Charge transfer driven by electron correlation: a non-Dyson propagator approach

A hole charge created in a molecular system, for instance, by ionization, can migrate through the system solely driven by electron correlation. This charge transfer due to electron correlation is referred to as charge migration. We introduce in this work a new ab initio method analyzing charge migration due to electron correlation in molecules. This method, a third-order "non-Dyson" propagator approach, aims in the long run, in particular, at the calculation of charge migration in relatively large molecules such as oligopeptides. First results of the new non-Dyson method are compared with a previously used propagator approach.     

Implementation and use of a direct, partially integral-driven non-Dyson propagator method for molecular ionization

The Green's function ADC(3) scheme has been for many years a successful method to predict theoretically the ionization (and electron affinity) spectrum of molecules. However, a dramatic enhancement of the method's power has come only recently, with the development of an approximation method to the one-particle Green's function which does not make direct use of the Dyson equation. In the present work, we present an efficient computer implementation of this novel approach, with first comparative tests demonstrating its enormous computational advantage over the conventional approach.     

Electron propagator calculations show that alkyl substituents alter porphyrin ionization energies

The effect of alkyl substituents on the four lowest vertical ionization energies of porphyrins is determined with ab initio electron propagator calculations on porphine and octamethylporphyrin. With the use of the partial third-order approximation, predicted ionization energies are in close agreement with recent photoelectron spectra. These data and the associated Dyson orbitals, which describe changes in electronic structure that accompany photoionization, enable assignment of photoelectron spectra and determination of alkyl-induced shifts. Hyperconjugation is most evident in the Dyson orbitals associated with the third and fourth ionization energies of octamethylporphyrin and is least prominent in the Dyson orbital of the second ionization energy. There is a positive correlation between the shift in an ionization energy produced by alkyl substitution and the degree of hyperconjugation in the associated Dyson orbital. Alkyl substitutions, therefore, may be employed to adjust the ionization energies of porphyrins and, consequently, their reactivity patterns that depend on charge-transfer capabilities and disposition to electrophilic attack.     

Acidity predictions in an electron propagator approach

An alternative way to calculate vertical ionization potentials (VIP) and vertical electron affinity (VEA) is the application of Koopman's theorem, using the electron propagator theory. In the present work, the results of the application of this theorem using the electron propagator formalism have been compared with the experiment in order to validate different basis set. Using the basis set with the best performance, the acidity tendencies in some substituted acetic acid molecules have been analyzed by correlating the proton affinity (PA) with molecular electronegativity (χ) and hardness (η); these last indexes were obtained from the calculated VIP and VEA considering the finite difference approximation. The above correlations were compared with equivalent correlations using the energy of the frontier Hartree–Fock orbitals and the corresponding Kohn–Sham orbitals, which were calculated with the B3LYP‐DFT procedure. The results indicate that the electron propagator theory could be an interesting alternative to evaluate reactivity indexes, since this theory gives reliable values of VIP and VEA. It was also found that (i) the VIP values are very close to experiment, with only a 0.38% of error; (ii) acceptable results are inferred for VEA; (iii) a triple zeta quality function works quite well in these calculations, and particularly the 6‐311G(d,p) basis set is the best, as it had been reported; and (iv) using the depronation energy (DPE), good results were obtained in the correlations δDPE‐VEA and δDPE‐χ. The results tested that P3 approximation in the electron propagator approach can be a new and interesting alternative in predicting VIP, VEA, and some reactivity indexes, such as χ and η, at least for the compounds studied. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Ab initio electron propagator calculations on the ionization energies of free base porphine, magnesium porphyrin, and zinc porphyrin

Ab initio electron propagator methods are applied to the prediction, assignment, and interpretation of the valence photoelectron spectra of free base porphine and of magnesium and zinc porphyrins. Tests of various approximate self-energies, including the partial third (P3), the outer valence Green's function, and the nondiagonal, renormalized second-order (NR2) methods are performed. Basis set effects and reduced active orbital spaces are examined as well. The P3 method and the one-electron picture of ionization that accompanies it are validated for the first two cationic states and for states with sigma holes that are localized in nitrogen, lone pair regions. In the remaining pi-hole states, there is significant shake-up character and NR2 results provide useful diagnostics of correlation effects.     

Calculation of valence electron vertical ionization potentials using a limited Cl approach

A method is outlined for the calculation of valence electron vertical ionization potentials based on CNDO/2 and CNDO/S SCF molecular ground states improved by including a limited number of doubly excited configurations and ionic states obtained from a single Cl calculation considering a limited set of singly and doubly excited configurations based on the closed shell ground state MO's of the parent molecule. From numerical results on carbon dioxide, sulphur dioxide, ethylene, and trans-butadiene it is shown that the Cl procedure leads to the right sequence of ionic states and their reasonable relative location in contrast to respective Koopmans' ionic states predictions.     

