Polarization dependent density functional

Chandra and his coworkers have developed analytical theories to predict and explain the interfacial solvation dynamics. For example, Chandra et al. [61] have developed a time-dependent density functional theory to predict polarization relaxation at the solid-liquid interface. They find that the interfacial molecules relax more slowly than does the bulk and that the rate of relaxation changes nonmonotonically with distance from the interface They attribute the changing relaxation rate to the presence of distinct solvent layers at the interface. Senapati and Chandra have applied theories of solvents at interfaces to a range of model systems [62-64]. 

The drastical enhancement of the TPA cross section in the presence of the solvent for the two-photon polymerization initiator [4-trans-[p-(N,N-Di- -butylamino)-p-stilbenyl vinyl piridinc (DBASVP) has been illustrated in a recent work by Wong et al. [112]. The DBASVP is the typical D-tt-A molecule exhibiting the positive solvatochromism (scheme 7). Hence, the lowest excited state of the DBASVP molecule has been found to be a CT state, which completely dominates the linear absorption spectrum. Wong et al. have combined the time-dependent density functional theory and the polarized continuum model (PCM) to evaluate the solvatochromic shift, TPA cross-section, and oxidation potential of the DBASVP molecule in different solutions. 

The simplest polarization propagator corresponds to choosing an HF reference and including only the h2 operator, known as the Random Phase Approximation (RPA), which is identical to Time-Dependent Hartree-Fock (TDHF), with the corresponding density functional version called Time-Dependent Density Functional Theory (TDDFT). For the static case co= 0) the resulting equations are identical to those obtained from a coupled Hartree-Fock approach (Section 10.5). When used in conjunction with coupled cluster wave functions, the approach is usually called Equation Of Motion (EOM) methods. ... 

In a later paper, Casida et used this formalism to calculate the excitation energies of some smaller molecules (N2, CO, CH2, and C2H4). In Table 12 we have collected their results for N2 and in Table 13 those for CO. Those for N2 can be compared directly with those of Table 11 obtained with an exact-exchange method. The results of both tables show that the time-dependent density-functional methods give results that are almost as accurate as those of the sophisticated correlation methods (like coupled-cluster, configuration-interaction, multiple-configuration, or polarization-propagator methods) and considerably... 

A special problem where the time-dependent density-functional theory could be useful is that of calculating the polarizability and hyperpolarizability (Section 12). It turned out that although accurate results could be achieved for smaller molecules (partly, however, requiring a careful choice of the approximate density functional), severe problems could turn up (but did not always) when considering extended systems. It might mean that the current density functionals are lacking an explicit dependence on the polarization, but further studies are needed in order to clarify this point. 

Excitation energies and transition moments can in principle be obtained as poles and residua of polarization propagators as discussed in Section 7.4. However, only in the case that the set of operators hn in Eq. (7.77) is restricted to single excitation and de-excitation operators q i,qai is it computationally feasible to determine all excitation energies. This restricts this approach to single-excitation-based methods like the random phase approximation (RPA) discussed in Sections 10.3 and 11.1 or time-dependent density functional theory (TD-DFT). 

This approximation is better known as the time-dependent Hartree—Fock approximation (TDHF) (McLachlan and Ball, 1964) (see Section 11.1) or random phase approximation (RPA) (Rowe, 1968) and can also be derived as the linear response of an SCF wavefunction, as described in Section 11.2. Furthermore, the structure of the equations is the same as in time-dependent density functional theory (TD-DFT), although they differ in the expressions for the elements of the Hessian matrix E22. The polarization propagator in the RPA is then given as... 

Orlova et al. (2003) theoretically studied the mechanism of the firefly bioluminescence reaction on the basis of the hybrid density functional theory. According to their conclusion, changes in the color of light emission by rotating the two rings on the 2-2 axis is unlikely, whereas the participation of the enol-forms of oxyluciferin in bioluminescence is plausible but not essential to explain the multicolor emission. They predicted that the color of the bioluminescence depends on the polarization of the oxyluciferin molecule (at its OH and O-termini) in the microenvironment of the luciferase active site the... 

Magyar, R.J., Mujica, V., Marquez, M. and Gonzalez, C. (2007) Density-functional study of magnetism in bare Au nanodusters Evidence of permanent size-dependent spin polarization without geometry relaxation. Physical Review B -Condensed Matter, 75,144421-1—144421-7. 

Atomic density functions are expressed in terms of the three polar coordinates r, 6, and multipole formalism, the density functions are products of r-dependent radial functions and 8- and -dependent angular functions. The angular functions are the real spherical harmonic functions ytm (8, ), but with a normalization suitable for density functions, further discussed below. The functions are well known as they describe the angular dependence of the hydrogenic s, p, d,f... orbitals. 

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