Theory Of Electron Correlation Research Articles

Size-consistent Brueckner theory limited to double and triple substitutions

A general Brueckner-type theory of electron correlation, including double and triple substitutions, is presented (BDT theory). This has the properties of (1) exactitude for three electrons and (2) size consistency. A Møller-Plesset type of perturbation analysis shows that this is identical in fifth order to coupled cluster theory with single, double and triple substitutions based on Hartree-Fock (CCSDT). The BDT equations, however, are considerably simpler than those of CCSDT. Some preliminary applications of BDT theory are discussed.

Third-order electron correlation theory of electronic Raman scattering for rare-earth ions in crystals: Effective-tensor-operator formulation.

Third-order electron correlation theory of electronic Raman scattering for rare-earth ions in crystals: Effective-tensor-operator formulation.

A fifth-order perturbation comparison of electron correlation theories

Electron correlation theories such as configuration interaction (CI), coupled-cluster theory (CC), and quadratic configuration interaction (QCI) are assessed by means of a Møller-Plesset perturbation expansion of the correlation energy up to fifth order. The computational efficiencies and relative merits of the different techniques are outlined. A new augmented version of coupled-cluster theory, denoted as CCSD(T), is proposed to remedy some of the deficiencies of previous augmented coupled-cluster models.

Third order a b i n i t i o calculations of amplitudes of two-photon absorption for ions across the lanthanide series

The third-order electron-correlation theory of two-photon absorption in rare earth ions in crystals has been extended by the effective operators arising from doubly excited configurations. The approach defined in terms of one-particle effective operators has been applied to the Pr+3, Nd+3, Eu+3, Gd+3, Tb+3, and Tm+3 ions. The relative importance of third-order contributions and their properties across the lanthanide series are presented. The discussion is based on the numerical results of exact ab initio calculations performed within the perturbed-function approach.

Relativistic autoionisation of bound states of negative ions: Be-

Negative ions have bound excited states which decay via relativistic autoionisation. An application of a state-specific theory of electron correlation and relativistic effects in the Breit-Pauli approximation to the Be- 1s22s2p2 4P metastable state has yielded for the lifetimes of its three J levels: J=5/2: 1.0*10-6 s, J=3/2: 2.0*10-3 s, J=1/2: 8.0*10-8 s. The only other complete information on such decay dynamics is based on the experimental measurements of the He- 4Po levels. The large dispersion among the J levels is due to the effects of final-state correlation, of cancellation and of non-orthonormality.

Multichannel relativistic autoionisation of negative ions: the 1s2s2p36S5/20metastable state of Be-

Be- has been predicted to have three bound states of which the 1s2s2p2 6S56/0 decays to a multichannel continuum via relativistic autoionisation. Application of a state-specific theory of electron correlation, relativistic effects and interchannel coupling has yielded tau =8.3*10-3 s for the lifetime of this level.

Controlled orthogonalization of localized orbitals

AbstractThe electron correlation theories for extended systems require an orthogonal and at the same time well‐localized virtual orbital system. An iterative method is suggested, by which extremely nonorthogonal basis sets can be orthogonalized without destroying the localization, in contrast to other well‐known procedures. With the help of a general formulation of the problem not only the localization but other properties can be achieved as well. The method is compared to Löwdin's orthogonalization. Calculations for model and real systems were carried out and the convergence properties and the stability of the fixed points of the iterative procedure were investigated.

The linked singles and doubles model: An approximate theory of electron correlation based on the coupled-cluster ansatz

From the diagrammatic construction of the full coupled-cluster theory of all single and double excitations, a linearized theory, a direct configuration interaction theory (CISD), a CEPA-like theory, and a linked singles and doubles (LSD) theory are separated. These theories are then compared with one another, with the results from full fourth-order perturbation theory, and with exact results when available. The LSD model, corresponding to the removal of unlinked terms of the CISD, and its spin adapted version, appear most accurate in Pariser–Parr–Pople studies where the exact numbers are known. Examples within the localized bond model are given indicating that this model is also the most successful of those examined in generating not only the basis set correlation, but the necessary delocalization and polarization required to correct for the zeroth-order local description.