Investigation of ethynylpyridines using the electron propagator theory

The optimized geometry, dipole moment, and HOMO–LUMO gap for three monoethynylpyridines and six diethynylpyridines have been computed using DFT/B3LYP/6‐311++g(3df,3p) level of theory, and the first 11 vertical ionization energies and electron affinity of these compounds have been calculated using various electron propagator decouplings. The outer valence Green's function approximant of the electron propagator theory offers closest agreement with experimental photoelectron spectrum, and the results for structural suitability, dipole moment, HOMO–LUMO gap, ionization energies, and electron affinity indicate that 2‐ethynylpyridine among monoethynylpyridines and 2,6‐diethynylpyridine among diethynylpyridines may be useful precursors for the preparation of conducting polymers. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112:426–439, 2012     

EOM/propagator ionization potentials: Prediction of complete valence-shell ionization spectra using direct diagonalization

It is shown that the major features of complete valence-shell ionization spectra can be predicted using direct diagonalization. A comparison is made with the 2p-h Tamm-Dancoff approximation, and results are presented for the ethylene molecule using a h₃ manifold containing over 23000 operators.     

Relativistic contributions to single and double core electron ionization energies of noble gases

We have performed relativistic calculations of single and double core 1s hole states of the noble gas atoms in order to explore the relativistic corrections and their additivity to the ionization potentials. Our study unravels the interplay of progression of relaxation, dominating in the single and double ionization potentials of the light elements, versus relativistic one-electron effects and quantum electrodynamic effects, which dominate toward the heavy end. The degree of direct relative additivity of the relativistic corrections for the single electron ionization potentials to the double electron ionization potentials is found to gradually improve toward the heavy elements. The Dirac-Coulomb Hamiltonian is found to predict a scaling ratio of ～4 for the relaxation induced relativistic energies between double and single ionization. Z-scaling of the computed quantities were obtained by fitting to power law. The effects of nuclear size and form were also investigated and found to be small. The results indicate that accurate predictions of double core hole ionization potentials can now be made for elements across the full periodic table.     

Application of the independent electron pair approach to the calculation of excitation energies,ionization potentials,and electron affinities of first row atoms

Excitation energies, first ionization potentials and electron affinities of first row atoms are calculated with a spin-adapted independent electron pair approximation (IEPA) combined with the direct determination of pair natural orbitals (PNOs). To enable comparison with molecular calculations Gaussian basis sets are used which are small enough to be also applicable to molecules. IEPA results for the above mentioned properties are accurate to 0.1–0.3 eV which is almost one order of magnitude better than the corresponding SCF-results. The same accuracy can be expected for molecules in which a localization of the doubly and singly occupied orbitals is possible, for instance for small hydrides. This is supported by the results of calculations on carbon hydrides.     

Pulsed-field ionization electron spectroscopy and binding energies of alkali metal-dimethyl ether and -dimethoxyethane complexes

Lithium and sodium complexes of dimethyl ether (DME) and dimethoxyethane (DXE) were produced by reactions of laser-vaporized metal atoms with organic vapors in a pulsed nozzle cluster source. The mono-ligand complexes were studied by photoionization and pulsed field ionization zero electron kinetic energy (ZEKE) spectroscopy. Vibrationally resolved ZEKE spectra were obtained for Li(DME), Na(DME) and Li(DXE) and a photoionization efficiency spectrum for Na(DXE). The ZEKE spectra were analyzed by comparing with the spectra of other metal-ether complexes and with electronic structure calculations and spectral simulations. Major vibrations measured for the M(DME) (M=Li,Na) ions were M-O and C-O stretches and M-O-C and C-O-C bends. These vibrations and additional O-Li-O and O-C-C-O bends were observed for the Li(DXE) ion. The M(DME) complexes were in C2v symmetry with the metal atom binding to oxygen, whereas Li(DXE) was in a C2 ring configuration with the Li atom attaching to both oxygen atoms. Moreover, the ionization energies of these complexes were measured from the ZEKE or photoionization spectra and bond dissociation energies were derived from a thermodynamic cycle.     

