Propagator, coupled cluster polarization

CCPPA coupled cluster polarization propagator approximation... 

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)... 

CCPPA Coupled Cluster Polarization Propagator Approximation... 

Korona T, Przybytek M, Jeziorski B. Time-independent coupled cluster theory of the polarization propagator. Implementation and application of the singles and doubles model to dynamic polarizabilities and Van der Waals constants, 2006. Submitted to Mol. Phys 104 2302-2316... 

CCDPPA coupled-cluster doubles polarization propagator approximation (Section VII. E),... 

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-... 

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... 

By the end of the 1980s, state of the art methods of quantum chemistry, such as coupled cluster, configuration interaction, fourth order perturbation theory (MP4), second-order polarization propagator (SOPPA, multiconfigu-rational linear response (MCLR) etc., had been applied to the calculation of... 

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... 

J.E. Del Bene, I. Alkorta, I.J. Elguero, A systematic comparison of second-order polarization propagator approximation (SOPPA) and equation-of-motion coupled cluster singes and doubles (EOM — CCSD) spin — spin couphng constants for selected singly bonded molecules, and the hydrides NH3, H2O, and HF and their protonated and deprotonated ions and hydrogen-bonded complexes, J. Chem. Theor. Comput. 4 (2008) 967-973. 

Relativistic calculations of NMR properties of RgH ion (where Rg = Ne, Ar, Kr, Xe), Pt shielding in platinum complexes, and Pb shielding in solid ionic lead(II) halides have been reported in this review period. For the Rg nucleus in the RgH ions, the following methods were used and results compared with each other non-relativistic uncorrelated method (HF), relativistic uncorrelated methods, four component Dirac Hartree-Fock method (DHF) and two-component zeroth order regular approach (ZORA), non-relativistic correlated methods using second order polarization propagator approach SOPPA(CCSD), SOPPA(MP2), respectively coupled cluster singles and doubles or second order Moller-Plesset, and... 

MP) perturbation theory, linearized coupled cluster and multiconfigurational self-consistent field (MCSCF) wavefunctions are commonly employed as approximate reference states in polarization propagator approximations and will be discussed in Sections 10.3 and 10.4. 

However, other attempts have been made to improve on the treatment of electron correlation in SOPPA. Three SOPPA-like methods have thus been presented. All are based on the fact that a coupled cluster wavefunction gives a better description than the Mpller-Plesset first- and second-order wavefunctions, Eqs. (9.66) and (9.70). In the second-order polarization propagator with coupled cluster singles and doubles amplitudes-SOPPA(CCSD)-method (Sauer, 1997), the reference state in Eqs. (3.160) to (3.163) is approximated by a linearized CCSD wavefunction... 

This keeps essentially the structure of the SOPPA equations but replaces in all matrix elements the first-order MP doubles correlation coefficients, Eq. (9.67), and the second-order MP singles correlation coefficient, Eq. (9.71), by coupled cluster singles and doubles amplitudes. In the earlier coupled cluster singles and doubles polarization propagator approximation (CCSDPPA) (Geertsen et al., 1991a), a precursor to SOPPA(CCSD), this was done only partially and in particular not in the second-order correction to the density matrix Very recently, a third method (Kjaer... 

Geertsen, J., Eriksen, S., and Oddershede, J. (1991a). Some aspects of the coupled cluster based polarization propagator method. Adv. Quantum Chem., 22, 167-209. 

Sauer, S. P. A. (1997). Second order polarization propagator approximation with coupled cluster singles and doubles amplitudes - SOPPA(CCSD) The polarizability and hyperpolarizabihty of Li. J. Phys. B At. Mol. Opt. Phys., 30, 3773-3780. 

Other ab initio MO calculations of spin-spin couplings include those based upon polarization propagator methods, e.g. RPA, SOPPA and the coupled cluster single and double polarization propagator approximation (CCSDPPA). These three methods have been used to calculate the C contributions to the values of /(C-H) and for... 

In SOPPA the equations for the polarization propagator are solved by retaining all terms second order in the fluctuation potential. The reference state is a correlated Moller Plesset wavefunction with the corresponding correlation coefficients. The zeroth-order wavefunction is a single reference SCF ground state. Correlation is introduced via the fluctuation potential. SOPPA includes dynamical correlation, but not nondynamical effects. The same technique can be applied to other methods, e.g., coupled cluster, giving CCSDPPA where the cluster amplitudes replace the correlation coefficients used in SOPPA. 

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