Purpose of Module

This module aims at building a bridge between surface hopping (SH) [1] and more accurate methods (summarized with the term QUANTUM in the following) like multiconfigurational time dependent hartree (MCTDH) [2] and variational multiconfigurational gaussian (vMCG) [3] by exploiting both types of methods to overcome the shortcomings of the other in a hybrid approach called the SHARC-gym [4].

In the computational simulation of molecular movements and reactions various degrees of simplification have been introduced. From exact quantum dynamics available only to model a few degrees of freedom up to huge coarse-grained simulations capable to model whole proteins different levels of sophistication are available. Exact quantum dynamics and methods that will converge to the exact result are capable to shed insight into the most intricate of mechanisms at the heart of processes like photosynthesis. Unfortunately, the use of these methods is hampered by the unfavorable scaling of the simulation time with the size of the investigated system, limiting those approaches to a few dozen degrees of freedom. During the last decades, surface hopping has risen to be one of the most popular approaches for the simulation of events that involve more than a single electronic state and more than 10 atoms. This popularity is due to the ease of implementation of an SH algorithm and the possibility to plug in properties calculated using any of the most popular quantum chemistry packages. However, while the foundations of SH are easy to grasp, the ad hoc nature of SH means that there is never any guarantee that the simulated dynamics for a given system resembles results obtained via more elaborate methods that do not suffer from such crude approximations. Many of the shortcomings of SH have been highlighted in the scientific literature and remedies to overcome those have been proposed. This means that a whole range of various additional parameters and flavours of SH exist at present that are combined or used exclusively at the will of the user, hoping that these corrections will result in a more accurate modelling of the problem at hand.

The SHARC-gym allows the user to overcome this uncertainty by combining SH and QUANTUM methods in a hybrid fashion. The method follows an iterative procedure which is briefly stated here (see also Ref [4]):

  1. Hamiltonian loop: The aim of this loop is to select the most important degrees of freedom using SH so that a stripped-down Hamiltonian can be used in QUANTUM dynamics. For this,a full-dimensional SH dynamics is conducted which serves as a reference throughout this loop.From this full-D SH reference, the degrees of freedom (molecular vibrations, movement or even electronic states) that drive the observed dynamics can be determined. Using these essential degrees of freedom, a new model with reduced dimensionality is constructed and a new SH simulation calculated. If this new simulation still contains the most important features of the dynamics, even more degrees of freedom can be cut from the Hamiltonian and the SH dynamics is repeated. Once too many modes have been stripped away and the results diverge from the full-D SH reference, this process is stopped and the Hamiltonian that was used before this last dynamics is used in the subsequent Parameter loop.
  2. Parameter loop: In this loop, the reduced Hamiltonian is used in a QUANTUM simulation which serves as a QUANTUM reference throughout the loop. Now that a QUANTUM reference in this reduced Hamiltonian is available, the plethora of parameters available in SH can be validated for this system. If the initially used set of SH parameters was found to perform well, then the SHARC-gym is finished, resulting in a QUANTUM-validated set of parameters for the full-D SH dynamics and a reduced Hamiltonian that captures the essential dynamics of the much bigger system. If the best set of SH parameters diverges from the set that has been used to determine the reduced Hamiltonian, this new set of parameters has to be used again in the Hamiltonian loop and the process has to be repeated as a whole until the best agreement is found.

The hybrid approach of the SHARC-gym enables the use of more accurate QUANTUM methods on a subset of degrees of freedom of larger systems that - as a whole - cannot be treated using a QUANTUM method. This selection of important degrees of freedom is based solely on another dynamics result, eliminating the bias of selecting a set of reactive coordinates beforehand. The SH dynamics benefit from a validation of the chosen parameters against the QUANTUM reference. Furthermore, the SHARC-gym provides a huge amount of possible test systems to quantify the shortcomings of different parameters of SH or even SH as a whole as the SHARC-gym may result in a QUANTUM reference which disagree with all the different flavours of SH.The current implementation of the SHARC-gym uses the SH code SHARC [5] [6] and the set of QUANTUM methods implemented in QUANTICS [7].

[1]J.C. Tully, R. K. Preston: Trajectory surface hopping approach to nonadiabatic molecular collisions: The reaction of H+ with D2,J. Chem. Phys,55, 562 (1971).
[2]M.H. Beck,A. Jackle, G. A. Worth, H.-D. Meyer: The multiconfiguration time-dependent hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets,Phys. Rep.,324, 1 (2000).
[3]G.W. Richings, I. Polyak, K.E. Spinlove, G.A. Worth,I. Burghardt, B. La-sorne: Quantum dynamics simulations using Gaussian wavepackets: the vMCG method,Int Rev Phys Chem,34, 269 (2015).
[4](1, 2) S.Gomez, M. Heindl, A. SzabadiandL. Gonzalez: From Surface Hopping to Quantum Dynamics and Back. Finding Essential Electronic and Nuclear Degrees of Freedom and Optimal Surface Hopping Parameters,J. Phys. Chem. A,123, 8321 (2019).
[5]S.Mai, P. Marquetand, L. Gonzalez: Nonadiabatic Dynamics: The SHARC Approach, WIREs Comput. Mol. Sci.,8, e1370 (2018)
[6]S.Mai, M. Richter, M. Heindl, M. F. S. J. Menger, A. Atkins, M. Ruckenbauer, F. Plasser, L. M. Ibele, S. Kropf, M. Oppel, P. Marquetand, L. Gonzalez:SHARC2.1: Surface Hopping Including Arbitrary Couplings — Program Package for Non-Adiabatic Dynamics, (2019)
[7]G.A. Worth, K. Giri, G. W. Richings, M. H. Beck, A. J ̈ackle, H.-D. Meyer:QUANTICS, a suite of programs for molecular QUANTum dynamICS simulations, Version1.1 (2015)

Background Information

The SHARC-gym is currently available from a GitHub repository. It needs a working SHARC installation which is available for free from Future development will make the SHARC-gym available as a built-in in SHARC and will feature improved functionalities to easily use the QUANTICS set of quantum dynamics methods in combination with SHARC-gym.

Building and Testing

The SHARC-gym consists of a set of Python scripts written in Python 2.7. To build a working SHARC installation follow the corresponding installation guide (SHARC installation ).

A test example for the SHARC-gym is available on the SHARC-gym GitHub page. Entering the testcase directory, follow the instructions written in instructions.txt.

Source Code

The source code can be found in the SHARC-gym repository on GitHub.