Interpolation Methods for Molecular Potential Energy Surface Construction

Abstract

The concept of a potential energy surface (PES) is one of the most important concepts in modern chemistry. A PES represents the relationship between the chemical system’s energy and its geometry (i.e., atom positions) and can provide useful information about the system’s chemical properties and reactivity. Construction of accurate PESs with high-level theoretical methodologies, such as density functional theory, is still challenging due to a steep increase in the computational cost with the increase of the system size. Thus, over the past few decades, many different mathematical approaches have been applied to the problem of the cost-efficient PES construction. This article serves as a short overview of interpolative methods for the PES construction, including global polynomial interpolation, trigonometric interpolation, modified Shepard interpolation, interpolative moving least-squares, and the automated PES construction derived from these.

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

“…PESs is, of course, not limited to such applications, and their use and construction were the subjects of recent reviews focused on fitting, 4 interpolation methods, 5 and on the use of neural networks. 6 As the determination of molecular PESs has been a topic of much discussion for more than 90 years, this list is far from complete.…”

Performance Evaluation of DFTB1 and DFTB2 Methods in reference to the Crystal Structures and Molecular Energetics of Siloxaalkane Molecular Compass

“…For this convergence efficiency, the exceptional credit goes to the SCC type computing features of the DFTB2 which actually enables us to incorporate the electronic resonance effects and Mulliken atomic charges interactions into its self-consistent iterative procedures practically, and to derive the corresponding nuclear forces with significant accuracy promptly. But, some inconsistencies ( = 0.76 (DFTB1 + PBC),  = 0.78 (DFTB2 + PBC),  = 0.77 (DFTB2 + PBC + dispersion energy corrections) though are still observed in the Xray produced SiOSi bond angles ( = 0.88), they all lie in the satisfactory range in regard to the quantum mechanical approximations adopted to model the DFTB + in order to treat the partial ionic and double bond characters as present in Si−O−Si linkages, and to address the related long range nonbonding interactions [39]. Similarly, unlike in non-crystalline molecular condition (subsection 3.1.1), the Xray derived bond length datasets for the concerned heteroatomic CSi bond spinaxis are very accurately reproduced by the both DFTB2 and DFTB1 under PBC with and without "dispersion energy corrections".…”

Portable Models for Entropy Effects on Kinetic Selectivity

“…In these cases, one sometimes constrains other degrees of freedom, but that of course introduces other approximations of which one must be conscious when interpreting results. Methods involving interpolation between well-chosen points on PESs have shown promise, but these can be prohibitively expensive if extensive coverage of a PES is desired …”