Geometry Optimizations and Transition State Searching

Prat-Resina X, JM Bofill, A Gonzalez-Lafont, JM Lluch (2004) Geometry optimization and transition state search in enzymes Different options in the microiterative method. Int. J. Quantum Chem 98 (4) 367-377... 

Transition state search algorithms rather climb up the potential energy surface, unlike geometry optimization routines where an energy minimum is searched for. The characterization of even a simple reaction potential surface may result in location of more than one transition structure, and is likely to require many more individual calculations than are necessary to obtain equilibrium geometries for either reactant or product. 

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

Kinds of Calculations. So far in this chapter, single-point, geometry optimization, and frequency calculations have been mentioned (Sections 15.11 and 15.13). Other important kinds of calculations are discussed in later sections (transition-state searches, reaction-path following, PES scans in Section 15.26 inclusion of solvation effects in Section 15.22). 

ADF enables geometry optimizations in Cartesian and internal coordinates. An initial Hessian estimate speeds up the optimizations. Various constraints can be imposed. Transition-state searches, intrinsic reaction coordinates, and linear transit calculations are available to further analyze the energy path from reactants, via the transition state, to the final products. Finite difference and analytic second derivatives " yield IR frequencies and Hessians. These Hessians are helpful in finding and characterizing transition states. 

The output for a transition state search is of course similar to that for a minimization. Quantities such as the Cartesian geometry, the SCF energy, the forces, parameter values, and displacements are common to both TS searches and minimizations and are printed out in the same way. The first difference occurs in the treatment of the starting Hessian for the indole minimization (O Fig. 10-2) a default Hessian, diagonal in the underlying space of primitive internals, is used whereas the TS search started with a full, albeit approximate, Cartesian Hessian which needs to be transformed into internal coordinates. This transformation is done once only, on the first optimization cycle, as thereafter the Hessian will be updated. 

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