The one-particle Green's function method in the Dirac-Hartree-Fock framework. II. Third-order valence ionization energies of the noble gases, CO and ICN

In this paper we present the third-order extension of the four-component one-particle propagator method in the non-Dyson version of the algebraic diagrammatic construction (ADC) for the calculation of valence ionization energies. Relativistic and electron correlation effects are incorporated consistently by starting from the Dirac-Hamiltonian. The ADC equations derived from the Feynman diagrams can hereby be used in their spin-orbital form and need not be transformed to the spin-free version as required for a nonrelativistic treatment. For the calculation of the constant self-energy contribution the Dyson expansion method was implemented being superior to a perturbational treatment of sigma(infinity). The Dirac-Hartree-Fock- (DHF-) ADC(3) was applied to the calculation of valence photoionization spectra of the noble gas atoms, carbon monoxide and ICN now also reproducing spin-orbit features in the spectrum. Comparison with DHF-ADC(2), nonrelativistic ADC(3), and experimental data was made in order to demonstrate the characteristics and performance of the method.     

Study of the photoelectron and electron momentum spectra of cyclopentene using benchmark Dyson orbital theories

A complete study of the valence electronic structure and related electronic excitation properties of cyclopentene in its C(s) ground state geometry is presented. Ionization spectra obtained from this compound by means of photoelectron spectroscopy (He I and He II) and electron momentum spectroscopy have been analyzed in details up to electron binding energies of 30 eV using one-particle Green's function (1p-GF) theory along with the outer-valence (OVGF) and the third-order algebraic diagrammatic construction [ADC(3)] schemes. The employed geometries derive from DFT/B3LYP calculations in conjunction with the aug-cc-pVTZ basis set, and closely approach the structures inferred from experiments employing microwave spectroscopy or electron diffraction in the gas phase. The 1p-GF/ADC(3) calculations indicate that the orbital picture of ionization breaks down at electron binding energies larger than approximately 17 eV in the inner-valence region, and that the outer-valence 7a' orbital is also subject to a significant dispersion of the ionization intensity over shake-up states. This study confirms further the rule that OVGF pole strengths smaller than 0.85 foretell a breakdown of the orbital picture of ionization at the ADC(3) level. Spherically averaged (e, 2e) electron momentum distributions at an electron impact energy of 1200 eV that were experimentally inferred from an angular analysis of EMS intensities have been interpreted by comparison with accurate simulations employing ADC(3) Dyson orbitals. Very significant discrepancies were observed with momentum distributions obtained from several outer-valence ionization bands using standard Kohn-Sham orbitals.     

New relativistic ANO basis sets for transition metal atoms

New basis sets of the atomic natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically symmetric atoms. These calculations include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the experimental values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals.     

Electronic structure and properties of transition metal-benzene complexes.

A comprehensive theoretical study of the geometries, energetics, and electronic structure of neutral and charged 3d transition metal atoms (M) interacting with benzene molecules (Bz) is carried out using density functional theory and generalized gradient approximation for the exchange-correlation potential. The variation of the metal-benzene distances, dissociation energies, ionization potentials, electron affinities, and spin multiplicities across the 3d series in MBz complexes differs qualitatively from those in M(Bz)(2). For example, the stability of Cr(Bz)(2) is enhanced over that of CrBz by almost a factor of 30. On the other hand, the magnetic moment of Cr(Bz)(2) is completely quenched although CrBz has the highest magnetic moment, namely 6 mu(B), in the 3d metal-benzene series. In multidecker complexes involving V(2)(Bz)(3) and Fe(2)(Bz)(3), the metal atoms are found to couple antiferromagnetically. In addition, their dissociation energies and ionization potentials are reduced from those in corresponding M(Bz)(2) complexes. All of these results agree well with available experimental data and demonstrate the important role the organic support can play on the properties of metal atoms/clusters.     

Fluorine as a pi donor. Carbon 1s photoelectron spectroscopy and proton affinities of fluorobenzenes

The carbon 1s ionization energies for all of the carbon atoms in 10 fluorine-substituted benzene molecules have been measured by high-resolution photoelectron spectroscopy. A total of 30 ionization energies can be accurately described by an additivity model with four parameters that describe the effect of a fluorine that is ipso, ortho, meta, or para to the site of ionization. A similar additivity relationship describes the enthalpies of protonation. The additivity parameters reflect the role of fluorine as an electron-withdrawing group and as a pi-electron donating group. The ionization energies and proton affinities correlate linearly, but there are four different correlations depending on whether there are 0, 1, 2, or 3 fluorines ortho or para to the site of ionization or protonation. That there are four correlation lines can be understood in terms of the ability of the hydrogens at the site of protonation to act as a pi-electron acceptor. A comparison of the ionization energies and proton affinities, together with the results of electronic structure calculations, gives insight into the effects of fluorine as an electron-withdrawing group and as a pi donor, both in the neutral molecule and in response to an added positive charge.     

