effect, the parameter will be negative. For others experiencing a large RT effect, the parameter will be larger than 1.

Electronically Nonadiabatic Effects on the Quantum Dynamics of the Ha + BeHb+ → Be+ + HaHb; Hb + BeHa+ Reactions

Nonadiabatic effects are ubiquitous and play an important role in many chemical processes. Here, the adiabatic and nonadiabatic quantum scattering calculations of the H + BeH⁺ reaction are performed using the time-dependent wave packet method based on an accurate diabatic potential energy matrix that includes the lowest two electronic states and their couplings. The resulting integral cross sections reveal that the nonadiabatic effect significantly inhibits the reactivity of the BeH⁺-depletion channel but enhances that of the H-exchange channel. The vibrational excitation is suppressed, but the translational excitation is promoted for the H₂ product in the BeH⁺-depletion channel when the nonadiabatic coupling is included. However, the nonadiabatic coupling has a mild effect on the H-exchange product-state distribution. When the nonadiabatic effect is considered, the differential cross sections of the H₂ product become less polarized because of the formation of an excited-state complex, whereas the corresponding results of the H-exchange channel only present an increase in the magnitude at the backward region.