Polarization propagator method

When Jens Oddershede was elected a Fellow of the American Physical Society in 1993, the citation read For contribution to the theory, computation, and understanding of molecular response properties, especially through the elucidation implementation of the Polarization Propagator formalism. Although written more than a decade ago, it is still true today. The common thread that has run through Jens work for the past score of years is development of theoretical methods for studying the response properties of molecules. His primary interest has been in the development and applications of polarization propagator methods for direct calculation of electronic spectra, radiative lifetime and linear and non-linear response properties such as dynamical dipole polarizabilities and... 

From the Orbital Implementation of the Kinetic Theory to the Polarization Propagator Method in the Study of Energy Deposition Problems... 

Orbital Implementation of the Kinetic Theory and the Polarization Propagator Method to equation (5) was cast in terms of CAB contributions, i.e.,... 

In order to calculate the GOS, one requires the excitation energies and the generalized transition moments. Oddershede and Sabin had already started in 1992 the investigation of the GOS and the stopping cross section in the first Bom approximation by means of the polarization propagator method [78]. 

Finally - and equally important - Jens contribution to the formal treatment of GOS based on the polarization propagator method and Bethe sum rules has been shown to provide a correct quantum description of the excitation spectra and momentum transfer in the study of the stopping cross section within the Bethe-Bloch theory. Of particular interest is the correct description of the mean excitation energy within the polarization propagator for atomic and molecular compounds. This motivated the study of the GOS in the RPA approximation and in the presence of a static electromagnetic field to ensure the validity of the sum rules. 

As was the case for the absorption spectrum, different calculations of the band MCD of ZnP and MgP have produced different interpretations of the observed spectral features. Solheim et al. have recently calculated the MCD spectra of ZnP, MgP, and NiP using their complex polarization propagator method and a hybrid... 

One somewhat displeasing detail in the approximate polarization propagator methods discussed in the previous section is the fact that concern needs to be made as to which formulation of wave mechanics that is used. This point has been elegantly resolved by Christiansen et al. in their quasi-energy formulation of response theory [23], in which a general and unified theory is presented for the evaluation of response functions for variational as well as nonvariational electronic structure methods. 

In describing polarization propagator methods it is instructive to start out with the simplest consistent method of the kind, namely the random-phase approximation (RPA). Within the framework we use here, RPA is described as the approximation to the general equation of motion (Eq. (58)) in which we set h = hj and assume 0> = HF>, that is, use the simplest truncation in both Eqs (64) and (89). It is convenient to split hj up into p-h and h-p excitation operators... 

Very recently we have formulated and tested a new coupled-cluster polarization propagator method (Geertsen and Oddershede, 1986a). We still use a perturbation expansion of the reference state but we replace the Rayleigh-Schrodinger correlation coefficients (i =1,2)... 

For a review of the theory and implementation of the polarization propagator method, see J. Oddershede, P. Jorgensen, D.L. Yaeger, Polarization Propagator Methods in Atomic and Molecular Calculations, Compt. Phys. Rep. 2 (1984) 33 J. Oddershede, Propagator Methods, Adv. Chem. Phys. 69 (1987) 201 S.P.A. Sauer, Molecular Electromagnetism. A Computational Chemistry Approach, Oxford University Press, 2011, chapters 2 10. 

The static and dynamic polarizability of the polyyne (C2 H2) series is treated in the TDHF and correlated second order polarization propagator methods by Dalskov et al.2i2 The calculated polarizabilities are extrapolated to the infinitely... 

The described polarization propagator method circumvents the problem of the unbounded Hamiltonian term Er, but with its aid only dipole polarizabilities (a) and not hyperpolarizabilities (P, etc.) can be calculated. 

In this substection we will shortly discuss the computational methods used for calculation of the spin-spin coupling constants. Two main approaches available are ab initio theory from Hartree-Fock (or self-consistent field SCF) technique to its correlated extensions, and density function theory (DFT), where the electron density, instead of the wave function, is the fundamental quantity. The discussion here is limited to the methods actually used for calculation of the intermolecular spin-spin coupling constants, i. e. multiconfigurational self consistent field (MCSCF) theory, coupled cluster (CC) theory and density functional theory (DFT). For example, the second order polarization propagator method (SOPPA) approach is not... 

The complex polarization propagator method has been applied to the calculations of dipole-dipole dispersion coefficients of pyridine, pyrazine, and r-tetrazine. These calculations refer to the electronic ground states as well as the first excited states of 7t—>7t character <2004MI321>. Calculations of static and dynamic polarizabilities of excited states by means of DFT have been performed <2004JCP9795>. 

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... 

Approximate polarization propagator methods are thus obtained by truncating the set of operators and by using an approximate reference state Mpller-Plesset... 

J. Oddershede, P. Jprgensen and D. L. Yeager, Polarization Propagator Methods in Atomic and Molecular Calculations, Comput. Phys. Rep. 2, 33-92 (1991). 

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