Silicon-nitrogen bonding in silatranes: assignment of photoelectron spectra

Silicon-nitrogen bonding and the photoelectron spectra of hydro-silatrane and methyl-silatrane, XSi[OCH2CH2]3N (X = H and Me), were studied with ab initio electron propagator theory, many-body methods, and density functional models. A linear vibronic coupling (LVC) model was employed to estimate vibrational widths of the ionization bands and to study the dependence of the ionization energies on the molecular geometry. Particular attention was given to coordinates that change the Si-N distance and the strength of the donor-acceptor interaction between these two atoms. The ionization energy of the highest occupied molecular orbital has a very strong geometrical dependence which leads to an unusually large vibrational width in the corresponding photoelectron band. The assignment of this band in methyl-silatrane, which was controversial for a long time, is resolved by the present study. The calculated photoelectron spectra allow for clear assignment of at least three more bands in the observed spectra. The present results demonstrate the important role of electrostatic interactions in Si <-- N bonding and in the outer-valence ionization energies of the silatranes.     

A generalized any particle propagator theory: Assessment of nuclear quantum effects on electron propagator calculations

In this work we propose an extended propagator theory for electrons and other types of quantum particles. This new approach has been implemented in the LOWDIN package and applied to sample calculations of atomic and small molecular systems to determine its accuracy and performance. As a first application of the method we have studied the nuclear quantum effects on electron ionization energies. We have observed that ionization energies of atoms are similar to those obtained with the electron propagator approach. However, for molecular systems containing hydrogen atoms there are improvements in the quality of the results with the inclusion of nuclear quantum effects. An energy term analysis has allowed us to conclude that nuclear quantum effects are important for zero order energies whereas propagator results correct the electron and electron-nuclear correlation terms. Results presented for a series of n-alkanes have revealed the potential of this method for the accurate calculation of ionization energies of a wide variety of molecular systems containing hydrogen nuclei. The proposed methodology will also be applicable to exotic molecular systems containing positrons or muons.     

New relativistic atomic natural orbital basis sets for lanthanide atoms with applications to the Ce diatom and LuF3

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are included as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.     

Reactivity and core-ionization energies in conjugated dienes. Carbon 1s photoelectron spectroscopy of 1,3-pentadiene

The high-resolution carbon 1s photoelectron spectrum of trans-1,3-pentadiene has been resolved into contributions from the five inequivalent carbon atoms, and carbon 1s ionization energies have been assigned to each of these atoms. Spectra have also been measured for propene and 1,3-butadiene at better resolution than has previously been available. The ionization energies for the sp2 carbons are found to correlate well with activation energies for electrophilic addition and with proton affinities. Comparing the results for 1,3-pentadiene with those for ethene, propene, and 1,3-butadiene as well as with results of theoretical calculations makes it is possible to assess the effect of the terminal methyl group in 1,3-pentadiene. As in propene, the methyl group contributes electrons to the beta carbon through the pi system. In addition, there is a significant (though smaller) contribution from the methyl group to the terminal (delta) CH2 carbon, also through the pi system. Most of the effect of the methyl group is present in the ground-state molecule. There are only relatively small contributions from the methyl group to the ionization energies from redistribution of charge in the pi system in response to the removal of a core electron. In addition to these specific effects, there is an overall decrease in average ionization energy as the size of the molecule increases as well as effects that are specific to the conjugated systems in 1,3-butadiene and 1,3-pentadiene. The results provide insight into the reactivity and regioselectivity of conjugated dienes.     

