Hartree-Fock Basis Research Articles

Inner-shell excitations of water molecule

Theoretical results for the generalized oscillator strength (GOS) and optical oscillator strength (OOS) have been obtained for the excitations from the ground state X 1Σ + to the inner-shell (O1s) 1A 1(1a 1→4a 1), 1B 2(1a 1→2b 2), 1B 1(1a 1→2b 1) electronic states within the first Born approximation (FBA). The target electronic wave functions were determined using the configuration-interaction method, with a Hartree-Fock basis for the occupied molecular orbitals, and improved virtual orbitals for the virtual space. Relaxation and correlation effects were explicitly taken into account. We present, as well, results for the generalized oscillator strength of the first valence A 1B 1 excited state, in connection with the discussion of the inner-shell problem. The results were compared with the available experimental and theoretical data.

Calculations of Core-Excited States in Li

We report on progress in the calculation of three-electron states making use of B-spline basis sets. In particular we discuss the advantages and disadvantages of using a Hartree-Fock basis (expanded in B-splines) compared to the use of hydrogenic basis states. Preliminary results are presented for the 2S terms in Li below the 1s2s 3S limit at 64.4 eV. The 2S terms have been studied less extensively than other core-excited states in Li. In this particular case the choice of basis has a large influence on the quality of the results.

Self-consistent determination of the one-body density matrix and particle-hole excitations

We develop a procedure recently proposed for the treatment of correlations in finite Fermi systems in a more consistent way than the random phase approximation (RPA). The one-body density matrix in the correlated ground state is now no more assumed to be diagonal in the Hartree-Fock basis. An expression is rather provided where this quantity is expressed in terms of the X and Y amplitudes of the particle-hole phonon operators. A set of RPA-like equations depending only on the one-body density matrix is then constructed by means of the method of linearized equations of motion and solved via an iterative procedure. The procedure is employed to calculate spectra and strength distributions of several neutral and charged Na and Li metal clusters within the jellium approximation. Improvements are observed with respect to standard RPA calculations.

Molecular cluster models of aluminum oxide and aluminum hydroxide surfaces

Ab initio, molecular orbital calculations for two different Hartree-Fock basis levels were performed on clusters in the system Al-O-H, and tested by comparing derived vibrational frequencies to the measured values for aluminum oxides and aluminum oxyhydroxide minerals. Models were chosen to reflect surface groups that may be present on aluminous minerals such as α-Al2O3 (corundum) and Al(OH)3 (gibbsite). Protonation and deprotonation reactions on bridging and terminal oxygen or hydroxyl sites were modeled to investigate the effects of solution pH on the structure of surface groups. Relative deprotonation energies, including solvation effects, were calculated for each site using the self-consistent isodensity polarized continuum model of Keith and Frisch (1994), and then used to predict the order in which each particular surface group protonates.

Optical and generalized oscillator strengths for theB1Σ+,C1Σ+, andE1Πvibronic bands in the CO molecule

Theoretical results for the generalized oscillator strength and optical oscillator strength (OOS) have been obtained for the excitations from the ground vibronic state ${X}^{1}{\ensuremath{\Sigma}}^{+}$ $(\ensuremath{\nu}=0)$ to the vibrational levels ${v}^{\ensuremath{'}}=0,1$ of the ${B}^{1}{\ensuremath{\Sigma}}^{+}$, ${C}^{1}{\ensuremath{\Sigma}}^{+}$, and ${E}^{1}\ensuremath{\Pi}$ electronic states within the first Born approximation. The target electronic states were determined using the configuration-interaction method, with a Hartree-Fock basis for the occupied molecular orbitals, and improved virtual orbitals for the virtual space. We discuss recent optical and electron impact measurements and reexamine previous OOS results for these processes.

