The course of a molecular vibration can be followed by calculating the potential and kinetic energy at various times. Two extreme conditions can be identified: (a) gas phase, in which the total energy is a constant through time, there being no damping of the kinetic energy allowed, and (b) liquid phase, in which kinetic energy is always set to zero, the motion of the atoms being infinitely damped.
All possible degrees of damping are allowed. In addition, the facility exists to dump energy into the system, appearing as kinetic energy. As kinetic energy is a function of velocity, a vector quantity, the energy appears as energy of motion in the direction in which the molecule would naturally move. If the system is a transition state, then the excess kinetic energy is added after the intrinsic kinetic energy has built up to at least 0.2 kcal/mol.
For ground-state systems, the excess energy sometimes may not be added; if the intrinsic kinetic energy never rises above 0.2 kcal/mol then the excess energy will not be added.
The IRC is a purely geometric structure, that is, it is time-independent. A plot of the IRC has two axes: potential energy and reaction coordinate. While potential energy is easy to understand - it's just the heat of formation - the meaning of the reaction coordinate is not so obvious. To understand the meaning used here, consider the first half of a reaction, going from reactants to the transition state. In this discussion, it is a requirement that the Potential Energy Surface (PES) increases monotonically in going from reactant(s) to the transition state. If this requirement is not true, then the PES can be divided into two or more sections in such a manner that in each section the requirement is true. The discussion that follows woiuld then apply to each section.
Both reactants and transition state have well-defined geometries. For the transition state, it is the stationary point on the PES which is the highest point on the minimum energy path from reactants to products. If the reactant is a single entity, e.g. the keto-enol tautomerization reaction, then it is that entity in its lowest energy configuration. If the reactant consists of two entities, e.g. the Diels Alder reaction or the Sn2 CH3Cl + F(-) reaction, then it is the associated complex. If no associated complex is formed, then it is the two isolated species.
The "length" of the reaction coordinate can be defined as follows: In the definition of the Cartesian geometry, let both the transition state and the reactants share the same center of mass. No rotation is permitted. Given that the coordinate of atom i in the reactant(s) is Ri(x,y,z), and the corresponding coordinate in the products is Pi(x,y,z), then the length, L, of the reaction coordinate is:
L = (Σi(Ri(x,y,z) -Pi(x,y,z))2)1/2
The reaction coordinate is represented by a set of points. The difference in geometry between each adjacent point on the reaction coordinate can be defined in a similar manner. By default, the step-size is 0.05 Angstroms, so the difference, Δl between the geometries of two points, X(j) and X(j+1), on a reaction coordinate is:
Δl = 0.05 = (Σi(X(j)i(x,y,z) -X(j+1)i(x,y,z))2)1/2
Note that the addition of all the step-sizes is not equal to the length of the reaction coordinate. It would only be equal if the reaction coordinate involved all atoms moving in straight lines; as this only occurs in diatomic reactions, this condition is normally not satisfied. In the output, the difference between each pair of points is a constant, when X-PRIORITY is in force, and the distance from the transition state is also printed.
Unlike the IRC, the default coordinate for the DRC is time, with a default step size of 0.1 fs. For long trajectories, particularly those of several picoseconds, a time step on 1 or more femtoseconds is suggested.