Density matrix approach to orbital relaxation dynamics in ionization

Dynamical response of electrons to a hole generated during ionization is formulated in time domain with the density matrix equations in the time‐dependent unrestricted Hartree–Fock approximation. Time evolutions of orbital energies and electron‐density distributions are computed for K‐shell and M‐shell ionizations of a Na atom by taking into account nonlinear coupling of density matrices beyond linear response. When the hole is generated so slowly that the adiabatic theorem is satisfied, the simulation eventually converges to the state of a fully relaxed Na⁺ ion. A rapid generation of a K‐shell hole (within about 1 fs) leads to a breakdown of the adiabatic theorem, triggering a collective oscillation of the electrons with the period of sub‐femtoseconds. The shake‐up effect associated with strong orbital relaxation in inner‐shell ionization is manifested as a mixing of occupied and unoccupied states in the density matrix.     

Ab initio studies of the electronic structure and density of states of metallic beryllium

Hartree–Fock–Roothaan studies are reported for low-lying electronic states of metallic beryllium as modeled by a moiety of 135 beryllium atoms. The system corresponds to 16 coordination shells of a central Be with internuclear separations derived from the lattice constants of the bulk metal. The calculations become tractable by use of the full D_3h symmetry of the system at both the integrals and self-consistent-field stages and by employing ab initio effective potentials for the 1s electrons of each beryllium atom. Ionization potentials, binding energies, orbital energies, electric field gradients, nuclear-electrostatic potentials, diamagnetic shielding constants, second moments, and Mulliken populations are calculated for selected electronic states. The calculated ionization potential for the lowest state agrees to within 10% of the experimental bulk work function. A density-of-states analysis for that state is reported and compared with band structure calculations.     

Examination of several density functionals in numerical Kohn–Sham calculations for atoms

We studied several exchange‐only and exchange–correlation energy density functionals in numerical, i.e., basis‐set‐free, nonrelativistic Kohn–Sham calculations for closed‐shell ¹S states of atoms and atomic ions with N electrons, where 2≤N≤120. Accurate total energies are presented to serve as reference data for algebraic approaches, as do the numerical Hartree–Fock results, which are also provided. Gradient‐corrected exchange‐only functionals considerably improve the total energies obtained from the usual local density approximation, when compared to the Hartree–Fock results. Such an improvement due to gradient corrections is not seen in general for highest orbital energies, neither for exchange‐only results (to be compared with Hartree–Fock results), nor for exchange–correlation results (to be compared with experimental ionization energies). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 227–241, 2001     

Dyson-corrected orbital energies for the perturbative treatment of electron correlation

The effect of replacing the Hartree–Fock one-particle energies with ionization potentials obtained from inverse Dyson equation when calculating electron correlation energies perturbatively is investigated. Though the energy shifts vary from system to system, the slight decrease of the resulting excitation energies at around equilibrium geometries leads to a slight increase of the correlation energies in most cases. In the dissociation limit the inverse Dyson equation opens the gap, thus nondiverging potential curves emerge even at the restricted Hartree–Fock (RHF)+RS2 level. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 713–719, 1998     

A preliminary ab initio investigation of the fate of the oxirane cation after vertical ionization of the oxirane molecule

A set of significant sections of the lowest energy hypersurfaces of the oxirane cation C₂H₄O⁺ are presented and discussed with the purpose of investigating the most probable rearrangement pathways following the initial ionization process. It is shown that the most important geometrical parameters involved in such processes are the ∠COC valence angle and the torsional angle of the two CH₂ groups. The most favoured rearrangement processes involve the second vertical ionization state from which it is possible to pass to a more stable open planar form via a conrotatory torsion of the two CH₂ groups and a moderate energy barrier. Other rearrangement processes involving a linear form are still possible. The calculations have been performed using a CI procedure starting from the molecular orbital space of the neutral parent molecule.     

