Core polarization and relativistic effects competition in the first ionization potentials for some systems in the Cu,Ag, and Au isoelectronic sequences

Single-configuration relativistic Hartree–Fock values of the first ionization potentials for Cu through Kr⁷⁺, Ag through I⁶⁺, and Au through Pb³⁺ are computed in “frozen” and “relaxed core” approximations with and without allowance for core polarization. Effects of polarization of the atomic core by the valence electron are included by introducing a polarization potential in the one-electron Hamiltonian of the valence electron. The core polarization potential depends on two parameters, the static dipole polarizability of the core α and the cut-off radius r₀, which are chosen independently of the ionization potential data. It is demonstrated that by including the core polarization potential with α and r₀ parameters, which are simply chosen instead of being empirically fitted, it is still possible to account, on the average, for at least 70% of the discrepancy between the single-configuration relativistic Hartree–Fock ionization potentials and the experiment, a discrepancy usually ascribed to the contribution of valence-core electron correlations, and to bring the theoretical ionization potentials to an average agreement with experiment of around 1%. It can be concluded from this study that for low and medium Z elements the core polarization dominates for neutral systems or systems in low ionization stages, whereas for highly ionized systems the relativistic effects prevail. For heavy elements, however, the core polarization influence is comparable to the relativistic one only for neutral systems, whereas for ions the relativistic effects are overwhelmingly predominant.     

The assignment of the ionization potentials of formaldehyde by an (e, 2e) experiment

The angular variation of the binding energy spectrum in an electron-electron coincidence experiment indicates that the third and fourth ionization potentials of formaldehyde are due to the 5a₁ and 1b₂ orbitals respectively. The vertical ionization potentials of the 4a₁ and 5a₁ orbitals are found to be 21.15 ± 0.15 and 34.2 ± 0.2 eV respectively.     

Outer shell ionization potentials for ethane by a many-body Green's function method

A calculation based upon the many-body Green's function method is employed to obtain the outer shell vertical ionization potentials of the ethane molecule. An extended basis set is employed to represent the approximate optical potential, derived by the functional derivative approach, as well as the one-electron Green's function. The results obtained confirm a²E_g state for the ion arising from the first ionization process. Supported by a fellowship of the Scuola Normale Superiore.     

Theoretical studies of molecular ions. Vertical ionization potentials of the nitrogen molecule

The ²Σ⁺_g, ²Π_u, and ²Σ⁺_u vertical ionization energies of nitrogen are obtained by using our theory of molecular electron affinities and ionization potentials, which permits the direct calculation of the ion-molecule energy differences. The contributions of charge redistribution and correlation energy change to the calculated ionization potentials are evaluated. The computational efficiency of the method is illustrated and comparisons are made with recent experimental results.     

Ionization and appearance potentials in organic chemistry. II—Appearance potentials and enthalpy differences for the stereoisomers of methylbicyclo[4.4.0]decanes

The ionization potentials for the stereoisomers of trans-fused 2- and 3-methylbicyclo[4.4.0]decanes and the appearance potentials for the ions at m/e 137 [M–CH₃]⁺, 109, 96, 95 and 82 were measured by the electron impact method. The ionization potentials and appearance potentials of the [M–CH₃]⁺ ions appeared to be equal for each of the epimers. Appearance potentials of the other ions were always lower for the less stable epimer. No quantitative correlation was observed between the difference in the appearance potentials for any ions and the differences in enthalpies of the ground states.     

Calculation of vertical ionization potentials of difluoramine by perturbation corrections to koopmans' theorem

The vertical ionization potentials of difluoramine are calculated by perturbation corrections to Koopmans' theorem. The calculation shows that difluoraimine has three overlapping bands between 15 and 16 eV. The calculated results compare well with the experimental values. The photoelectron spectrum of difluoramine is compared with that of OF₂ and CH₂F₂.     

Ionization and appearance potentials in organic chemistry. I—energetic aspects of the mass spectra of stereoisomeric 4-substituted N-alkyl-2-methyldecahydroquinol-4-ols

The ionization potentials for the stereoisomers of trans-fused 1,2-dimethyl- and 1-ethyl-2-methyl-4-R-decahydroquinol-4-ols (R?C?CH, CH?CH₂ or C₂H₅) and the appearance potentials for the [M–CH₃]⁺ and [M–C₂H₅]⁺ ions (loss of 2-CH₃ and 4-C₂H₅ groups potential, respectively) were measured by using the electron impact method. The ionization and appearance potential for [M–CH₃]⁺ are always lower for the isomers with the axial 2-CH₃ group. For the C-2 epimers, the difference between the appearance potentials for the [M–CH₃]⁺ ion values is likely to be equal to the enthalpy differences between the ground states of the epimers and the dissociation energy differences between the axial and equatorial C₂–CH₃ bonds. The appearance potentials for [M–C₂H₅]⁺ for the C-4 epimers possessing the 4-C₂H₅ group were very similar. At the same time, the appearance potentials for the [M–CH₃]⁺ ions were lower for less stable epimers which had an axial 4-C₂H₅ group.     

