Model potentials for molecular calculations. II. The spd-MP set for transition metal atoms Sc through Hg

Model potential parameters and valence orbitals were generated for the transition metal atoms Sc through Hg. They are named the spd-MPs and are supplementary to the sd-MPs presented in the preceding article. The outermost core np electrons were treated explicitly together with valence nd and (n + 1)s electrons, and the remaining electrons were replaced by a model potential. The model potential parameters and valence orbitals were determined in the same way as the sd-MPs. Major relativistic effects (via the mass velocity and Darwin terms) were also incorporated in the spd-MPs for the second-and third-row transition metal atoms. The results of numerical nonrelativistic Hartree-Fock (HF) calculations for the first-row transition metal atoms and of the quasirelativistic HF calculations with Cowan and Griffin's method for the second-row and third-row transition metal atoms were used as reference data in determination of the spd-MPs.     

Valence electronic structures of CH2BrCl and CF2BrCl: binding energy spectra and electron momentum distributions

The binding energy spectra (BES) of valence shells of CH2BrCl and CF2BrCl have been measured at a series of different azimuthal angles by an (e, 2e) electron momentum spectrometer employing noncoplanar symmetric geometry at an impact energy of 1200 eV plus binding energy. The experimental momentum profiles (XMPs) are extracted from the sequential BES and compared with the theoretical ones calculated by using Hartree-Fock (HF) and density functional theory (DFT-B3LYP) calculations with 6-311G, 6-311++G**, and aug-cc-pVTZ basis sets. In general, the DFT-B3LYP calculations using the larger basis sets 6-311++G** and aug-cc-pVTZ describe the XMPs well for both molecules. Moreover, the pole strengths of main ionizations from the inner valence orbitals 2a', 3a', and 1a' of CH2BrCl are determined, and the controversial ordering of two outer valence orbitals 3a' ' and 6a' of CF2BrCl has also been assigned unambiguously.     

Two-electron valence indices from the Kohn-Sham orbitals

The recent Hartree-Fock (HF) difference approach to the chemical valence indices (ionic and covalent), formulated in the framework of the pair-density matrix, is implemented within the Kohn-Sham (KS) density functional theory (DFT). The valence numbers are quadratic in terms of displacements of the molecular spin-resolved charge-and-bond-order (CBO) matrix elements, relative to values in the separated atoms limit (SAL). It is shown that the global valence represents a generalized “distance” quantity measuring a degree of similarity between the two CBO matrices: the molecular and SAL. Numerical values for typical molecules exhibiting single and multiple bonds demonstrate that the KS orbitals give rise to these new bond valences in good agreement with both chemical and HF predictions. This KS bond multiplicity analysis is applied to the chemisorption system including the allyl radical and a model surface cluster of molybdenum oxide. It is concluded that the quadratic valence analysis represents a valuable procedure for extracting useful chemical information from standard DFT calculations. © 1997 John Wiley & Sons, Inc.     

The HeHe Coulomb and exchange interaction energy

The Coulomb and exchange interaction energy between two helium atoms is calculated, increasing systematically the basis set, by a supermolecular method which excludes the superposition error by using non-orthogonal orbitals. At 5.6 bohr an energy limit of 9.69 K is found at the Hartree-Fock level; for correlated wavefunctions the corresponding value is 11.86 K using only s orbitals, 10.70 K including p orbitals and 10.58 K adding d orbitals.     

Application of minimization methods in calculating atoms with several open shells

Basing on minimization methods, earlier suggested algorithms for the solution of a many-electron problem in Hartree-Fock-Roothaan approximation for systems with close and open shells extend over Roothaan-Hartree-Fock atomic theory (Roothaan-Bagus method). In present work the expressions for energy derivatives with respect to elements of density matrices and nonlinear parameters of atomic orbitals — orbital exponents — have been obtained to solve Hartree-Fock (HF) equations in algebraic approximation. It is possible to create an algorithm of the first-order minimization or quasi-Newton method on their basis. Calculations of atoms and ions with several open shells were carried out by minimization methods. The energy values, close to the results of numerical solution of HF equations with high accuracy of virial relation, were gained using a sufficiently narrow basic set of Slater-type AO.     

