Correlation Energy Contributions Research Articles

Basis set and correlation effects on computed hydrogen bond energies of the dimers (AHn)2: AHn=NH3, OH2, and FH

Basis set expansion and correlation effects on computed hydrogen bond energies of the dimers (AHn)2, AHn=NH3, OH2, and FH, have been evaluated. The addition of diffuse functions is the single most important enhancement of split-valence plus polarization basis sets, leading to a significant lowering of hydrogen bond energies at all levels of theory. In general, basis set enhancement effects do not appear to be additive. The correlation energy contribution increases the stabilization energies of these neutral hydrogen bonded complexes, with the second order Mo/ller–Plesset term being the dominant term.

Binding energy analysis of solid hydrogen fluoride

Ab initio energy band structure calculations of infinite single and double HF chains are performed. Interaction energies within and between the linear macromolecules are deduced. As an alternative way for the decomposition of the binding energy tetrameric HF clusters are investigated. Second order perturbation theory is applied to calculate the correlation energy contributions. The interaction of the elementary cell with its neighboring cells in the same layer is repulsive. A binding energy is obtained for the interaction with cells in different layers. The cohesive energy is about - 2 kcal mol -1 with respect to a single HF dimer. The results show that the binding energy in molecular crystals can be determined with the help of molecular cluster calculations.

Electronic excitations in semiconductors. II. Application of the theory to diamond

A previously developed theory for calculating electronic excitations in semiconductors is applied to diamond. The starting point is a self-consistent-field calculation within a given basis set of Gaussian-type orbitals. From that the fully correlated electronic wave function and correlation energy are calculated. The reduction of the direct energy gap and the widths of valence and conduction bands due to correlations are studied and compared with experiments. The results can be understood in terms of simple physical pictures. The largest correlation energy contribution results from the polarization cloud of the excited electron and hole pair, but changes in the ground-state correlations due to the presence of the excited electron are also of importance. Intra-atomic correlations such as relaxation effects are only estimated from molecular calculations. A detailed comparison with other methods is made, in particular with the local approximation to the density-functional formalism.

Correlation energy from compton scattering and positron annihilation data

AbstractThe second moments of Compton profiles are used to obtain electronic energies. It is proposed that the second moment of a line‐slit positron annihilation angular correlation curve, in comparison with the second moment of Compton profiles, can yield the correlation energy contribution to the cohesive energy of a material. The need for correcting the PAAC data for the positron enhancement factor and thermalization effects is examined. Numerical estimates of the errors involved are given for sodium and lithium and the possible applicability of the proposal is shown.

An ab initio study of the geometry, energy, and selected force constants for the three planar conformers of carbonic acid, and the bicarbonate ion; and of the energy for the reaction H2O + CO2 → H2CO3

AbstractAb initio calculations using the unscaled 4‐31G basis set have been carried out on the cc, tc, and tt conformers of carbonic acid and the bicarbonate ion, with full geometry optimization assuming the structures to be planar. The complete harmonic force field is reported for the (most stable) tt conformer and for the bicarbonate ion, also selected quadratic force constants for the cc and tc conformers. The changes in certain bond lengths and stretching force constants in the cc → tc, tc → tt, and cc → tt conformer conversion reactions are indicative of intramolecular hydrogen bonding, CO…HO and HO…HO, which is examined in greater detail by partitioning the overall conformer conversion energy into distortion and bonding energy components. The fundamental vibration frequencies for the tt conformer and the bicarbonate ion are calculated from the force constant matrices, and hence, using a scaling factor based on a comparison of calculated and experimental values for the bicarbonate ion and trans‐formic acid, a value is predicted for the zero‐point energy of the tt conformer. A new estimate of ΔH˚ for the hydration reaction, H2O + CO2 → H2CO3, at 298 K in the gas phase; is made from thermochemical data, +20.2 ± 3.4 kJ mol−1, which, together with estimates of (H298˚ – H0˚) and the zero‐point energy for H2CO3, gives +8.1 ± 7.0 kJ mol−1 for ΔET(expt). ΔET calculated from the 4‐31G basis set data is ‐29.1 kJ mol−1. Comparison of the experimental value, the Hartree–Fock limit value, and values calculated with a variety of basis sets for the bond separation reaction, CO2 + CH4 → 2H2CO, suggests that the differences, ΔET(expt) minus ΔET(SCF), are due mainly to basis set limitations and not substantial correlation energy contributions.

Electron correlations in the ground state of diamond

The correlated ground-state wave function and energy of diamond are calculated. The calculations are done in order to demonstrate that electron correlations in solids can be treated with the same accuracy as in small systems. This is achieved by applying a recently developed Local Approach to the correlation problem. The approach requires a SCF calculation as a starting point. We present such a calculation for diamond by applying a method due to Stoll and Preuss which uses localization potentials. The correlation energy is analysed in terms of inter- and intraatomic correlation energy contributions. The results are used to calculate the binding energy of diamond.

