Calculations on the helium isoelectronic sequence using Coulomb Green's function variables

Calculations on the ground states of the helium isoelectronic series are carried out using variational wavefunctions of the form ψ (x,y), in which x and y are the combinations r₁ + r₂ ± r₁₂ occurring in the Coulomb Green's function. The results for helium are the most accurate to date using a two-variable wavefunction accounting for 71.5% of the correlation energy.     

Visualization of electron correlation in a series of helium S states

Electron correlation has been studied for a series of helium S states represented by a variety of wavefunctions, the best of which are accurate Hylleraas—Kinoshita functions. The states studied are the ground state, the lowest excited ¹S and ³S states, and the (2s)² and (2p)² doubly-excited ¹S states. Primary data is obtained from graphs of the conditional probability density as a function of the radial distance r₂ and the interelectronic angle θ₁₂, given that r₁ is fixed at various distances. Such graphs make clear the extent to which characteristics such as angular and radial correlations, and Fermi and Coulomb holes, are consequences of the relative motion of electrons in two-electron atoms.     

Visualization of electron correlation in ground states of He and H−

For the ground states of He and H^?, conditional probability densities d(r₂,θ₁₂r₁) for finding two electrons in different relative positions have been calculated for several wavefunctions including simple one-configuration wavefunctions and Hylleraas—Kinoshita type functions. The calculations, including graphing, were all carried out on a desktop computing calculator.     

On the evaluation of non-adiabatic coupling matrix elements for large scale CI wavefunctions

The implementation of a recently proposed technique for evaluating matrix elements of the form 〈Ψ_J(r;R)|∂Ψ_I(r;R)/t6R_α〉_r using analytic gradient techniques is described. The Ψ_K(r;R) are developed from state-averaged multiconfiguration self-consistent-field/configuration interaction (CI) wavefunctions. The CI wavefunctions are determined using the shape driven graphical unitary group approach. The method is shown to be considerably more efficient than presently existing approaches based on divided differences. As an illustration of the potentialities of this approach non-adiabatic coupling matrix elements are determined for the collinear charge transfer reaction: Mg(¹S) + FH(¹Σ⁺)→MgF(²Σ⁺)+H(²S).     

Pointwise bounds for the electron density and estimates of an expectation value for one-electron systems

Pointwise bounds for wavefunctions of a class of Schrödinger operators for one-electron systems are used to obtain pointwise bounds for the electron density, as well as estimates for the expectation value (r^?1).     

The effect of electron correlation on one-electron properties in the 2 3S and 2 1S excited states of the helium atom

The density difference ΔD(r₁), defined as the difference between the exact and the Hartree-Fock radial density functions is reported for the 2 ³S and the 2 ¹S excited states of the helium atom. The density differences in both cases resemble the inverse of the helium ground-state density difference, but are more long-ranged due to the diffuseness of the excited states. The effect of electron correlation on one-electron distributions is also demonstrated by comparison of (r₁ⁿ) expectation values and several indices of the relative sizes of atoms. Electron correlation leads to a contraction of the Hartree-Fock electron clouds.     

Correlation energy correction as a density functional. A model of the pair distribution function and its application to the first- and second-row atoms and hydrides

A scheme for correlation energy corrections E_c based on asymptotic properties of the effective pair distribution function g(r₁; r₂) and correlation energy densities ϵ_c{ϱ(r₁)} has been considered. To obtain ϵ_c{ϱ(r₁)} model functions g(r₁; r₂) are used in the local spin density approximation (LSDA). This model yields the correct high-density limit for the homogeneous electron gas ϵ_c{ϱ} and reproduces empirical E_c values with an average error amounting to 2.2% for the first- and second-row closed-shell atoms, 5.6% for the first-row hydrides XH and 3.4% for the second-row hydrides XH.     

Introduction of the shell structure into the Thomas—Fermi energy density functional for neutral atoms

The Thomas—Fermi energy density functional is constructed for the Na atom using H-like wavefunctions. Minimization of the functional with respect to the Z in the wavefunctions leads to the energy value ot ?166.35 e_O²/a_O, which compares favorably with the Hartree—Fock value of ?161.8 e_O²/a_O.     

A non local density functional calculation of the diamagnetic susceptibilities and other electronic properties of noble gases and closed-shell ions

The non local weighted-density approximation (WDA) to the exchange-correlation potentialV _xc (r) is used to compute electron densities, ionization potentials and electron affinities of several atoms and ions. Especial care is taken in calculating and discussing 〈r ²〉 in noble gas atoms. Good results are obtained for all those quantities, but it is critical that the WDA is applied in such a way that it preserves the correct larger behaviour ofV _xc (r). A comparison of the calculated electron density with that of the Hartree-Fock method shows the effects of coulomb correlation. The density rearrangements upon the introduction of correlation agree qualitatively with the results of Configuration-Interaction calculations     

Spatial correlation of atomic electrons: He

For any two-electron wavefunction whose angular dependence is given in terms of the spherical harmonics of the individual electrons and/or o₁₂, where o₁₂ is the interelectronic angle. a transformation is generated which reduces |ψ(r₁, r₂, o₂, o₁, o₁₂ )|² to |ψ(r₁, r₂, o₁₂)|². Geometric aspects of electron correlation are analyzed in terms of this resulting three-coordinate function, with specific application to a number of wave functions for doubly-excited helium. Angular correlation has been studied by integrating |ψ(r₁, r₂, o₁₂)|² over its radial dependence to yield p(o₁₂), the probability density function for the interelectronic angle. Trends of p(o₁₂) for doubly-excited states of the helium atom are related to a number of quantities including energies and autoionization widths. These trends can be rationalized in terms of a simple classical model. The full spatial correlation involving |ψ(r₁, r₂, o₁₂)|² is explored by the use of three-dimensional graphs for some of these states.     

