Charge overlap effects dependence on the nature of the interaction

The He-He, He-H(1s), H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for studying how charge overlap effects in second-order dispersion energies vary as a function of the nature of the interacting species. The non-expanded second-order energy and the corresponding multipole R ^-1 expansions, through all powers of R ^-1, are obtained for each interaction using Unsöld's average energy approximation. The results are used to discuss the limitations of the usefulness of the R ^-1 expansions.     

Padé approximation methods applied to the intermolecular force series

The H(1s)-H⁺, He-He, H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for investigating the use of the Padé approximation method in summing the R ^-1 intermolecular force series. Various Padé approximants and partial sums of the R ^-1 expansions of the second-order Coulomb interaction energies are compared with the corresponding non-expanded results for each interaction. The computations are based on Unsöld's average energy approximation and on exact results for the H(1s)-H interaction. The results indicate that the Padé approximation method is a simple, useful way to remove some of the difficulties associated with the slow rate of convergence of the R ^-1 force series but that it does not alleviate the problems associated with the asymptotic divergent nature of the series. The results for the H(1s)-H⁺ interaction illustrate a possible difficulty in using Unsöld's method in the calculation of interaction energies.     

Ab initio calculations of multipole moments,polarizabilities and long-range interaction coefficients for the azabenzene molecules

Using LCAO-SCF wave functions on the monomers and a non-empirical Unsöld procedure for the second-order properties we have calculated the (2 ^l ) multipole moments (up to l=6), the (l,l') multipole polarizabilities (up to l + l' = 6) and the related long-range coefficients describing the electrostatic, induction and dispersion interactions for the different azabenzene molecules. The agreement with available experimental data is good, in particular for the dipole polarizabilities. The anisotropy of the long-range interaction potential is dominated by the electrostatic contributions, although the dispersion terms, especially the mixed-pole terms (l≠l') for even n (C₈, C₁₀), also contribute significantly; the induction energy is rather small. The π contributions to the polarizabilities and the dispersion interactions are found to be larger than earlier estimates. Moreover, it is shown by calculating the dipole polarizabilities of some (aza)naphthalenes and (aza)anthracenes, that a bond polarizability model can be applied effectively only if the delocalized π electrons are considered separately from the σ electrons.     

Variational calculations of the static polarizability of H2 and of the dipole-dipole contribution to the dispersion energy between two hydrogen molecules

The convergence of variation-perturbation calculations using non-linear variation parameters has been examined for the static polarizability of H₂ and for the coefficient (C₆) of the R ^-6 term in the multipole expansion of the H₂-H₂ dispersion energy. Using a correlated ground state wavefunction, and one excited state for each of the parallel and perpendicular components of the polarizability, a single variational parameter for each state gave 96 per cent of the exact value of α_⊥ and 91 per cent of the exact value of α_‖. A second variational parameter for the parallel component gave 94 per cent of α_‖. The same procedure gave the spherical average and anisotropy of C₆ to an accuracy of about 90 per cent. By extending the calculations into the region where overlap of the orbitals of the two molecules becomes significant, it is shown for the end-on configuration that the C₆ R ^-6 term underestimates the dispersion energy near the van der Waals' minimum by roughly 10 per cent.     

Derivatives of the eigenvalues of the hamiltonian to fifth order

Results of CPMET calculations on the He-He potential are presented. The effect of inter-intra coupling is shown to be far from negligible (about 30 per cent of the binding energy). Since the coupling must vanish with increasing R the previous striking agreement between experiment and ab initio calculations must be regarded as somewhat fortuitous. This is likely to be a principal reason for the present disagreement between ab initio and perturbation theoretical values for the long-range interatomic energy constants.     

On the evaluation of high-order interaction energies using pseudo state methods

General expressions for the coefficients of the R ^-1 multipole expansion of the third and fourth-order interaction energies are derived in (pseudo) spectral form for the interaction of two S-state atoms. Explicit accurate results, for the H(ls)-H(ls) interaction, are obtained for the lead O(R ^-11) third-order energy and the lead O(R ^-12) fourth-order energy by using one centre pseudo state methods. These calculations, together with the appropriate second-order results, furnish an accurate expression for the total long-range interaction energy through O(R ^-12) and illustrate the applicability of the pseudo state approach for the evaluation of high-order interaction energies.     

