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

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.