Core-valence correlation potentials based on density functional theory. Applications to valence-electron-only calculations on Na and K diatomics

The core-valence correlation potential has been derived for Na and K employing atomic calculations which make use of the density functional formula worked out by Lee, Yang and Parr based on Colle-Salvetti approach. The numerical potential is fitted with a small number of Gaussians leading to a very simple expression for an one-electron corevalence correlation operator? _cv . The core-valence correlation corrections can be computed by applying? _cv on a quite general class of wavefunctions. Applications of the? _cv operator within the framework of valence-electron-only calculations using effective Hamiltonians are presented for Na and K atoms, for Na₂, K₂, NaK and their cations. Almost all the corrections calculated for the physical properties due to the core-valence correlation lead to results which are in good agreement with those obtained from much more sophisticated treatments and experimental data.     

Effects of anharmonicity on non-radiative transitions in polyatomic molecules

The effect of anharmonicity on the non-radiative transition in large molecules is examined within the Morse potential surface model. The vibrational wavefunctions are assumed to be the product of the harmonic and Morse oscillator wavefunctions. The method of factorization introduced by Gelbart et al. is used for the evaluation of a density weighted Franck-Condon factor. As an example, we choose the intersystem crossing ³ B _1u→¹ A _1g in benzene. The numerical calculation shows that the anharmonicity causes an increase by a numerical factor ～ 10³ in the non-radiative transition rate. The electronic energy distribution over the vibrational modes in the final state is determined and compared with that obtained using the harmonic potential surface model.     

Accuracy of first-order wavefunctions for ten-electron atomic systems

It is demonstrated that for Ne-like systems, the zeroth-plus-first-order wavefunctions, obtained within Rayleigh—Schrödinger perturbation theory based on H₀ = H_HF, are of the same accuracy as variational wavefunctions obtained in CI calculations using very extensive sets of singly and doubly excited configurations. Variational correlation energies for Na⁺, Mg²⁺ and Ar⁸⁺ are reported for the first time.     

Structure of small molecular hydrogen clusters

The ground state energies and structural properties of small (H₂) _N ,N=2?7, are calculated using the variational Monte Carlo method. These wavefunctions include both short- and long-range correlation effects that are important in the binding of van der Waals clusters. We have investigated these clusters using shadow wavefunctions and found that the coupling to shadow variables raises the energy in all cases, implying that the ground states of these small clusters are properly described as quantum liquids rather than solid structures.     

Studies on allophanate-urethane networks based on hydroxyl terminated polybutadiene: effect of isocyanate type on the network characteristics

Polyurethane networks containing allophanate groups, based on hydroxyl terminated polybutadiene and various diisocyanates, such as toluene diisocyanate, 4,4^′ di(isocyanatocyclohexyl) methane and isophorone diisocyanate were synthesized at various NCO/OH equivalence ratios (r-values) ranging from 1.0 to 1.5. Mechanical properties such as tensile strength, stress at 100% elongation, equilibrium relaxation modulus increase and % elongation at break decreases with r-value. Crosslink density (ν_e) for the networks was determined using swell methods. Crosslink density values calculated from equilibrium relaxation modulus were found to be close to those obtained from swell data. Crosslink density (ν_t) was theoretically calculated assuming complete reaction between the functional groups. The ratio, ν_e/ν_t decreases with r-value. Linear fits with good correlation coefficients were obtained between network parameters and mechanical properties. Dynamic mechanical studies show that the r-value does not influence the glass transition temperature. Thermal decomposition studies using thermogravimetric technique indicate that the decomposition is in multiple stages.     

Use of electron-density contours from FSGO model wavefunctions: nonbonded radius of atoms and molecular anisotropy of the plarizability for some diatomic systems

Electron density contours (0.002 au) obtained from FSGO model wavefunctions are used to estimate “naturally partitioned” length (L_p) and width (W_p). The quantity L_p/W_p ? 1 is shown to be proportional to experimental molecular anisotropy (K) of polarizability. Predicted |K| values are used to estimate |α_| ? α| for a series of diatoms.     

Long-range interaction between Hg*(1,3P1) and noble gas atoms

The long-range, van der Waals interaction is considered for the system M^*(nsnp ^1,3P₁)/noble gas (¹S₀), where M^* is any atom with two valence electrons outside closed shells. An important “correlation” effect is shown to arise due to the different symmetry properties of the spatial parts of the singlet and triplet wavefunctions; this is the direct analogue of the effect of angular correlation in the ground-state problem. Detailed calculations are carried out for Hg^*(6s6p ^1,3P₁) interacting with the noble gases.     

Solubility of amphenicol bacteriostats in CO2

The solubilities of three veterinary amphenicol bacteriostats, chloramphenicol, florfenicol and thiamphenicol, were measured in supercritical carbon dioxide (SC-CO₂) by a re-circulating method at temperatures of 313.15 and 333.15 K and pressures ranging from 11.0 to 49.0 MPa. These compounds displayed very limited solubility in SC-CO₂ (10⁻⁵ to 10⁻⁷ mole fraction) over the range of experimental conditions. Chloramphenicol had the highest observed solubility of the three amphenicols, while the solubilities of florfenicol and thiamphenicol were almost an order of magnitude lower. The experimental solubility data were correlated with seven known density-based models. The density models (ln y versus ln ρ or ln ρ_r) gave better correlation than the semi-log scale of ln y versus ρ_r. Four models for ln E versus density correlations also gave better correlation than the semi-log scale of ln y versus ρ_r by introducing the enhancement factor E. The correlation accuracy of all the seven models mainly depends on the system investigated, measured density and temperature range.