Quantum-chemical modeling of photoelectron spectra and electronic structure of <Emphasis Type="Italic">tris</Emphasis>-β-diketonates of 3<Emphasis Type="Italic">d</Emphasis>-metals Sc,Ti, V

The electronic structure and ionization energies of chelate complexes were calculated for transition metals Sc, Ti, and V using the Hartree-Fock (HF)SCF ab initio approximations. As the number of d electrons increases in the series of these compounds, the sequence of HF orbitals does not agree any longer with the PES bands and with the data obtained in the density functional theory approximation. Using the configuration interaction (CI) method considerably improves agreement with experiment. For the vanadium complex containing an odd d electron in the ionized state, the HF orbitals become a rough approximation for the CI decomposition, hindering the interpretation of the ionic states.Original Russian Text Copyright © 2004 by V. I. Vovna and I. S. OsmushkoTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 651–659, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Multi-channel reaction matrix theory and configuration-interaction in the discrete and in the continuous spectrum. Inclusion of closed channels and derivation of quantum defect theory

We present a derivation of Multichannel Quantum Defect Theory (MQDT) which is based on the configuration-interaction in the continuum (CIC) and reaction matrix (K-matrix) formalisms, generalized so that closed channels are included. The whole development focuses on obtaining and utilizing eigenfunctions composed of smooth parts only. Whereas the theories of Seaton and Fano depend on the use of irregular or unbound functions, ours does not. No separation of configuration space into inner and outer space is necessary. Furthermore, the present theory allows in a practical way the transfer of information from one part of the spectrum to another byinterpolation — as opposed to the standard ab initio MQDT which is limited toextrapolation from the continuous to the discrete spectrum. The formalism is developed for the physically important Coulomb potential. However, its structure is such that it allows the easy determination of those parts which must be altered to accomodate extension to other potentials. Furthermore, it permits the execution of reliable calculations which employ a basis of numerical fixed-core Hartree-Fock (HF) functions for the singly excited configurations, of multiconfigurational HF (MCHF) for the spectroscopic valence states and of analytic virtual orbitals for the correlation vectors.     

SCF wavefunctions and energies for valence states and excited states of carbon and nitrogen

Wavefunctions and energies are reported for the (2s)ⁿ(2p)^m states of neutral carbon and nitrogen using the fixed double-zeta bases employed by Clementi to describe the ground state of these atoms. In addition, the wavefunctions and energies for a number of valence states are given, including the so-called sp³ valence state of carbon. Calculated energies of the valence states agree well with those obtained from experiment. The corresponding valence-state orbitals are useful in semi-empirical quatum-mechanical calculators, such as the maximum overlap method.     

On the nodal structure of single-particle approximation based atomic wave functions

The nodal structures of atomic wave functions based on a product of spatial orbitals, namely, restricted, unrestricted, and generalized valence bond wave functions, are shown to be equivalent. This result is verified by fixed node-diffusion Monte Carlo simulations for atoms up to Ne. Also for a molecular system, Li(2) at the equilibrium geometry, a multideterminantal generalized valence bond wave function does not improve the nodal surfaces of a restricted Hartree-Fock wave function.     

Interactions of Li, Ca, and Al with aromatic carbon materials: an ab initio study

The interactions of benzene (C6H6), naphthalene (C10H8), and perinaphthene (C13H9) with metal atoms (Li, Ca, and Al) were studied using second-order M?ller-Plesset perturbation theory. By analyzing the frontier molecular orbitals, geometric structures, binding energies, and charge transfers, it was found that these metal atoms can bond strongly with C13H9, but can only bond weakly with C6H6 and C10H8. The bonding nature between a metal atom and C13H9 at their ground state depends significantly on the valence orbital of the metal atom and the pi-bonding distribution of the aromatic hydrocarbons. The spindly shaped 3p valence orbital of an Al atom results in the deviation of the adsorption site to the edge of C13H9, whereas the ball-shaped 2s/4s valence orbitals of a Li and a Ca atom facilitate their overlap with the second lowest unoccupied molecular orbital of C13H9. Further, Hartree-Fock and density-functional theory methods were demonstrated generally to be unreliable in describing the interactions of metal atoms with these pi systems.     

