Adaptive fitting of potential energy surfaces of small to medium-sized molecules in sum-of-product form: Application to vibrational spectroscopy

Abstract

A semi-automatic sampling and fitting procedure for generating sum-of-product (Born-Oppenheimer) potential energy surfaces based on a high-dimensional model representation is presented. The adaptive sampling procedure and subsequent fitting relies on energies only and can be used for re-fitting existing analytic potential energy surfaces in sum-of-product form or for direct fits from ab initio computa- tions. The method is tested by fitting ground electronic state potential energy surfaces for small to medium sized semi-rigid molecules, i.e., HFCO, HONO, and HCOOH, based upon ab initio computations at the CCSD(T)-F12/cc-pVTZ-F12 or MP2/aug-cc-pVTZ levels of theory. Vibrational eigenstates are computed using block improved relaxation in the Heidelberg MCTDH package and compared to available experimental and theoretical data. The new potential energy surfaces are compared to the best ones currently available for these molecules, in terms of accuracy, including of resulting vibrational states, required numbers of sampling points, and number of fitting parameters. The present procedure leads to compact expansions and scales well with the number of dimensions for simple potentials such as single or double wells.

Vibrational dynamics of formic acid and its dimer: FTIR and Raman jet spectroscopy and theory

“…Peaks in the 8 contour move closer together and the entire envelope shifts towards lower wavenumbers. Similarly for HCOOD, the simulated branches align very well with the observed maxima, 105 reinforcing the assignment of the two most intensive peaks to 0 and 2 . With 0 and 2 as anchor points, we can also determine the band centre in HCOOD, (1039.5 + 1023.5)∕2 = 1031.5 cm −1 .…”

“…[21, 22, 27-30, 98, 99] and Refs. [24,55,[100][101][102][103][104][105] where the formic acid monomer is of secondary interest or used as a benchmarking reference.…”

“…Since the high-resolution band centre of HCOOH must be rounded off to 1033 cm −1 , we shall round the HCOOD band centre to 1031 cm −1 . 105 The 8 band centre is estimated by adding the shift of the band contour (−2 cm −1 ) to the high-resolution band centre of HCOOH (1033.47 cm −1 ). From the ground state rotational constants in Ref.…”

On the vibrations of formic acid predicted from first principles

“…12 Whereas an ill-defined coordinate system can introduce artificial correlation, a well-choosen one may minimize the correlation between the different degrees of freedom. 13 The main focus of this section is not a to give a comprehensive review of available vibrational methods, for which already vast literature is available, 4,[14][15][16][17][18][19] but rather to give an overview of selected concepts and methods necessary for discussing the literature on formic acid, reviewed below. We also shall not discuss the computation of intensities, but emphasize the importance of the development of e.g.…”

“… 12 Whereas an ill-defined coordinate system can introduce artificial correlation, a well-choosen one may minimize the correlation between the different degrees of freedom. 13 …”