Soft X-ray emission and the d band width in nickel

It is shown that recent theories of electron correlation in transition metals can explain the widths of the L2,3 and M2,3 soft X-ray emission spectra of Ni. The author shows calculations, based on an accurate band structure, which include correlations through a self-energy. The latter quantity has been calculated several times in connection with photoemission, and one finds that its effects are similar in X-ray emission. The relative widths of the L2,3 and M2,3 spectra are also briefly discussed.

Superconducting transition temperatures of vapour quenched Ag-In and Ag-Sn multilayers

Sequences with up to 17 layers of alternate films of In and Ag respectively Sn and Ag were deposited onto a liquid helium cooled substrate and studied in situ. A plot of the superconducting transition temperature against the number of films yields a zig-zag variation superimposed on a smoothly increasing curve. This agrees qualitatively with a recent theory for electron correlation in adjacent superconducting layers, operating in conjunction with a proximity effect.

On the theory of electronic correlations in solids

A formalism is presented for the computation of long range as well as short range correlations in the electronic ground state of a solid. It is based on a Local Approach to the correlation problem which was successfully tested before for small molecules. The method connects two approaches to the correlation problem. One is that of the RPA which is often applied in solid state physics and describes the long range aspects of the correlated electronic motions. The other is that of quantum chemistry which tries to calculate to high accuracy the short range part of the correlation problem. The method is variational in nature. The approximations which have been made exclude the application of the present formalism to strongly correlated systems such as valence fluctuating systems.

Valence bond perturbation theory for electron correlation

A second-order valence bond perturbation treatment (VB–PT) of electron correlation which utilizes the self-consistent valence bond wavefunction as an initial approximation is described. In trial calculations on H2 and LiH, at the equilibrium intranuclear distance, the accuracy is comparable to third-order Hartree–Fock perturbation theory (HF–PT). However, the computation time for VB–PT increases only as NK4 (N is the number of electrons; K the number of basis functions) whereas HF–PT, and other treatments of similar accuracy, are N2K4 procedures. Other advantages of VB–PT include a correct qualitative description of bond dissociation in zeroth-order; an exact breakdown of the perturbation energy into a sum over pairs; potentially weak mixed pair correlations; and the possibility of atoms-in-molecules methods to do away with the basis set problem.

New interpretations, anomalous degeneracies, and SO(4) theory for electron correlation in first-row atoms and multiply-excited states

Geometrical and computational interpretations are offered for configuration-mixed ..cap alpha.. (1s/sup d/2s/sup 2/2p/sup m/) + ..beta.. (1s/sup d/2p/sup m/+2) (where d = 0 or 2) valence states based on new profiles of L-shell mixing coefficients, correlation energies, and pair-function angular distributions for both ground and excited states. When viewed for species having the same degree of ionization Z-N, the profiles constructed for the internal and semi-internal ''nondynamical'' correlation energies computed by Sinanoglu's ''non-closed-shell many-electron theory'' are found to display a striking, approximate particle-hole symmetry with respect to total L-shell occupancy. Near-degeneracy-type correlation energy for /sup 3/P and /sup 1/D levels of C-like atoms becomes exactly degenerate when the same radial functions are used for both states. The mixing structure for all L-shell states is described accurately by an N-electron operator ..lambda.. (N) = ..sigma../sub i/< j (A/sub i/-A/sub j/)/sup 2/ with single-particle SO(4) generators A/sub i/ like the Runge-Lenz vector. ..lambda.. (N) represents an approximate ''correlation invariant'' for L-shell mixings.

Electron correlation theories and their application to the study of simple reaction potential surfaces

AbstractThis paper serves two purposes. The first is to describe an implementation of the coupled cluster theory with double substitutions (CCD) previously developed by Cizek. The second is to apply this method and closely related fourth‐order perturbation methods to some simple molecules and reaction potential surfaces. These studies show that CCD theory gives results close to those of a Møller‐Plesset perturbation treatment to fourth order in the space of double and quadruple substitutions MP4(DQ). Addition of contributions from single substitutions at fourth order makes little change in predicted relative energies. Preliminary results on the potential surfaces for 1,2‐hydrogen shifts in C2H2, HCN, CH2O, and N2H2 are discussed and compared with previous studies.

