Frequency-dependent polarizability, linear response theory

The last method used in this study is CCSD linear response theory [37]. The frequency-dependent polarizabilities are again identified from the time evolution of the corresponding moments. However, in CCSD response theory the moments are calculated as transition expectation values between the coupled cluster state l cc(O) and a dual state... 

Self-Consistent Field Linear Response Theory and Application to Ceo. Excitation Energies, Oscillator Strengths and Frequency-Dependent Polarizabilities. 

The second approach is used by Baerends and co-workers. They use linear response theory, but instead of calculating the full linear response function they use the response function of the noninteracting Kohn-Sham system together with an effective potential. This response function can be calculated from the Kohn-Sham orbitals and energies and the occupation numbers. They use the adiabatic local density approximation (ALDA), and so their exchange correlation kernel, /xc (which is the functional derivative of the exchange correlation potential, Vxc, with respect to the time-dependent density) is local in space and in time. They report frequency dependent polarizabilities for rare gas atoms, and static polarizabilities for molecules. 

The third approach is that used by Salahub and co-workers. They initially used DFT RPA but recendy have reported an implementation of time-dependent density functional response theory (TD DFRT). Their Kohn-Sham linear response function involves a coupling matrix, K, which in the RPA case contains only the response to coulomb terms, but in their present implementation contains exchange and correlation response terms. Their K is time independent as they work within the adiabatic approximation. They calculate the frequency dependent polarizability from a sum-over-states (SOS) formula, and hence have to calculate the excitation spectrum. 

R. Cammi and J. Tomasi, Nonequilibrium solvation theory for the polarizable continuum model - a new formulation at the SCF level with application to the case of the frequency-dependent linear electric-response function, Int. J. Quantum Chem., (1995) 465-74 B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798-807 R. Cammi, L. Frediani, B. Mennucci, J. Tomasi, K. Ruud and K. V. Mikkelsen, A second-order, quadratically... 

The application of the Lorentz-Lorenz equation gives a convincing demonstration of the general similarity of the linear response in gas and liquid but its application in the liquid introduces an approximation which has not yet been quantified. A more precise objective for the theory would be to calculate the frequency dependent susceptibility or refractive index directly. For a continuum model this may lead to a polarizability rigorously defined through the Lorentz-Lorenz equation as shown in treatments of the Ewald-Oseen theorem (see, for example Born and Wolf, plOO),59 but the polarizability defined in this way need not refer to one molecule and would not be precisely related to the gas parameters. 

R. Cammi and J. Tomasi, Int. J. Quantum Chem., 29, 465 (1995). Nonequilibrium Solvation Theory for the Polarizable Continuum Model A New Formulation at the SCF Level with Application to the Case of the Frequency-Dependent Linear Electric Response Function. 

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