Antisymmetrized random phase approximation for quasi-elastic scattering in nuclear matter: Non-relativistic potentials

Many-body techniques for the calculation of quasi-elastic nuclear matter response functions in the fully antisymmetrized random phase approximation on a Hartree-Fock basis are discussed in detail. The methods presented here allow for an accurate evaluation of the response functions with little numerical effort. Formulae are given for a generic non-relativistic potential parameterized in terms of meson exchanges; on the other hand, relativistic kinematical effects have been accounted for.

Interaction-driven equilibrium and statistical laws in small systems: The cerium atom

It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently strong. This interaction mixes the unperturbed shell-model (Hartree-Fock) basis states and produces chaotic many-body eigenstates. As a result, an interaction-induced statistical equilibrium emerges in the system. This equilibrium is due to the off-diagonal matrix elements of the Hamiltonian. We show that it can be described by means of temperature introduced through the canonical-type distribution. However, the interaction between the particles can lead to prominent deviations of the equilibrium distribution of the occupation numbers from the Fermi-Dirac shape. Besides that, the off-diagonal part of the Hamiltonian gives rise to the increase of the effective temperature of the system (statistical effect of the interaction). For example, this takes place in the cerium atom which has four valence electrons and which is used in our work to compare the theory with realistic numerical calculations.

Conformational analysis of carbonic anhydrase inhibitors using ab initio molecular orbital methods. 1. Rotational isomerism in methane sulfonamide anion, CH 3 -SO 2 -NH −

Ab initio calculations have been performed on methane sulfonamide anion. Geometries have been optimized using Hartree-Fock basis sets up to 6-31+G*, and single-point calculations employing those Hartree-Fock geometries have been performed at levels up to MP2/6-311++G**. In addition, geometry optimizations for the 0°, 90°, 150°, and 180° conformers have been carried out at the MP2/6-31G*, MP2/6-31+G*, and MP2/6-311++G** levels. Vibrational frequencies have been calculated using the HF/4-31G*, MP2/6-31G*, and MP2/6-31+G* geometries. All calculations at or above the 4-31G* level agree that H—N—S—C ˜90° is the global minimum. The H—N—S—C = 180° conformer is clearly higher in energy although the relative energy of this conformer varies from 0.36 to 1.03 kcal/mol for the post-HF calculations depending on basis set. The H—N—S—C = 180° conformer appears to be a very shallow local minimum. However, the potential energy surface is quite flat in this region, and the highest-level calculations, including MP2 optimizations and vibrational frequency analysis, are ambiguous on this point. The conformer with an H—N—S—C torsion of 0° is a transition state with a relative energy ˜8 kcal/mol.

Relativistic many-body calculations of energies of n = 3 states for boron-like sodium

Energies of 2s23l, 2s2p(1P)3l, 2s2p(3P)3l and 2p23l states (with l = s, p, d) for B-like Na are calculated. These perturbation-theory calculations make use of a frozen-core relativistic Hartree-Fock basis sets. The calculations include Coulomb and Breit contributions from first- and second-order diagrams for both diagonal and non-diagonal matrix elements. Corrections for the frequency-dependent Breit interaction are taken into account in lowest order and corrections for the Lamb shift are also included. Contributions from three-electron diagrams are compared with those from one- and two-electron diagrams. Comparisons are made with available experimental data; we find good agreement in most cases with experimental term-splitting values in ions with small nuclear charge.

The charge response of a meson-correlated relativistic Fermi gas

The quasielastic longitudinal electromagnetic response function R_L is studied within the context of a model that extends our previous investigations of pionic correlations and currents. Four mesons are now employed (pion, rho, sigma and omega, via the Bonn potential) and the many-body dynamics are extended to the full random-phase approximation built upon a Hartree-Fock basis. Wherever possible the Lorentz covariance of the problem is respected. The first three energy-weighted moments of the reduced response are computed, namely, the zeroth moment (Coulomb sum rule), the first moment (related to the position of the quasielastic peak) and the second moment (related to the peak width or variance). We discuss how with a modest downward adjustment of the Fermi momentum it is possible to obtain the expected zeroth and second moments; this implies that the nuclear system has a lower density than that required when using the free relativistic Fermi gas and accordingly that the interaction effects are weaker than one might initially find.