Ab initio studies on hydrogen bonded chains. I. Equilibrium geometry of the infinite,linear chain of hydrogen fluoride molecules

The idealized case of an infinite, linear chain of hydrogen fluoride molecules is studied at the Hartree—Fock level with the aid of the crystal orbital method. Extended gaussian basis sets have been used to compute the equilibrium structure and the stabilization energy (hydrogen bond energy) per HF molecule. It is demonstrated that near Hartree—Fock limit results for this model system account for a large part of the observed differences between isolated dimers in the gas phase and the infinite periodic crystal. For the infinite chain the following results were obtained: r_HF = 1.721 bohr, r_FF = 5.049 bohr and ΔE (hydrogen bond energy per HF) = 5.9 kcal/mole.     

CH3OOH和CH3CH2OOH的表征和活性：光电子能谱的研究

The ionization energies of MHP （CH3OOH） and EHP（CH3CH2OOH） nave been determined by Hel photoelectron spectroscopy （PES） measurement and both Gaussian-2 （G2） calculation and Hartree-Fock （HF） method on the basis of Koopmans theorem at 6.311＋G^＊ basis set level for the first time. The assignment and characterization of PE spectra of MHP and EHP were also supported by the G2 and HF calculations. The first ionization energies of MHP and EHP are 9.87 and 9.65 eV, respectively. Higher solubility of EHP in the atmosphere was attributed to their lower ionization energy values.     

Atomic orbital deformation in bond formation: energy effects

Changes in the radial dependence of atomic orbitals which accompany electronegativity equalization during molecule formation may be monitored by the parallel use of flexible and constrained basis sets in molecular orbital calculations. The stabilization associated with orbital deformation in molecules like BH₃ or CH₄, which contain many bonding MOs in the valence shell, is due to an increase in the attractive, one-electron term in the molecular energy expression relative to the electron repulsion term. The stabilization which occurs in molecules with an excess of non-bonding electrons in the valence shell is due to reduced interelectronic repulsion.     

Ab initioMO calculations on the acidities of water and methanol,and hydrogen bond energies of the conjugate ions with a water molecule

The acidities, deprotonation energies, of water and methanol were calculated by the use of the ab initio self-consistent-field (SCF ) molecular orbital (MO ) method with electron correlation computed by the thirdorder Møller–Plesset perturbation method and configuration interaction with double excitations. Zero-point vibrational energy correction translational energy change, and the PV work term were included to evaluate the accurate acidities. The calculated acidity difference including these corrections was 7 kcal/mol, which is somewhat smaller than the experimental ones (9.5–12.5 kcal/mol) recently determined. The hydrogen bond energies of the conjugate ions (OH^? and CH₃O^?) with a water molecule were calculated to be 2.3 kcal/mol near the Hartree–Fock limit; this energy only amounts to 25% of the (total) hydration energy difference between the two negative ions. The aqueous solvation effect on the acidity scale was discussed.     

An ab initio molecular orbital study of the protonation of amines

Ab initio molecular orbital calculations using an 8 ^s , 3 ^p ; 3 ^s Gaussian basis set, with contraction, have been used to study a series of primary amines XNH₂, where X = H, CH₃, OH, F, CN, CHO, and NO₂. The geometries of the corresponding ammonium ions have been optimised and the energy differences have been used to estimate relative proton affinities. The 1 ^s orbital energies for both the amines and ammonium ions, when corrected for the effects of charges on the other atoms in the molecule by use of an ESCA equation, give a good correlation with the computed charge on the nitrogen atom.     

Ab initio calculations on furan with a new computer program

Two ab initio calculations with different basis sets have been performed on the molecule furan, C₄H₄O. The calculations were done with a new computer program, REFLECT, which is presented. A preliminary analysis of the molecular wave functions has been made by looking at total and orbital energies and also by means of a population analysis. One inner shell ionization energy has been calculated by taking the difference in total energy for the molecule and the corresponding ion. The result is compared with the ionization energy obtained from Koopmans' theorem.     

