Light Particle Nonadiabatic Probability 2

Available identifiers

MaRDI QIDQ6775404

FSSH-2 probability for a nonadiabatic transition of the light particle(s) subsystem, induced by the heavy particle(s) dynamics

Description

Numerical problems due to the (near) divergence of the nonadiabatic coupling tensor elements are circumvented here, thus allowing much longer time steps than in Tully's traditional FSSH-1.

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Defining Formula: $\begin{array}{rlr}{P}_{mn}(t,t+\mathrm{\Delta }t)& \equiv & \frac{{\rho }_{mm}(t)-{\rho }_{mm}(t+\mathrm{\Delta }t)}{{\rho }_{mm}(t)}\\ c(t+\mathrm{\Delta }t)& =& \exp (-\mathrm{i}E\mathrm{\Delta }t/\hslash )\mathrm{\Gamma }(t,t+\mathrm{\Delta }t)c(t)\end{array}$

$E$ symbol represents Light Particle Eigen Energy

$\mathrm{\Delta }t$ symbol represents Time Step

$\hslash$ symbol represents Planck Constant

$\rho$ symbol represents Light Particle Density Matrix

$c$ symbol represents Light Particle Expansion Coefficient

$t$ symbol represents Time

$P$ symbol represents Light Particle Nonadiabatic Probability 2

$\mathrm{\Gamma }$ symbol represents Light Particle Time Overlap

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