Intra-atomic Correlation Effects Research Articles

Some effects of intra-atomic electron correlation on XPS multiplet splittings

Large deviations between experimental and theoretical values for XPS exchange splittings have been attributed to intra-atomic correlation effects. It is shown here how these can reduce exchange splittings by a factor which is roughly independent of the valence electron configuration, spin state, or covalency. The use of splittings to measure such effects may therefore be justified, in spite of the large contributions from correlation.

Theory of the hydrogen interstitial impurity in germanium

The self-consistent pseudopotential method is used to study the electronic structure of the hydrogen interstitial impurity in Ge. The impurity is considered to be at the site of tetrahedral symmetry and strong intra-atomic correlation effects are included. It is found that a singly occupied H-$1s$ deep donor state exists, a result consistent with positive muon spin rotation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) experiments. This state lies at least 1 eV, and perhaps as much as 6 eV, below the Ge valence-band maximum. An examination of the charge density suggests only a small tendency of H to bond with the neighboring Ge atoms. It is tentatively concluded that this deep donor state is the one probed by ${\ensuremath{\mu}}^{+}\mathrm{SR}$ experiments but that H migrates to impurity- or defectrelated complexes or forms of molecular hydrogen rather than remaining as an isolated interstitial impurity.

Natural states of interacting systems and their use for the calculation of intermolecular forces. II. Natural states in the asymptotic 1/ R expansion

The asymptotic natural states i.e. the natural states of the subsystems in the various terms of the asymptotic expansion of the primitive wavefunction of the supersystem are defined. Integro-differential equations are derived that allow the direct calculation of these asymptotic natural states and from them, the terms C 6, C 8 etc. in the asymptotic 1/ R expansion of the interaction energy. A pictorial interpretation of these states is given and the rapid convergence of the expansion in natural states is explained. The transferability of certain matrix elements is demonstrated and a virtually exact combination rule for the calculation of the C k coefficients between different atoms from those for like atoms is obtained- The effects of intraatomic electron correlation on the C k as well as the justification of a core-valence separation are discussed.

An approximate treatment of intra-atomic correlation in Hartree-Fock calculations: the Hg2(X1Σg+) potential

Atomic and molecular properties dependent on the valence electrons are sensitive to intra-atomic correlation effects, and these tend to be largest in atoms of high atomic number where accurate ab initio computations are difficult. A simple model potential method is proposed for including correlation effects in Hartree-Fock calculations. Application is made to an electron-gas computation of the Hg2(X1 Sigma g+) potential.

A calculation of the well depth for a pair of helium atoms

A new methods is proposed for the elimination of the basis superposition error in the calculation of small potentials. The method which involves CI is applied to the calculation of the well depth of He 2. It includes interatomic and intraatomic correlation effects simultaneously. A value for the well depth of 10.54 K at R = 3.03 au is obtained, in excellent agreement with current theoretical estimates.

On the exchange polarization effects in the interaction of two helium atoms

The induction and the dispersion components of the exchange polarization energy are calculated for the interaction of two ground-state helium atoms. The calculations are made within the framework of a double perturbation theory with the neglect of all intra-atomic correlation effects. Two zeroth-order operators, the Hartree and the Hartree-Fock are considered, the former yielding much better results than the latter. At the van der Waals minimum the exchange polarization energy is positive and decreases the interaction energy by about 7 per cent. The calculated value of a well depth amounts to 13·4 K, which should be considered as an upper limit because of the neglect of intra-atomic correlation. When approximately corrected for the latter a lower limit of 10·7 K is obtained. It is also shown that over 90 per cent of the exchange dispersion energy can be obtained by using a simplified formula involving only one two-electron integral over a relevant pair function.

