Diagrammatic Many-body Perturbation Theory Research Articles

Perturbation calculation of molecular correlation energy using Gaussian-type geminals. Second-order pair energies of LiH and BH

The second-order pair energies of LiH and BH are calculated using Rayleigh–Schroedinger perturbation theory. The first-order perturbed pair functions are expanded in terms of explicitly correlated Gaussian functions. The nonlinear parameters entering the Gaussian geminals are optimized with reference to crude SCF functions according to the method proposed previously. The final values of the second-order pair energies are then calculated using accurate SCF orbitals. At this final stage only the linear parameters are reoptimized. The calculated second-order correlation energies of LiH and BH are compared with recent diagrammatic many-body perturbation theory results. The basis sets composed of two optimized Gaussian geminals for each spin-adapted pair function are shown to give quite reliable second-order correlation energies. The results obtained with four geminals for each pair function are superior to the most accurate many-body perturbation theory data. It is stressed that the nonlinear parameters of Gaussian geminals can be given a simple physical interpretation which facilitates their reasonable guess. The first-order pair functions represented in terms of Gaussian geminals have a very attractive compact and simple form. If properly optimized they can also provide highly accurate values of the second-order molecular correlation energies.

Nuclear field theory

By using path integral techniques nuclear field theory (NFT) is developed for Fermi systems interacting via a general two-body force. The NFT Lagrangian is strictly derived. As a by-product, the corresponding graphical rules are obtained. The relation between the NFT and the conventional Feynman diagrammatic many-body perturbation theory is established for processes connecting initial and final states, too.

Diagrammatic perturbation theory applied to the ground state of the water molecule

The diagrammatic many-body perturbation theory is applied to the ground state of the water molecule within the algebraic approximation. Using four different basis sets, the total energy, the equilibrium OH bond length, and the equilibrium HOH bond angle are examined. The latter is found to be a particularly sensitive test of the convergence of perturbation expansions. Certain third-order results, which incorporate all two-, three-, and four-body effects, show evidence of good convergence properties.

Diagrammatic perturbation theory. The ground state of the carbon monosulfide molecule

Diagrammatic many-body perturbation theory is employed in a study of the ground state of the carbon monosulfide molecule for bond lengths close to the equilibrium value. The calculations are complete through third order in the energy within the algebraic approximation. Two different zero-order Hamiltonians are considered and all two-, three-, and four- body terms are determined for the corresponding perturbation expansions. Many-body effects are found to be very important. Padé approximants to the energy expansion are constructed and upper bounds are evaluated. Almost 53% of the estimated correlation energy is recovered. The variation of components of the correlation energy with nuclear separation is investigated. Spectroscopic constants are also calculated.

Comparison of high-order many-body perturbation theory and configuration interaction for H 2O

Diagrammatic many-body perturbation theory, coupled with a recursive computational procedure, is employed to obtain the correlation energy of H 2O within a 39-STO basis set by evaluating all double-excitation diagrams through twelfth order without any approximations. This provides, for the first time, the complete double-excitation diagrams contributions to the correlation energy, which is −0.28826 hartree, compared with a correlation energy of −0.27402 hartree obtained from a configuration interaction calculation which includes all double excitations. The difference of 0.0142 hartree includes the “size consistency” correction to the all-double-excitations CI energy, due to the “pathological” unliked-diagram terms remaining in that result, but also involves certain fourth- and higher-order rearrangement diagrams. Contrary to conventional belief, the unshifted, or Møller-Plesset partitioning of the hamiltonian provides a much more rapid convergence of the perturbation series that does the shifted, or Epstein-Nesbet partitioning. In both cases. Padé approximants enhance the convergence of the series considerably. A simple variation-perturbation scheme based on the first-order MBPT wavefunction is sufficient to provide 97.5% of the all-doubles CI correlation energy.

