Symmetric functions, such as Permutationally Invariant Polynomials (PIPs) and Fundamental Invariants (FIs), are effective and concise descriptors for incorporating permutation symmetry into neural network (NN) potential energy surface (PES) fitting. The traditional algorithm for generating such symmetric polynomials has a factorial time complexity of , where is the number of identical atoms, posing a significant challenge to applying symmetric polynomials as descriptors of NN PESs for larger systems, particularly with more than 10 atoms. Herein, we report a new algorithm which has only linear time complexity for identical atoms. It can tremendously accelerate generation process of symmetric polynomials for molecular systems. The proposed algorithm is based on graph connectivity analysis following the action of the generation set of molecular permutational group. For instance, in the case of calculating the invariant polynomials for a 15-atom molecule, such as tropolone, our algorithm is approximately 2 million times faster than the previous method. The efficiency of the new algorithm can be further enhanced with increasing molecular size and number of identical atoms, making the FI-NN approach feasible for systems with over 10 atoms and high symmetry demands.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1021/acs.jctc.4c01447 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
New Algorithms to Generate Permutationally Invariant Polynomials and Fundamental Invariants for Potential Energy Surface Fitting.
J Chem Theory Comput
January 2025
State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, People's Republic of China.
Symmetric functions, such as Permutationally Invariant Polynomials (PIPs) and Fundamental Invariants (FIs), are effective and concise descriptors for incorporating permutation symmetry into neural network (NN) potential energy surface (PES) fitting. The traditional algorithm for generating such symmetric polynomials has a factorial time complexity of , where is the number of identical atoms, posing a significant challenge to applying symmetric polynomials as descriptors of NN PESs for larger systems, particularly with more than 10 atoms. Herein, we report a new algorithm which has only linear time complexity for identical atoms.
View Article and Find Full Text PDFFull-dimensional accurate potential energy surface and dynamics for the unimolecular isomerization reaction CH3NC ⇌ CH3CN.
J Chem Phys
January 2025
School of Chemistry and Chemical Engineering and Chongqing Key Laboratory of Chemical Theory and Mechanism, Chongqing University, Chongqing 401331, China.
The reaction CH3NC ⇌ CH3CN, a model reaction for the study of unimolecular isomerization, is important in astronomy and atmospheric chemistry and has long been studied by numerous experiments and theories. In this work, we report the first full-dimensional accurate potential energy surface (PES) of this reaction by the permutation invariant polynomial-neural network method based on 30 974 points, whose energies are calculated at the CCSD(T)-F12a/AVTZ level. Then, ring polymer molecular dynamics is used to derive the free energy barrier of the reaction at the experimental temperature range of 472.
View Article and Find Full Text PDFResurgence of Chern-Simons Theory at the Trivial Flat Connection.
Commun Math Phys
December 2024
Institut des Hautes Études Scientifiques, Le Bois-Marie 35 rte de Chartres, 91440 Bures-sur-Yvette, France.
Some years ago, it was conjectured by the first author that the Chern-Simons perturbation theory of a 3-manifold at the trivial flat connection is a resurgent power series. We describe completely the resurgent structure of the above series (including the location of the singularities and their Stokes constants) in the case of a hyperbolic knot complement in terms of an extended square matrix (, )-series whose rows are indexed by the boundary parabolic -flat connections, including the trivial one. We use our extended matrix to describe the Stokes constants of the above series, to define explicitly their Borel transform and to identify it with state-integrals.
View Article and Find Full Text PDFNoise-induced entrainment of the circadian clock by thermoperiods in tomato: A computational approach.
J Theor Biol
February 2025
Department of Mathematics, Swinburne University of Technology, Hawthorn, Vic 3122, Australia. Electronic address:
The endogenous circadian rhythm (approximately 24 h) allows plants to adapt to daily light and temperature variations. Although the mechanism of photoperiod entrainment has been studied extensively, entrainment to diurnal temperature rhythms remains poorly understood. Here we investigate the stochastic entrainment of the circadian clock in the model crop tomato, subject to different thermoperiods.
View Article and Find Full Text PDFAutomated potential energy surface development and quasi-classical dynamics for the F- + SiH3I system.
J Chem Phys
November 2024
MTA-SZTE Lendület "Momentum" Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary.
Article Synopsis
- The study focuses on developing a potential energy surface (PES) for the F- + SiH3I system, aiming to understand its gas-phase reactions using quasi-classical dynamics simulations.
- The PES is created using an automated process with Robosurfer, which handles various computational tasks and enhances the fitting set using a robust electronic structure calculation method, addressing potential issues in convergence and accuracy.
- Simulations reveal high reactivity in the system, with two primary product types (SN2 and proton abstraction) being observed, along with various other reactions, and the study also explores dynamics through trajectory animations.
Want AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!