Transition state optimization of periodic systems using delocalized internal coordinates

In this work, we adapt our algorithm for relaxations of periodic systems (Bucko et al. in J Chem Phys 122: 124508, 2005) in delocalized internal coordinates of Baker et al. (J Chem Phys 105: 192, 1996) for the use in transition state geometry optimizations. The abilities of our algorithm are demonstrated on examples of relaxations of atomic positions and cell geometries of systems with and without additional geometric constraints that include transition states for reactions of molecules in the gas phase, reconnection of H atoms in the one-dimensional periodic chain of H-2 molecules, proton transfer in zeolite chabazite, partial desorption of crotonaldehyde from the MgO surface, and a pure affine shear deformation of Al. A simple approximate initial Hessian is suggested, in which only the matrix elements corresponding to atoms actively participating in reaction of interest are determined accurately at a DFT level, while remaining elements, typically related to inactive atoms and lattice vectors components, are defined on a basis of a simple empirical model. The calculations employing the approximate Hessian are shown to be more effective compared to simulations carried out with exact initial Hessian, in which all elements related to atomic positions are computed at the DFT level.