A new module for constrained multi‐fragment geometry optimization in internal coordinates implemented in the MOLCAS package

Abstract

A parallel procedure for an effective optimization of relative position and orientation between two or more fragments has been implemented in the MOLCAS program package. By design, the procedure does not perturb the electronic structure of a system under the study. The original composite system is divided into frozen fragments and internal coordinates linking those fragments are the only optimized parameters. The procedure is capable to handle fully independent (no border atoms) fragments as well as fragments connected by covalent bonds. In the framework of the procedure, the optimization of relative position and orientation of the fragments are carried out in the internal "Z-matrix" coordinates using numerical derivatives. The total number of required single points energy evaluations scales with the number of fragments rather than with the total number of atoms in the system. The accuracy and the performance of the procedure have been studied by test calculations for a representative set of two- and three-fragment molecules with artificially distorted structures. The developed approach exhibits robust and smooth convergence to the reference optimal structures. As only a few internal coordinates are varied during the procedure, the proposed constrained fragment geometry optimization can be afforded even for high level ab initio methods like CCSD(T) and CASPT2. This capability has been demonstrated by applying the method to two larger cases, CCSD(T) and CASPT2 calculations on a positively charged benzene lithium complex and on the oxygen molecule interacting to iron porphyrin molecule, respectively.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table

“…In Ref. , we introduced a new procedure for numerical geometry optimization of frozen fragments, which is based on displacements of internal coordinates (M olcas module geo). In this approach, a partial Z‐matrix is constructed and it is used to define Cartesian coordinates, which correspond to displacements of internal coordinates.…”

Constrained numerical gradients and composite gradients: Practical tools for geometry optimization and potential energy surface navigation

“…The tests presented in this work show that, by performing this partial numerical differentiation, the accuracy of the final constrained optimization is not significantly affected. Comparison with a method with similar features shows a competitive performance based on the total number of energy evaluations and accuracy of the final result, while the present method is expected to have a better scaling as the number of fragments (or unconstrained degrees of freedom) increases.…”

“… Performance of the present constrained optimization method for various systems taken from Ref. (Set III). The numbers appearing in the figure legend refer to different values of the energy convergence criterion (in units of E h ).…”

“…Finally, in the case of Set III, starting structures for the constrained optimization were taken from Ref. to ease comparison with that work. We note that in this case, the deformation is generally larger than for the other benchmark sets.…”

“…[7][8][9][10] However, to the best of our knowledge, there has been no attempt to apply a similar reduction of dimensionality to the computation of numerical gradients. A recent method published by Vysotskiy et al [11] takes a similar approach, but instead of explicitly calculating the gradient it fits the PES on a local grid over the reduced dimensions.…”