Kramers' restricted hartree—fock method for polyatomic molecules using ab initio relativistic effective core potentials with spin—orbit operators

A two-component Kramers' restricted Hartree–Fock method (KRHF) has been developed for the polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin–orbit operators at the Hartree–Fock (HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculation of spin–orbit interactions at the HF level. KRHF calculations have been performed for the HX, X₂, XY(X, Y = I, Br), and CH₃I molecules. It is demonstrated that the orbital energies from KRHF calculations are useful for the interpretation of spin-orbit splittings in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced, and bond energies are significantly decreased by the spin–orbit interactions.     

An analysis of the through-bond interaction using the localized molecular orbitals with ab initio calculations—II : Lone-pair orbital energies in bicyclo compounds: 7-azabicyclo[2.2.1]heptane and 2-azabicyclo[2.2.2]octane,and their n-methyl derivatives

Ab intio SCF MO calculations using STO-3G basis set were performed on 7-azabicyclo[2.2.1]heptane, N-methyl-7-azabicyclo[2.2.1]heptane, 2-azabicyclo[2.2.2)octane, N-methyl-2-azabicyclo[2.2.2)octane, and their model molecules. The orbital energies obtained by these calculations were compared with the experimental ionization potentials The canonical MOs obtained for the model molecules were then transformed into the localized Mos. With the use of the localized MOs thus obtained, the lone-pair orbital energies were pursued in the light of the through-space and/or the through-bond interactions between thw specified localized MOs. As a result of this analysis, it was found that the effects of the inner shell orbitals, 1s electrons of the N atom, and of the neighbouring N-C bonds of the skeleton (through-bond interaction) play a dominant role in the interaction with the lone-pair orbitals. It was also found that the effect of the N-Me group on the lone-pair orbital energy is considerably important.     

Variation of parameters in Becke‐3 hybrid exchange‐correlation functional

We have investigated the consequences of varying the three parameters in Becke's hybrid exchange‐correlation functional, which includes five contributions: Hartree–Fock exchange, local exchange, Becke's gradient exchange correction, local correlation, and some form of gradient correlation correction. Our primary focus was upon obtaining orbital energies with magnitudes that are reasonable approximations to the electronic ionization potentials; however, we also looked at the effects on molecular geometries and atomization enthalpies. A total of 12 parameter combinations was considered for each of three different gradient correlation corrections: the Lee–Yang–Parr, the Perdew‐86, and the Perdew–Wang 91. Five molecules were included in the study: HCN, N₂, N₂O, F₂O, and H₂O. For comparison, a Hartree–Fock calculation was also carried out for each of these. The 6‐31+G** basis set was used throughout this work. We found that the ionization potential estimates can be greatly improved (to much better than Hartree–Fock levels) by increasing the Hartree–Fock exchange contribution at the expense of local exchange. In itself, this also introduces major errors in the atomization enthalpies. However, this can be largely or even completely counteracted by reducing or eliminating the role of the gradient exchange correction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 227–238, 2000     

Atomic calculations with an effective one-body potential

The accuracy of a new effective one-body potential is assessed by the study of the electronic structure of atoms from He to Kr. The exchange part of this potential is obtained from a local approximation. Several simplified representations of the electronic density which lead to analytic Coulomb potentials are tested. It is shown that the introduction of the shell structure of the density is necessary, at least for third row atoms. The screening parameters of the potential are variationally optimized with respect to the total energy of the atom. With the most elaborate form of the Coulomb potential which contains one screening parameter for each shell, the comparison of the results with exact Hartree–Fock calculations is very promising. The relative difference is on the order of 10^?5 for the total energy and on the order of 10^?2 for the orbital energies. Multiplet splitting is reproduced accurately and F^? is predicted to be stable (in contrast some others local potentials) by an amount of 0.046 a.u., compared with 0.050 a.u. for an exact Hartree–Fock calculation.     

