A VARIATIONAL CENTROID DENSITY PROCEDURE FOR THE CALCULATION OF TRANSMISSION COEFFICIENTS FOR ASYMMETRIC BARRIERS AT LOW-TEMPERATURE

The low temperature behavior of the centroid density method of Voth, C handler, and Miller (VCM) [J. Chem. Phys. 91, 7749 (1989)] is investig ated for tunneling through a one-dimensional barrier. We find that the bottleneck for a quantum activated process as defined by VCM does not correspond to the classical bottleneck for the case of an asymmetric barrier. If the centroid density is constrained to be at the classical bottleneck for an asymmetric barrier,the centroid density method can give transmission coefficients that are too large by as much as five o rders of magnitude. We follow a variational procedure, as suggested by VCM, whereby the best transmission coefficient is found by varying th e position of the centroid until the minimum value for this transmissi on coefficient is obtained. This is a procedure that is readily genera lizable to multidimensional systems. We present calculations on severa l test systems which show that this variational procedure greatly enha nces the accuracy of the centroid density method compared to when the centroid is constrained to be at the barrier top. Furthermore, the rel ation of this procedure to the low temperature periodic orbit or ''ins tanton'' approach is discussed. (C) 1995 American Institute of Physics .