An empirical chemical potential of the atomic core for non-transition element

An empirical relation between the energy of an atomic ion and its charge is determined from the experimental ionization potentials for non-transition elements. The definition of chemical potential μ_c and effective charge Z_c of the atomic core is postulated. Both are shown to be closely related to the classical electronegativity.     

Calculation of Vertical Ionization Potentials of Oxygen Difluoride,Difluoramine, and Difluoromethane by Local Density Approximation

The vertical ionization potentials of OF₂, HNF₂, and CH₂F₂ were computed by the deMon density functional program. The results are compared with earlier calculations and with experiment. The average absolute deviation of the 21 computed ionization potentials of the outer valence electrons from experiment is 0.44 eV, which compares well with 0.37 eV for frozen-orbital configuration-interaction calculations. Although this performance is not as good as perturbation corrections to Koopmans' theorem, the computation requirements are much less demanding.     

Semiempirical potential curves of N2 and CO computed with the MS-Xα theory

Potential energy curves of N₂⁺ and CO⁺ have been obtained by mapping vertical ionization potentials onto the potential energy curves of the corresponding parent species. The vertical ionization potentials used in this mapping procedure were computed using the MS-Xα formalism in the muffin-tin approximation. The mapping procedure reduces the error inherent in the direct use of total statistical energies within the muffin-tin approximation     

Calculation of vertical ionization potentials of H2O and Ne by many-body Rayleigh-Schrödinger perturbation theory

The vertical ionization potentials of H₂O and Ne are calculated by many-body Rayleigh-Schrödinger perturbation theory up to third order. The comparison of the present method with the other approaches is done.     

Calculation of vertical ionization potentials using the one-body green's function: Ne,Mg and H2O

The valence and core ionization potentials of Ne, Mg, and H₂O have been calculated by using the one-body Green's function. The self-energy part was taken to include the second order and the ω²-dependent terms, third order in the perturbation.     

Molecular model potentials: Combination of atomic boxes

A new Combination of Atomic Boxes (CAB) molecular orbital model is introduced, having the following characteristics:

1. Atomic model potentials are one-dimensional potential boxes of finite depth U _A and of length L _A, the box-parameters being chosen to give valence electron ionization energies.
2. Explicit molecular model potentials are constructed by combining all the model potentials of the atoms in the molecule.
3. A minimum computational effort leads to rigorous solutions of the resulting Schroedinger equation.

The model is tested on a large variety of π-electron systems containing atoms of four rows of the periodic system. Branched and cyclic molecules are also treated. The comparison of the calculated first and higher ionization and first excitation energies with the observed data gives the mean deviations 0.540 eV and 0.388 eV resp. The common physical basis of the CAB and the model-pseudopotential methods is discussed. The constant potential within the box is a consequence of the partial cancellation of the electrostatic potential by a repulsive term representing the Pauli principle. It is shown that CAB is not restricted to π-electrons but can be extended to σ-electron systems as well.     

Charge transfer reactions in alkane and cycloalkane systems. Estimated ionization potentials

