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

Abstract

The minimum energy structures, i.e., trans-HONO, cis-HONO, HNO, and OH + NO, as well as the corresponding transition states, i.e., TS, TS, and TS, on the ground state potential energy surface (PES) of HONO have been characterized at the CCSD(T)-F12/cc-pVTZ-F12 level of theory. Using the same level of theory, a six-dimensional (6D) PES, encompassing the trans- and cis-isomers as well as the associated transition state, is fit in a sum-of-products form using neural network exponential fitting functions. A second PES is developed based on ab initio data from CCSD(T) computations extrapolated to the complete basis set (CBS) limit. The PES fits, based on 90 neurons, are accurate (RMSEs ≈ 10 cm) up to 10 000 cm above the energy minimum. The PESs are validated by computing vibrational energies using block improved relaxation with the multi configuration time dependent Hartree (MCTDH) approach. The vibrational frequencies obtained on the PESs are compared to available experimental measurements, previous theoretical computations based on a CCSD(T)/cc-pVQZ(-g functions) PES, and anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory obtained using second-order vibrational perturbation theory. The results suggest that these are the best available PESs for HONO, and thus, should be suitable for a variety of dynamics studies, including quantum dynamics with MCTDH where the sum-of-products form can be exploited for computational efficiency.

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

“…In addition to the 1D and 2D grid data, geometries were selected randomly from within the space spanned by the 6D grid (ranges considered for each of the chosen coordinates). Preliminary investigation 74 into the use of 1D and 2D grids along normal mode coordinates shows no de¯nitive improvement in the quality of the PES; however, further testing remains to be carried out. However, the choices of geometries were restricted using an energy¯lter, 32,35,37 i.e.…”

“…Details on the basis functions chosen as well as size of the primitive grids, number of grid points, and, for HFCO and HONO, number of single particle functions, including those in combined modes, are provided in the original papers. 39,58,75,74 In this paper, the focus is on the details of the PES¯tting, as well as the quality of the PESs as assessed through the computed vibrational frequencies, as discussed in the following section.…”

“…For the NN-expnn PESs that have been developed based on direct¯ts to ab initio data by our group, 39,58,75,74 the initial interest has been in the computation of vibrational frequencies. As high quality experimental data sets of vibrational frequencies over broad spectral ranges are known for many molecules, comparison to this experimental data provides a stringent test of the quality of the PES (beyond RMSEs for the training and test data sets).…”

“…39 For the 6D vibrational problems of HFCO and HONO, block improved relaxation 94 was used to compute the vibrational state energies. 75,58,74 Improved relaxation 43,[94][95][96] was used to obtain wavefunctions and assign the vibrational states. Details on the basis functions chosen as well as size of the primitive grids, number of grid points, and, for HFCO and HONO, number of single particle functions, including those in combined modes, are provided in the original papers.…”

“…3, the utility of this speci¯c potential energy surface¯tting approach is exempli¯ed through discussion of the applications (drawn from our own work) to several speci¯c molecules: CS 2 , 39 HFCO, 75,58 and HONO. 74 Finally, a brief summary and potential future directions are outlined in Sec. 4.…”