Comparison of perturbative and multiconfigurational electron propagator methods

Ionization energies below 20 eV of 10 molecules calculated with electron propagator techniques employing Hartree-Fock orbitals and multiconfigurational self-consistent field orbitals are compared. Diagonal and nondiagonal self-energy approximations are used in the perturbative formalism. Three diagonal methods based on second- and third-order self-energy terms, all known as the outer valence Green's function, are discussed. A procedure for selecting the most reliable of these three versions for a given calculation is tested. Results with a polarized, triple ζ basis produce root mean square errors with respect to experiment of approximately 0.3 eV. Use of the selection procedure has a slight influence on the quality of the results. A related, nondiagonal method, known as ADC (3), performs infinite-order summations on several types of self-energy contributions, is complete through third-order, and produces similar accuracy. These results are compared to ionization energies calculated with the multiconfigurational spin-tensor electron propagator method. Complete active space wave functions or close approximations constitute the reference states. Simple field operators and transfer operators pertaining to the active space define the operator manifold. With the same basis sets, these methods produce ionization energies with accuracy that is comparable to that of the perturbative techniques. © 1996 John Wiley & Sons, Inc.     

Monte Carlo configuration interaction applied to multipole moments,ionization energies,and electron affinities

The method of Monte Carlo configuration interaction (MCCI) (Greer, J. Chem. Phys. 1995a, 103, 1821; Tong, Nolan, Cheng, and Greer, Comp. Phys. Comm. 2000, 142, 132) is applied to the calculation of multipole moments. We look at the ground and excited state dipole moments in carbon monoxide. We then consider the dipole of NO, the quadrupole of N₂ and of BH. An octupole of methane is also calculated. We consider experimental geometries and also stretched bonds. We show that these nonvariational quantities may be found to relatively good accuracy when compared with full configuration interaction results, yet using only a small fraction of the full configuration interaction space. MCCI results in the aug‐cc‐pVDZ basis are seen to generally have reasonably good agreement with experiment. We also investigate the performance of MCCI when applied to ionisation energies and electron affinities of atoms in an aug‐cc‐pVQZ basis. We compare the MCCI results with full configuration interaction quantum Monte Carlo (Booth and Alavi, J. Chem. Phys. 2010, 132, 174104; Cleland, Booth, and Alavi, J. Chem. Phys. 2011, 134, 024112) and “exact” nonrelativistic results (Booth and Alavi, J. Chem. Phys. 2010, 132, 174104; Cleland, Booth, and Alavi, J. Chem. Phys. 2011, 134, 024112). We show that MCCI could be a useful alternative for the calculation of atomic ionisation energies however electron affinities appear much more challenging for MCCI. Due to the small magnitude of the electron affinities their percentage errors can be high, but with regards to absolute errors MCCI performs similarly for ionisation energies and electron affinities. © 2013 Wiley Periodicals, Inc.     

Molecular photoionization cross sections in electron propagator theory: angular distributions beyond the dipole approximation

Corrections to dipole approximation results for angular distributions in photoionization of first-row hydrides have determined by using Dyson orbitals calculated with ab initio electron propagator theory and by considering the full multipole expansion for the incident photon representation. The relative importance of first-order corrections which consist of electric quadrupole and magnetic dipole terms and of higher-order terms has been estimated as a function of photon energy. Multipole corrections to the dipole approximation depend on photon energy and on the characteristics of the Dyson orbitals.     

Substituent effects on the electron affinities and ionization energies of tria-, penta-, and heptafulvenes: a computational investigation

The extent of substituent influence on the vertical electron affinities (EAs) and ionization energies (IEs) of 43 substituted tria-, penta-, and heptafulvenes was examined computationally at the OVGF/6-311G(d)//B3LYP/6-311G(d) level of theory and compared with those of tetracyanoquinodimethane (TCNQ) and tetrathiafulvalene (TTF) as representing strong electron-acceptor and -donor compounds, respectively. The substituents X at the exocyclic positions of the fulvenes were either NH(2), H, or CN, while the substituents Y at the ring positions were H, Cl, F, CN, or NH(2). The variations of the EAs and IEs were rationalized by qualitative arguments based on frontier orbital symmetries for the different fulvene classes with either X or Y being constant. The minimum and maximum values found for the calculated EAs of the tria-, penta-, and heptafulvenes were 0.51-2.05, 0.24-3.63, and 0.53-3.14 eV, respectively, and for the IEs 5.27-9.96, 7.07-10.31, and 6.35-10.59 eV, respectively. Two of the investigated fulvenes outperform TCNQ (calcd EA = 2.63 eV) and one outperforms TTF (calcd IE = 6.25 eV) with regard to acceptor and donor abilities, respectively. We also evaluated the properties of bis(fulvene)s, i.e., compounds composed of a donor-type heptafulvene fused with an acceptor-type pentafulvene, and it was revealed that these bis(fulvene)s can be designed so that the IE and EA of the two separate fulvene segments are retained, potentially allowing for the design of compact donor-acceptor dyads.     

