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.

Problem-free time-dependent variational principle for open quantum systems

“…Numerical values of the parameters are taken from Ref. 29 for the twodimensional model of the bis(methylene) adamantyl radical cation: ω 1 = 7.743 × 10 −3 a.u., ω 2 = 6.680 × 10 −3 a.u., d = 5.289 × 10 −3 a.u., and c = 9.901 × 10 −4 a.u. The dissipative part is introduced through bilinear coupling of the system coordinates x α with coordinates of harmonic bath oscillators.…”

A scheme for a single molecule phase-shift gate in a solid matrix

“…This property is interesting not only from a fundamental viewpoint [2][3][4][5][6][7][8][9][10][11][12] but also for its applications. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] Since a quantum system is inevitably coupled to the environment, the investigation of geometric phases in open quantum systems has also attracted considerable attention. [7][8][9][10][11][12][28][29][30][31][32][33][34][35][36][37][38][39][40] The phase-shift gate as a quantum logic operator is an important element of quantum computation.…”

The adiabatic limit of the exact factorization of the electron-nuclear wave function

“…However, for a real electronic state ϕ BO R (r), A BO ν (R) identically vanishes, andε BO (R) contains the diagonal correction to the BO energy. 34,35 These corrections to the BO energy, being O(M −1 ν ), are often neglected. The purpose of Secs.…”

“…In Eq. (24) we consider the term on the right-hand-side, removing the explicit dependence on the units of momentum, i.e., √ M 0 e 0 , and we insert the expansion (34), to get…”