Ionization potentials,electron affinities,electronegativities, and hardnesses of fractional charged atoms from the density-functional theory

The electron-correlation and self-interaction corrected generalized exchange local-spin-density functional theory with the Gopinathan, Whitehead, and Bogdanovic Fermi-hole parameters has been employed to give self-consistent field calculations for the quark atoms, the first- and second-order positive ions, and the first- and second-order negative ions of the quark atoms with fractional nuclear charges $ Z = N \pm \frac{1}{3} $ and $ Z = N \pm \frac{2}{3} $. A special technique to obtain the converged second-order negative ions is discussed. The first and second ionization potentials and electron affinities are calculated by the differences of the total energies between the ionized and nonionized systems and compared with the empirical inter-extrapolation results. The agreement between the present calculations and the inter-extrapolated results is excellent for the ionization potentials and reasonably good for the electron affinities of the quark atoms. Finally, the calculated ionization potentials and electron affinities are used in obtaining the electronegativities and hardnesses for these quark atoms.     

Ionization potentials and electron affinities of carbo- and heterocyclicπ-conjugated molecules

The correlations of the observed ionization potentials and electron affinities with the orbital energies of SCF-MO's calculated by the variable- modification of the Pariser-Parr-Pople method were examined for 30 conjugated molecules including heterocycles. A simple linear relation has been found between the ionization potential and the energy of the highest occupied SCF-MO as well as between the electron affinity and the energy of the lowest vacant SCF-MO. The ionization potential and electron affinity are estimated by using these empirical relations for 24 conjugated heteromolecules of biochemical interest.

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Zusammenfassung PPP-Rechnungen nach der variables-Methode an 30 carbo- und heterocyclischen-Systemen zeigen eine gute Korrelation der experimentellen ionisationspotentiale und Elektronenaffinitäten mit den Energien der höchsten besetzten bzw. tiefsten unbesetzten SCF-MOs. Die so erhaltenen Regressionsgeraden wurden zur Bestimmung vos Ionisationspotentialen und Elektronenaffinitäten vos 24 biochemisch interessanten Heterosystemen herangezogen.

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Résumé Examen pour 30 molécules conjuguées des corrélations entre potentiels d'ionisation et affinités électroniques expérimentales avec les énergies des orbitales moléculaires SCF de la méthode de Pariser-Parr-Pople à variable. Une relation linéaire simple a été trouvée entre le potentiel d'ionisation et l'énergie de la plus haute orbitale moléculaire occupée ainsi qu'entre l'affinité électronique et l'énergie de la plus basse orbitale vacante. Ces relations empiriques permettent d'estimer les potentiels d'ionisation et l'affinité électronique de 24 molécules conjugées d'intérêt biochimique.

     

Charge localization in stacked radical cation DNA base pairs and the benzene dimer studied by self-interaction corrected density-functional theory

The incomplete cancellation of the electron self-interaction can be a serious shortcoming of density-functional theory especially when treating odd-electron systems. In this work, several popular and potentially viable correction schemes are applied in order to characterize the electronic structure of stacked molecular pairs, consisting of a neutral molecule and adjacent radical cation, as a function of separation distance. The unphysical sharing of the positive charge between adjacent molecules separated by 6-7 A is corrected for by applying a new empirical scheme proposed by VandeVondele and Sprik [Phys. Chem. Chem. Phys. 2005, 7, 1363] with a unique choice of parameters. This method is subsequently applied to characterize the electronic structure of two neighboring guanines excised from a canonical Arnott B-DNA structure and will be used in future investigations of certain model DNA fibers.     

Analysis of the equation-of-motion theory of electron affinities and ionization potentials

An analysis of the equation-of-motion (EOM) method for computing molecular electron affinities and ionization potentials is presented. The method is compared with the Dyson equation approach of Green function theory. Particular emphasis is devoted to clarifying the similarities between these two theories when carried out to second and to third order. The Epstein—Nesbet hamiltonian and the notion of diagonal scattering renormalization have been used to systematize this comparison.     