Geometry,basis set,and correlation energy dependence of computed protonation energies of imino bases

The nitrogen protonation energies of the imino bases HN?CHR, where R is H, CH₃, NH₂, OH, and F, have been evaluated to determine the dependence of absolute and relative protonation energies on geometry, basis set, and correlation effects. Reliable absolute protonation energies require a basis set larger than a split-valence plus polarization basis, the inclusion of correlation, and optimized geometries of at least Hartree–Fock 4-31G quality. Consistent relative protonation energies can be obtained at the Hartree–Fock level with smaller basis sets. Extending the split-valence basis set by the addition of polarization functions on all atoms decreases the computed absolute Hartree–Fock nitrogen protonation energies of the imino bases HN?CHR except when R is F, but increases the oxygen protonation energies of the carbonyl bases O?CHR.     

Self-consistent molecular hartree—fock—slater calculations. IV. On electron densities,spectroscopic constants and proton affinities of some small molecules

The use of the Xα exchange approximation in calculations on small molecules is studied. Electron densities are very similar to Hartree—Fock densities, as judged from density difference maps. The statistical total energy, E_Xα, is used in order to calculate R_eB_e, ω₃ and D_e of a series of diatomic molecules. The agreement with experiment is again similar to that in Hartree—Fock calculations. Proton affinities can also be calculated very well. The Hartree—Fock—Slater and Hartree—Fock models show on the whole very analogous behaviour. These results are obtained by using accurate, unapproximated, potentials and densities.     

Explicitly correlated configuration interaction studies using spherical Gaussians. II. Exploratory studies on LiH

Ab initio self-consistent-field and configuration interaction studies have been carried out on the ground state of the LiH molecule at its equilibrium distance. Floating spherical Gaussian basis orbitals (FSGO ) were employed, along with spherical Gaussian correlation factors, using the procedure described in the preceding paper. A near-Hartree–Fock function was found using only 13 FSGO . Exploratory configuration interaction studies recovered approximately 73% of the inner shell correlation energy and approximately 56% of the total correlation energy with five configurations plus the Hartree–Fock configuration. These studies indicate that, by using spherical Gaussian correlation factors, direct introduction of interelectronic coordinates into trial wave functions can be accomplished for molecular systems. It was also shown that correlating configurations need not utilize the full Hartree–Fock basis, but may use substantially smaller bases and still recover correlation energy effectively. Finally, the results indicate that, in spite of their improper cusp behavior, FSGOS and spherical Gaussian correlation factors can be used for construction of high accuracy wave functions.     

Pauli repulsion in the open shell species BeH and Co+

Using the natural bond orbital method, one may associate the valence bond configuration and Lewis structure concepts to wave functions consisting of molecular orbitals and thus gain intuitive insight into the molecular potential energy curves. Natural bond orbital analysis of the restricted open shell Hartree–Fock and unrestricted Hartree–Fock wave functions for the BeH ground state provides an intuitive model to help understand the nature of the bonding in this open shell species. The contrasting behavior of the bonding orbitals for different spins can be attributed to differences in the Pauli repulsive interactions with the lonepair orbitals. Such behavior occurs in BeH(²Σ) but does not in CO⁺(²Π) because the Pauli repulsion depends on the orbital overlap.     

Cluster calculations of the H2O/Pt(111) system

The electronic interaction between water and a Pt(111) surface as evaluated for different Pt_x(H₂O)_y clusters is discussed. Hartree–Fock–Slater (HFS ) one-electron ground state energies, ionization potentials, partial densities of states, and Mulliken occupation numbers are related to bonding shifts, as well as initial and final state screening for different orientations of the molecule. The formation of Pt? H₂O bonds are sensitive to the orientation since surface oriented H atoms bridge the spatial separation between O 2p and Pt 5d orbitals and thus increase the intermixing of metal and adsorbate orbitals. The dipole moment and the net charge of the H₂O molecule is also discussed. Finally, approximations of the metal–H₂O potential for use in statistical models of the liquid–metal interface are suggested.