The splitting of atomic orbitals with a common principal quantum number revisited: np vs. ns

Atomic orbitals with a common principal quantum number are degenerate, as in the hydrogen atom, in the absence of interelectronic repulsion. Due to the virial theorem, electrons in such orbitals experience equal nuclear attractions. Comparing states of several-electron atoms that differ by the occupation of orbitals with a common principal quantum number, such as 1s(2) 2s vs. 1s(2) 2p, we find that although the difference in energies, ΔE, is due to the interelectronic repulsion term in the Hamiltonian, the difference between the interelectronic repulsions, ΔC, makes a smaller contribution to ΔE than the corresponding difference between the nuclear attractions, ΔL. Analysis of spectroscopic data for atomic isoelectronic sequences allows an extensive investigation of these issues. In the low nuclear charge range of pertinent isoelectronic sequences, i.e., for neutral atoms and mildly positively charged ions, it is found that ΔC actually reverses its sign. About 96% of the nuclear attraction difference between the 6p (2)P and the 6s (2)S states of the Cs atom is cancelled by the corresponding interelectronic repulsion difference. From the monotonic increase of ΔE with Z it follows (via the Hellmann-Feynman theorem) that ΔL > 0. Upon increasing the nuclear charge along an atomic isoelectronic sequence with a single electron outside a closed shell from Z(c), the critical charge below which the outmost electron is not bound, to infinity, the ratio ΔC/ΔL increases monotonically from lim(Z→Z(c)(+))ΔC/ΔL=-1 to lim(Z→∞)ΔC/ΔL=1. These results should allow for a more nuanced discussion than is usually encountered of the crude electronic structure of many-electron atoms and the structure of the periodic table.     

CFCl3分子2e和4a1轨道的电子动量谱研究

由于工业的迅速发展,使得空气质量急剧下降,因此对影响大气的分子进行深入研究变得非常必要．本实验室已经对影响环境的甲烷[1]、丙烷[2]、CO2[3]等分子进行了电子动量谱研究,为环保提供了有用的数据．CFCl3作为工业广泛应用的气雾剂和制冷剂原料,它的大量使用导致了大气中臭氧的减少[4]．前人已用光电子谱学的方法[5-8]研究了CFCl3,我们又用电子动量谱的手段对CFCl3分子进行了进一步的研究,即从波函数的层次上详细了解CFCl3的电子结构．     

The consequences of neglecting permutation symmetry in the description of many-electrons systems

The consequences of neglecting the permutation symmetry of the Hamiltonian of many-electrons system are examined. From the comparison of wave functions based on methods, which take (generalized valence bond [GVB]) and do not take (Hartree-Fock) the permutation symmetry into account, it is shown that neglecting the permutation symmetry leads to false concepts, misinterpretations, and unjustifiable approximations when dealing with many-electrons systems, atoms, and molecules. In particular, it is shown that how the double occupancy of atomic and molecular orbitals, the exchange integral, the correlation energy, and the so-called “nondynamic” correlation energy are related to neglecting the permutation symmetry.     