A semi-empirical MO theory for ionization potentials and electron affinities

A method for calculating the vertical ionization potentials and electron affinities according to their fundamental definition as differences between energies of the singlet ground and doublet ionized states is developed for cyclic hydrocarbons. The method adopts a new approach based on the central idea of a recent ab initio IP and EA calculation in which orbital exponents are optimized for both ground and ionized states. Hence, all the semi-empirical parameters of the MO theory are written as functions of the effective nuclear charge which, in turn, is made self-consistent with the molecular electronic charge distribution of the species. Although the MO theory is developed in the π electron approximation, the changes in the σ electron density, resulting from the loss or gain of a π electron, are explicitly considered in the calculation. The theory is compared to the earlier work of Hoyland and Goodman and tested against the first five polyacenes and on the condensed ring aromatics phenanthrene, pyrene, and perylene. Except for perylene, the results are in close agreement with the latest photoelectron spectroscopic measurements.     

Core ionization potentials from self-interaction corrected Kohn-Sham orbital energies

We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the "DeltaKohn-Sham" method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter alpha is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique alpha=0.72 and basis set larger than 6-31G, the core ionization energies (IPs) of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.     

Localized orbital corrections for the calculation of ionization potentials and electron affinities in density functional theory

This paper describes the extension of a previously reported empirical localized orbital correction model to the correction of ionization potential energies (IP) and electron affinities (EA) for atoms and molecules of first and second row elements. The B3LYP localized orbital correction version of the model (B3LYP-LOC) uses 22 heuristically determined parameters that improve B3LYP DFT IP and EA energy calculations on the G2 data set of 134 molecules from a mean absolute deviation (MAD) from experiment of 0.137 to 0.039 eV. The method significantly reduces the number of outliers and overall MAD to error levels below that achieved with G2 wave function based theory; furthermore, the new model has zero additional computational cost beyond standard DFT calculations. Although the model is heuristic and is based on a multiple linear regression to experimental errors, each of the parameters is justified on physical grounds, and each provides insight into the fundamental limitations of DFT, most importantly the failure of current DFT methods to accurately account for nondynamical electron correlation.     

The density functional theory study on the ionization potentials and electron affinities of cytosine-formamide complexes

Accurate adiabatic and vertical ionization potentials (IPs) and valence electron affinity (EA) of cytosine and cytosine-formamide complexes have been determined using density functional theory B3LYP. Comparison has been made with the data from a recently published study, as well as earlier studies on cytosine. For cytosine-formamide complexes it is found that the hydrogen bond interactions between cytosine and formamide play a more important role in the process of electron attachment than in the process of electron detachment. Meanwhile, the hydrogen bond interactions facilitate the adiabatic electron detachment and attachment but have different effects on the vertical electron detachment and attachment with different positions of formamide. The article is published in the original.     

Ionization potentials and electron affinities of Cu,Ag, and Au: Electron correlation and relativistic effects

The electron correlation and relativistic effects on ionization potentials and electron affinities of Cu, Ag, and Au are investigated in the framework of the coupled cluster method and different 1-component approximations to the relativistic Dirac-Coulomb Hamiltonian. The first-order perturbation approach based on the massvelocity and Darwin terms is found to be sufficiently accurate for Cu and Ag while it fails for Au. The spin-averaged Douglas-Kroll no-pair method gives excellent results for the studied atomic properties. The ionization potentials obtained within this method and the coupled cluster scheme for the electron correlation effects are 7.733(7.735) eV for Cu, 7.461(7.575) eV for Ag, and 9.123(9.225) eV for Au (experimental values given in parentheses). The calculated (experimental) electron affinity results for Cu, Ag, and Au are 1.236(1.226), 1.254(1.303), and 2.229(2.309) eV, respectively. There is a marked relativistic effect on both the ionization potential and electron affinity of Ag which sharply increases for Au while Cu exhibits only a little relativistic character. A similar pattern of relativistic effects is also observed for electric dipole polarizabilities of the coinage metal atoms and their ions. The coupled cluster dipole polarizabilities of the coinage metal atoms calculated in this article in the Douglas-Kroll no-pair formalism (Cu: 46.50 au; Ag: 52.46 au; Au: 36.06 au) are compared with our earlier data for their singly positive and singly negative ions. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 557–565, 1997     

