Fast-Computing Potential Energy Surfaces from Specific Reaction Parameter Hamiltonians
Résumé
Obtaining the potential energy surface (PES) of a system is often a complex and tedious task. Normally it involves the calculation of thousands of ab initio energy points followed by a fitting process, which can be more or less difficult depending on both the topography of the PES and/or the analytical form used to fit it. For this reason, the development of tools that provide fast results but yet of acceptable accuracy is highly desirable.
In the present work we address this issue through the use of specific reaction parameters (SRP) for semi-empirical methods (as implemented in MOPAC [1]) that will best describe a reference set of ab initio points within a given accuracy. To this purpose, we define a target rms-like function that contains the weighted differences between energies and frequencies of the normal modes of the selected molecule. This function is then minimized by a series of codes/scripts that rely on the non-linear optimization NLopt library [2]. In our particular implementation, we use the Multi-Level Single-Linkage (MLSL) global optimization algorithm [3], coupled with the Bound Optimization BY Quadratic Approximation (BOBYQA) for a subsequent local optimization [4].
We have tested this methodology for the fit of the ground state PES of a series of systems of increasing dimensionality, namely: NO (1D), NO2 (3D) and HONO (6D). All single point ab initio calculations have been carried out at the Second-
Order Perturbation Theory of Complete Active Space Self-Consistent Field level (CASSCF//CASPT2), using the ANO-L basis sets. We have subsequently used these SRP-PES for the computation of vibrational eigenstates with a standard
approach and the Lanczos diagonalization as well as with the Multiconfigurational Time-Dependent Hartree (MCTDH) method [5]. Our preliminary results indicate that the optimized SRP constitute an efficient way of computing ground state PES for small-medium systems.
References:
[1] J. Stewart. Mopac2016. http://openmopac.net/
[2] J. S.G. Johnson. The NLopt nonlinear-optimization package. http://ab-initio.mit.edu/nlopt
[3] A.H.G. Kan and G.T. Timmer. Math. Program., 39, 57-78 (1987).
[4] M.J.D. Powell. Cambridge NA Report NA2009/06, University of Cambridge, pages 26-46 (2009).
[5] M.H. Beck, A. Jäckle, G.A. Worth, and H.D. Meyer. Phys. Rep., 324, 1-105 (2000).