## Second-Order Differencing Scheme

This module, SodLib, 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, J. Comp Phys, 94, 59-80, 1991. Within this scheme the time interval is determined through dividing hbar by the eigenvalue of the Hamiltonian operator with the largest absolute value. This routine has been implemented and tested as an added functionality within the Quantics software package available through CCPForge.

Quantics is a package to study chemical reactions of molecules whose main developer (G. Worth, University College London) is a member of E-CAM’s WP3 – Quantum Dynamics. It incorporates a variety of quantum dynamical methods joined by the fact that the state system is usually described via wavefunctions (containing the quantum analogue of the information given by positions and velocities for classical atoms). It is increasingly used by the computational chemistry community for scientific applications. Work is on-going in E-CAM to improve its scalability (see E-CAM deliverable D7.2 ) and add new functionalities in view of applications to study materials and light harvesting complexes.

**Module documentation can be found here, including a link to the source code.**

### Practical application and exploitation of the code

The module is currently being used in a Phd thesis and the results of this application will provide benchmarks for a model describing proton-transfer in a condensed phase system.