Dipole moments from atomic-number-dependent potentials in analytic density-functional theory

Molecular dipole moments of analytic density-functional theory are investigated. The effect of element-dependent exchange potentials on these moments are examined by comparison with conventional quantum-chemical methods and experiment for the subset of the extended G2 set of molecules that have nonzero dipole moment. Fitting the Kohn-Sham [Phys. Rev. 140, A1133 (1965)] potential itself makes a mean absolute error of less than 0.1 D. Variation of alpha (Slater's [Phys. Rev. 81, 385 (1951)] exchange parameter) values has far less effect on dipole moments than on energies. It is argued that in variable alpha methods one should choose the smaller of the two rather than the geometric mean of the two alpha values for the heteroatomic part of the linear-combination-atomic-orbital density. Calculations on the dipole moment of NH(2)(CH)(24)NO(2) are consistent with earlier calculations and show that varying the differences between alpha values for atoms with different atomic numbers has only short-ranged electrostatic effects.     

Effect of the Perdew-Zunger self-interaction correction on the thermochemical performance of approximate density functionals

The Perdew-Zunger self-interaction-corrected density functional theory (SIC-DFT) was implemented self-consistently using a quasi-Newton direct minimization method. We calculated SIC-DFT energies for a number of atoms and molecules using various approximate density functionals, including hybrids. Self-interaction errors (SIE) of these functionals were compared and analyzed in terms of contributions from valence and core orbitals. We also calculated enthalpies of formation of the standard G2-1 set of 55 molecules and found that self-interaction-correction (SIC) improves agreement with experiment only for the LSDA functional, while all other functionals show worse performance upon introducing SIC. This is the first systematic study of the effect of SIC on thermochemical properties. We found no direct connection between the magnitude of the SIE contained in a functional and its performance for thermochemistry. Approximate functionals with large self-interaction errors can accurately reproduce enthalpies of formation. Our results do not support the popular belief that a smaller SIE of hybrid functionals is the main reason for their higher accuracy.     

Effect of self-interaction error in the evaluation of the bond length alternation in trans-polyacetylene using density-functional theory

The calculation of the bond-length alternation (BLA) in trans-polyacetylene has been chosen as benchmark to emphasize the effect of the self-interaction error within density-functional theory (DFT). In particular, the BLA of increasingly long acetylene oligomers has been computed using the M?ller-Plesset wave-function method truncated at the second order and several DFT models. While local-density approximation (LDA) or generalized gradient corrected (GGA) functionals strongly underestimate the BLA, approaches including self-interaction corrections (SIC) provide significant improvements. Indeed, the simple averaged-density SIC scheme (ADSIC), recently proposed by Legrand et al. [J. Phys. B 35, 1115 (2002)], provides better results for the structure of large oligomers than the more complex approach of Krieger et al. [Phys. Rev. A 45, 101 (1992)]. The ADSIC method is particularly promising since both the exchange-correlation energy and potential are improved with respect to standard LDA/GGA using a physically appealing correction, through a different route than the more popular approach through the Hartree-Fock exchange inclusion within the hybrid functionals.     

The self-consistent determination of the ion and neutral molecule wavefunctions in a theory of electron affinities and ionization potentials

In this paper, we discuss the validity of our earlier derivation of a theory of molecular electron affinities and ionization potentials. We show how one can improve upon our original derivation, which was not entirely consistent, by iteratively calculating both the ion and neutral molecule wavefunctions. Most importantly, we demonstrate that the electron affinities and ionization potentials which are obtained by using our original theory are correct through third order, even though the derivation of this theory contains an inconsistency.     