Minimizing effective many-body interactions

A simple two-level model is developed and used to test the properties of effective interactions for performing nuclear structure calculations in truncated model spaces. It is shown that the effective many-body interactions sensitively depend on the choice of the single-particle basis and they appear to be minimized when a self-consistent Hartree-Fock basis is used.

How accurate are molecular mechanics predictions for fullerenes? A benchmark comparison with Hartree-Fock self-consistent field results

As research into the growing family of fullerene compounds continues to expand, theoreticians making predictions about these large carbon clusters are interested in reliable approaches to reduce the computational expense of calculations. Here we show that an empirical method, molecular mechanics (MM3), can be effectively used to optimize the geometries of fullerenes and consequently reduce the time required for more elaborate quantum mechanical calculations. Equilibrium structures and heats of formation were predicted for 22 fullerences ranging from C[sub 28] to C[sub 120] using MM3. The MM3 geometries are found to be in good agreement with those obtained by the minimum basis Hartree-Fock self-consistent field (SCF) method. However, the heats of formation obtained with MM3 and SCF are quite different. At the MM3 optimized geometry, an SCF energy point was calculated for each structure and found to be very close to the fully optimized SCF energy. This procedure yields accurate energy differences between isomers at a fraction of the computational cost. We propose other ways of using MM3 to speed ab initio calculations as well. 40 refs., 7 figs., 4 tabs.

Charge exchange in many-body time-dependent processes.

Dynamical processes involving charge exchange betwen atoms and solid surfaces are studied within an Anderson-Newns model. We performed a perturbative treatment of the correlation term starting from a time-dependent Hartree-Fock basis, and calculated the probabilities of the final atomic charge states by using the Green-function formalism for irreversible processes. We analyzed the negative-ion fraction, assuming an Anderson symmetric case, and considering the electronic correlation effects up to a second perturbative order, for two ``extreme'' model systems: the two-level one, and a solid within the wide-band approximation.

Ground state properties and optical response of LixNa4−x, x=0–4: An a b i n i t i o study

The ground state properties of LixNa4−x (x=0–4) were investigated using extended basis Hartree–Fock calculations. The existence of substitution isomers was found for the mixed alkali clusters and planar singlet ground states were found for all clusters, including the isomers. The optical response of the clusters was modeled via configuration interaction—singles (CIS) in the hope of helping to interpret the experimental data. CIS results were found comparable to experiment at lower excitation energies, but inadequate at higher energies due to the neglect of doubles and higher excitations. Some exploration of the excited state surfaces of Li4 and of one isomer of Li2Na2 is also reported. Comparisons are made between CIS calculations, experiment, and multireference doubly excited configuration interaction calculations.

On the resolution of an apparent conflict in the relation between position and momentum operators within the Hartree–Fock approximation

Time-dependent Hartree–Fock theory leads to two apparently quite different expressions relating matrix elements of the electronic position and momentum operators, depending upon whether a single-particle or a many-particle matrix element is used as the starting point. The two expressions are shown to be equivalent, in a complete Hartree–Fock basis set, by means of explicit use of the commutation properties of r with V and J on the one hand, and self-consistency relations and Brillouin’s theorem on the other.

Two approaches to the computational determination of molecular structure: the torsional angle in tolane and the effect of fluorination on the structure of oxirane

