When do we need to account for the geometric phase in excited state dynamics ?

Abstract

We investigate the role of the geometric phase (GP) in an internal conversion process when the system changes its electronic state by passing through a conical intersection (CI). Local analysis of a two-dimensional linear vibronic coupling (LVC) model Hamiltonian near the CI shows that the role of the GP is twofold. First, it compensates for a repulsion created by the so-called diagonal Born-Oppenheimer correction (DBOC). Second, the GP enhances the non-adiabatic transition probability for a wave-packet part that experiences a central collision with the CI. To assess the significance of both GP contributions we propose two indicators that can be computed from parameters of electronic surfaces and initial conditions. To generalize our analysis to N-dimensional systems we introduce a reduction of a general N-dimensional LVC model to an effective 2D LVC model using a mode transformation that preserves short-time dynamics of the original N-dimensional model. Using examples of the bis(methylene) adamantyl and butatriene cations, and the pyrazine molecule we have demonstrated that their effective 2D models reproduce the short-time dynamics of the corresponding full dimensional models, and the introduced indicators are very reliable in assessing GP effects.

Cited by in corpus (6)

• Why do mixed quantum-classical methods describe short-time dynamics through conical intersections so well? Analysis of geometric phase effects
• An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry's phase and "magnetic" forces
• A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model
• Problem-free time-dependent variational principle for open quantum systems
• Geometric phase effects in excited state dynamics through a conical intersection in large molecules: N-dimensional linear vibronic coupling model study
• Geometry of quantum hydrodynamics in theoretical chemistry