Green's function calculations of ground-state correlation energies

A computationally convenient and numerically stable procedure is reported for the direct calculation of ground-state correlation energies employing one-particle Green's functions.     

Auger spectra by the Green's function method

Auger energies are calculated from the poles of the one-particle and particle—particle Green's functions. The theory is applied to the hydrogen fluoride molecule.     

Green's function calculations on the Auger spectra of CO

The Auger spectra of carbon monoxide have been calculated by the Green's function method and the unsolved assignment problems have been studied. Electron correlation plays an important role in all parts of the spectra. The results favour the assignment of the 250 eV peak in the C (KVV) spectrum as mainly 4σ¹5σ¹.     

Symmetry-adapted correlation function for semiclassical quantization

We study a very simple method to incorporate quantum-mechanical symmetries, including the permutational symmetry on an equal footing with spatial symmetries, into the semiclassical calculation of correlation functions. This method is applied to the calculation of energy spectra to verify its validity by reproducing quantum energy levels for systems of bosons (symmetrized) and fermions (antisymmetrized). The mechanism of how the phase-space structure of classical dynamics is linked with the relevant quantum symmetry is discussed.     

Calculations on the helium isoelectronic sequence using Coulomb Green's function variables

Calculations on the ground states of the helium isoelectronic series are carried out using variational wavefunctions of the form ψ (x,y), in which x and y are the combinations r₁ + r₂ ± r₁₂ occurring in the Coulomb Green's function. The results for helium are the most accurate to date using a two-variable wavefunction accounting for 71.5% of the correlation energy.     

Green's function calculations on the complete valence ionization spectra of HF,HCl, HBr AND HI

The ionization spectra of the entire valence region are calculated for HF, HCl, HBr and HI. For the two ionization processes of lowest energy the common molecular orbital picture of ionization applies, whereas this picture breaks down for ionization from the inner valence α-orbital. For HF and HCl basis set effects on the calculated outer-valence ionization energies are investigated and accurate values are computed using large basis sets. The calculated inner valence ionization spectra are compared with recent (e, 2e)-measurements.     

The absorption and circular dichroism bandshapes of chromophore aggregates as studied by a modified Green's function theory

A modified Green's function method is applied to calculating the aggregate bandshape whereby a decoupling approximation for vibrationally averaging the Green's function is used to include thermal and static effects as well in terms of the correction shift of the chromophore bandshape. The utility of the present method is shown by a sample calculation of the absorption and circular dichroism bandshapes of a model dimer.     

The He(II) photoelectron spectra of the fluorosubstituted ethylenes and their analysis by the Green's function method

The 30.4 nm He(II) photoelectron spectra of the fluorosubstituted ethylenes have been recorded. The assignment of all main bands is obtained from many-body Green's function calculations. The results from the semi-empirical HAM/3 method lead to a nearly identical assignment. For the mono- and difluoroethylenes, an unambiguous interpretation of the spectra can be established from empirical considerations alone. The set of spectra has been reexamined with respect to the “perfluoro-effect” rules. Also discussed are the ionisation energies as a function of the geminal FCF bonding angle and the similarity of the spectra of the cis and trans isomers of 1,2-difluoroethylene. Additional weak bands were detected in the energy region 21–24 eV in all spectra and were attributed to “shake-up” transitions on the basis of 2ph-Tamm-Dancoff Green's function calculations. The orbital model of ionisation breaks down for the ionisation out of the F(2s) and C(2s) orbitals in general. The calculations reveal a charge transfer character of the excitations accompanying ionisation from the C(2s) orbitals.     