Simple Non‐Local Calculation of Jellium Metal Surface Properties

AbstractThe gradient expansion for the kinetic, exchange, and correlation energy contributions to the surface energy and work function of jellium metals is investigated. For the gradient correction of the exchange‐correlation the coefficient given by Geldart and Rasolt and the first gradient coefficient of Gupta and Singwi are used. The surface energy is determined from the variational principle for the energy, using parametrized trial functions for the electron density. The calculated surface energies are in agreement with some other nonlocal calculations. The work functions are calculated both, from the classical expression of Lang and Kohn and from less density‐profile‐sensitive expression. The calculated values of the work functions are in excellent agreement with the results of Lang and Kohn.

The optical activity of tetrahydroquinoline in the random-phase approximation. The importance of the correlation energy contributions to the optical activity

The random-phase approximation is applied to analyse the circular dichroism of the lowest electronic transitions of this molecule. The RPA equations are reduced to effective eigenvalue equations and the effective Hamiltonians analysed in Tamm-Dancoff (TD) and correlation interactions. It is shown that correlation provides important contributions and is essential to predict the correct sign of the lowest electronic transitions.

The energy and electron density of states of H in transition metals. IV. Improvements of the theory

For pt.III see ibid., vol.8, p.775-84 (1978). Calculations of the energy, Delta E, of hydrogen in the transition metals Pd, Rh and Ni previously reported were in error because of an inaccurate approximation used for the exchange and correlation energy contribution xi xc. Corrected results are presented and now disagree with the experimental results. The theory has therefore been critically reexamined and several refinements considered in detail. It is shown that the original theory correctly included the non-orthogonality of the basis functions. Further, the inclusions of second-neighbour sites of the impurity in the Vdd' matrix and gradient corrections to the exchange and correlation potential are shown to have little effect. The original perturbation treatment of the Vss' matrix has been tested by treating the g=0 orthogonal plane waves more rigorously through a Wannier-function representation. Significant changes occur at low energies in the electron density of states but the Delta E values are little affected. It is possible that the g not=0 Wannier functions could produce significant effects. A model calculation for a non-spherical impurity potential shows that a spherically symmetric screened Coulomb potential may be inadequate to describe hydrogen in transition metals.

The instability of the planar structure of carbanion ?:CH2-CN

Ab initio SCF calculations using uniform quality extended basis set supplemented with polarization functions predict a slightly pyramidal carbanion centre in ⊖:CH2-C≡N. This finding is in contrast to the usual finding of planar geometry of carbanion centres generated next to other conjugative groups. Although the predicted barrier to pyramidal inversion is very small (∼0.1 kcal/mole) it is estimated that correlation energy contributions, neglected in any SCF calculations, may be too small to remove the barrier. The present results confirm earlier experimental findings that counter-ion and solvent effects can have a dominant role in determining the geometry of this unusual ion in actual chemical systems.

Correlation energy contributions to reaction heats

AbstractNew, more accurate, Hartree‐Fock limit energies (EHF) for ethane and ethylene are obtained from SCF total molecular energie using Ermler and Kern's procedure. These results, together with EHF values for other small closed shell molecules, are employed to calculate correlation energy (Ec) contributions to reaction heats. Cancellation to within 98% of the total Ec involved, and often to more than 99%, is found for a wide variety of chemical reactions, which strongly suggests that there are systematic regularities in the contribution to Ec from the different kinds of electron pairs in the valence shell. Assuming trictly localized pairs occupying orbitals having strongly directional character, Ec for the valence shell is evaluated in terms of Ec per lone pair, Ec per XH bond, and Ec per X/X shared pair for Ne and for molecules containing first row atoms, where X is C, N, O, and F.

Lowest order corrections to excitation energies

It is shown that the excitation energy obtained by subtracting total energies for the ground and excited state is consistent through second order in the electronic repulsion if the total energies are obtained from separate Hartree—Fock calculations on the ground and excited state and augmented with the corresponding first order pair correlation energy contributions. Numerical examples indicate that calculations for individual excitations give an unsufficient description of excitation energies for close lying excited states.

Theory of the lattice energy, equilibrium structure, elastic constants, and pressure-induced phase transitions in alkali-halide crystals

The interionic forces in alkali-halide crystals are calculated theoretically, using a modified electron-gas treatment including corrections to the kinetic, exchange, and correlation energy contributions. These results are used to predict the equilibrium bond distances and lattice energies, the pressure-volume phase diagrams, and the elastic constants of the lithium, sodium, potassium, and rubidium fluorides, chlorides, bromides, and iodides. Both the $B1$ (rock salt) and $B2$ (cesium chloride) lattice types are considered, and the pressure-induced phase transition between them is predicted. First- and second-nearest-neighbor short-range interactions between the ions have been included for the $B1$ phase, while third-nearest-neighbor interactions were also needed for the $B2$ phase. The average magnitude of the deviation between the predicted and observed bond distances is 2%, lattice energy 2%, and elastic constants 10%. The pressure variation of the elastic constants for NaCl has also been predicted, up to the onset of a shear instability.

