MSA

Monomial Symmetrization for Creating Permutationally Invariant Polynomials and Potential Energy Surface (PES) Fitting

MSA 2.0.1 https://github.com/szquchen/MSA-2.0/releases/tag/v2.0.1

The Software
MSA is software that produces polynomials and their gradient of a desired maximum order that are invariant with respect to permutations of like atoms. These are called permutationally invariant polynomials (PIPs).  Optionally these PIPs and gradients are used in linear regression to fit electronic energies and gradients given in standard format at nuclear configurations in Cartesian coordinates. There is an option to weight the energies and also to change the Morse range parameter.  Default values are in the file param.inp and they can be used as is, or changed in the interactive script shown in the video below. We suggest that the user experiment with both parameters to achieve an optimum precision of the fit.

A  data set for CH4 is provided as part of the download of MSA.zip folder. This is not needed if you are just generating PIPs.   Below is a sample:  no. of atoms, energy in hartree, atom label followed by cartesian coords in angstroms and cartesian components of grad (if inputed) in hartree/bohr blank otherwise. Based on the order of atoms the symmetry label is 4 1.  This indicates that the full permutation group of the 4 H atoms will be used.  A reduced symmetry, for example, 2 2 1 could also be used, but that is not done in this case.

5
-40.48132472
H -0.10095840 -0.41955010 -1.31205540 0.00475800 -0.00753200 0.00876200
H -0.33382290 -1.64227710 -0.08089010 0.00501000 -0.01045300 -0.00392400
H 0.27898620 0.01183520 0.37889600 0.00242100 0.01037400 0.00814600
H -1.41320490 -0.14046190 -0.03074290 -0.00415000 0.00917100 0.01147400
C -0.41724430 -0.55439810 -0.28616510 -0.00804000 -0.00155500 -0.02444600

A Short Video on Creating a PIP Basis and Fitting 
In the video we take you through the process of using this MSA software and provide an example for a fit of the H3O2– potential.4  We assume the MSA folder has been downloaded and unzipped. The driver is “msa.py”.   Note the default value of the Morse range parameter used in the fit in the video is 2 bohr.  A value of 3 bohr was used in ref. 4 and this gave smaller fitting root mean square errors. The wall clock time to generate the basis is about 2 minutes and also several minutes to do the fit.  This is on a single 2018 Intel. CoreTM i7-8750H processor.

What is Needed in Order to Run the Codes

  • For the PIP basis
  • C++ compiler. We used the GNU Compiler Collection on our Linux cluster (“GCC 4.4.7 20120313 (Red Hat 4.4.7-16)) in the example. Freely available.
  • Perl.  We used Perl v5.10.1 (*) built for x86_64-linux-thread-multi. Freely available.
  • Python. We used Python 2.6.6 and 3.8.5 and versions in between
  • For fitting
  • Fortran 90 compiler. We used the Intel® Fortran Compiler (“ifort 15.0.0 20140723”) in the example.  gfortran is also included as an option in the makefile.
  • The “dgelss” subroutine from LAPACK, which is embedded in Intel® Math Kernel Library (Intel® MKL). Freely available
  • Users have to provide the data set of electronic energies.

References About the MSA Software
1. Xie, Z., Bowman, J.M. Permutationally Invariant Polynomial Basis for Molecular Energy Surface Fitting via Monomial Symmetrization. J. Chem. Theory Comput. 2010, 6, 26-34.  Nandi, A. Qu, Chen, Bowman, J.M. Using Gradients in Permutationally Invariant Polynomial Potential Fitting: A Demonstration for CH4 Using as Few as 100 Configurations, J. Chem. Theory Comput. 2019, 15, 2826-2835. Please cite these as the primary references to the MSA software.

2. PL Houston, et al.,Permutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methods, J. Chem. Phys. 2022 156, 044120

3. PL Houston, C Qu, Q Yu, R Conte, A Nandi, JK Li, JM Bowman, PESPIP: Software to fit complex molecular and many-body potential energy surfaces with permutationally invariant polynomials,  J. Chem. Phys. 2023 158, 044109 .  This is about enhanced PIPs and fast grad evaluation using Mathematica notebooks.  This software can be downloaded from https://github.com/PaulLHouston/PESPIP

4.Assessing Permutationally Invariant Polynomial and Symmetric Gradient Domain Machine Learning Potential Energy Surfaces for H3O2–  Priyanka Pandey, Mrinal Arandhara, Paul L. Houston, Chen Qu, Riccardo Conte, Joel M. Bowman, and Sai G. Ramesh, J. Phys. Chem. A, 2024 128 , 3212-3219.

Contact Information
Joel Bowman: jmbowma at emory.edu

Funding
Funding from the National Science Foundation, Army Research Office and NASA is acknowledged.