Brueckner determinant

More promising in that respect are Brueckner CC (B-CC) methods, where the orbitals are determined in the presence of the correlation perturbation so that the amplitudes of the single excitations vanish, i.e., Ti = 0. Though B-CC methods can be applied to both closed- and open-shell systems, they offer particular advantages in the treatment of symmetry breaking problems, as the corresponding Brueckner determinant is generally more stable than the ROHF reference. ... 

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. 

Abstract We discuss the high-density nuclear equation of state within the Brueckner-Hartree-Fock approach. Particular attention is paid to the effects of nucleonic three-body forces, the presence of hyperons, and the joining with an eventual quark matter phase. The resulting properties of neutron stars, in particular the mass-radius relation, are determined. It turns out that stars heavier than 1.3 solar masses contain necessarily quark matter. 

H Brueckner, P Jaek, M Langer, H Godel. Liquid chromatographic determination of D-amino acids in cheese and cow milk. Implication of starter cultures, amino acid racemases, and rumen microorganisms on formation, and nutritional considerations. Amino Acids 2 271-284, 1992. 

In 1958, Nesbet extended Brueckner s theory for infinite nuclear mat-ter to nonuniform systems of atoms and molecules. By consideration of the CISD problem in which the electronic Hamiltonian is diagonalized within the basis of the reference and all singly and doubly excited determinants, Nesbet explained that Brueckner theory allows one to construct a set of orthonormal molecular orbitals for which the correlated wavefunction coefficients for all singly excited determinants vanish. Unfortunately, the construction of the set of orbitals that fulfill this Brueckner condition can be determined only a posteriori from the single excitation coefficients computed in a given orbital basis. As a result, the practical implementation of Brueckner-orbital-based methods has... 

Cluster Singles, Doubles, and Triples Calculations with Hartree-Fock and Brueckner Orbital Reference Determinants A Comparative Study. 

The admixture of singly excited configurations (with respect to the SCF determinant) via their interaction with doubly excited ones is exactly equivalent to a replacement of Hartree-Fock by Brueckner (best-overlap) orbitals. Expectation values of simple one-electron operators like x, r, (3z — r )j2 etc., have been calculated (35) for H2 in its... 

The Brueckner orbital variant of CC should also be mentioned. CCSD puts in all single excitation effects via the wavefunction exp(Ti + T2) o- We can instead change the orbitals ip, in Oo in this wavefunction until Tj = 0. These orbitals are called Brueckner orbitals and define a single determinant reference B instead of o that has maximum overlap with the correlated wave-function. Since B-CCD " (or BD) effectively puts in Tj, it will give results similar but not identical to those from CCSD (they differ in fifth order). For BH, the corresponding B-CCD errors are 1.81, 2.88, and 5.55, compared to 1.79, 2.64 and 5.05, for CCSD as a function of R. . See also B-CCD for symmetry breaking problems. ... 

Now we turn to the evaluation of fourth- and higher-order corrections. The largest of these is the correction that arises when the approximate Brueckner orbitals obtained by solving Eq. (74) for 6(f>v are replaced by the chained Brueckner orbitals determined by solving the second-order quasiparticle equation... 

Sptpp, the associated one-particle effective Hamiltonian that corresponds to the reference independent particle determinant. Usually this will be a Hermitian operator, but in some cases like Brueckner, that might not be the case. That, too, is not really a problem [12]. 

Brueckner-Goldstone (BG) MBPT [91,92] was used for the determination of atomic correlation energies and polarizabilities and soon applied... 

In this context, it is pertinent to recall that in many cases one can obtain the so-called best overlap orbitals [64] of DODS type which are produced by the given many-electron wave function. These orbitals were considered in [65] where they were identified with spin-polarized Brueckner orbitals. However, they exist if and only if the so-called nonsinglet Brueckner instabihty conditions are satisfied. At last, if the correct spin-projected determinant is involved in the consideration, then it is always possible to construct the best overlap orbitals of DODS type for the given exact or approximate state vector ). These orbitals were recently introduced [62] and named the spin-polarized extended Bmeckner (SPEB) orbitals. By construction, they maximize T). 

The best overlap orbitals are not the same as the natural spin orbital, but are probably very close (choosing the best unitary transformation of the best overlap orbitals). In a Cl expansion, the singly substituted determinants disappear if the best overlap orbitals of the same Cl problem are used. The best overlap orbitals are also called Brueckner orbitals (BO), after the American physicist Keith Brueckner, or are referred to as correlation corrected orbitals. 

Before giving the definition of the unitary transformation we should fix the PD. A simple choice for this is to use the determinant which has the maximal overlap with the reference function active orbitals accordingly wiU lead to the exact Brueckner orbitals in the active space [19,33]. 

Correlation methods that can use quasi-restricted Hartree-Fock (QRHF) or Brueckner orbital reference determinants include CCSD, CCSDT, CCSD(T), CCSDT-1, CCSDT-2, and CCSDT-3. 

A second type of reference determinant that is sometimes of value is that made up of Brueckner orbitals. The latter have the property that the single excitation amplitudes are zero (there are different Brueckner orbitals for CCSD, CCSDT-1, and so on). In our opinion, the most important use of Brueckner orbitals is in the study of symmetry breaking problems, as Brueckner orbitals frequently do not break symmetry. ... 

CCSD(TQ). These can be used with RHF and UHF references. CCSD(T), properly generalized, can also be used with ROHF and more general reference determinants, such as QRHF and Brueckner. 

Denoyer, E. R., Brueckner, P., and Debrah, E. (1995). Determination of trace impurities in semiconductor-grade hydrofluoric acid and hydrogen peroxide by ICP-MS. At. Spectrosc. 16(1), 12. 

At this point, we mention that the orbital-rotation parameters may also be determined by extending the projeetion manifold to the single excitations, replacing the orbital conditions (13.8.22) by the amplitude equations (13.8.20) for the singles. This approach is called Brueckner coupled-cluster (BCC) theory [5,31,32]. In BCC theory, neither the energy nor the amplitude equations depend on the multipliers and no multipliers must be set up to obtain the BCC wave function. 

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