Direct and efficient discretization of a harmonic bath
The parameters of a harmonic bath and its coupling to the system of interest are often specified in terms of a spectral density function. In order to treat the bath by classical trajectory methods, it is important to discretize the bath into modes of different frequencies and coupling values. This is frequently achieved by choosing the frequencies on a regular grid with a fixed spacing. We have shown that a more efficient discretization is achieved by partitioning the spectral density into modes that correspond to equal fractions of the reorganization energy. In the special case of the Ohmic spectral density, this approach gives rise to a logarithmic frequency grid. The procedure leads to faster convergence with respect to the number of discrete harmonic bath modes.
Further, we have developed a procedure for determining the parameters of the discrete bath directly from the classical time correlation function (which is often obtained through molecular dynamics calculations), avoiding numerical computation of the spectral density by means of a discrete Fourier transform. Convergence is obtained using a shorter time length of the response function, leading to significant computational savings.