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.
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Inelastic Charge‐Transfer Dynamics in Donor–Bridge–Acceptor Systems Using Optimal Modes
A time‐convolutionless master equation approach for computing state‐to‐state rates was developed in which the coupling between states depends on the nuclear coordinates. This approach incorporates a fully quantum‐mechanical treatment of both the nuclear and electronic degrees of freedom and recovers the well‐known Marcus expression in the semiclassical limit. A significant breakthrough was made in using this approach by tying it to a fully ab initio quantum chemical approach for determining the diabatic states and electron‐phonon coupling terms, allowing unprecedented accuracy and utility for computing state‐to‐state electronic transition rates. The Weinstein group at the University of Sheffield reported recently upon a series of donor‐bridge‐acceptor (DBA) molecular triads whose electron‐transfer (ET) pathways can be radically changed by infrared light excitation of specific intramolecular vibrations. Once the diabatic states and couplings are determined, the TCLME approach is used to compute the time‐correlation functions and state‐to‐state golden‐rule rates.
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- NSF-PAR ID:
- 10061101
- Date Published:
- Journal Name:
- Advances in chemical physics
- ISSN:
- 0065-2385
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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