Herman-Kluk propagator

When we express the electronic DoF in Eq. (134) in terms of the new variables (135a) and (135b), perform the integration over Xo. and employ the complex notation introduced in Eq. (125), the Herman-Kluk propagator can be written in the following form [100] ... 

B. Semiclassical Herman-Kluk-Type Frozen Gaussian Wavepacket Propagation Method... 

Herman-Kluk method, direct molecular dynamics, Gaussian wavepacket propagation, 380—381 Hermite basis functions ... 

In the past two decades, a variety of semiclassical initial-value representations have been developed [105-111], which are equivalent within the semiclassical approximation (i.e., they solve the Schrodinger equation to first order in H), but differ in their accuracy and numerical performance. Most of the applications of initial-value representation methods in recent years have employed the Herman-Kluk (coherent-state) representation of the semiclassical propagator [105, 108, 187, 245, 252-255], which for a general n-dimensional system can be written as... 

Since the classical treatment has its restrictions and the applicability of the quantum OCT is limited to low-dimensional systems due to its formidable computational cost, it would be very desirable to incorporate the semiclassical method of wavepacket propagation like the Herman-Kluk method [20,21] into the OCT. Recently, semiclassical bichromatic coherent control has been demonstrated for a large molecule [22] by directly calculating the percent reactant as a function of laser parameters. This approach, however, is not an optimal control. 

Most of the applications of initial-value representation methods in recent years have employed the Herman-Kluk (coherent-state) representation of the semiclassical propagator,which for a general n-dimensional system can be written as... 

Herman M F, Kluk E and Davis H L 1986 Comparison of the propagation of semiclassical frozen Gaussian wave functions with quantum propagation for a highly excited enharmonic oscillator J. Chem. Phys. 84 326... 

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