Rate constants of change transfer reactions k_CT, involving C₃? C₉ alkanes and cycloalkanes, have been determined in an ion cyclotron resonance mass spectrometer. The rate constants are significantly lower than the corresponding rate constants for collision when the reaction is less than about 0.5 eV exothermic for linear alkane ions, or less than about 0.2 eV exothermic for cycloalkane ions. In this region of low reaction efficiency, the efficiency of reaction with linear or branched alkanes seems to depend primarily on reaction exothermicity. (The efficiencies of reaction of a given ion with cyclic alkanes also depend on ΔH_rn, but are higher than for reactions with other compounds). Although the lowered reaction efficiencies probably result, at least in part, from unfavorable Franck–Condon factors in the energy range near the ionization onset, quantitative correlations between reaction efficiency and estimated relative Franck–Condon factors were not observed. When the enthalpy of reaction is small (less than about ?0.15 eV), it is seen that the reverse charge transfer can also occur, and equilibrium is established under the conditions of these experiments. From the observed equilibrium constants, values for the standard free energy change are derived, and assuming that ΔS is small for electron transfer equilibria, values of ΔH_rn are estimated. In the case of the equilibria involving cyclohexane ion, these values of ΔH_rn lead to estimates of the ionization potentials of methylcyclopentane, 3-methylpentane, n-octane, 2,2-dimethylbutane, and 2,3-dimethylbutane, which are lower than the ionization potentials of cyclohexane, that is, <9.88 eV, although all these compounds had previously been reported to have ionization potentials above 10.03 eV. That the ionization potentials are indeed lower than 10.03 eV is confirmed by determining the quantum yields of ionization with 10.03-eV photons. It is pointed out that the conclusions reached here apparently also apply to the charge transfer reactions of alkane ions in the liquid phase.     

pH,Definition and measurement at high temperatures

In this review paper, the NBS scale and its limitations are briefly discussed. The magnitude of liquid junction potentials and some calculated values are presented. The use of a molality scale for hydrogen electrode concentration cells at high temperatures is described, and results from measurements on ionization equilibria are summarized. Use of this scale is also recommended for certain circumstances with cells without liquid junction. As an alternative activity scale, use of the Pitzer ion-interaction treatment for ions is recommended for special cases. Finally, reference data are presented for _±HCl in HCl(aq) to 350°C and (HCl+NaCl)(aq) to 200°C that were derived by use of the Pitzer ion-interaction treatment.Presented at the Second International Symposium on Chemistry in High Temperature Water, Provo, UT, August 1991.     

A semi-empirical MO theory for ionization potentials and electron affinities. II. Vertical and adiabatic values,benzenoid and nonbenzenoid aromatic hydrocarbons,and conjugated molecules with heteroatoms

Further developments of a recent semiempirical, variable effective charge MO theory for calculation of ionization potentials (IP ) and electron affinities (EA ) as energy differences between separately minimized ground and ionized states are reported. The method is extended to adiabatic as well as vertical IPS and EAS by including core repulsion and σ bond compression energies in the total energy. The method is generalized to heteroatomic systems and is simplified by neglecting penetration integrals. As before, only two molecular parameters, the vertical IPS of benzene and naphthalene, are required to set the magnitude of the σ changes associated with the polarization of the core during loss or gain of a π charge. Twenty-seven aromatic molecules are studied, including polyacenes, condensed ring compounds, nonbenzenoids with five and seven member rings, nonplanar molecules, and heteroatomics with N⁺, as in pyridine, N⁺², as in pyrrole, and O⁺², as in furan. The results are within 0.2 eV of the photoelectron spectroscopic vertical IPS and the predicted vertical-adiabatic separation is consistent with the shape of the first band. The calculated EAS are within 0.2 eV of the observed values. The calculation is used to predict the IP and EA of the ionic photosensitizing cyanine dye, pinacyanol. The values obtained are consistent with the latest measured IP and EA of the adsorbed dye, corrected for surface and aggregation polarization effects.     

Calculation of vertical ionization potentials by configuration interaction

The ionization potentials of H₂O, N₂, C₂H₂, and HCN were calculated by frozen-orbital configuration interaction using doouble-zeta and double-zeta plus polarization functions basis sets. The results are compared to the observed values and to those from Rayleigh—Schrödinger perturbation theory. The effects of higher excitations are estimated and discussed.     

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     

Ab initio MRD-CI study of ethane: The 14–25 eV PES region and Rydberg states of positive ions

Ab initio calculations of the MRD-CI type are reported for various states of the C₂H₆⁺ ion in two different nuclear geometries and the results are compared with the experimentally observed ethane PES in the 14–25 eV region. The calculated vertical IP values for ionization out of the 1e_u, 2a_2u and 2a_1g MO's respectively agree well with the locations of the three ionization maxima in this spectral range. The analogous findings for excitation out of the relaxed ionic ground state find several relatively low-lying species which occupy a 2pσ* MO in addition to states resulting from simple ionization of the neutral molecule. A number of Rydberg states are also calculated at the relaxed-ion geometry, from which results it is determined that the quantum defects for such species are from 0.40–0.45 units smaller than for their counterparts in neutral systems; these findings are clearly consistent with a decrease in the core penetrability of the Rydberg electron as the effective charge is increased to Z = 2.