Calculated Ionization Energies Research Articles

Theoretical studies on pteridines. 2. Geometries, tautomer, ionization and reduction energies of substrates and inhibitors of dihydrofolate reductase

AbstractAb initio SCF calculations with STO‐3G and 3‐21G basis sets are reported for approximately 85 pteridines of interest to the study of the reaction and inhibition mechanisms of dihydrofolate reductase. These include tautomeric, protonated, deprotonated, reduced and 6‐substituted forms of the 2‐amino‐4‐oxo‐ and 2,4‐diamino‐pteridines, many of which are not easily amenable to experimental investigation. Full geometry optimizations at the SCF/STO‐3G level for 30 such pteridines have been performed. A step‐wise computational protocol designed to identify the minimum level of theory necessary for reliable prediction of relative tautomer, reduction and ionization energies has been developed in an effort to minimize the cost of calculations for this reasonably large N‐heterobicylic system. In general, SCF/STO‐3G results were found to be inadequate while SCF/3‐21G results obtained with STO‐3G optimized geometries agreed with all available experimental evidence with the exception of the relative acidity of 6‐methyl‐7,8‐dihydropterin. Correlation graphs relating experimental pKa's to the calculated ionization energies are presented: these are of potential predictive value. An analysis is given of the importance of resonance substructures, such as the guanidinium and extended‐guanidinium groups, in stabilizing some preferred tautomeric and ionized forms, and in explaining the observed geometry changes.

Hole localization in ionized and bound excitation states of monovalent copper halides

Abstract The results of self-consistent field calculations on the ground states, ionized stated and some excited states of the clusters [CuCl4]3−, [CuBr4]3−, [Cu4Cl]3+ and [Cu2Cl]+ are presented and discussed. The Madelung field of the rest of the crystal has been incorporated in the calculations. High and low point-group symmetries are considered, showing the importance of relaxing symmetry constraints. The calculated ionization energies show good overall agreement with experiment; however, the calculated crystal field splitting of the 3d levels is much smaller than the observed one. The calculated 3d–4s-like excitation energies are very sensitive to both the external field and the basis sets used, and more studies are required before firm conclusions can be drawn. The results indicate that at the level of the single-configuration SCF approximation, open-shell orbitals describing 3d holes are strongly localized on copper. Their ‘covalency’ is small, so that a seemingly necessary contribution to an understanding of the spectral properties is missing at this level of approximation, which includes one-electron band theory.

Electronic structure and identification of deep defects in GaP

We report a theoretical study of the Ga vacancy, the P antisite defect (i.e., a P atom occupying a normally Ga site), and carbon impurities at Ga sites. The analysis employs a modified version of the self-consistent Green's-function method that was previously used to describe deep centers in Si. In all three cases, the number, orbital content, and relative energy positions of the localized states can be understood in terms of simple models, as in the case of corresponding centers in Si. In particular, we find that, in all cases, the gap state consists primarily of atomiclike $p$ orbitals centered on the four nearest neighbors, revealing that deviations from $s{p}^{3}$-hybrid character are possible even without any relaxation of the surrounding lattice. In the case of the antisite defect, we find an ${A}_{1}$ bound state in the gap which is consistent with the EPR spectra that led to the identification of the defect. The calculated ionization energies are in agreement with optical data and more recent deep-level-transient-spectroscopy data. In the case of the Ga vacancy, we find a ${T}_{2}$ level in the gap above an ${A}_{1}$ resonance inside the valence bands, and in the case of carbon, we find a deep ${A}_{1}$ level in the gap. These results contradict key assumptions that led to the identification of the NRL-1 EPR signal as the ${V}^{2\ensuremath{-}}$ charge state of the Ga vacancy. More recent experiments redetermined some of the parameters of NRL-1 and reassigned the center to the neutral state of the Ga vacancy. Here, we discuss the interplay between experiment and theory that led to the new identification and describe existing difficulties that limit our ability to construct a detailed model which is consistent with all experiments and with theory.