Two types of structural problems are distinguished in relation to the nature of the quantumchemical methods suitable for their resolution. One problem concerns the chemical conclusions that can be drawn from intercomparison of the structures of a family of related molecules. For such a study, relatively low-level computational methods can be employed, because residual errors for a given structural parameter due to neglect of electron correlation and use of only a mediumsized Hartree-Fock basis set are nearly invariant to minor changes in the rest of the molecule. Such a study is illustrated by a set of structural evaluations of oxirane (ethylene oxide) and of all its possible fluorinated derivatives. The other class of problems consists of situations in which absolute values of structural parameters are required, either because the molecule under study has no close chemical relatives or because the chemically interesting question requires knowledge of the absolute value of one parameter for its resolution. Such a problem is illustrated by a study of the barrier inhibiting torsion about the CC bond of tolane (diphenylacetylene). The structural effects of successive fluorination of oxirane are found to parallel very closely those previously reported for fluorinated cyclopropanes. Even minor effects, such as the greater shortening of a C-F bond when it is cis to another C-F group compared to the shortening when it is in a trans configuration, are reproduced. The large-scale calculations on tolane, C 6K 5-CC-C 6H 5, made using a 6-311G ∗∗ basis set and MP2 treatment of electron correlation would have exceeded the storage capacity of our Cray computer without use of a new “direct correlation” method which makes unnecessary the storage of two-electron integrals over atomic basis functions. The equilibrium geometry of tolane is found to have the two phenyl rings coplanar. A barrier of 0.64 kcal mol −1 is found at the energy maximum at a torsional angle of 90 °.

Double Auger effect in the multiparticle perturbation theory framework

Within the framework of multiparticle perturbation theory (MPT), we investigate the correlation process of decay of an interior atomic vacancy accompanied by emission of two electrons simultaneously, i.e., the double Auger effect. In the lowest nonvanishing order of MPT, with respect to the interelectron interaction, expressions are obtained for calculation of the partial amplitudes and the probability of transitions in atoms with filled shells. Approximate formulas are discussed for the value of the probability in concrete transitions. Results are introduced and discussed for the numerical calculation of the double Auger transition 1s−1→2s−22p−1q1q2 in Ne expressed in the Hartree-Fock basis of wave functions.

A numerically stable procedure for calculating M�ller-Plesset energy derivatives, derived using the theory of Lagrangians

When Moller-Plesset energy derivatives are determined in the canonical Hartree-Fock basis, singularities or instabilities may arise due to degeneracies among the occupied or unoccupied orbitals. If a non-canonical basis is used these singularities disappear. Numerically stable expressions are presented for the molecular gradient and Hessian of the second-order Moller-Plesset energy, obtained by differentiating a fully variational Lagrangian of the energy constructed in a non-canonical representation. By using a non-canonical representation, singularities and instabilities are avoided, and the variational property of the Lagrangian ensures that Wigner's 2n + 1 rule is satisfied for the orbital derivatives and that the multipliers satisfy the stronger 2n + 2 rule. It is shown that the most expensive step in the calculation of the Hessian scales as Mn 4o, where M is the number of independent Cartesian distortions, n the total number of orbitals, and o the number of occupied orbitals.

On the choice of orbital bases for configuration interaction

We study the CI energy dependence on one-particle orbital bases obtained as SCF solutions of a general parametrized Fock operator which reduces to the Hartree–Fock mean field as a special case. In the case of single excitation CI, exact analytical expressions are derived for the curvature of the CI energy surface at the Hartree–Fock point. Numerical applications to N2 and H2O show that the convergence rate of the CI expansion can be drastically increased by an appropriate and largely system independent choice of the mean field parameters. In all configuration spaces, except single plus double excitation CI, the Hartree–Fock basis is found to be the worst orbital basis for use in CI, suggesting in general that the common-practice procedure of optimizing within a given physical model as the first step to go beyond the model itself can be a very inefficient strategy.

Optimization of wave function and geometry in the finite basis Hartree-Fock method

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTOptimization of wave function and geometry in the finite basis Hartree-Fock methodMartin Head-Gordon and John A. PopleCite this: J. Phys. Chem. 1988, 92, 11, 3063–3069Publication Date (Print):June 1, 1988Publication History Published online1 May 2002Published inissue 1 June 1988https://doi.org/10.1021/j100322a012RIGHTS & PERMISSIONSArticle Views946Altmetric-Citations64LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (858 KB) Get e-Alerts