Application of R-matrix method to electron-H<Subscript>2</Subscript>S collisions in the low energy range

Electron-H₂S collision process is studied using the R-matrix method. Nine low-lying states of H₂S molecule are considered in the R-matrix formalism to obtain elastic integral, differential, momentum transfer and excitation cross sections for this scattering system. We have represented our target states using configuration interaction (CI) wavefunctions. We obtained adequate representation of vertical spectrum of the target states included in the scattering calculations. The cross sections are compared with the experiment and other theoretical results. We have obtained good agreement for elastic and momentum transfer cross sections with experiment for entire energy range considered. The differential cross sections are in excellent agreement with experiment in the range 3–15 eV. A prominent feature of this calculation is the detection of a shape resonance in ²B₂ symmetry which decays via dissociative electron attachment (DEA). Born correction is applied for the elastic and dipole allowed transition to account for higher partial waves excluded in the R-matrix calculation. The electron energy range is 0.025–15 eV.     

A simple route to the energy shift between an electrically polarizable molecule and a magnetically susceptible molecule via the electromagnetic energy density

The van der Waals dispersion interaction between a molecule that is electrically polarizable and one that is magnetically susceptible, is recalculated within the framework of non-relativistic quantum electrodynamics. The energy shift is obtained in a simple way by calculating the response of a test polarizable body to the electromagnetic energy density due to a second source molecule. It is confirmed that the near-zone asymptote of the potential between an electric dipole polarizable molecule and a paramagnetic one varies as R ^{? 4}. Inclusion of the often neglected diamagnetic coupling term, however, results in an R ^?5 dependent short-range behaviour, which is seen to dominate over the paramagnetic contribution in the near-zone. For larger intermolecular distances, the expected R ^?7 dependence on separation is found for both paramagnetic and diamagnetic susceptible molecules interacting with an electric dipole polarizable one.     

Molecular ions in ultracold atomic gases: computed electronic interactions for MgH<Superscript>+</Superscript>(X<Superscript>1</Superscript>Σ<Superscript>+</Superscript>) with Rb

The electronic structures of the manifold of potential energy surfaces generated in the lower energy range by the interaction of the MgH⁺(X¹Σ⁺)  cationic molecule with Rb(²S)  neutral atom are obtained over a broad range of Jacobi coordinates from strongly correlated ab initio calculations which use a Multireference (MR) wavefunction within a Complete Active Space (CAS) approach. The relative features of the lowest five surfaces are analyzed in terms of possible collisional outcomes when employed to model the ultracold dynamics of ionic molecular partners.     

Spin-Hamiltonian parameters and tetragonal distortion due to the Jahn–Teller effect for Cu2+ centres in trigonal Zn(BrO3)·6H2O crystal

The spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants ⁶⁵A_// and ⁶⁵A_⊥) for the tetragonal Cu²⁺ centres in trigonal Zn(BrO₃)·6H₂O crystal are calculated from the complete diagonalization (of energy matrix) method (CDM) based on the cluster approach. In the CDM, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and the contributions to the spin-Hamiltonian parameters from both the spin-orbit coupling parameter of central d⁹ ion and that of ligand ion are included. The calculated spin-Hamiltonian parameters of Zn(BrO₃)·6H₂O: Cu²⁺ show good agreement with the experimental values and the tetragonal elongation (characterized by ΔR=R_// ? R _⊥, where R_// and R _⊥ represent the metal-ligand distances parallel with and perpendicular to the C₄ axis) due to the static Jahn–Teller effect is obtained from the calculations. The results are discussed.     

Off-shell variation in the binding energy of triton

Phase-shift-equivalent potentials are used to study the sensitivity of triton binding energy (E _T) to the off-shell behaviour of two-nucleonT matrix in a translationally-invariant basis of harmonic oscillator wavefunction. For a smaller value of inverse range parameterλ (1.95 fm⁻¹), which is close to the attractive range of our model potential, a 21% variation in the triton binding energy is obtained. For the other value ofλ an off-shell variation of about 28% inE _T is obtained.     

Photoionization of the ground1 S e and twenty lowest excited states of the Ne-like Fe16+

TheR-matrix method is used to calculate cross-sections for the photoionization of Ne-like Fe¹⁶⁺ from ground 2s ²2p ⁶¹ S ^e and excited states belonging to 2s2p ⁶ 3l and 2s ²2p ⁵ 3l configurations. Configuration interaction wavefunctions are used to represent two target states of Fe¹⁷⁺ ion retained in theR-matrix expansion. The cross-sections are obtained as a function of kinetic energy (ε _k) of the ejected electron from 10 to 24 Ry. For low kinetic energy the cross-sections show series of Rydberg states which converge onto² S ^e threshold Fe¹⁷⁺. The calculations are carried out in the LS coupling.     