Cluster calculations of intermediate states in the catalyzed conversion of CH 3OH to CH 2O on a Cu(100) surface

The Hartree-Fock-Slater (HFS) calculations of a CH 3OCu 5 cluster symbolizing methoxide bound to a Cu(100) surface are presented. Adsorption geometry, molecular orbitals, and symmetry properties of the CH 3O group in terms of one-electron energies, charge distributions, and partial densities of states (PDOS) are discussed. A comparison of calculated ionization energies and measured binding energies supports the occupation by methoxide of the hollow adsorption site. The electron distribution of the hydrogen atoms has been analyzed for different geometries and is shown to be a sensitive probe of the oxidation from methoxide (CH 3O)/methyl (CH 3) to formaldehyde (CH 2O)/methylene (CH 2).

The frozen-core approximation with a nonempirical polarisation potential: the sodium isoelectronic sequence

Orbital wavefunctions of a large number of levels Na I, Mg II, Al III and Cl VII have been calculated using a frozen-core Hartree-Fock approximation which includes a nonempirical polarisation potential derived from polarised core orbitals. The calculated ionisation energies are in very good agreement with precise measurements. Electric dipole oscillator strengths derived from the computed wavefunctions and energies are found to be of generally high accuracy.

Ground states of molecules. 56. MNDO calculations for molecules containing sulfur

AbstractMNDO has been extended to sulfur, but without inclusion of 3d AOs. Calculations are reported for heats of formation, geometries, dipole moments, and ionization energies of a variety of sulfur‐containing molecules. The average discrepancy between calculated and observed heats of formation is larger than for compounds of other elements, a difference probably due, at least partly, to the lower accuracy of the thermochemical data for sulfur compounds. The calculated dipole moments agree well with experiment as do the calculated ionization energies, except for those corresponding to ionization from sulfur “lone‐pair” orbitals which are too high by ca. 1 eV, probably as a result of the neglect in NDDO of interactions between inner and valence shell orbitals. As in the case of other third‐period elements, the calculated heats of formation of compounds of sulfur in its higher valence states (SIV, SVI) were too positive by large amounts, due presumably to the neglect of 3d AOs.

Multimode Jahn–Teller and pseudo-Jahn–Teller effects in BF+3

The ionic states of BF3 exhibit striking vibronic coupling effects. These effects are investigated using ab initio calculated ionization energies and vibronic coupling constants. The two Jahn–Teller active modes show interference effects in all bands of E symmetry. In the 2A1′ ionic state single quanta of a degenerate vibration are excited. They borrow their intensities from the adjacent 2E′ state by means of a pseudo-Jahn–Teller interaction. The symmetry of BF+3 in its nondegenerate ground state is predicted to be lowered due to two-mode pseudo-Jahn–Teller interaction with the second excited state. This interaction is surprisingly strong and leads to an interesting vibronic structure. The vibrational fine structure in all experimental spectra is reproduced satisfactorily. The earlier discrepancies in assigning the three lowest lying ionic states are explained.

Electrostatic and relaxation effects in ionization of molecular dimers and intermolecular complexes

AbstractThe shifts in ionization energies which occur when a molecule is incorporated as an asymmetric dimer or in an intermolecular complex are analyzed theoretically. MOSCF calculations with 4–31G basis sets were performed on closed‐ and open‐shell states of (HF)2, H2O·HF, and their valence–hole ions, as well as on the heterodimers incorporating the higher homologues CH3F, CH3OH, and (CH3)2O. The analysis concerns the influence of electrostatic, polarization, and charge transfer effects associated with complexation on the initial molecular state of each monomer system, as well as monomer–dimer differences in the electronic relaxation mechanism considered as a final state effect in the ionization process. The calculated ionization energy shifts which agree well with the experimental data available for (CH3)2O·HF, show that the shifts are dominated by electrostatic effects, but some effects arising from differences in molecular size and electric polarizability of the monomers can be discerned.

