## PaPIM: A code for Quantum Time Correlation Functions

PaPIM code is a package to study the (quantum) properties of materials, and in particular time correlation functions, via the so-called mixed quantum-classical methods. In these schemes, quantum evolution is approximated by appropriately combining a set of classical trajectories for the system. Several quantum effects, for example, the possibility to find atoms in classically forbidden regions (tunneling), are reproduced at a manageable fraction of the cost of exact solutions.

The PaPIM module is a high-performance Fortran 90/95 MPI parallelized package for calculating system’s time-dependent observables. The code represents the current optimized assembly of the following modules:

- PIM_wd and PIM_qcfmodules (described in deliverable D3.3) for exact quantum sampling of the Wigner phase space probability distribution function and the corresponding calculation of specific quantum correlation functions, respectively;
- ClassMC module (described in D3.1) for Monte Carlo sampling of classical Maxwell-Boltzmann distribution and calculation of corresponding correlation-functions;
- PotMod module (described in D3.1), a library for model potentials and interfaces to external codes for potential energy calculations used by the sampling modules. This module is currently being enhanced with an interface to couple PaPIM with the CP2K package for electronic structure calculations;
- AuxMod module (described in D3.1) which provides a tailored set of MPI commands used for code parallelisation as well as input handling subroutines.

##### Practical application and exploitation of the code

The code has been extensively used for the calculation of the infrared absorption spectrum of CH_{5}^{+} in the gas phase. [1] This highly flexible molecule is considered a standard benchmark of approximate quantum methods, and has experimental interest, for example, in the context of green chemistry. The calculations performed with PaPIM were used to benchmark both the PIM method for time-correlation functions [2] and to realize the code performance analysis.

Through collaborations the code is also currently employed by several groups in their study of: properties of H_{2} molecules in clathrates (materials for capture and storage of hydrogen and CO_{2} in energy applications (University College Dublin); infrared characterisation of molecules, and from it understand the effect that the environment has on their chemical properties, in the atmosphere (Université Pierre et Marie Curie); hydrogen at extreme pressures in the context of geophysical applications (Ecole Normale Supérieure Paris); new potentials to efficiently characterise the chemical reactivity of small water clusters, again with possible applications on the physics of the atmosphere in reactions related to greenhouse effect (University of Bochum).

More description of the code and its systematic tests are reported in the E-CAM deliverable D3.3.

[1] O. Asvany, P. K. P, B. Redlich, I. Hegemann, S. Schlemmer, D. Marx Understanding the infrared spectrum of bare CH5+

*Science*

**309**(2005) 1219 [2] M. Monteferrante, S. Bonella, G. Ciccotti Quantum dynamical structure factor of liquid neon via a quasiclassical symmetrized method

*J. Chem. Phys.*

**138**(2013) 054118