A study of interpolating moving least-squares method on fitting potential energy surface

Abstract

Interpolating moving least-squares method (IMLS) is a highly accurate fitting method. There are a lot of studies on how to use IMLS to fit potential energy surfaces (PESs). However, there are still only few IMLS-fitted PESs for 4-atom systems based on data calculated at electronic structure method. The purpose of the current study is to find more efficient ways to use IMLS to fit ab initio or DFT PES of 4-atom. Three methods have been investigated to fit the PES of CO[subscript 2] + O using points computed at B3LYP/3-21G level. Dawes et al. developed the dynamics-driven IMLS method by fitting HONO at the HF/cc-pVDZ level. [R. Dawes, A. F. Wagner and D. L. Thompson, J. Phys. Chem. A, 113, 4709 (2009).] In current study, the dynamics-driven IMLS method is used to fit the CO[subscript 2] + O PES for collision energy below 57.7 kcal/mol for 992 data points. There is good agreement between opacity functions at three collision energy below 57.7 kcal/mol calculated using classical trajectories with the IMLS potential and those from direct dynamics trajectories. Since ab initio or DFT calculation is only performed for the data point calculation, the method can be used to fit PES of highly accurate theoretical method only by changing the ab initio or DFT method. In the second method, grids of specified range of CO[subscript 2] + O PES are calculated. A new range is determined to include points below 70 kcal/mol. The RMS error of energy and gradients are 0.19 kcal/mol and 13 kcal/(mol [angstrom]) respectively with 528 data points selected from the range by random points. In the third method, an algorithm is developed to search for all the points below the cutoff energy 60 kcal/mol. The results show that the algorithm successfully finds the points below the cutoff energy. The algorithm is used to fit the points of energy below 60 kcal/mol. The points below 60 kcal/mol are fitted using 1287 DFT points. However, there are many DFT calculations required in the last two methods besides the data point calculation. Much more work is needed to develop these two methods in order to fit PES of highly accurate theoretical method.