Photoelectron spectroscopic study of simple hydrogen-bonded dimers. II. The methanol dimer

HeI photoelectron spectra of a supersonic jet of methanol vapor have been obtained by using the temperature-controlled supersonic nozzle beam photoelectron spectrometer recently constructed in our laboratory. A HeI spectrum attributable to the methanol dimer (CH 3OH) 2 has been deduced by spectrum stripping. The first ten vertical ionization energies and the first adiabatic ionization energy of (CH 3OH) 2 have been determined from the stripped spectrum. Ab initio SCF MO calculations of ionization energies have also been carried out for (CH 3OH) 2 on the basis of Koopmans' theorem. The lower bound of the dissociation energy of (CH 3OH) 2 + has been estimated to be 1.2 ± 0.2 eV from the adiabatic ionization energies of the monomer and dimer. The equilibrium structure of (CH 3OH) 2 is also discussed.

The Electronic Structure of Closed Shell Metallocenes in the Ground State and in the Cationic Hole-States

The electronic structure of tne closed shell metallocenes bis(π-cyclopentadienyl)magnesium (1), bisbenzene chromium (2), ferrocene (3) and cyclopentadienyl benzene manganese (4) has been studied in the ground state as well as in the low-lying cationic states. The computational framework is a semiempirical INDO Hamiltonian, the theoretical framework for the investigation of the cationic hole-states is the Green's function method. The calculated ionization energies are compared with the photoelectron (PE) spectra of the four closed shell metallocenes. The interrelation between theoretically determined reorganization energies and the localization properties of the orbital wave functions or the nature of the transition metal center is analyzed. General rules concerning the validity of Koopman's theorem in transition metal complexes are formulated.

Effects of relativity in the He(I) Photoelecron Spectrum of CI 4

Valence ionization energies of tetraiodomethane (CI 4) obtained with He(I) photoelectron spectroscopy are presented. The interpretation is based on the results of Hartree-Fock-Slater (HFS) calculations using STF basis sets of triple-zeta quality. Effects of relativity have been taken into account through a perturbation treatment to first order in the square of the fine structure constant. The excellent agreement between experiment and theory illustrates that the HFS scheme including a relativistic perturbation approach is a reliable method for the calculation of ionization energies of molecules containing heavy atoms.

Errors in the Slater transition state method for spin-polarized calculations of localized core levels

In analogy to the Slater transition state method for calculating ionization energies, which takes account of electronic relaxation effects, one may construct an unrelaxed transition state method, which gives Xα ionization energies which are the analog of Koopmans’ theorem ionization potentials of Hartree–Fock theory. As the unrelaxed method is more algebraically tractable, it can be analyzed in detail. Comparisons of unrelaxed transition state energies and unrelaxed Xα total energy differences for LCAO calculations reveal an anomalous error for spin-polarized localized core orbitals. This discrepancy is shown to arise from poor convergence of the series used to derive the transition state energy. Similar discrepancies are shown to exist in relaxed transition state calculations.

The polarised frozen-core approximation: Oscillator strengths for the boron isoelectronic sequence

Orbital wave functions of a large number of ns-, np-, and nd-levels of the first five members of the boron isoelectronic sequence have been calculated using a frozen-core Hartree-Fock procedure augmented by an l-dependent core polarisation potential. The calculated ionisation energies are generally in very good agreement with observations. Electric dipole oscillator strenghts have been derived from the calculated orbitals and energies and have been used to yield simple interpolation formulae for f-values of higher members of the sequence. They are expected to be of high accuracy in many cases.

∆SCF and Transition Operator (TO) Calculations in the Theoretical Determination of Vertical Ionization Energies in Transition Metal Compounds

The interrelation between theoretically determined vertical ionization potentials in transition metal compounds based on the ∆SCF approximation (Iv,j ∆SCF) and based on the “transition operator (TO)” method (Iv,j TO) has been investigated. Numerical results in the outer valence region have been obtained by means of semiempirical INDO calculations. The difference between the calculated ionization energies (Iv,j ∆SCF and Iv,j TO) is enlarged with increasing atomic numbers of the transition metal center due to noncompensating terms in third order of perturbation. The neces­sary conditions for the imbalance of both theoretical procedures are large two-electron interaction integrals and highly populated transition metal hole-states. Both requirements are enhanced by going from the left side of the 3d series to the extreme right. For d4-d6 complexes a simplified expression for Iv,j ∆SCF has been derived containing only one third order element.