Theoretical study of the molecular ions SiH −5 and SiH −3

Ab initio HF and Cl calculations were performed to determine the equilibrium geometry of SiH − 5 and SiH − 3, the barrier for internal rotation (SiH − 5) and inversion (SiH − 3) and the stability of SiH − 5 and further to study the effect of electron correlation on reaction energies. The gaussian-type basis included d and f functions on Si and a p set on II. The D 3h structures of SiH − 5 is lower in energy than the C 4v structure by 2.9(3.2) kcal/mol (corresponding HF results in parentheses). SiH − 3 has C 3v structure, the inner-ion barrier computed is 26.2 (27.3) kcal/mol. SiH − 5 turns out to be stable with respect to SiH 4 + H − by 20.3 (13.8) kcal/mol, but it is unstable with respect to SiH − 3 ← H 2 by 6.3 (5.6) kcal/mol. These results show that electron correlation has a small effect on barriers of inversion (SiH − 3) or pseudorotation (SiH − 5), but may have a pronounced effect on reaction energies even if all systems involved have closed shells. The correlation energy contributions are analyzed in terms of intrapair and interpair terms in order to get a better understanding of the influence of correlation on reaction and activation energies.

Correlation energy contribution to the ammonia inversion barrier

Diagrammatic many-body double-perturbation theory is used to study the correlation contribution to the inversion barrier in ammonia. With a one-center solution as the zero-order function, the perturbation energy diagrams are shown to be of three types: Hartree-Fock diagrams (geometry dependent), atom-like correlation diagrams (geometry independent) and non-atom-like correlation diagrams (geometry dependent). Only the third class of diagrams enter into the correlation correction to the barrier. These diagrams, which appear first in third order, contribute a small fraction (1%) of the total correlation energy. We estimate from them that the correlation energy contribution to the barrier is small (less than 10% of the total barrier), although the bond length dependence of the correlation correction is such that it is difficult to obtain an exact value for it.

The influence of electron correlation on reaction energies. The dimerization energies of BH3 and LiH

Results of rigorous computations employing extended Gaussian-type basis sets are reported for BH3, B2H6, LiH, and Li2H2 in their respective equilibrium geometries. The dimerization energy of BH3 is calculated as −20.7 kcal/mol within the Hartree-Fock approximation and as −36.6 kcal/mol if electron correlation is included. The corresponding results for the dimerization of LiH are −47.3 kcal/mol and −48.3 kcal/mol. Partitioning of the correlation energy contributions allows to attribute the effect of electron correlation to the increase of next neighbour bond interactions on the dimerization of BH3 and LiH. The difficulties of accurate computations of reaction energies are discussed in detail.

LCAO-MO-SCF calculations using Gaussian basis functions. X. AlLi-SCF results and implications for choosing configurations for configuration interaction calculations

Ab initio LCAO-MO-SCF calculations have been performed for the lowest 1Σ+ state of AlLi. The results give a potential curve indicative of a chemically bound species but with the ESCF minimum lying slightly above the sum of the comparable SCF energies of the separated atoms. Analysis of the probable correlation energy contributions and an estimate of their magnitudes leads to an estimate of −1.5 eV for the correlation energy contribution to the binding in AlLi. This should be sufficient to permit the AlLi species to exist. The Li in AlLi is electron deficient compared to the Li atom itself. An examination of population analysis results for unoccupied orbitals leads to interesting insight into which virtual orbitals will correlate certain specific electron pairs or certain of the occupied molecular orbitals. The relationship suggests a very logical and systematic method for helping to choose a priori the best truncated set of virtual orbitals for configuration interaction calculations.

Analysis of Magnetic Field Effects on the Correlation Energy of a Quantum Plasma: Quantum Strong-Field Limit

The correlation energy of a degenerate electron plasma in an extremely high magnetic field is calculated taking account of the dominant local principal plasmon mode's zero-point energy, as well as the statically shielded electron-electron interaction energy involving the quantum strong-field counterpart of the Debye-Thomas-Fermi static-shielding law. Other Plasmon-mode-resonance correlation-energy contributions are estimated in the quantum strong-field limit, and shown to be small for an extremely high magnetic field.

Simple models of correlation in atoms

Expectation values of various atomic operators are given for a 1s1s′ correlation split wavefunction, and are used in a simple variational calculation allowing for angular correlation in the 1S state. The radial and angular correlation energy contributions obtained are roughly additive.

Origin of the dimerization energy of BH 3 to B 2H 6

The Hartree-Fock and correlation energy contributions to the dimerization energy of BH 3 have been calculated as 8.4 and 16.8 kcal/mole, respectively. The latter is mainly due to the increase in the number of pairs of nearest neighbour bonds. We estimate the dimerization energy at 36 + 5 kcal/mole.