A knowledge of the mechanism associated with a chemical reaction, going from reactants to products, is of paramount importance in understanding chemical behavior. Computationally, it is desired to determine the lowest energy path along the reaction coordinate for the rearrangement of atoms when going from the reactants to the products. This is commonly referred to as the reaction minimum energy path (RMEP). The RMEP can consist of many maxima and minima. The maxima are first-order saddle points or transition states while the minima are stable intermediates (long- or short-lived) along the reaction coordinate. From this information, one can calculate the thermodynamic and kinetic data associated with the chemical reaction.
The determination of the RMEP for a chemical reaction can be a daunting computational problem even for the simplest of reactions. The Nudged Elastic Band (NEB) method provides a convenient computational tool for calculating the RMEP connecting a set of reactants and products. The NEB method is a two ended method requiring a reactant and product supermolecule. In calculating the RMEP, the NEB minimization process only requires the calculation of gradients (first derivatives of the energy with respect to displacement of the nuclei) making it a computationally inexpensive approach. We have interfaced the NEB code [published by Alfonso and Jordan, J Comp Chem 24 (2003) 990-996] to the quantum mechanical software packages Gaussian 2009, ACES II, ACES III, CFOUR and DMol3. We further modified the code to include variable spring constants, climbing image and the FIRE optimizer [Bitzek, Koskinen, Gahler, Moseler and Gumbsch, Phys Rev Letters 97 (2006) 170201(1-4)] in the NEB software package. The FIRE optimizer is well suited for minimizing the NEB forces. The Simplified Generalized Simulated Annealing (SGSA) procedure [Dall'Inga Junior, Silva, Mundim and Dardenne, Genetics and Molec. Biol., 27, (2004) 616-622] is used to search for the global minimum of the reactant and product supermolecules. We have interfaced the GSA with DMol3, Mopac93, Mopac2009 and Gaussian 2009. In our implementation of the GSA, the optimization search can be restricted to defined torsion angles, internal coordinates and Cartesian coordinates. The transition states are refined with the modified dimer method [Heyden, Bell and Keil, J Chem Phys 123 (2005) 224101(1-14)], which we have also interfaced to the above QM codes. The bonding characteristics of the generated molecular structures are studied using the atoms in molecules software InteGriTy [Katan, Rabiller, Guezo, Oison and Souhassou, J Appl Crsyt 36 (2003) 65-73] to generate molecular graphs. All graphics and animations involving molecules was rendered using PyMOL, courtesy of DeLano Scientific LLC, Palo Alto, California.