Interpretation of CO/Pt photoemission data via relattvistic cluster calculations

Small clusters modeling various surfaces of platinum are employed in relativistic molecular orbital calculations. The results are correlated with existing ultraviolet (UPS) and X-ray (XPS) photoelectron spectra. The Pt valence band consists of two complexes, d 5 2 and d 3 2 , separated by spin-orbit splitting. The UPS result for clean Pt(111) conforms to a schematic description of the Pt d-band. The calculated ionization energies for the adsorbed CO compare well with UPS and XPS data.

Ionization energies of the N2, CO, CO2, N2O, C2H2 and SiH4 molecules calculated by universal model potential

A modified XαSW method with universal potential (MXαSWU) was used to calculate ionization energies of the N2, CO, CO2, N2O, C2H2 and SiH4 molecules. The calculated energies are in agreement with experiment and other calculations.

Hartree-Fock-Slater-LCAO studies of the acetylene-transition metal interaction: II. Chemisorption on Fe and Cu; cluster models

Self-consistent Hartree-Fock-Slater-LCAO studies have been performed for (geometrically distorted) C 2H 2 molecules interacting with Fe and Cu clusters of one to three atoms, which model the π, di-σ, μ 2 and μ 3 adsorption sites on Fe(110), (100) and Cu(111), (100) and (110) surfaces. The results have been compared with previous data for Ni surfaces (paper I). Calculated ionization energies are in fair agreement with the measured ones (from UPS): a bonding shift of the acetylene π u levels, relative to the 3σ g level, is found in all cases, but also a larger splitting of these π u levels occurring on Cu, compared with Fe and Ni. This difference is due to a different C 2H 2-metal interaction: on Fe and Ni we find π to metal donation and (more substantial) metal to π ∗ back donation, on Cu the first effect is dominated by a strong interaction between the occupied acetylene π u (and 3σ g) levels and the filled metal levels which are present in the same energy range (only in Cu, due to the lower lying 3d and 4s bands). This relatively strong (net repulsive) interaction explains the larger π u level splitting and, also, the observation that C 2H 2 binds weaker to Cu (it desorbs, at higher temperature, and does not dissociate) than to Fe and Ni.

Broken orbital-symmetry and the description of hole states in the tetrahedral [CrO 4] − anion. I. Introductory considerations and calculations on oxygen 1s hole states

The localization of holes in systems containing spatially equivalent sites is discussed in terms of a simple one-particle model in which quantum mechanical delocalization effects compete with essentially classical polarization or dielectric relaxation effects. The predictions of the model for a tetrahedral system like CrO − 4 compare favourably with the results of symmetry unrestricted SCF calculations on O 1s hole states. The connection with a Cl treatment using symmetry-restricted MOs is discussed. The calculated ionization energies are finally compared with XPS measurements on Na 2CrO 4. To this end the crystal surrounding of the CrO − 4 anion has been represented by a point charge model and the ensuing Modelung field was included in the SCF calculations. In contrast to the Td restricted result of 551.4 eV, the completely localized C 3v results of 532.6 eV is in satisfactory agreement with the experimental data which are found around 530.0 eV.

The frozen orbital approximation for calculating ionization energies with application to propane

In the frozen orbital approximation (FOA), the influence of reorganization on correlation contributions to ionization energies is neglected. It is particularly useful in calculations for large molecules because of the advantage that only one integral transformation is required for the calculation of all ionic states. In connection with the concept of independent orbital correlation contributions, the dimensions of the CI matrices can be drastically reduced. The method is applied to the calculation of the valence ionization energies of propane, and compared to more rigorous ab initio results and a recent calculation in which inner valence shell contributions to electron correlation are neglected. The ordering of the first three ionizations in the photoelectron spectrum of propane, which has not been definitively assigned, is shown to be 2B1(2b1),2A1(6a1) and 2B2(4b2), in agreement with Koopmans' theorem.

Fractional occupation in the hartree-fock method

It is shown that ϵ i HF = ϵ i Xα if we allow fractional occupation in the Hartree-Fock formalism and substitute the local Xα potential for the non-local exchange potential. Calculations of ionization energies of closed-shell atoms show that the proposed method is as accurate, and simpler than the standard transition-operator techniques.