# Geometric phase effects in excited state dynamics through a conical intersection in large molecules: N-dimensional linear vibronic coupling model study.

@article{Li2017GeometricPE, title={Geometric phase effects in excited state dynamics through a conical intersection in large molecules: N-dimensional linear vibronic coupling model study.}, author={Jiaru Li and Lo{\"i}c Joubert-Doriol and Artur F. Izmaylov}, journal={The Journal of chemical physics}, year={2017}, volume={147 6}, pages={ 064106 } }

We investigate geometric phase (GP) effects in nonadiabatic transitions through a conical intersection (CI) in an N-dimensional linear vibronic coupling (ND-LVC) model. This model allows for the coordinate transformation encompassing all nonadiabatic effects within a two-dimensional (2D) subsystem, while the other N - 2 dimensions form a system of uncoupled harmonic oscillators identical for both electronic states and coupled bi-linearly with the subsystem coordinates. The 2D subsystem governs…

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## References

SHOWING 1-10 OF 56 REFERENCES

### Geometric phase effects in low-energy dynamics near conical intersections: a study of the multidimensional linear vibronic coupling model.

- PhysicsThe Journal of chemical physics
- 2013

In molecular systems containing conical intersections, a nontrivial geometric phase (GP) appears in the nuclear and electronic wave functions in the adiabatic representation of an N-dimensional linear vibronic coupling model.

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

- PhysicsThe Journal of chemical physics
- 2014

Using examples of the bis(methylene) adamantyl and butatriene cations and the pyrazine molecule, it is 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.

### Why Do Mixed Quantum-Classical Methods Describe Short-Time Dynamics through Conical Intersections So Well? Analysis of Geometric Phase Effects.

- PhysicsJournal of chemical theory and computation
- 2015

Using two-dimensional linear vibronic coupling models, this work unravels how the MQC methods can effectively mimic the most significant dynamical GP effects: compensation for repulsive diagonal second-order nonadiabatic couplings and transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.

### Investigation of geometric phase effects in photodissociation dynamics at a conical intersection

- Physics
- 2014

### Effect of the geometric phase on nuclear dynamics at a conical intersection: Extension of a recent topological approach from one to two coupled surfaces.

- PhysicsThe Journal of chemical physics
- 2008

The approach is exact, and uses simple topology to separate the wave function into contributions from Feynman paths that wind different numbers of times, and in different senses, around the conical intersection.

### Nonequilibrium Fermi golden rule for electronic transitions through conical intersections.

- Physics, ChemistryThe Journal of chemical physics
- 2011

A simple analytical expression for the time evolution of electronic populations at finite temperature is developed, which can be seen as a nonequilibrium generalization of the Fermi golden rule due to aNonequilibrium character of the initial photoinduced nuclear distribution.

### Diabolical conical intersections

- Physics
- 1996

In the Born-Oppenheimer approximation for molecular dynamics as generalized by Born and Huang, nuclei move on multiple potential-energy surfaces corresponding to different electronic states. These…

### Theoretical Study of Geometric Phase Effects in the Hydrogen-Exchange Reaction

- PhysicsScience
- 2005

A simple topological argument is used to extract reaction paths with different senses from a nuclear wave function that encircles a conical intersection, which causes the cancellation in geometric phase effects of the hydrogen exchange reaction.

### Studies of the Jahn-Teller effect .II. The dynamical problem

- PhysicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1958

This paper examines the vibronic energy levels of a symmetrical non-linear molecule in a spatially doubly degenerate electronic state which is split in first order by a doubly degenerate vibrational…

### Short-time dynamics through conical intersections in macrosystems. I. Theory: effective-mode formulation.

- PhysicsThe Journal of chemical physics
- 2006

The derivation of the effective Hamiltonian is presented, first introduced by Cederbaum et al. and analyzed in some detail, and several special cases and topological aspects are discussed.