The Chebyshev Scheme (CH)

Purpose of Module

This module implements the Chebyshev integration scheme for exact wavefunction propagation on the grid. This routine has been implemented and tested within the Quantics quantum dynamics package which is available on CCPForge. The purpose of the module is to be used in quantum dynamical propagation problems as described by Leforestier et al. [1Lef]

Background Information

Currently, the Chebyshev integration scheme resides within the Quantics software package available through CCPForge.

The module consists of a main routine, chebstep, which uses a separate routine bessjn to generate the real Bessel coefficients of integer order. Both are referenced and documented within the cheblib routine, and for further information on the Chebyshev integration scheme see Tal-Ezer et al. [1Tal]


A test example (test89.inp) is provided for the Chebyshev integration scheme and can be found in the directory ~/quantics/elk_inputs. This test works for Quantics Revision 787. The Quantics README file will help you to install the Quantics code. The test can be done through the following command

$ quantics test89.inp

A more detailed test documentation for Quantics code developers can be found in this link

Source Code

The source code for the Chebyshev propagator can be found within the Quantics software which can be downloaded via gitlab. You firstly need to make an account (at gitlab). The Quantics project has a private repository so you also need to be a member of the project to clone it into your computer, then type:

Within the Quantics program, explicit code for the Chebyshev routine is located in the file ~/quantics/source/lib/ode/cheblib.f90.


[1Lef]C. Leforestier, R. H. Bisseling, C. Cerjan, M. D. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, R. Kosloff J. Comp. Phys. 94 (1991) 59 DOI:
  1. Tal‐Ezer, R. Kosloff J. Chem. Phys. 81 (1984) 3967 DOI: 10.1063/1.448136