Polyatomic molecular potential energy surfaces by interpolation in local internal coordinates

Abstract

We present a method for expressing a potential energy surface (PES) for polyatomic molecules as an interpolation of local Taylor expansions in internal coordinates. This approach extends and replaces an earlier method which was only directly applicable to molecules of no more than four atoms. In general, the local Taylor expansions are derived from ab initio quantum calculations. Here, the methodology is evaluated by comparison with an analytic surface for the reactions H+CH4⇌H2+CH3. Approximately 1000–1300 data points are required for an accurate 12-dimensional surface which describes both forward and backward reactions, at the energy studied.

Quasi-classical trajectory study of the dynamics of the Cl + CH4→ HCl + CH3 reaction

“…PESs that encompass all the degrees of freedom have, however, been reported, including hypersurfaces derived from fits to ab initio points of LEPS (London-Eyring-Polanyi-Sato) functions augmented by bending potential terms. 15,18,27 A first accurate, fully dimensional ab initio PES was generated by Castillo et al 20 using the iterative interpolation method of Collins and coworkers, [28][29][30][31] and was subsequently employed for QCT calculations. In this latter study, QCISD electronic structure calculations were carried out with an aug-cc-pVDZ basis set, and the scaling all correlations method 32,33 was used to correct inaccuracies of the applied level of theory to reduce the computed barrier height.…”

Molecular Potential Energy Surfaces by Interpolation

“…So, in this tradition, we choose a set of molecular configurations on such a reaction path as an initial data set to describe the PES via Eq. (8). Already, we have just about exhausted our intuition as to where data points should be located.…”

“…This problem has been discussed in detail elsewhere. [8,11,14] The relevant solution here is to choose an independent set of 3N-6 linear combinations of the Z i as internal coordinates at each data point Z(n). This can be achieved as follows.…”

Modified Shepard interpolation of gas-surface potential energy surfaces with strict plane group symmetry and translational periodicity

“…The representation of the gas-surface PES is similar in both spirit and implementation to the modified Shepard interpolation that has been used for some time for representing molecular [45][46][47][48][49][50] and gas-surface 16,44,[52][53][54][55][56][57] PESs. The PES is determined by the energies and the first and second order derivatives of the energy at a set of "data point" geometries.…”

“…Building on the success of modified Shepard interpolation for building the PESs for gas phase reactions in an algorithm often called Grow, [45][46][47][48][49][50][51] modified Shepard interpolation has been used to represent the PES in gas-surface reactions. 44,[52][53][54][55] This approach has several advantages, including being able to treat polyatomic adsorbates, simple and seamless treatment of reactive or nonreactive collisions, physisorption, chemisorption and surface catalysed reactions, and strict interpolation of known energies.…”