Phase quantization of chaos in the semiclassical regime

Since the early stage of the study of Hamilton chaos, semiclassical quantization based on the low-order Wentzel-Kramers-Brillouin theory, the primitive semiclassical approximation to the Feynman path integrals (or the so-called Van Vleck propagator), and their variants have been suffering from difficulties such as divergence in the correlation function, nonconvergence in the trace formula, and so on. These difficulties have been hampering the progress of quantum chaos, and it is widely recognized that the essential drawback of these semiclassical theories commonly originates from the erroneous feature of the amplitude factors in their applications to classically chaotic systems. This forms a clear contrast to the success of the Einstein-Brillouin-Keller quantization condition for regular (integrable) systems. We show here that energy quantization of chaos in semiclassical regime is, in principle, possible in terms of constructive and destructive interference of phases alone, and the role of the semiclassical amplitude factor is indeed negligibly small, as long as it is not highly oscillatory. To do so, we first sketch the mechanism of semiclassical quantization of energy spectrum with the Fourier analysis of phase interference in a time correlation function, from which the amplitude factor is practically factored out due to its slowly varying nature. In this argument there is no distinction between integrability and nonintegrability of classical dynamics. Then we present numerical evidence that chaos can be indeed quantized by means of amplitude-free quasicorrelation functions and Heller's frozen Gaussian method. This is called phase quantization. Finally, we revisit the work of Yamashita and Takatsuka [Prog. Theor. Phys. Suppl. 161, 56 (2007)] who have shown explicitly that the semiclassical spectrum is quite insensitive to smooth modification (rescaling) of the amplitude factor. At the same time, we note that the phase quantization naturally breaks down when the oscillatory nature of the amplitude factor is comparable to that of the phases. Such a case generally appears when the Planck constant of a large magnitude pushes the dynamics out of the semiclassical regime.     

Energy quantization of chaos with the semiclassical phases alone

The mechanism of energy quantization is studied for classical dynamics on a highly anharmonic potential, ranging from integrable, mixed, and chaotic motions. The quantum eigenstates (standing waves) are created by the phase factors (the action integrals and the Maslov index) irrespective of the integrability, when the amplitude factors are relatively slowly varying. Indeed we show numerically that the time Fourier transform of an approximate semiclassical correlation function in which the amplitude factors are totally removed reproduces the spectral positions (energy eigenvalues) accurately in chaotic regime. Quantization with the phase information alone brings about dramatic simplification to molecular science, since the amplitude factors in the lowest order semiclassical approximation diverge exponentially in a chaotic domain.     

Analytical results for the classical and semiclassical coordinate probability distribution function of anharmonic oscillators

The classical and Wigner—Kirkwood semiclassical distribution functions for single and double-well anharmonic oscillators with ? = p?²/2m + k₂x?² + k_2nx?²ⁿ are given in closed form. Applications in the theory of electron diffraction are discussed briefly.     

Conical intersections and semiclassical trajectories: comparison to accurate quantum dynamics and analyses of the trajectories

Semiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, full-dimensional quantum mechanical scattering calculations are carried out for all five systems at energies that allow for electronic de-excitation via the seam of CIs. Several semiclassical trajectory methods are tested against the accurate quantum mechanical results. For four of the five model systems, the diabatic representation is the preferred (most accurate) representation for semiclassical trajectories, as correctly predicted by the Calaveras County criterion. Four surface hopping methods are tested and have overall relative errors of 40%-60%. The semiclassical Ehrenfest method has an overall error of 66%, and the self-consistent decay of mixing (SCDM) and coherent switches with decay of mixing (CSDM) methods are the most accurate methods overall with relative errors of approximately 32%. Furthermore, the CSDM method is less representation dependent than both the SCDM and the surface hopping methods, making it the preferred semiclassical trajectory method. Finally, the behavior of semiclassical trajectories near conical intersections is discussed.     

Double-ionization auger satellites obtained by the green's function method

A three-particle Green's function approach is used to obtain triple ionization potentials and double-ionization Auger satellites. Electron correlation is included beyond reorganization. Transition energies and intensities are calculated for the hydrogen fluoride molecule. The assignment of the 629 eV structure to double-ionization satellites is confirmed.     

Comparison between equations-of-motion and green's function methods for the particle-hole response function

We show that, apart from a few differences, the equations-of-motion method of McKoy et al. provides the leading correction to the random phase approximation (with exchange) in the fully renormalized response function (density-density correlation function). Thus, their equations-of-motion method is shown to be equivalent to a partial summation of infinite sets of terms in the perturbation expansion of the response function.