The exchange coupling in Cr3On (n = 0-3) clusters

The structures of neutral and cationic Cr3On0,+ (n = 0-3) clusters are calculated with density functional theory employing the BLYP and BP86 functionals. Gas-phase CrnOm clusters are produced by laser vaporization and characterized with time-of-flight mass spectrometry. The ionization energies of Cr3On (n = 0-2) are determined with threshold photoionization spectroscopy using tunable laser light in the 4.5-5.60 eV range. On the basis of a comparison between experimental and calculated ionization energies, ground-state structures were assigned. The influence of sequential addition of oxygen on the exchange coupling between the chromium atoms is investigated providing evidence for enhanced ferromagnetic coupling of chromium atoms in both the neutral and cationic Cr3On0,+ clusters. This evidence of superexchange interaction through oxygen extends earlier ideas to control the magnetic interactions in the chromium dimer via chemical reactions with oxygen toward larger chromium clusters.     

Communication: Ionization potentials in the limit of large atomic number

By extrapolating the energies of nonrelativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row of the periodic table, even as Z → ∞. The local density approximation for the exchange contribution becomes more accurate (or even exact) in this limit. Extended Thomas-Fermi theory matches the shell average of both the ionization potential and density change.     

Relativistic theory of an inhomogeneous electron liquid in relation to atomic binding energies

Experimentally determined ionization potentials in the literature are used to plot the binding energies for neutral atoms as a function of atomic number Z for Z?=?2–30, 32, 36, 42. From this pretty smooth plot we have subtracted non-relativistic Hartree–Fock binding energies, using both available numerical values and the almost analytical result, based on the non-relativistic Thomas–Fermi statistical theory valid for large Z. The difference is still relatively smooth. For Mo, with Z?=?42, the difference is about 70 atomic units. This difference is then analyzed using first relativistic theory of an inhomogeneous electron liquid and then the Local Density Approximation (LDA), and for Mo their results yield approximately 88 and 67 atomic units respectively. We infer that a highly accurate relativistic many-electron theory will therefore be needed before reliable electron correlation energies can be extracted from the experimental binding energies for atoms heavier than Argon. This fact has prompted us to use available LDA calculations to confront three theoretical predictions of the Z dependence of non-relativistic electron correlation energies at large Z.     

Intermediate state representation approach to physical properties of dicationic states

The second-order algebraic construction (ADC(2)) approach to the two-particle (pp) propagator, devised to compute double ionization energies and associated spectroscopic amplitudes, is reformulated and extended using the concept of intermediate state representations (ISR). The ISR formulation allows one to go beyond the general limitations inherent to the propagator approach, as here (N-2)-electron wave functions and properties become directly accessible. The (N-2)-electron ISR(2) equations for a general one-particle operator have been derived and implemented in a recent version of the double ionization ADC(2) program. As a first test of the method, the dipole moments of a series of 2h states of LiH, HF, and H(2)O were computed and compared to the results of a full configuration interaction (FCI) treatment. The dipole moments obtained at the ADC(2)/ISR(2) computational level are in good agreement with the FCI results.     

Electron impact ionization of atomic hydrogen

The role of Coulomb-correlation in electron impact ionization of atomic hydrogen is investigated. Triple differential cross sections are calculated using the first order multiple scattering theory taking into account the propper asymptotic behaviour of the final state wavefunction. A semi-empirical procedure is outlined to choose the effective charges consistent with several physically required limits. A comparison with recent experimental data is made; the observed agreement strongly suggests the importance of asymptotic Coulomb-correlation in ionization even at high energies. The first order approximation used here for the hydrogen case is easily generalizable for ionization of several electron atoms at not too large scattering angles and not too low incident energies.     

Complete basis set, the MP2 ab initio, and hybrid density functional theory evaluation of ionization potential and electron affinity for PH, PH2, PHF, PF, and PF2

A systematic study was performed on the small molecular systems built from phosphor, hydrogen and fluorine with the target being to evaluate accurately their ionization potentials and electron affinities, as well as influence fluorine on the ionization potential of phosphor as a central atom. To determine the accuracy of hybrid density functional methods for computing those energies, ionization energies for hydrogen, fluorine and phosphor were calculated and compared with the experimental and CBSQ values. To demonstrate the accuracy of this method, both the ionization potential and the electron affinity for phosphorus and fluorine atoms were calculated and compared with the experimental data. For both PF and PF₂, an identical electron affinity of 0.72 eV and for PH and PHF 1.0 eV were suggested.     

Slater-like model for carbon 1s core ionization energies of halomethanes.

