Code template
On this page an example of the CCS code 1 is presented. This is a template which has been used in many other projects as a starting point. For other projects modifications included new routines for the Hamiltonian and its derivatives as well as different algorithms for CS basis set sampling. The main driver is main.for.
The main input files are:
incn_nd.inp sets initial position of the wave packet and compression parameters of the basis set
grid_nd.inp sets the parameters of the basis set (its dimensionality, size, energy interval and limits on CS grid initial coordinates and momenta) The number of degrees of freedom (dimensionality) must also be set in the file arr_prm.cm
dynm_nd.inp sets parameters of propagation (time step, number of steps, etc)
The main output file is:
acf_fun.out is for the autocorrelation function.
The program also calls some LAPACK routines.
The input files and the file arr_prm.cm which sets the dimensionality of the system are provided in separate directories for 6D, 10D and 32D Henon-Heiles potential.
The program calculates autocorrelation function of the wave packet propagated in Henon-Heiles potential. The Figs.1a, 1b, 1c, 1d and Figs. 2a, 2b, 2c. 2d show the autocorrelation function for 6D and 10D potentials. Figs. 3a,3b present spectrum of the autocorrelation functions for 32D system. The results are similar to those obtained in our early (and not so efficient) CCS calculation D.V.Shalashilin and M.S.Child J.Chem.Phys. 115 5367 (2001) and in MCTDH calculation by M.Nest and H.-D Meyer in J.Chem.Phys. 117 10499 (2002).
In the present calculation the basis of CS is sampled from a Gaussian distribution biased to the center of propagating wave packet. The width of this distribution is not equal to the width of the propagating Coherent State. It is given by a compression parameter set in the input file incn_nd.inp. The compression depends on the size of the CS basis set. For a small basis zi compression parameter must be set bigger in order to provide an accurate representation of the propagating wave packet at initial time. The accuracy of representation can be checked by calculating the norm of the propagating wave packet z for this chosen basis. The compression is set such that the norm is close or exceeds 0.99. For 32D problem only 4 modes are initially excited. The rest is a bath. Compression factor for bath modes was substantially higher then for system modes.
Calculations required very small CS basis sets and therefore were very fast. For example 10D calculation reproduces well first and second recurrences with only 100 CS. Initial rapidly decaying part of the autocorrelation function is reproduced with the basis of only 10 CS. More details can be found in D.V.Shalashilin and M.S.Child J.Chem.Phys. 128 054102 (2008)