A test of quantum transition state theory for a system with two degrees of freedom

Abstract

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Rate constants calculation with a simple mixed quantum/classical implementation of the flux-flux correlation function method

“…A similar behavior was reported for calculations performed with the quantum transition state theory and the mixed-Q/C theory by Pollak and co-worker. 18,19 The comparison between full-QM and mixed-Q/C results is very good for fast friction conditions. This agreement is remarkable considering that for all values of f, the frequency of the bath mode is higher than the frequency of the quantum mode.…”

“…Since then, it has been used to assess other approximate methods. [13][14][15][16][17][18][19][20] We have obtained results for a wide array of parameters for temperatures between 140 and 300 K. In all cases we carried out both full-quantum ͑full-QM͒ and mixed-Q/C computations. In this way we were able to perform a quantitative assessment of the mixed approach.…”

Quantum Smoluchowski equation: escape from a metastable state

“…We now discuss the classical and vacuum limits of quantum Smoluchowski equation (8). As mentioned earlier in the classical limit, D qo reduces to Einstein's classical diffusion coefficient k B T /γ.…”

“…where V n (x) is the n-th derivative of the the classical potential which gets modified by the quantum corrections. To solve quantum Smoluchowski equation (8) it is therefore necessary to calculate the corrections δ X2 (t) , δ X3 (t) , etc. To this end we return to operator Eq.…”

“…The theory of quantum Brownian motion is one of the major issues in physics and chemistry today. Its tremendous success in the treatment of various phenomena in quantum optics [1], quantum tunneling and coherence effects in condensed matter physics [2][3][4], activated processes in chemical physics [5][6][7][8][9][10] is now well-documented in the current literature. While the noise operator and density operator semigroup methods formed the core of development in quantum optics in sixties and seventies, real time path integrals attracted wide attention since eighties.…”