Based on the atomic electron affinity EA, the average energy of the valence-shell electrons EI and the polarizability alpha, the charge effect and the relaxation effect were evaluated for the carbon 1s core ionization energies of halomethanes CHnY4-n-mZm (Y, Z=F, Cl, Br, I). The charge effect was scaled by the electronegativity discrepancy (the discrepancy of EA and the discrepancy of EI between the C and H or halogen atom in the C-H or C-halogen chemical bond). The relaxation effect (induced dipole) was scaled by the charge on the carbon atom together with the polarizability of the H and halogen atoms. Further, the electrostatic relaxation shielding DeltaSi of the carbon 1s electron in the halomethane was expressed by the charge effect together with the relaxation effect. By introducing DeltaSi into the Slater model, a Slater-like model was obtained for calculating the carbon 1s core ionization energy E1,C of halomethane, whose correlation coefficient r is 0.99985 and the average absolute error is only 0.041 eV between the calculated and the experimental carbon 1s core ionization energies for 27 halomethanes. Also the cross-correlation was tested by the leave-one-out (LOO) cross-validation method, and the obtained model has good predictive ability and stability (the correlation coefficient rcv is 0.99976, the average absolute error between the predicted and the experimental values is only 0.052 eV). The proposed model perhaps lays a good foundation for computing the core ionization energies of various atoms in more complex molecules.     

Ionization energy of atoms obtained from GW self-energy or from random phase approximation total energies

A systematic evaluation of the ionization energy within the GW approximation is carried out for the first row atoms, from H to Ar. We describe a Gaussian basis implementation of the GW approximation, which does not resort to any further technical approximation, besides the choice of the basis set for the electronic wavefunctions. Different approaches to the GW approximation have been implemented and tested, for example, the standard perturbative approach based on a prior mean-field calculation (Hartree-Fock GW@HF or density-functional theory GW@DFT) or the recently developed quasiparticle self-consistent method (QSGW). The highest occupied molecular orbital energies of atoms obtained from both GW@HF and QSGW are in excellent agreement with the experimental ionization energy. The lowest unoccupied molecular orbital energies of the singly charged cation yield a noticeably worse estimate of the ionization energy. The best agreement with respect to experiment is obtained from the total energy differences within the random phase approximation functional, which is the total energy corresponding to the GW self-energy. We conclude with a discussion about the slight concave behavior upon number electron change of the GW approximation and its consequences upon the quality of the orbital energies.     

Study of the molecular structure, ionization spectrum, and electronic wave function of 1,3-butadiene using electron momentum spectroscopy and benchmark Dyson orbital theories

The scope of the present work is to reconcile electron momentum spectroscopy with elementary thermodynamics, and refute conclusions drawn by Saha et al. in J. Chem. Phys. 123, 124315 (2005) regarding fingerprints of the gauche conformational isomer of 1,3-butadiene in electron momentum distributions that were experimentally inferred from gas phase (e,2e) measurements on this compound [M. J. Brunger et al., J. Chem. Phys. 108, 1859 (1998)]. Our analysis is based on thorough calculations of one-electron and shake-up ionization spectra employing one-particle Green's function theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. Accurate spherically averaged electron momentum distributions are correspondingly computed from the related Dyson orbitals. The ionization spectra and Dyson orbital momentum distributions that were computed for the trans-conformer of 1,3-butadiene alone are amply sufficient to quantitatively unravel the shape of all available experimental (e,2e) electron momentum distributions. A comparison of theoretical ADC(3) spectra for the s-trans and gauche energy minima with inner- and outer-valence high-resolution photoelectron measurements employing a synchrotron radiation beam [D. M. P. Holland et al., J. Phys. B 29, 3091 (1996)] demonstrates that the gauche structure is incompatible with ionization experiments in high-vacuum conditions and at standard temperatures. On the other hand, outer-valence Green's function calculations on the s-trans energy minimum form and approaching basis set completeness provide highly quantitative insights, within approximately 0.2 eV accuracy, into the available experimental one-electron ionization energies. At last, analysis of the angular dependence of relative (e,2e) ionization intensities nicely confirms the presence of one rather intense pi(-2) pi(*+1) satellite at approximately 13.1 eV in the ionization spectrum of the s-trans conformer.     

Decoupled Hartree–Fock methods. I. Calculations for atoms with orthogonalized orbitals

By a proper approximation of the interaction term in a many-electron Hamiltonian the Hartree-Fock equations are decoupled. Making use of this simplification one obtains a good initial guess for the wave function with minimal computational work. Refining the procedure, the exact HF limit can be achieved. Total energies, ionization potentials and excitation energies for light atoms are calculated.