Van der Waals constants for alkaline earth-noble gas pairs

The long-range R−6 interaction between alkaline earth and noble gas atoms is considered from both classical and quantum-mechanical viewpoints. Intra-atomic electron correlation effects are shown to be important for these systems. The relevant van der Waals coefficients are calculated with the use of an accurate, correlated wavefunction in the case of Be and from oscillator strength sum rules for the other alkaline earth atoms.

Metal-insulator transitions and Hund's rule coupling in degenerate narrow bands

The intra-atomic exchange (Hund's rule mechanism) and the intra-atomic correlation effects on electron hoppings are examined to determine their roles in the 'metal-insulator transition' and magnetic ordering in degenerate narrow bands. A trial function is proposed with minimum polarity for the ground state of a correlated electron system. The tight-binding bands are then constructed and show a narrowing of the bulk part of the density of states due to the restriction on electron hopping by the intra-atomic interactions. The critical correlation energies for the ferromagnetic and the paramagnetic states are calculated, but not for the antiferromagnetic state. The ratio of these two critical energies provides a condition for metallic ferromagnetism.

Effect of Intra-atomic Correlation on London Dispersion Interactions: Use of Double-Perturbation Theory

A simple double-perturbation-theory method is outlined for the calculation of the first-order effects of intra-atomic electron correlation on the dipole polarizability at imaginary frequencies, and on the London coefficient for interactions between two-electron systems. Both single-parameter Slater and Hartree—Fock orbitals are used as zero-order wavefunctions. The static polarizability of helium and the London coefficient for helium—helium interactions found with the Hartree—Fock wavefunction are (in atomic units) 1.3346 and 1.382, respectively; accepted values are 1.384 and 1.47. The extensions of this method to larger systems, higher multipole interactions, and more complicated zero-order wavefunctions are discussed.

Long-Range Interaction of Helium Atoms. A. Calculations

The interaction of two nonoverlapping helium atoms is evaluated using the many-electron theory of atoms and molecules with a Hirschfelder—Linnett-type of pair function, a Hylleraas intra-atomic correlation function, and a two-term atomic Hartree—Fock orbital. Previous work (previous paper) showed that the ``nonoverlapping'' region is separations over 3.7 Å. In atomic units we find V=−1.353R6−13.25R8−52.45R10−94.45R10for the dipole—dipole (using three variable parameters), dipole—quadrupole (two parameters), quadrupole—quadrupole (one parameter), and dipole—octupole (one parameter) interactions. The accepted correct value of the first coefficient is about 1.47. About 21% of the R−6 coefficient is due to three-electron effects which arise as matrix elements between the two-electron terms in the wavefunction. Neglecting intra-atomic correlation effects we obtain a coefficient of −1.644 for the first term. An error of 25% results if only a one-term atomic orbital is used. The relation of these results to many approximate methods of calculation is also discussed.

Electronic structure of the first row hydrides BH, CH, NH, OH and FH. I. Ground states

Some recent calculations by the self-consistent field molecular orbital method are generalized to allow for electron correlation. Correlations between the motions of the valence electrons are introduced explicitly by means of configuration interaction, whilst the effects of intra-atomic electron correlation are estimated semi-empirically. Both forms of correlation, but especially the latter, are found to have a profound effect on the calculated properties of the hydrides. The total electronic energies obtained in the final calculations fall consistently above the experimental values by an almost constant amount (0.5 to 0.7 eV). The wave functions and dipole moments of the molecules are analyzed in the frameworks of both the valence-bond and molecular orbital theories.

The Bindng Energy of the Nitrogen Molecule

A recent self-consistent field molecular orbital calculation on the nitrogen molecule by Scherr is extended to include configuration interaction. In this way the calculated binding energy De is increased from 1.19 electron volts to 3.29 electron volts. The extended calculation is then modified to make allowance for the effects of intra-atomic electron correlation. The result of this modified calculation (De>9.18 ± 0.5 eV) is consistent only with the higher of the two spectroscopic values (7.52, 9.91 eV). Configuration interaction is much less important in the modified calculation than in the orbital calculation.