Density functional perturbation theory energy change

Problem was solved by application of intrinsic reaction coordinate (IRC) procedure in combination with Density Functional Theory and second order Moller-Plesset perturbation theory methods [35]. It was demonstrated that potential energy surface around boat conformation is extremely fiat (Fig. 19.2) and contains wide plateau where energy of molecule remains almost the same. Conformation of cyclohexene ring is changed from one twist-boat to symmetric another twist-boat via boat conformation representing a central point of plateau. Width of plateau in terms of value of the C3-C4-C5-C6 torsion angle slightly depends on method of calculations (Table 19.2) and is varied within 30 0°. 

Time-dependent response theory concerns the response of a system initially in a stationary state, generally taken to be the ground state, to a perturbation turned on slowly, beginning some time in the distant past. The assumption that the perturbation is turned on slowly, i.e. the adiabatic approximation, enables us to consider the perturbation to be of first order. In TD-DFT the density response dp, i.e. the density change which results from the perturbation dveff, enables direct determination of the excitation energies as the poles of the response function dP (the linear response of the KS density matrix in the basis of the unperturbed molecular orbitals) without formally having to calculate a(co). 

This quantity can be viewed as a generalization of Fukui s frontier MO concept and plays a key role in linking Frontier MO Theory and the HSAB principle. It can be interpreted either as the sensitivity of a system s chemical potential to an external perturbation at a particular point r, or as the change of the electron density p(r) at each point r when the total number of electrons is changed. The former definition has recently been implemented to evaluate this function,but the derivative of the density with respect to the number of electrons remains by far the most widely-used definition. The second order derivative of the energy with respect to the external potential is the linear response function xCi tO called the polarizability kernel... 

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