Coupled cluster propagator method

The use of Cl methods has been declining in recent years, to the profit of MP and especially CC methods. It is now recognized that size extensivity is important for obtaining accurate results. Excited states, however, are somewhat difficult to treat by perturbation or coupled cluster methods, and Cl or MCSCF based methods have been the prefen ed methods here. More recently propagator or equation of motion (Section 10.9) methods have been developed for coupled cluster wave functions, which allows calculation of exited state properties. 

More recently Equation Of Motion (EOM) methods have been used in connection with other types of wave functions, most notably coupled cluster.Such EOM methods are closely related to propagator methods, and give working equations which are similar to those encountered in propagator theory. 

Computationally, the present approach rests on the QVC coupling scheme in conjunction with coupled-cluster electronic structure calculations for the vibronic Hamiltonian, and on the MCDTH wave packet propagation method for the nuclear dynamics. In combination, these are powerful tools for studying such systems with 10-20 nuclear degrees of freedom. (This holds especially in view of so-called multilayer MCTDH implementations which further enhance the computational efficiency [130,131].) If the LVC or QVC schemes are not applicable, related variants of constructing diabatic electronic states are available [132,133], which may extend the realm of application from the present spectroscopic and photophysical also to photochemical problems. Their feasibility and further applications remain to be investigated in future work. 

It is well known that electron correlation plays a key role in understanding the most interesting phenomena in molecules. It has been the focal point of atomic and molecular theory for many years [1] and various correlated methods have been developed [2]. Among them are many-body perturbation theory [3] (MBPT) and its infinite-order generalization, coupled cluster (CC) theory [4,5], which provides a systematic way to obtain the essential effects of correlation. Propagator [6-9] or Green s function methods (GFM) [10-14] provide another correlated tool to calculate the electron correlation corrections to ionization potentials (IPs), electron affinites (EAs), and electronic excitations. 

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)... 

Electronic correlation in extended systems remains a central problem despite impressive progress in recent years. For small systems a number of very powerful methods have reached a high degree of accuracy thanks to a combination of formal algebraic and numerical techniques. These include configuration interaction,1-5 propagator methods,2,4 5 many-body perturbation procedures,3-5 and coupled-cluster methods.4 For extended systems density functional methods6,7 dominate the scene. Certain forms of correlation are taken into account by such methods, but how and to what extent are still unclear.8... 

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... 

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... 

About two-thirds of the propagation reactions in the table are exothermic, and one-third thermoneutral or endothermic. In all cases, the energy needed is much lower than the one necessary to initiate the chain of reactions. Again as before, BMK results are of comparable quality to G4 or CCSD(T), although the CBS-APNO calculations exhibit smaller deviations from the experimental values for this set of reactions. Needless to stress, the BMK calculations are faster and cheaper than the composite or coupled cluster methods, especially when larger molecules are considered. 

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. 

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. 

---