Fast Marching Method for Calculating Reactive Trajectories for Chemical Reactions

We present a method for computing classical Newtonian trajectories that minimize the path length or transit time from reactant to product. Our approach is based on a generalization of the fast-marching method, which allows us to construct the solution of the Hamilton-Jacobi equation for the action that optimizes the desired quantity. The resulting “reactive paths” can be interpreted as reaction coordinates but, unlike more conventional choices, they contain dynamical information about the chemical system of interest.     

Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem

The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations, or even exact expressions, for the Fukui function for electron attachment.     

An example where orbital relaxation is an important contribution to the Fukui function

Density-functional electronic structure calculations are performed on the molecules Cr2(hpp)4, Mo2(hpp)4, and W2(hpp)4, where the bridging ligand, hpp, is the anion of 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine. The calculated electronic densities are used to determine the Fukui functions. These molecules are unique not only in their ability as electron donors but also because orbital relaxation plays a decisive role in their reactivity. Unlike other examples in the literature, the reactivity of these compounds cannot be expressed solely in terms of the highest occupied and lowest unoccupied Kohn-Sham orbitals but only using the Fukui function, which includes the effects of orbital relaxation.     

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄−S−C₆H₄−S′−Au′₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.