Brueckner

Another technique, called Brueckner doubles, uses orbitals optimized to make single excitation contributions zero and then includes double excitations. This is essentially equivalent to CCSD in terms of both accuracy and CPU time. 

A slightly improved form of this equation is the renormalized Davidson correction, which is also called the Brueckner correction ... 

Brueckner Doubles energies, optionally including triples and quadruples (BD, BD(T), BDfTQl). 

Comparatively little space will therefore be devoted to some rather recent approaches, such as the plasma model of Bohm and Pines, the two-body interaction method developed by Brueckner in connection with nuclear theory, Daudel s loge theory, and the method of variation of the second-order density matrix. This does not mean that these methods would be less powerful or less impor-... 

In conclusion, we observe that the elementary partitioning method described in this section is of value not only for numerical purposes and for estimating the remainder but also for studying theoretical problems connected with conventional perturbation theory and with Brueckner s approximation for treating many-particle systems. 

B. Some Recent Developments Bohm-Pines Plasma Model, Brueckner s Approximation... 

Brueckner, K. A., Phys. Rev. 96, 508, Nuclear saturation and two-body forces. II. Tensor forces/ ... 

Goldstone, J., Proc. Roy. Soc. [London] A239, 267, Derivation of the Brueckner many-body theory. ... 

Rodberg, L. S., Ann. Phys. 2, 199, The many-body problem and the Brueckner approximation."... 

Table III displays VEDEs obtained with the Brueckner-reference methods discussed in Section 5.2 and augmented, correlation-consistent, triple- basis sets [41]. AEDEs include zero-point energy differences and relaxation energies pertaining to geometrical relaxation on the neutral s potential energy surface. The average absolute error with respect to experiment is 0.05 eV [26].

The Brueckner-reference method discussed in Section 5.2 and the cc-pvqz basis set without g functions were applied to the vertical ionization energies of ozone [27]. Errors in the results of Table IV lie between 0.07 and 0.17 eV pole strengths (P) displayed beside the ionization energies are approximately equal to 0.9. Examination of cluster amplitudes amd elements of U vectors for each ionization energy reveals the reasons for the success of the present calculations. The cluster operator amplitude for the double excitation to 2bj from la is approximately 0.19. For each final state, the most important operator pertains to an occupied spin-orbital in the reference determinant, but there are significant coefficients for 2h-p operators. For the A2 case, a balanced description of ground state correlation requires inclusion of a 2p-h operator as well. The 2bi orbital s creation or annihilation operator is present in each of the 2h-p and 2p-h operators listed in Table IV. Pole strengths are approximately equal to the square of the principal h operator coefiScient and contributions by other h operators are relatively small. 

K. A. Brueckner, The Many-Body Problem. J. Wiley and Sons, Inc., New York, 1959. 

Valeev, E. F., Schaefer III, H. F., 1998, The Protonated Water Dimer Brueckner Methods Remove the Spurious C] Symmetry Minimum , J. Chem. Phys., 108, 7197. 

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