Calculation of the electronic structure of metalloporphyrin dianions by the restricted Hartree-Fock method

The metalloporphine dianions (Me-P)^2– with D_4h symmetry for the nuclear skeleton have an e_g ² electronic configuration, which generates the triplet state ³A_2g and the three single states ¹B_1g, ¹B_2g, and ¹A_1g. With the aid of projection operators of the symmetry group, SCF equations have been formulated for such systems with open shells of degenerate orbitals, where the Roothaan method is not directly applicable. Calculations of the individual states of (Me-P)^2– and its analogs have been performed by the proposed method in the -electronic approximation. In accordance with Hund's rule, it has been found that the lowest level in the multiplet is the triplet level and that the subsequent singlet levels of (Me-P)^2– are 340 (¹B_1g), 2560 (¹B_2g), and 3010 (¹A_1g cm^–1 above it. A comparison of the -electron densities of (Me-P)^2– and Me-P has revealed, first, that the additional charge is distributed along the periphery of the macrocycle (the maximum increase takes place at the bridging atoms) and, second, that a number of bonds are strengthened, rather than weakened. The results obtained correlate well with the data on the reactivity and vibrational spectra of the dianions of porphyrins.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 2, pp. 153–160, March–April, 1986.     

Soliton states in polyacetylene chains with consideration of electron correlation

The stationary states of a longtrans-(CH)_N chain have been considered in the ppp-Peierls model; electron correlation was taken into account with the aid of a wave function constructed from variable geminals. The states of a chain with a pair of neutral solitons, which have local minima of the total energy lying 1.6 eV above the ground state, have been determined numerically by finding a self-consistent approximation of the electronic system and the lattice deformations. The soliton pair is stable only when the kinks in the lattice are at a sufficient distance, and it is stabilized significantly by electron correlation. The influence of the correlation of the electrons and the kinks in the lattice on the position of excited levels of different symmetry and alternant character has been considered.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 4, pp. 385–393, July–August, 1986.We thank A. A. Ovchinnikov for some useful discussion.     

Visualization of electron correlation in a series of helium S states

Electron correlation has been studied for a series of helium S states represented by a variety of wavefunctions, the best of which are accurate Hylleraas—Kinoshita functions. The states studied are the ground state, the lowest excited ¹S and ³S states, and the (2s)² and (2p)² doubly-excited ¹S states. Primary data is obtained from graphs of the conditional probability density as a function of the radial distance r₂ and the interelectronic angle θ₁₂, given that r₁ is fixed at various distances. Such graphs make clear the extent to which characteristics such as angular and radial correlations, and Fermi and Coulomb holes, are consequences of the relative motion of electrons in two-electron atoms.     

ππ*Transition of ethylene: electron correlation and Rydberg character

The excited single (ππ*) state of planar ethylene is calculated in a GTO basis set by a second-order perturbation method. It is shown that the transition energy is nearly independent of the Rydberg character of the π* orbital and therefore electron correlation is introduced.     

Visualization of electron correlation in autoionizing states above the 3p threshold in magnesium

The conditional probability density has been calculated for a number of autoionizing states (AIS) in Mg above the 3p threshold. The correlation in such high energy AIS has not been extensively studied and provides insight into the rovibrator behavior of two-electron atoms. The calculations have been done by configuration interaction (CI) with a B-spline basis. This allows for the simultaneous study of the effects of electron correlation and the widths and angular distribution of photoelectrons in multiphoton ionization. The states have been assigned approximate vibrational quantum numbers, and a correlation between the approximate quantum numbers and the photoelectron distribution is observed. Probability distribution for one electron when the other, represented by the small spike, is at its most probable distance from the nucleus. This is a distribution for the doubly-excited 1S(e) state commonly labeled as the 4s2 state.     

Symmetry effects in the radiation damping of degenerate states

Radiation damping of three atoms in a radiation field is studied for both a linear and closed-chain configuration. One atom of the system is initially excited. Use is made of the Heitler-Ma perturbation procedure up to second order. The discussion is developed in terms of the symmetry of the interactions within the system. The interactions arising from dipole transitions perpendicular to the plane of the closed chain are shown to be similar to the interactions in a two-atom system, and the results are extended to cover larger rings.     

Influence of electron correlation effects on the solvation of Cu2+

Hybrid QM/MM MD simulations including electron correlation effects at MP2 level were performed to obtain an accurate picture of the solvation structure and the Jahn-Teller effect of the Cu2+ ion.     

Influence of delocalization on the stability of dianions: study of a systematic series of dianions with growing electronic localization

The electronic stability of a dianion is influenced by the degree of delocalization of its electrons, but it is generally not possible to separate this influence from other effects. Here, we investigate by theoretical means the sequence of dianions consisting of phen-1,4-ylenbis(ethynide) and seven of its derivatives obtained by hydrogenating the benzene core in several steps. These dianions are structurally similar and mainly differ by the degree of delocalization of their electrons. We present geometries and electron detachment energies computed at a correlated level of theory. The results point to a classification of the eight dianions in three distinct groups of electronic stability. We are able to explain this grouping by a simple resonance structure picture, which demonstrates why the dianions with more delocalized electrons are less stable.     