Core-level positive-ion and negative-ion fragmentation of gaseous and condensed HCCl3 using synchrotron radiation

We investigated the dissociation dynamics of positive-ion and negative-ion fragments of gaseous and condensed HCCl(3) following photoexcitation of Cl 2p electrons to various resonances. Based on ab initio calculations at levels HF/cc-pVTZ and QCISD/6-311G?, the first doublet structures in Cl L-edge x-ray absorption spectrum of HCCl(3) are assigned to transitions from the Cl (2P(3/2),(1/2)) initial states to the 10a(1)(?) orbitals. The Cl 2p → 10a(1)(?) excitation of HCCl(3) induces a significant enhancement of the Cl(+) desorption yield in the condensed phase and a small increase in the HCCl(+) yield in the gaseous phase. Based on the resonant photoemission of condensed HCCl(3), excitations of Cl 2p electrons to valence orbitals decay predominantly via spectator Auger transitions. The kinetic energy distributions of Cl(+) ion via the Cl 2p → 10a(1)(?) excitation are shifted to higher energy ～0.2 eV and ～0.1 eV relative to those via the Cl 2p → 10e(?) excitation and Cl 2p → shape resonance excitation, respectively. The enhancement of the yields of ionic fragments at specific core-excited resonance states is assisted by a strongly repulsive surface that is directly related to the spectator electrons localized in the antibonding orbitals. The Cl(-) anion is significantly reinforced in the vicinity of Cl 2p ionization threshold of gaseous HCCl(3), mediated by photoelectron recapture through post-collision interaction.     

Power-gap law and the dynamical constraints on angular momentum transfer in rotationally inelastic molecular collisions

The model proposed by Dexheimer, Durand, Brunner and Pritchard has been developed and tested on CO₂H₂, CO₂He, Na₂He, Na₂Ne and N₂Ar. This model explains the rapid decrease in the rotationally inelastic integral cross sections with increase in the amount of rotational energy transfer (∣ΔE∣) in the region ∣ΔE∣ > ∣ΔE∣^*, ∣ΔE∣^* is foun to depend on the reduced mass of the system, the moment of inertia of the molecule, the initial rotational state, and the interaction potential. Data for the systems studied show quantitative agreement with the predictions of the model.     

A comparison of perfect pairing and molecular orbital methods for the calculation of molecular properties of HF and HF+

The perfect pairing and molecular orbital methods are compared using minimum bases of Slater-type orbitals for the calculation of properties of HF and two states of HF^*. A discussion is given of the calculations of bond lengths and of valence and core ionization potentials.     

环己烯分子2b和3a轨道的电子动量谱学研究

The electron momentum profile for inner valence orbitals 2b and 3a of cyclohexene (C6H10) was firstly studied by the binary (e,2e) electron momentum spectroscopy (EMS), at the impact energy of 1200 eV plus binding energy using symmetric non-coplanar kinematics. The complete valence shell binding energy spectrum of C6H10 was also obtained. The experimental momentum profile of the summed orbitals was compared with Hartree Fock (HF) and density functional theory (DFT) methods with various basis sets. The experimental measurement was well described by the HF and DFT calculations except for the low-p region (p<0.25 a.u.). Experimental small “turn-up” effects of momentum profile in the low-p region could be due to the distorted wave effects.     

Basis Set Orbital Relaxation in Atomic and Molecular Hydrogen Systems

Orbital relaxation (OR) amounts to variation of the orbital exponents in hydrogen molecules and ions relative to the exponents of the isolated atom; it is represented as the sum of the one- and two-center contributions depending on the effective atomic charge and on the presence of other atoms in the molecule. The procedure for isolating the contributions of the exponent includes treatment of the OR of hydrogen in a special set of neutral and charged atoms and molecules with certain multiplicities of their electronic states. Within the framework of the spin-unrestricted Hartree-Fock method, we found and discussed the optimal values of the exponents of the basis orbitals of hydrogen atoms and molecules using the minimal split valence-shell basis set, the basis set that includes the polarization function, and the expanded set of grouped natural orbitals. A simple energy model is suggested for OR. Expressions are derived for evaluating the exponents of the relaxed orbitals in hydrogen-containing systems.Original Russian Text Copyright © 2004 by A. I. Ermakov, A. E. Merkulov, A. A. Svechnikova, and V. V. Belousov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 973–978, November–December, 2004.