Many-body perturbation theory quadruples

Bartlett R J and Purvis G D 1978 Many-body perturbation theory coupled-pair many-electron theory and the importance of quadruple excitations for the correlation problem int. J. Quantum Chem. 14 561-81... 

R. J. Bartlett and G. D. Purvis, Int. ]. Quantum Chetn., 14,561 (1978). Many-Body Perturbation Theory, Coupled-Pair Many-Electron Theory, and the Importance of Quadruple Excitations for the Correlation Problem. 

Early comparisons of this sort were based on work by Handy and coworkers [37], who developed an efficient direct FCI approach in terms of determinants. Using a double-zeta (DZ) basis set, they considered stretching the 0-H bond lengths in the H2O molecule to 1.5 and 2.0 times their equilibrium values. The FCI results showed that even the restricted Hartree-Fock (RHF) based fourth-order many-body perturbation theory (MBPT) approach [38], which includes the effect of single, double, triple and quadruple excitations, did not accurately describe the stretching of the bond the error increased from 0.6 kcal/mole at to 10.3 kcal/mole... 

Bartlett, R. J., Purvis, G. D. (1978). Many-body perturbation theory, coupled-pair many-electron theory, and the importance of quadruple excitation for the correlation problem. International Journal of Quantum Chemistry, 14, 561-581. 

The fact that in a configuration interaction expansion unlinked cluster contributions can only be accounted for by including quadruple- (and higher-order) excitations is one of the principal drawsbacks of the method. In contrast, such contributions are automatically accounted for without explicitly computing higher-order terms, in some cluster-based methods and in many-body perturbation theory. In this sense the ci expansion is much less compact and less efficient than these approaches and becomes progressively less efficient as the number of electrons increases. 

The many body perturbation theory has been applied to obtain higher accuracy in ab initio calculations of molecular properties. Pople etal. [181] have developed analytic derivative methods at second order perturbation theory level (MBPT(2)). Simandiras et al. [184] have derived specific expressions for analytic determination of dipole moment derivatives at MBPT(2). Dierksen and Sadlej [229] have shown by applying finite field MBPT in studying dipole and quadruple polarizabilities of the CO molecule that fourth and even higher level of MBPT is required to achieve satisfactory results. 

The ab initio method used to obtain the potential surface employs many-body perturbation theory (MBPT) relative to an unrestricted Hartree-Fock (UHF) reference function. Correlation is treated to fourth order in MBPT and includes contributions from all single, double, and quadruple excitations. A Gaussian basis of double zeta plus polarization functions (DZP) is used. This model is computationally efficient and has been shown to provide accurate force fields and geometries and reliable thermochemical data for a wide variety of molecular systems.It has also been used to calculate reaction paths for some triatomic systems. 

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