Second-Order Differencing Scheme (SOD)

Purpose of Module

This module provides exact wavefunction propagation using the second-order differencing (SOD) integrator scheme to solve the time-dependent Schrödinger equation as described by Leforestier et al. [Lef] Within this scheme the time interval is determined through dividing \hbar by the eigenvalue of the Hamiltonian operator with the largest absolute value.

Background Information

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


A test example (test90.inp) is provided for the SOD 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 test90.inp

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

Source Code

The source code for the second-order differencing 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 SOD routine is located in file ~/quantics/source/lib/ode/sodlib.f90.


[Lef]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: