Importance Of Electron Correlation Research Articles

Basis set and correlation effects on geometry of octahedral second-row transition-metal complexes

An extensive investigation of the basis-set effect on the predicted geometry of the redox pair [Ru(NH3)6]2+/3+ is presented. Basis sets where the core electrons have been replaced with a relativistic core potential as well as all-electron basis sets were tested. Best agreement with observations was obtained with the all-electron basis set MIDI augmented with a set of f-type polarization functions on the metal center. Other properties such as the vibration spectrum, the relative energy of the high-spin and low-spin states, and geometry changes upon oxidation/reduction of the central metal are discussed. The importance of electron correlation on the predicted geometry was estimated at the MP2, MP3, MP4(SDQ), CCSD, and CCSD(T) levels of theory. The MIDI(f) basis set is then used for other octahedral second-row transition-metal complexes and some other related complexes. The electronic spectrum of [Ru(NH3)6]2+ is also calculated using two different CI computational schemes. Surprisingly good agreement between the predicted electronic spectrum and the observed spectrum are obtained using one of the CI computational schemes. © 1996 John Wiley & Sons, Inc.

Structure and stability of molecular carbon: Importance of electron correlation.

The electronic structure of medium-size molecular carbon is determined by a variety of methods, including density functional, quantum chemistry, and quantum Monte Carlo approaches. We demonstrate (i) significant differences between the mean-field methods in determining the minimum energy structure of a set of ${\mathrm{C}}_{10}$ and ${\mathrm{C}}_{20}$ isomers, and (ii) the crucial importance of an accurate account of electron correlation which enables us to predict, e.g., that of the available geometries for ${\mathrm{C}}_{20}$ the relaxed graphite fragment (bowl) is lower in energy than either the ring or fullerene isomers.

Analytic energy derivatives for ionized states described by the equation-of-motion coupled cluster method

The theory for analytic energy derivatives of excited electronic states described by the equation-of-motion coupled cluster (EOM-CC) method has been generalized to treat cases in which reference and final states differ in the number of electrons. While this work specializes to the sector of Fock space that corresponds to ionization of the reference, the approach can be trivially modified for electron attached final states. Unlike traditional coupled cluster methods that are based on single determinant reference functions, several electronic configurations are treated in a balanced way by EOM-CC. Therefore, this quantum chemical approach is appropriate for problems that involve important nondynamic electron correlation effects. Furthermore, a fully spin adapted treatment of doublet electronic states is guaranteed when a spin restricted closed shell reference state is used—a desirable feature that is not easily achieved in standard coupled cluster approaches. The efficient implementation of analytic gradients reported here allows this variant of EOM-CC theory to be routinely applied to multidimensional potential energy surfaces for the first time. Use of the method is illustrated by an investigation of the formyloxyl radical (HCOO), which suffers from notorious symmetry breaking effects.

Neutral and negative donors in quantum dots

Using a method introduced earlier, the exact solutions of ground states of neutral donor (D0) centres in different quantum dots (QDs) have been obtained, and, taking the Chandrasekhar-type function as a trial function, the ground states of negative donor (D-) centres in QDs have been calculated. The dimensionality and potential-shape effects of QDs on the binding energies EB(D0) and EB(D-) of D0 and D- centres have been studied. The ratio sigma of EB(D0) to EB(D-) has clearly demonstrated the so-called freeze-out effect in different QDs. According to the value of sigma obtained, calculated results of different quantum-well structures can be checked and compared with others. It has been shown that the freeze-out effect and the electron-correlation effect are strongly dependent on the dimensionality of QDs and weakly dependent on the potential shape, and that the polarization term of the trial function not only brings in the important electron-correlation effect but also modifies the behaviour of the single-electron orbitals.

Valence electron momentum distributions of the hydrogen halides. I. Comparison of EMS measurements and calculations using Hartree—Fock limit and configuration interaction wavefunctions for hydrogen fluoride.

The valence orbital momentum profiles of hydrogen fluoride have been obtained using electron momentum spectroscopy at an impact energy of 1200 eV. The present results show significant differences from earlier measurements. (J. Electron Spectry. Relat. Phenom. 21 (1980) 71) for the (3σ) −1 ionization but are in good agreement for the (1π) −1 processes. The measurements are compared with calculations ranging from minimum basis set to highly saturated basis sets essentially at the Hartree-Fock limit and also with numerical Hartree-Fock calculations. The experimental momentum resolution is incorporated into the calculations using the recently developed GW-PG resolution folding method (Chem. Phys. 159 (1992) 347). The significant discrepancy remaining between SCF limit calculations and experiment indicates the importance of electron correlation and relaxation effects in describing the momentum profile corresponding to the removal of the 1π electron. These effects are investigated using multireference singles and doubles CI calculations of the full ion-neutral overlap distribution and considerable improvement in the agreement between theory and experiment is then achieved.

Study of Electron Correlations in Pb n2+-Clusters

The ground state properties of Pb-clusters are investigated using a many-body Hamiltonian with intra and inter-atomic Coulomb interactions. By solving the model exactly we obtain that Pb is metastable (lifetime τ > 1040s) and that it has isosceles geometry (bondangle Θ ≃ 124°). The importance of electron correlations for the stability of doubly charged clusters is discussed. By comparison between the exact solution and several variational approaches we particularly show that both the metastability and isosceles shape of Pb result mainly from antiferromagnetic quantum spin-fluctuations.

Electron correlations and spin-orbit interaction in two-photon ionization of closed-shell atoms: A relativistic time-dependent Dirac-Fock approach.

Electron-correlation and spin-orbit-interaction effects are known to play an important role in the quantitative description of multiphoton ionization of heavy atoms. In this paper an ab initio approach to two-photon ionization (2PI) of closed-shell atoms in the framework of the relativistic time-dependent Dirac-Fock theory is proposed. This formulation is known to contain important electron-correlation corrections and includes the spin-orbit interaction by use of relativistic wave functions. Computational results for nonresonant 2PI total cross sections of the rare gases are given. The approach is suitable for calculations of angular distributions, branching ratios, and autoionizing resonances.

Fully numerical complex-coordinate Hartree-Fock calculations for alkaline-earth resonance states.

A fully numerical multiconfiguration Hartree-Fock program has been modified for performance of calculations on atomic quasibound states using the complex-coordinate (dilation) technique. We present single-configuration calculations for the lowest $^{2}$P\ifmmode^\circ\else\textdegree\fi{} states of ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, along with results of some small-scale multiconfiguration investigations of the Mg resonance. An instability originating in difficulty satisfying orthogonality constraints prevents a full multiconfiguration treatment of this resonance. Single-configuration dilated Hartree-Fock calculations predict $^{2}$P\ifmmode^\circ\else\textdegree\fi{} shape resonances for all these systems, though recent extensive calculations show the Ca, Sr, and Ba ions to be bound. Nonetheless, we think it is significant that the dilated numerical method can easily carry out fully variational computations on these heavy atoms, and our results, in conjunction with those of other studies, shed light on the importance of electron correlation in its effect upon the resonance parameters and its variation with progressively heavier alkaline-earth atoms. We also establish the feasibility of accounting for important correlation effects through the use of multiconfiguration approximations, though we have not attempted an accurate calculation in this work. Our Be, Mg, and Ca results agree well with previously published single-configuration dilated basis-set calculations, but no such calculations have been carried out for Sr or Ba. Finally, we investigate the dilational stability of the numerical method since this has been an important consideration in basis-set calculations. A simple exercise based on Cauchy's theorem shows that analyticity of the Hartree-Fock radial wave functions implies that the energy and other physical quantities are independent of the dilation parameter, and a high degree of such independence is demonstrated in our numerical results.

On the strength of electron correlations in high-T c superconducting copper oxides

We analyze the strength of electronic correlations in the half-filled antibonding Cu−O orbitals of high-Tc superconducting copper oxides by considering a Cu12O 17 n− cluster withn=8 or 10, respectively. The correlated ground state is calculated by the method of the local approach (LA) in a version which allows the treatment of stronger correlated electrons. As mean-field basis a semiempirical Hamiltonian of the ZDO (zero differential overlap) type has been adopted. It is found that the correlations are particularly strong in the Cu 3dx2−y2 orbitals. The nonintegral orbital occupation allows for valence fluctuations between Cu+ and Cu2+ in spite of the remarkable correlations. According to the present model excess holes are located at the oxygen sites. The theoretical findings are compared with the results of spectroscopic investigations. The present electronic-structure analysis allows for a straighforward rationalization of previous experimental measurements. The strong connection between the importance of electronic correlations and the symmetry properties of the electronic wave function is emphasized.

New results in atomic photoionisation at the Daresbury Synchrotron Radiation Source

A survey of recent experimental results in atomic photoionisation using the Daresbury Laboratory Synchrotron Radiation Source is presented. Three experiments are described: fluorescence from excited atomic ions, threshold electron behaviour near the double ionisation limit of He, and the measurement of absolute cross sections for atomic ions. The data yield fundamental information on the importance of electron correlation and autoionisation in atoms. Their relevance to recent theoretical ideas is discussed, with future developments of the experimental programme indicated.

Resonant electron transfer and L-shell excitation for41Nb31+and57La40+ions

Observations of resonant electron transfer and L-shell excitation (RTE) using coincidence techniques are reported for 41Nb31+ and 57La40+ ions colliding with H2. The measured RTE cross sections are about ten times larger than those previously found for RTE involving the K shell and constitute as much as half of the total L alpha beta X-ray production. Overall agreement with theory is reasonable but discrepancies similar to those previously reported for K-shell RTE exist. The results demonstrate the importance of electron correlation in the production of L vacancies for projectile energies where RTE is possible.

Nonlinear Optical Properties of Polyenes: Electron Correlation and Chain Conformation

ABSTRACTUsing a recently developed many-electron theory of second and third order nonlinear optical susceptibilities, microscopic descriptions of γxxxx(-3ω;ω,ω,ω) are presented for two conformations of polyenes. The importance of electron correlations and the effects of variation in conformation and chain length are discussed.

