Higher random phase approximation

T. Shibuya, V. McKoy, Higher Random-Phase Approximation as an Approximation to the Equations of Motion, Phys. Rev. A 2 (1970) 2208. 

HOHAHA HHPA Homonuclear Hartmann-Hahn Spectroscopy Higher Random Phase Approximation... 

Random phase approximation D = (K2 + b2)/2 works well for strong coupling (e.g., b > 10) and strong nonlinearity (e.g., K = 4.0), that waits for higher-order correction by Fourier path method [11,15,16], With K > 1.0, diffusion coefficients approach some constants as b —> 0 due to the breakup of the last KAM torus of each standard map, while with K < 0.9 and smaller b, they are expected to be evaluated by the stochastic pump or three resonance model and their extensions [12,17,18]. 

Apart from primary structural and energetic data, which can be extracted directly from four-component calculations, molecular properties, which connect measured and calculated quantities, are sought and obtained from response theory. In a pilot study, Visscher et al. (1997) used the four-component random-phase approximation for the calculation of frequency-dependent dipole polarizabilities for water, tin tetrahydride and the mercury atom. They demonstrated that for the mercury atom the frequency-dependent polarizability (in contrast with the static polarizability) cannot be well described by methods which treat relativistic effects as a perturbation. Thus, the varia-tionally stable one-component Douglas-Kroll-Hess method (Hess 1986) works better than perturbation theory, but differences to the four-component approach appear close to spin-forbidden transitions, where spin-orbit coupling, which the four-component approach implicitly takes care of, becomes important. Obviously, the random-phase approximation suffers from the lack of higher-order electron correlation. 

There do exist recent quantum chemical techniques which are size consistent. Among them, the Random Phase Approximation (RPA), its variants such as the Second-Order Polarization Propagator Approximation (SOPPA) [10], and the Coupled Cluster Approximation (CCA) [11] axe the most prominent and being widely used. In the SOPPA method, electron correlation effects are included in the two-particle polarization propagator to second order. The coupled cluster method uses an exponential ansatz through which higher-order exci-... 

At a higher computational level, the Kirkwood model gave [M]d+ 11.8° for the enantiomer. At a still higher level, Random Phase Approximation calculations were used to obtain an extensive catalog of transitions for (R,R)-( —)-31, which reproduced the... 

The last few years have seen some very exciting developments on yet higher rungs of the ladder of exchange-correlation functionals. In particular, approaches that explicitly account for correlation have emerged, such as the random phase approximation (RPA) within the adiabatic-connection-fluctuation-dissipation theorem. Very recently, RPA has been applied to solids and surfaces with some very encouraging results (e.g., [45-49]). 

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