Geometry optimization, constrained

The idea of constrained dynamics performed for a set of points along such a reaction path , i.e. for a set of fixed values of the reaction coordinate, A, is not specific to MD. Similar approaches have been commonly used in computational studies based on static quantum-chemical calculations. Such approaches are known as linear transit calculations, reaction path scans, etc. A set of constrained geometry optimizations with the constraint driving the system from reactants to products is a popular way to bracket a transition state, for instance. 

The basic output of an electronic structure calculation is the electronic and the total energy of the system for a certain nuclear geometry. When the energy is minimized as a function of a number of internuclear distances or bond angles, this is referred to as a (constrained) geometry optimization. This will normally give the equilibrium structure under the restraints of the geometrical model. 

Constrained geometry optimizations led to the potential energy surface shown in Figure 2. The three minima observed correspond to the structures shown in Figure 3. It is evident that the three minima are almost isoenergetic, and consequently the system can assume any of the three forms. 

Figure 2. Potential energy surface for the cysteine thiyl radical resulting from a constrained geometry optimization with respect to the C-Ca-Cp-Sy dihedral angle. Reproduced with permission from [128]. Copyright 2004, American Chemical Society.

De Vico, L., Olivucci, M., 8c Lindh, R. (2005). New general tools for constrained geometry optimizations. Journal of Chemical Theory and Computation, 1(5), 1029-1037. doi 10.1021/ct0500949. 

All computations were essentially DFT (B3LYP) constrained geometry optimizations and where conduced by means of the suite for electronic structure ab-initio studies NWChem [10]. 

There are several obstacles that make the use of the RSH difficult. First, the choice of the coordinates / is not trivial and requires either chemical intuition or a preliminary calculation with the RPH that reveals all LAMs. Once coordinates / have been selected, the reaction surface has to be mapped out by constrained geometry optimizations for a grid of / points. This in itself can be already very time consuming apart from the fact that an analytical function Vo R ) has to be derived to carry out the dynamics calculations. Frequencies, normal modes, and coupling coefficients are complicated functions of / , which are difficult to calculate and to interpret. 

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