Coupled-cluster series

Like the configuration interaction expansion, the coupled cluster series must be truncated for practical applications. The approximation... 

In the next section we derive the Taylor expansion of the coupled cluster cubic response function in its frequency arguments and the equations for the required expansions of the cluster amplitude and Lagrangian multiplier responses. For the experimentally important isotropic averages 7, 7i and yx we give explicit expressions for the A and higher-order coefficients in terms of the coefficients of the Taylor series. In Sec. 4 we present an application of the developed approach to the second hyperpolarizability of the methane molecule. We test the convergence of the hyperpolarizabilities with respect to the order of the expansion and investigate the sensitivity of the coefficients to basis sets and correlation treatment. The results are compared with dispersion coefficients derived by least square fits to experimental hyperpolarizability data or to pointwise calculated hyperpolarizabilities of other ab inito studies. 

To derive working expressions for the dispersion coefficients Dabcd we need the power series expansion of the first-order and second-order responses of the cluster amplitudes and the Lagrangian multipliers in their frequency arguments. In Refs. [22,29] we have introduced the coupled cluster Cauchy vectors ... 

The coupled cluster expression for frequency-dependent second hyperpolarizability, Eq. (30), can now be expanded in a Taylor series in its frequency arguments around its static limit as ... 

Wesendrup, R., Laerdahl, J.K and Schwerdtfeger, P. (1999) Relativistic Effects in Gold Chemistry. VI. Coupled Cluster Calculations for the Isoelectronic Series AuPt , Au2 and AuHg. Joumul of Chemical Physics, 110, 9457-9462. 

Fossgaard, O., Gropen, O., Eliav, E. and Saue, T. (2003) Bonding in the homologous series CsAu, CsAg, and CsCu studied at the 4-component density functional theory and coupled cluster levels. Journal of Chemical Physics, 119, 9355-9363. 

The relative weakness of the Sn - Cl bond in this case reflects a trend observed in all Group 14 compounds, in which bond dissociation energies (BDE) in a series MX n = 2-4) follow the order MX4 > MX3 and MX2 > MX3 [93]. For example, the bond energies in SnCU, SnCls, and SnCl2 are 84.2,42.9, and 91.1 kcalmoD based on our combined BAC-MP4 and coupled-cluster results. The relatively weak bond in SnCls makes the rate of Eq. 58 fast relative to Eq. 54, and thus not rate Hmiting. 

J. Paldus, Coupled Cluster Theory. In S. Wilson and G. H. F. Diercksen (Eds.) Methods in Computational Molecular Physics, NATO ASI series. Series B Physics, Vol. 293. (Plenum, New York, 1992), pp. 99-194. 

The coupled cluster (CC) method is actually related to both the perturbation (Section 5.4.2) and the Cl approaches (Section 5.4.3). Like perturbation theory, CC theory is connected to the linked cluster theorem (linked diagram theorem) [101], which proves that MP calculations are size-consistent (see below). Like standard Cl it expresses the correlated wavefunction as a sum of the HF ground state determinant and determinants representing the promotion of electrons from this into virtual MOs. As with the Mpller-Plesset equations, the derivation of the CC equations is complicated. The basic idea is to express the correlated wave-function Tasa sum of determinants by allowing a series of operators 7), 73,... to act on the HF wavefunction ... 

The second general approach to correlation theory, also based on perturbation theory, is the coupled-cluster method, which can be thought of as an infinite-order perturbation method. The coupled-cluster wave function T cc is expressed as a power series,... 

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