Low-rank sum-of-products finite-basis-representation (SOP-FBR) of potential energy surfaces

2020 ◽  
Vol 153 (23) ◽  
pp. 234110
Author(s):  
Ramón L. Panadés-Barrueta ◽  
Daniel Peláez
Keyword(s):  
Potential Energy ◽  
Potential Energy Surfaces ◽  
Finite Basis ◽  
Low Rank ◽  
Sum Of Products ◽  
Energy Surfaces ◽  
Finite Basis Representation

Fitting potential energy surfaces to sum-of-products form with neural networks using exponential neurons

2017 ◽  
Vol 16 (05) ◽  
pp. 1730001 ◽  
Author(s):  
Alex Brown ◽  
E. Pradhan
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Ab Initio ◽  
Potential Energy Surfaces ◽  
Quantum Dynamics ◽  
The Neural Network ◽  
Sum Of Products ◽  
High Level ◽  
Energy Surfaces ◽  
Dynamics Problems

In this paper, the use of the neural network (NN) method with exponential neurons for directly fitting ab initio data to generate potential energy surfaces (PESs) in sum-of-product form will be discussed. The utility of the approach will be highlighted using fits of CS2, HFCO, and HONO ground state PESs based upon high-level ab initio data. Using a generic interface between the neural network PES fitting, which is performed in MATLAB, and the Heidelberg multi-configuration time-dependent Hartree (MCTDH) software package, the PESs have been tested via comparison of vibrational energies to experimental measurements. The review demonstrates the potential of the PES fitting method, combined with MCTDH, to tackle high-dimensional quantum dynamics problems.

A ground state potential energy surface for HONO based on a neural network with exponential fitting functions

2017 ◽  
Vol 19 (33) ◽  
pp. 22272-22281 ◽  
Author(s):  
Ekadashi Pradhan ◽  
Alex Brown
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
Energy Surface ◽  
Exponential Fitting ◽  
Sum Of Products ◽  
State Potential ◽  
Vibrational Energies ◽  
Energy Surfaces

Using CCSD(T)-F12/cc-pVTZ-F12 and CCSD(T)/CBS ab initio energies, two different six-dimensional ground state potential energy surfaces for HONO have been fit in sum-of-products form using neural network exponential fitting functions and tested by computing vibrational energies with MCTDH.

VIBRATIONALLY AVERAGED POTENTIAL ENERGY SURFACES AND PREDICTED INFRARED SPECTRA OF THE He–18O13C18O AND He–16O13C16O COMPLEXES

2008 ◽  
Vol 07 (04) ◽  
pp. 707-717 ◽  
Author(s):  
YALI CUI ◽  
HONG RAN ◽  
DAIQIAN XIE
Keyword(s):  
Potential Energy ◽  
Normal Mode ◽  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Finite Basis ◽  
Lanczos Algorithm ◽  
Stretching Vibration ◽  
Representation Method ◽  
Energy Surfaces ◽  
Variable Representation

Vibrationally averaged potential energy surfaces for isotopic He–CO 2 complexes ( He –18 O 13 C 18 O and He –16 O 13 C 16 O ) are presented. Based on the latest ab initio potential of He –16 O 12 C 16 O (Ran H, Xie D, J Chem Phys128:124323, 2008.) including the Q3 normal mode for the v3 antisymmetric stretching vibration of the CO 2 molecule, the averaged potentials for both He –18 O 13 C 18 O and He –16 O 13 C 16 O are obtained by integrating the potential energy surfaces over the Q3 normal mode. The averaged potentials have T-shaped global minima and two equivalent linear local minima. The radial discrete variable representation/angular finite basis representation method and Lanczos algorithm are employed to calculate the related rovibrational energy levels. The calculated band origin shifts of He –18 O 13 C 18 O and He –16 O 13 C 16 O are 0.1066 and 0.0914 cm-1, respectively, which agree very well with the observed values of 0.1123 and 0.0929 cm-1. The calculated rovibrational transitions of He –18 O 13 C 18 O and He –16 O 13 C 16 O are also in very good agreement with the available experimental spectra.

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