About the calculation of exchange coupling constants using density-functional theory: the role of the self-interaction error

The effect of the correction of the self-interaction error on the calculation of exchange coupling constants with methods based on density-functional theory has been tested in simple model systems. The inclusion of the self-interaction correction cancels the nondynamical correlation energy contributions simulated by the commonly used functionals. Hence, such correction should be important in the accurate determination of exchange coupling constants. We have also tested several recent functionals to calculate exchange coupling constants in transition-metal complexes, such as meta-GGA functionals or new formulations of hybrid functionals. The influence of the basis set and of the use of pseudopotentials on the calculated J values has also been evaluated for a Fe(III) dinuclear complex in which the paramagnetic centers bear several unpaired electrons.     

Application of many-body rayleigh-schrödinger perturbation theory to calculation of ionization potentials and electron affinities

The ionization potentials and electron affinities are calculated by the use of the many-body Rayleigh-Schrödinger perturbation theory. This approach is elaborated up to the third order, where each perturbation contribution can be interpreted by the diagrammatic method. Some simple illustrative calculations of π-electron systems are carried out.     

DFT calculations of the ionization potentials and electron affinities of serinamide

Adiabatic and vertical ionization potentials (IPs) and valence electron affinities (EAs) of serinamide in the gas phase have been determined using density functional theory (DFT) B3LYP, B3P86, and B3PW91 methods with the 6‐311++G** and 6‐311G** basis sets, respectively. IPs and EAs of serinamide in solution have been calculated with the B3LYP method using the 6‐311++G** and 6‐311G** basis sets. Eight possible conformers of serinamide and its charged states in the gas phase have been optimized employing the DFT B3LYP method with 6‐311++G** and 6‐311G** basis sets, respectively. All the adiabatic and vertical ionization potentials (AIPs and VIPs) of eight serinamide conformers in our work are positive values, whether in the gas phase or in solutions; the IPs in solutions are smaller than the results in the gas phase and decrease with increased dielectric constants in solutions. This finding indicates that the cationic states in solutions are more stable than those in the gas phase. All EAs of eight serinamide conformers are negative values in the gas phase, indicating that the anionic states are unstable with respect to electron autodetachment, both adiabatically and vertically. In contrast, all other adiabatic electron affinities (AEAs) are negative values in solutions except for 6S in water; 7S in chloroform, acetone, and water; and 8S in acetone and water, and increase with increasing of dielectric constants in solutions. All vertical electron affinities (VEAs) are negative values in solutions; however, no good rule has been found for these values in solutions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Application of multiconfigurational many-body perturbation theory to the calculation of ionization potentials,electron affinities and excitation energ

Multiconfigurational many-body perturbation theory is applied to the problem of calculating ionization potentials, electron affinities, and excitation energies. H₂O, C₂H₄, and H₂ are studied, with correlation corrections through third order and inclusive of certain higher-order terms. Results are compared with those by other many-body theoretical methods.     

Synthesis, ionisation potentials and electron affinities of hexaazatrinaphthylene derivatives

Several hexaazatrinaphthylene derivatives and a tris(thieno)hexaazatriphenylene derivative have been synthesised by reaction of the appropriate diamines with hexaketocyclohexane. The crystal structure of 2,3,8,9,14,15-hexachloro-5,6,11,12,17,18-hexaazatrinaphthylene has been determined by X-ray diffraction; this reveals a molecular structure in good agreement with that predicted by density functional theory (DFT) calculations and pi-stacking with an average spacing between adjacent molecular planes of 3.18 A. Solid-state ionisation potentials have been measured by using UV photoelectron spectroscopy and fall in the range of 5.99 to 7.76 eV, whereas solid-state electron affinities, measured using inverse photoelectron spectroscopy, vary in the range -2.65 to -4.59 eV. The most easily reduced example is a tris(thieno)hexaazatriphenylene substituted with bis(trifluoromethyl)phenyl groups; DFT calculations suggest that the highly exothermic electron affinity is due both to the replacement of the outermost phenylene rings of hexaazatrinaphthylene with thieno groups and to the presence of electron-withdrawing bis(trifluoromethyl)phenyl groups. The rather exothermic electron affinities, the potential for adopting pi-stacked structures and the low intramolecular reorganisation energies obtained by DFT calculations suggest that some of these molecules may be useful electron-transport materials.