Diagrammatic perturbation theory: Many-body effects in the X1Σ+ states of first-row and second-row diatomic hydrides

Diagrammatic many-body perturbation theory is employed in a study of the X1Σ+ states oif first- and second-row diatomic hydrides at their respective equilibrium nuclear separations. All two-, three-, and four-body terms are determined through third-order in the energy within the algebraic approximation (i.e., parameterization of state functions by expansion in a finite basis). Padé approximants to the energy are constructed. From the first-order wavefunction rigorous upper bounds to the expectation value of the electronic energy are obtained from the Rayleigh quotient. Two different zero-order Hamiltonians are used, and the convergence properties of the resulting perturbation expansions are compared. In both schemes three- and four-body terms are significant, having a magnitude that is as much as 24% of the sum of the second- and third-order terms.

Plasmon satellite in the Auger emission spectrum of metals

The Auger emission spectrum of metals is studied using a diagrammatic many-body perturbation theory. The plasmon band on the low-energy side of the main emission band is obtained by a first-order theory. For aluminum, the ratio of the maximum intensity of the plasmon band to that of the parent $\mathrm{LVV}$ band is about 40%. The direct coupling of the plasmon to the outgoing Auger electron is found to play an important role in the calculation.

Many-body perturbation theory applied to electron pair correlation energies. I. Closed-shell first-row diatomic hydrides

Diagrammatic many-body perturbation theory is formulated through third order and applied to LiH, BH, and HF with various sizes of two-center Slater orbital basis sets. The most extensive calculations use 46 orbitals to recover 94, 95, and 97% of the experimental correlation energy for the three molecules, respectively, when the perturbation expansion is carried through third order with pair restrictions and including selections of higher-order diagrams via denominator shifts. A detailed analysis of the ’’pair’’ correlation energies relative to SCF occupied orbitals is given, including both inter- and intrapair contributions for the different spin cases.

A complete diagrammatic construction of PCILO method

In the present short communication, the diagrammatic many-body perturbation theory for the rederivation of PCILO method (perturbation configuration interaction using localized orbitals, see Theoret. Chim. Acta (Berl.)13, 1 (1969) and15, 100 (1969)) is consequently used. Using the Goldstone-Hugenholtz linked-cluster theorem, the diagrammatic expression for the exact ground-state energy is obtained. An application of the present approach to the low-lying excited and/or ionized states is also discussed.

Electron-Interaction Effects on the Soft X-Ray Emission Spectrum of Metals. I. Formalism and First-Order Theory

The soft x-ray emission spectrum of metals is studied using a diagrammatic many-body perturbation theory to account for the interactions between electrons. On the basis of a one-electron model, the emission spectrum gives a direct measure of the Fermi energy and is simply related to the conduction-electron density of states. In actual metals, however, the spectra are strongly modified by electron interactions, and these relations are no longer valid. A low-energy tail is introduced in place of a sharp emission threshold, and a satellite band appears which is associated with plasmon excitation in the metal. The first-order theory described here shows that certain interference terms play an important role in determining the emission intensity. For sodium, a satellite band is obtained with maximum intensity between 1% and 2% of the parent band, in agreement with observations by Rooke. The low-energy tail has a similar strength in the region of the satellite. The first-order theory, however, breaks down in the region of the parent band spectrum.

Validity of many-body approximation methods for a solvable model: (III). Diagram summations

The model N-fermion system studied in two previous papers is reconsidered in order to investigate the range of validity of diagrammatic many-body perturbation theory and various selective summations of higher order graphs. The familiar random phase approximation or bubble graph sum is shown to be the first term in an expansion in powers of 1/ N for which the coefficients are arbitrary functions of NV/ ε, where V is the interaction strength and ε is the level separation of the non-interacting system. However, the 1/ N expansion converges very slowly (if at all) for N < 40. Other corrections to the bubble sum which do not fit into such an expansion are shown to be much more important than the 1/ N corrections for small N. These are the exchange and self-energy graphs which correct for counting errors and violations of the exclusion principle when enumerating the states that a given particle can occupy. With these terms a rather good approximation to the excitation energy can be obtained, though the results are not quite as good as that obtained with fourth-order perturbation theory for small N, or for the whole range of N with the self-consistent linearization procedure described in a previous paper.