Core ionization energies of atoms and ions calculated using the generalized Sturmian method

The physical event of the umbrella inversion of ammonia has been studied in detail by application of the formalisms of frontier orbital theory, the density functional theory, the localized molecular orbital method, and the energy partitioning analysis. An intuitive structure for the transition state and dynamics of the physical process of structural reorganization prior to inversion have been suggested. The computation starts with the CNDO/2 equilibrium geometry, and thereafter the cycle proceeds through all the conformations of ammonia obtained by varying the ∠HNH angle in steps of 2° from its equilibrium value up to the transition state. The geometry of each conformation is optimized with respect to the length of the N–H bond. The glimpses of the charge density reorganization during the movement of the molecule from equilibrium conformation toward the transition state is computed in terms of dipole moment and the quantum mechanical hybridizations of bond pair and lone pair of N atom through the localized molecular orbitals (LMOs) of all the conformations. Results demonstrate that as the geometry of the molecule begins to evolve through the reorganization of structure, the N–H bond length and the dipole moment begin to decrease, and the trend continues up to the transition state. The dipole moment of the molecule at the suggested transition state is zero. The computed nature of quantum mechanical hybridization of bond pair and lone pair of the N atom as a function of reaction coordinates of the ∠HNH angles reveals that the percentage of s character of the lone pair hybrid decreases and that of the bond pair hybrid forming the σ(N–H) bond increases during the process of geometry reorganization from the equilibrium shape to the transition state. The rationale of the zero dipole moment of the transition state for inversion is not straightforward from its point‐group symmetry, but is self‐evident from its electronic structure drawn in terms of LMOs. The electronic structure of the transition state, which may be drawn in terms of the LMOs, seems to closely reproduce its suggested intuitive structure. The pattern of variation of dipole moment and nature of the changes of the percentage of the s character in the lone pair hybrid creating dipole with the evolution of geometry during the physical process of structural reorganization for the inversion are found to be nicely correlated according to the suggestion of Coulson. The profiles of the increasing strength of the N–H bond and the increasing percentage of s character of the bond pair hybrid of N atom forming this bond as a function of reaction coordinates are also found to be correlated in accordance with the suggestion of Coulson. The profile of global hardness as a function of reaction coordinate seems to demonstrate that the dynamics of the evolution of the molecular structure from equilibrium shape to the transition state following the course of suggested mode of structural reorganization conforms to the principle of maximum hardness (PMH). The profiles of parameters like the energies of highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO), the gap in energy between HOMO and LUMO, the global hardness, the global softness, and chemical potential as a function of reaction coodinates of a continuous structural evolution from equilibrium shape to the transition state mimic the potential energy diagram of the total energy. Both the frontier orbital parameters and the density functional quantities are found to be equally effective and reliable to monitor the process of necessary structural reorganization prior to the inversion of mofecules. An energy partitioning analysis demonstrates that the origin of barrier has no unique single source rather as many as four mutually exclusive but interacting one‐ and two‐center energy terms within the molecule entail the origin and the height of the barrier. From a close analysis of the results, it seems highly probable that the necessary structural reorganization prior to umbrella inversion of ammonia most realistically occurs following the course of normal modes of vibration of the molecule. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 1–26, 2000     

Excitation energies, electron affinities and ionization potentials of the transition metals V, Cr and Mn

 Configuration interaction calculations were carried out for neutral ground and excited states and positively and negatively ionized states of the V, Cr and Mn atoms. Energy convergence with respect to systematic expansion of both the one-electron and configuration bases was investigated for valence correlation. Contributions from core electrons to the differential correlation energies and relativistic effects were evaluated separately. Assuming additivity of these contributions, excitation energies, electron affinities and ionization potentials of the atoms were obtained. All calculated values were in excellent agreement with the observed values within a deviation of 0.056 eV except for the electron affinity of the V atom, which had a calculated value 0.110 eV larger than the experimental value. Received: 9 August 2000 / Accepted: 26 October 2000 / Published online: 3 April 2001     

Theoretical prediction of proton and electron affinities,gas phase basicities,and ionization energies of sulfinamides

Structural Chemistry - Sulfinamides, as an asymmetric synthesizer, especially in drug synthesis, play critical roles in organic chemistry. In this study, the gas phase ion energetics data including...