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 CH5+ in the gas phase.  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  and to realize the code performance analysis.
Through collaborations the code is also currently employed by several groups in their study of: properties of H2 molecules in clathrates (materials for capture and storage of hydrogen and CO2 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.
The PIM_wd module implements the exact quantum Wigner probability distribution function sampling algorithm of the Phase Integration Method , and is the main subroutine for the quantum correlation function calculations in the PaPIM code. The module samples the thermal Wigner density using a generalised Monte Carlo scheme for sampling phase space points. The scheme combines the Penalty  and Kennedy  algorithms to sample noisy probability densities. This is necessary because the estimator of the quantum thermal density is not known analytically but must be computed via a statistical average affected by uncertainty. The sampled points are the basis for the calculation of time-independent and time-dependent system observables.
The module was developed as the main component of the PaPIM code, but also as a standalone subroutine that can be easily implemented in other methods (e.g. the whole family of so-called linearised approximations of quantum dynamics) for which phase space sampling of the exact quantum Wigner probability distribution is required. Because the Phase Integration Method samples a set of independent phase space points, independent instances of the PIM_wd module can be run in parallel in order to parallelise the phase space sampling. In the PaPIM package, the parallelisation is accomplished using MPI, which has proved to provide good scalability of the PaPIM code. The module will also be adapted for HTC capabilities.
Practical application and exploitation of the code
The code has been extensively used for the calculation of the infrared absorption spectrum of CH5+ in the gas phase.  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.
This module is part of the modules in deliverable D3.3 which were developed during the E-CAM ESDW7.
In this report for Deliverable 3.3 of E-CAM , 6 software modules in quantum dynamics are presented. Four modules stem from some of the activities performed during the Extended Software Development Workshop (ESDW) held by E-CAM at University College Dublin in July 2017 and originate from input of E-CAM’s academic user base. The other two modules were developed following discussions with our industrial partner IBM, in the framework of E-CAM’s pilot project on Quantum Computing.
Following the order of presentation, the 6 modules are named: LocConQubit, OpenQubit, PaPIM, PIM_wd, PIM_qcf, Openmpbeads. They include code for generation of controlled pulses for qubits and for calculation of quantum time correlation functions and their documentation.
In this report, a short description is written for each module, followed by a link to the respective Merge-Request on theGitLab service of E-CAM. These merge requests contain detailed information about the code development, testing and documentation of the modules. A performance analysis for PaPIM, a package merging the functionality of several modules for quantum dynamics developed in E-CAM and structured to act as a high-performance container for future modules, is also presented. This analysis was performed by the E-CAM software group, in collaboration with the POP Center of Excellence for Computing Applications.
 S. Bonella, M. Mališ, A. O’Cais, and L. Liang, “D3.3.: Quantum dynamics e-cam modules ii,” Mar. 2018. [Online]. Available: https://doi.org/10.5281/zenodo.1210077.
Module ClassMC samples the system phase space using the classical Boltzmann distribution function and calculates the time correlation functions from the sampled initial conditions. For more information check the module documentation here.