The intermolecular potential of HF

The functional form of separate contributions to the intermolecular potential between small dipolar molecules has been analysed using the HF intermolecular potential as an example. The SCF energy was partitioned into first order electrostatic and exchange terms and higher order terms, called the polarization energy, which can be obtained by iterating the wavefunction to self consistency. A comparison was made for each term between a bipolar expansion about a single centre in each molecule and spherically symmetric site-site models. The overlap dependent part of the electrostatic energy could be combined with the exchange energy to give a single term which we call the repulsion energy and this was most accurately represented by a six term bipolar expansion. The polarization energy has a long range (R ^-6) component and an overlap dependent component and both could be separately represented by a two-term bipolar expansion. A semiempirical estimate was made of the dispersion energy and the total potential predicts a geometry of the HF dimer in good agreement with experiment. The predicted binding energy of the dimer is 17 kJ mol^-1 which is slightly smaller than a previous empirical estimate (23 kJ mol^-1).     

Ab initio potential energy curves and vibrational levels for the C and D 1Πu states of the hydrogen molecule

Two lowest eigenvalues of the Hamiltonian for the hydrogen molecule corresponding to the ¹Π_u symmetry have been calculated in the Born-Oppenheimer approximation. They represent the C and D states, respectively. Different highly flexible wavefunctions were used for both states and the calculations were performed for a wide range of internuclear distances: 1 ≤ R ≤ 12 a.u. for the C state, and 1 ≤ R ≤ 25 a.u. for the D state. The calculated potential energy curves are more accurate than any previous ab initio results for the above states. The vibrational Schrödinger equation for both states has been solved for H₂, HD, and D₂ using the Numerov method. The resulting energies and rotational constants are compared with the experimental values.     

Effects of reduction of the ionization potential on solutions of the Rankine-Hugoniot equations for Jovian entry

The influence predictions of three different reduction-of-the-ionization-potential models (Unsöld, Ecker-Weizel and Griem) on the calculated composition of hydrogen-helium shock layers for conditions that would be encountered during entry of the Jovian atmosphere is investigated. The comparisons indicate that the Ecker-Weizel model gives the largest ΔI and Griem's the smallest. The ΔI-model influence on the composition increases as the hydrogen mass fraction, entry velocity, and ambient density increase.     

A study of pion absorption by16O using realistic interactions—I. Twonucleon emission following bound-pion absorption

Matrix element of the Galilean invariant non-relativistic reduction of the pseudoscalar-pseudovector interaction has been calculated assuming the reaction to be a direct process with boundπ ⁻ being absorbed by a correlated pair of nucleons. The Hartree-Fock wavefunctions obtained with the unitary-model-operator approach starting with the realistic nucleon-nucleon interaction have been used forπ-capturing nucleon pair in the initial state. The calculations have been done with and without antisymmetrising the initial state wavefunction of the pion absorbing pair. For the final state nucleon-nucleon interaction has been taken into account. The strongπ-nucleus interaction together with the Coulomb interaction with the finite nuclear size on the bound pion wavefunction are taken into account. Angular distributions of the emitted nucleon-pair, the branching ratios and the total absorption rates are calculated for¹⁶O with and without antisymmetrisation effect. The calculated results are compared with the experimental and other theoretical work.     

Diagrammatic non-degenerate RSPT for evaluation of ground-state energy of simple open-shell molecular systems

The diagrammatic non-degenerate Rayleigh-Schrödinger perturbation theory and the coupled cluster approach are applied to the evaluation of the ground state energy of a simple open-shell molecular system described in the zeroth order approximation by a single determinant wavefunction. The corresponding hamiltonian is built up by the creation and annihilation operators introduced over an orthonormal set of restricted Hartree-Fock one-particle functions. The perturbation H₁ is composed of one- and two-particle terms, the one-particle term depending in an explicit way upon the type of restricted Hartree-Fock theory used. The efficiency of the elaborated theory is illustrated for the BeH molecule.     

Binding energy of a screened donor in a spherical quantum dot with a parabolic potential

A wavefunction is proposed for calculating the ground-state energy of a screened donor in a spherical quantum dot under a parabolic potential by a variational method. The donor is taken to be at the center of the quantum dot. Results are presented for four values of the screening parameter by the proposed wavefunction as well as for the hydrogenic donor case by a wavefunction used by Xiao et al.. To assess the accuracy of the results, ‘exact’ energies are also obtained by numerical integration of the Schrödinger equation. It is shown that the proposed wavefunction gives very good results in all cases including the hydrogenic donor case.