Self-consistent theory of electron correlation in the Hubbard model

Self-consistent theory of electron correlation in the Hubbard model

Green function theory of electron correlations above and below the Verwey transition in magnetite doped with impurities

The electron correlation effects in magnetite doped with impurities (MexFe3-xO4 with Me = Zn, Ni, Co, Ti, Sn, Li, Cr, Mg, Al, B-site vacancy) are studied on the basis of a Hamiltonian which describes the electron-electron and the electron-impurity interactions and is an extension of the Cullen-Callen model of magnetite. Treating this model in the case of low impurity concentrations x by means of a cluster approximation for Green functions the temperature dependence of the charge density oscillations around an isolated impurity and the Verwey transition temperature Tv(x) are calculated. The theoretical results for Tv(x) agree well with experiments except for titanium-substituted magnetite. For this ferrite the theory predicts an increase of Tv(x) with increasing x which represents a combined electron correlation and lattice structure effect.

The pairwise correlated generalized valence bond model of electronic structure. IV. Low lying S states of two-electron atoms and ions

Quantitative tests for theories of electron correlation are rare, since exact nonrelativistic energies are generally unknown. An important exception to this dilemma is found in the case of two-electron atoms. Accurate nonrelativistic energies are available for ground and excited states of two-electron atoms and ions. Comparison with these exact results provides an ideal testing ground for a theory of electron correlation. We have, therefore, carried out SCF calculations on the (1s,1s)1S ground state and on the (1s,2s)1S and (1s,2s)3S excited states of two-electron atoms for a wide range of nuclear charges. The resulting correlation energies (i.e., EEXACT−ESCF) are then compared to the overlap approximation we developed in an earlier paper. The observed correlation energies agree with the overlap approximation to within 2% for the singlet states. Hence, combining the overlap approximation for the correlation energy with the calculated SCF energy (i.e., the pairwise correlated generalized valence bond method) gives total energies two orders of magnitude more accurate than the SCF calculations, with only a trivial increase in computing effort. The agreement for triplet states is equally good for the pair of orbitals for which the 2s eigenvalue equals the ionization potential. However, discrepancies of 10% are found for the pair of orbitals for which the one-electron Hamiltonian is diagonal.

Gutzwiller theory of electron correlation at finite temperature

The Gutzwiller's scheme is extended to finite temperature in order to study the properties of electrons in strongly correlated metals. Using the quasichemical approximation we have constructed an orthogonal set of trial functions. These have a one-to-one correspondence to the Slater determinants with Bloch states. Our scheme for constructing this set of basis functions is independent of the perturbation theory. Based on this orthogonal set, the entropy of the correlated electrons has been derived from the thermodynamic equations. It has the correct behavior in the metallic phase except in the vicinity of the metal-nonmetal phase boundary. The electron effective mass and the Pauli spin susceptibility are found to be enhanced in a way similar to the Brinkman-Rice result for a correlated ground state. The Knight shift is also enhanced but the enhancement factor is much less than that for the susceptibility. However, the electronic specific heat is enhanced only for $\frac{{k}_{B}T}{\ensuremath{\Delta}}\ensuremath{\gtrsim}0.11$ ($\ensuremath{\Delta}$ is the bare bandwidth). For $\frac{{k}_{B}T}{\ensuremath{\Delta}}\ensuremath{\lesssim}0.11$ we need to consider the collective excitations such as paramagnons in order to have a complete treatment of the specific heat. Using an ellipsoidal density of states we have performed model calculations for a nonmagnetic state in order to illustrate the characteristic features of the strongly correlated electron system.

Note on the perturbation theory of electron correlation

The n-electron Hilbert space is partitioned into three parts by means of the projection operators P, Q, R such that P is associated with the known zeroth order wavefunction Φ, Q with the subspace of functions that are singly or doubly substituted with respect to Φ and R with the rest. The perturbation expansion based on this partition has some advantages compared with conventional expansions and is helpful for an analysis of correlation effects in π-electron systems.

Electron correlation in excited states and term splittings in the carbon-I isoelectronic sequence

The theory of electron correlation in excited states is used in evaluating spectroscopic quantities exemplified by the calculation of term level splittings among excited states of the carbon-I isoelectronic sequence. Agreement with experiment is generally better than 10%, which is 4–25 times better than that achieved by conventional Hartree-Fock (HF) calculations and 2–10 times better than that achieved by standard multiconfigurational HF calculations.