Abstract
The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.
Highlights
In the quantum description of molecular structure and dynamics, adiabatic approximations1–4 assume that the nuclei move infinitely slowly compared to electrons
The eigenfunctions are of the form ψenlec(r; q)ψvnib(q), where each electronic eigenfunction supports a complete set of vibrational eigenfunctions that depend only on the electronic state n and the vibrational coordinates q
Since the stabilization energy is much less than the vibrational frequency, this would be classified as a weak pseudo Jahn-Teller coupling
Summary
In the quantum description of molecular structure and dynamics, adiabatic approximations assume that the nuclei move infinitely slowly compared to electrons (or the electrons infinitely quickly with respect to nuclei). One may solve an electronic Schrodinger equation with a “clamped nuclei” Hamiltonian, which neglects the action of the nuclear kinetic energy operator on the electronic wavefunction, and may use each coordinate-dependent energy eigenvalue as the potential energy function in the vibrational Hamiltonian of the corresponding electronic eigenstate. In this approximation, the eigenfunctions are of the form ψenlec(r; q)ψvnib(q), where each electronic eigenfunction supports a complete set of vibrational eigenfunctions that depend only on the electronic state n and the vibrational coordinates q. One often useful semiclassical picture for the breakdown of the adiabatic approximation is of an electronic wavefunction which fails to “keep up” with changes in vibrational coordinates.
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