Inner-shell photoionisation in molecules: the carbon monoxide case

The inner-valence-shell photoionisation of CO has been studied by electron spectrometry using monochromatised synchrotron radiation in the region of 34 to 100 eV. The analysis of the experimental data and the quantitative comparison with theoretical calculations illustrate the important role electron correlation and shape resonances play in the explanation of the main features of these photoelectron spectra.

Excitation operators and the extended random phase approximation: II. Applications

The random phase approximation (RPA) and its extensions are tested by applying them to the π electron system of a series of linear polyenes in the PPP approximation, for which exact solutions are available. The importance of electron correlation is varied by altering the form of the electronic repulsion matrix elements in the PPP model. Emphasis is placed on a comparison between recently suggested refinements in the RPA and the more standard RPA scheme. The elements of the modifications of the RPA are illustrated by the simple example of ethylene. Calculations for longer polyenes (butadiene, hexatriene, and octatetraene) demonstrate that certain improvements in the RPA are essential if reliable results are to be obtained for highly correlated excited states. The results provide support for use of the extended RPA method in molecular excited state calculations.

Importance of electron correlation in computing molecular energies and structures of annulenes

Importance of electron correlation in computing molecular energies and structures of annulenes

Applications of a simple molecular wavefunction. Part 13.—Open-shell calculations for hydrogen-bridge structures

Calculations have been made, using open-shell many-determinant FSGO wave functions, for the species Li2H2, Be2H4 and B2H6 containing hydrogen bridge structures. Corresponding calculations have been made for the monomers to estimate the energy of dimerization. Comparison has been made between open-shell and closed-shell calculations in order to assess the importance of electron correlation in dimerization. Similar calculations have been performed for the non-classical structure of the ethyl cation containing one hydrogen atom in the bridge region; calculations were also made for the classical form in order to estimate the relative stability of the two forms.

Fundamental problems in the electronic structure of transition-metal oxides

The evolution of the electronic structure of a solid as it is formed from large interatomic separations to its equilibrium lattice configuration is analyzed. The importance of electronic correlations in the narrow-band regime is emphasized, particularly with regard to transport behavior. First, the case of a monovalent solid, such as Na, is analyzed in detail, and an effective one-electron representation, exact in the atomic limit, is introduced. It is shown that the ordinary band approximation fails miserably in this limit. Next, the more realistic case of a transition-metal oxide is considered. In the limit of strong correlations, it is emphasized that information deduced from optical experiments should not be used to analyze transport data within the band approximation, since the effective electronic density-of-states diagram can differ significantly from that derived from optical results. Finally, some fundamental difficulties in our present understanding are discussed.

The importance of electronic correlations for the calculation of X-ray and fast electron scattering by Be, B, C, N, O, F:II

The elastic, inelastic and total intensities of diffraction for fast electrons, the coherent, incoherent and total scattering for X-rays by the neon atom in its ground state have been studied using the atomic Bethe- Goldstone equations which give about 97.3% of the empirical correlation energy. The results are compared with those obtained with two CI wavefunctions and the Clementi wavefunction which give respectively 85% 53% and 20% of the correlation energy. The authors give also the Hartree- Fock results. It is shown that a properly correlated wavefunction is necessary when one wants to compare carefully the theoretical and experimental scattering intensities.

The importance of electronic correlations for the calculation of X-ray and fast electron scattering by Ne(1S)

The importance of electronic correlations for the calculation of X-ray and fast electron scattering by Ne(¹S)

Resonance and conjugation—II Factors determining bond lengths and heats of formation

Two previous papers presented interim reports of an investigation into the importance of resonance in conjugated systems. Further work has confirmed our earlier conclusions that resonance effects are unimportant in classical molecules, the bond lengths in them being determined by the state of hybridization of carbon; that the observed stabilization of such molecules is due to changes in bond energy with hybridization rather than to resonance; and that resonance stabilization plays a surprisingly small role even in benzene. A calculation is described which, starting from very limited experimental data, provides values for several CC bond lengths (ethylene, benzene, graphite) which agree excellently with experiment, a value for the sp 2- sp 2 CC bond length which agrees well with the value found in butadiene, diphenyl, etc., and a set of bond energies for CC and CH bonds of various types. Heats of formation for a number of hydrocarbons are calculated from these bond energies and compared with experiment. Agreement is excellent for paraffins, olefines, and acetylenes, confirming the lack of hyperconjugative stabilization in the latter. Deviations in cycloparaffins are ascribed to conformational effects (CHCH dipole repulsions). Butadiene shows an apparent resonance energy of 2 kcal/mole, less than a quarter of the stabilization energy; reasons are given for believing even this value to be much too large. The lack of resonance in butadiene is confirmed by a MO calculation of its effect on the bond lengths. When allowance is made for the effect of σ-bond compression, the resonance energy of benzene is found to be only about 10 kcal/mole, less than a quarter of the stabilization energy. Previous ideas concerning the importance of electron correlation in conjugated systems are clarified: it is shown that the neglect of such correlation invalidates existing methods of calculation, particularly in the case of classical molecules, and a method is suggested whereby such correlation effects might be taken into account. The significance of resonance theory is discussed. Various criticisms made by Mulliken in a recent paper are shown to be unjustified.