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On the derivation of semiclassical expressions for quantum reaction rate constants in multidimensional systems
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Image of FIG. 1.
FIG. 1.

Metastable potential well () with a barrier of height and unstable frequency ıω at the barrier top. Dashed line indicates the barrier potential ().

Image of FIG. 2.
FIG. 2.

Euclidean action as a function of the first order Fourier coefficient at temperatures lower than the crossover temperature, β > β. Classical instanton solution corresponds to the minimum of at .

Image of FIG. 3.
FIG. 3.

WKB action () (a), and exp ( − () − β) (b) for an Eckart barrier of height and temperature β > β.

Image of FIG. 4.
FIG. 4.

Instantons (solid lines) on classical PES. Longer instantons correspond to lower temperatures. Solid circle denotes the saddle point of PES. Coordinates and correspond to the unstable and stable normal coordinates at the saddle point, respectively.

Image of FIG. 5.
FIG. 5.

Reaction probability as a function of total energy for the 2D Eckart barrier in Eq. (6.1) . The height of the barrier is 0.425 eV.

Image of FIG. 6.
FIG. 6.

Thermal rate constant as a function of inverse temperature for 2D Eckart barrier, Eq. (6.1) . Solid line represents exact quantum results of Eq. (6.2) ; dashed line: transition state theory results; open circles: semiclassical instanton expressions in Eqs. (2.18) and (2.19) ; and solid circles: the improved semiclassical instanton expressions (3.65) and (4.42) . Atomic units are used.


Generic image for table
Table I.

Logarithm of thermal rate constant log as a function of inverse temperature. HT and LT stand for high and low temperature expressions. Atomic units are used.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the derivation of semiclassical expressions for quantum reaction rate constants in multidimensional systems