Polarizability, electric dynamic

The set of excitation energies consistent with the SCF parameterization of the wave function are those given by the random-phase approximation (RPA), in the sense that these are the locations of poles in the dynamic electric polarizability. The eigenvalues of A are not the RPA energy differences, and they often deviate significantly from them. 

Effective Hamiltonian Method for Dynamic Electric Polarizabilities. 

The molecular response tensors are characterized by peculiar properties and satisfy a series of very general quantum-mechanical relations. First we observe that the dynamic properties can be rewritten as a sum of the corresponding static property and a function multiplying the square of the angular frequency. Thus, for instance, in the case of dipole electric polarizability, using Eqn. (117),... 

According to the fluctuation-dissipation theorem [1], the electrical polarizability of polyelectrolytes is related to the fluctuations of the dipole moment generated in the counterion atmosphere around the polyions in the absence of an applied electric field [2-4], Here we calculate the fluctuations by computer simulation to determine anisotropy of the electrical polarizability Aa of model DNA fragments in salt-free aqueous solutions [5-7]. The Metropolis Monte Carlo (MC) Brownian dynamics method [8-12] is applied to calculate counterion distributions, electric potentials, and fluctuations of counterion polarization. 

The interfacial electric polarizability y, being an important dynamic characteristic of the particle surface charge, can be easily determined from the electro-optical effect dependence on the square of the electric field strength (Eq. 6). A significant increase in the particle dimensions as well as the low surface charge of the colloid-polymer complex complicate the electric polarizability determination near to the system s isoelectric point (Figure 2). The electric polarizabilities are calculated in this review only for polymer covered particles in stabilized suspensions. One way to obtain correct values... 

The dynamic dipole polarizability tensor a can be expressed through eq. (1.55) when both A and B operators are the electric dipole moment... 

In order to derive a quantum mechanical expression for the mixed dynamic electric dipole magnetic dipole polarizability tensor we have to evaluate the time-dependent expectation value of the electric dipole operator ( o(t) Aa l o(f)) in the presence of the time-dependent magnetic induction of left- or right-circularly polarized radiation... 

O Equation 11.84 defines the components of the dynamic electric dipole polarizability tensor, cCf,v -coa-, o)i), those of the first electric dipole hyperpolarizabUity,j8 v(/ (-Wa wi, W2), and those of the second electric dipole hyperpolarizabUity yf,v ((-coa coi, C02, (03). The combination of frequencies and the presence or absence of static fields characterize various nonlinear processes. The calculations can be done for any combination of frequencies satisfying O Eq. 11.85, but only selected examples of the most commonly studied optical phenomena will be discussed below (see, e.g., Willets et al. 1992 and Bogaard and Orr 1975 for more details). 

Choosing a non-zero value for uj corresponds to a time-dependent field with a frequency u, i.e. the ((r r)) propagator determines the frequency-dependent polarizability corresponding to an electric field described by the perturbation operator QW = r cos (cut). Propagator methods are therefore well suited for calculating dynamical properties, and by suitable choices for the P and Q operators, a whole variety of properties may be calculated. " ... 

As electric fields and potential of molecules can be generated upon distributed p, the second order energies schemes of the SIBFA approach can be directly fueled by the density fitted coefficients. To conclude, an important asset of the GEM approach is the possibility of generating a general framework to perform Periodic Boundary Conditions (PBC) simulations. Indeed, such process can be used for second generation APMM such as SIBFA since PBC methodology has been shown to be a key issue in polarizable molecular dynamics with the efficient PBC implementation [60] of the multipole based AMOEBA force field [61]. 

We shall consider here in more detail two models first a dynamic coupling approach, due to Weigang33, who considered optical activity deriving from the coupling of electric dipoles (the diene chromophore and the polarizable bonds around it) and second, a localized orbital investigation, which permits one to separate the contributions from the intrinsic diene optical activity and from the axial substituents. 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

Second-order perturbation sums are a second example in which one is interested in an average or integral over a spectral density. For example, the dynamic polarizability a of a system at a frequency co0 is related to the spectral density /(co) of the electric dipole moment of the system by... 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

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