Time-dependent coupled

Dispersion of Linear and Nonlinear Optical Properties of Benzene An Ab Initio Time-Dependent Coupled-Perturbed Hartree-Fock Study Shashi P. Kama, Gautam B. Talapatra and Paras N. Prasad Journal of Chemical Physics 95 (1991) 5873-5881... 

The field- and time-dependent cluster operator is defined as T t, ) = nd HF) is the SCF wavefunction of the unperturbed molecule. By keeping the Hartree-Fock reference fixed in the presence of the external perturbation, a two step approach, which would introduce into the coupled cluster wavefunction an artificial pole structure form the response of the Hartree Fock orbitals, is circumvented. The quasienergy W and the time-dependent coupled cluster equations are determined by projecting the time-dependent Schrodinger equation onto the Hartree-Fock reference and onto the bra states (HF f[[exp(—T) ... 

The solution of the time-dependent HF or KS Equation (2.184) can be obtained within a time-dependent coupled HF or KS approaches (TDHF or TDDFT) by expanding all the involved matrices (F, R, C and e) in powers of the field components. It has to be noted that the solvent-induced matrices present in F(,(R) depend on the frequency-dependent nature of the field as they depend on the density matrix R and as they are determined by the value of the solvent dielectric permittivity at the resulting frequency. 

RJ. Wheatley, Time-dependent coupled-cluster calculations of polarizabilities and dispersion energy coefficients. J. Comput. Chem. 29, 445 150 (2008)... 

Dalgaard E, Monkhorst HJ (1983) Some aspects of the time-dependent coupled-cluster approach to dynamic response functions. Phys Rev A 28 1217—1222. 

The experimental measures of these molecular electric properties involve oscillating fields. Thus, the frequency-dependence effects should be considered when comparing the experimental results . Currently, there are fewer calculations of the frequency-dependent polarizabilities and hyperpolarizabilities than those of the static properties. Recent advances have enabled one to study the frequency dispersion effects of polyatomic molecules by ab initio methods In particular, the frequency-dependent polarizability a and hyperpolarizability y of short polyenes have been computed by using the time-dependent coupled perturbed Hartree-Fock method. The results obtained show that the dispersion of a increases with the increase in the optical frequency. At a given frequency, a and its relative dispersion increase with the chain length. Also, like a, the hyperpolarizability y values increase with the chain length. While the electronic static polarizability is smaller than the dynamic one, the vibrational contribution is smaller at optical frequencies. ... 

In order to demonstrate the physical significance of asymjjtotic nonadiabatic transitions and especially the aiialj-tical theory developed an application is made to the resonant collisional excitation transfer between atoms. This presents a basic physical problem in the optical line broadening [25]. The theoretical considerations were mad( b( for< [25, 27, 28, 29, 25. 30] and their basic id( a has bec n verified experimentally [31]. These theoretical treatments assumed the impact parameter method and dealt with the time-dependent coupled differenticil equations imder the common nuclear trajectory approximation. At that time the authors could not find any analytical solutions and solved the coupled differential equations numerically. The results of calculations for the various cross sections agree well with each other and also with experiments, confirming the physical significance of the asymptotic type of transitions by the dipole-dipole interaction. 

Table 1 shows good agreement between the fully numerical solutions of the time-dependent coupled equations [27] and the present results obtained by matching the asymptotic analytical solutions, indicating the usefulness of the present analytical theory. 

Quantum Chemistry (1992) which is entirely devoted to molecular non-linear optics. The foundations of time-dependent coupled-perturbed Hartree Fock theory, referred to in Section 3.1.2, are beautifully described in Sections 12.5-12.7 of Roy McWeeny s book [7]. 

Reddington et al. (1973) performed a numerical solution of the time dependent coupled equations for K + I in the energy range 20-100 eV. He reproduced all features which we discussed in the previous section. Risking some monotony, we cite here their conclusion that the simple LZ-formula accounts well for the numerically computed transition probabilities. 

The 1960s also saw the first ab initio calculations of a(time-dependent uncoupled Hartree-Eock (TDUHE) method [35] and by the time-dependent coupled Hartree-Eock (TDCHE) method [36]. 

S. P. Kama, Chem. Phys. Lett., 214, 186 (1993). A Direct Time-Dependent Coupled Perturbed Hartree-Fock-Rootham Approach to Calculate Molecular (Hyper)polarizabilities. 

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