Influence of surface states on electron transport through intrinsic Ge nanowires

Solution-grown single-crystal Ge nanowires were used as conductive channels in field effect transistor devices to study the influence of surface states on their electron transport properties. Nanowires contacted with Pt electrodes using focused ion beam metal deposition exhibited linear current-voltage (IV) curves at room temperature with apparent resistivities ranging from 10(1) to 10(-1) Omega cm. In all cases, the nanowire conductance decreased with positive external electric fields applied perpendicular to the nanowire surface by a gate electrode, characteristic of p-type carrier accumulation at the nanowire surface. The field-induced change in conductance exhibited a time-dependent relaxation, with response time and magnitude of current decrease that depended on the nanowire surface chemistry. Nanowires treated with an organic passivation layer using a thermally initiated hydrogermylation reaction exhibited 2 orders of magnitude slower current relaxation and a smaller decrease in current relative to "bare" nanowires with oxidized surfaces.     

Crucial role of electron correlation in both the upper and lower states in optical transitions

The merits of the various methods, used for the determination of relativistic energies, are discussed on the basis of numerical results. It is concluded that, at present, the perturbation approach, based on the Pauli approximation of the Dirac-Breit equation, is more accurate (up to Z < 48) than the variational approach. Furthermore it is expected that, in any case, the prediction of ionization potentials and energy levels will be equally satisfactory by either method. Consequently, and taking into account the importance of the correlation effects (not only because of the contribution of the correlation energy but also because of their influence on the prediction of the hyperfine structure), it is suggested that it may be worthwhile to direct more efforts towards multiconfigurational Dirac-Breit-Pauli calculations.This work has been supported in part by the National Research Council of Canada.     

Application of Wigner and Husimi intracule based electron correlation models to excited states

A new approach to the electron correlation problem based on phase space intracules derived from the Wigner distribution is applied to excited states. The computed electron correlation energy reduces the mean absolute error in the prediction of the excitation energies of 55 atomic excited states from 0.65 eV for unrestricted Hartree-Fock to 0.32 eV. This compares favorably to a mean absolute deviation of 0.52 eV for second order Moller-Plesset perturbation theory and 0.35 eV for the Lee-Yang-Parr functional. An analogous correlation model based on the Husimi distribution is developed. Predicted correlation energies and excitation energies from this model are significantly worse than for the Wigner intracule based model. Alternative correlation kernels may be more suitable for the Husimi intracule based approach.     

Adiabatic perturbation theory for the degenerate case. II. Perturbation of degenerate bound states embedded in the continuum

An adiabatic formula for the contracted Hamiltonian in a reference space containing bound-state eigenfunctions of degenerate energy levels embedded in the continuum is derived. A general factorization theorem for the dynamic operatorS_α(0, – ∞/λ) is proved, and the cancellation of the pole singularities in the perturbation series of the contracted Hamiltonian in adiabatic form is discussed.     

Visualization of electron correlation in ground states of He and H−

For the ground states of He and H^?, conditional probability densities d(r₂,θ₁₂r₁) for finding two electrons in different relative positions have been calculated for several wavefunctions including simple one-configuration wavefunctions and Hylleraas—Kinoshita type functions. The calculations, including graphing, were all carried out on a desktop computing calculator.     

Limitations of density functional theory in application to degenerate states

It is shown that the claims that density functional theory (DFT) can handle orbitally degenerate states are ungrounded. The constraint search formulation of DFT allows one to determine a set of densities and eigenvalues for the degenerate term that, however, are neither observables, nor can they be used to solve the system of coupled equations for the nuclear motions to obtain observables, as in the wave function presentation. A striking example of the failure of the existing versions of DFT to describe degenerate states is provided by the Berry phase problem: the strong dependence of the results on the phase properties of the electronic wave function that are smeared out in the density formulation. The solution of the Jahn-Teller E-e problem illustrates these statements. For nondegenerate states with the full wave function taken in the adiabatic approximation as a product of the electronic and nuclear parts, the formulation of DFT is rigorous if and only if the dependence of the electronic wave function on nuclear coordinates is ignored. This lowers the accuracy of the results, in general, and may lead to erroneous presentation as in the case of molecular systems in strong magnetic fields. © 1997 by John Wiley & Sons, Inc.     

On the structure of the Clifford algebra unitary group adapted states in the many‐electron correlation problem

An attempt has been made to understand the structure of the Clifford algebra unitary group adapted many‐particle states from the conventional symmetric group point of view. Emphasizing the symmetric group result that the consideration of the spin‐independent Hamiltonian matrix over the many‐particle configuration functions (CFs) entails a particular subspace of their spatial parts only, attention is confined entirely in this subspace. Question of adapting the functions therein to the unitary group subduction chain is then shown to bring out an interesting lead to the Clifford algebra unitary group approach (CAUGA) states, thus underlining the motive and the essential gains of the CAUGA formulation. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 607–614, 2000     

Influence of structure on electron correlation effects and electron-water dispersion interactions in anionic water clusters

Electronic structure calculations at the level of second-order M?ller-Plesset perturbation theory have been performed on anionic water clusters, (H2O)n(-), in the n = 14-33 size regime. The contribution to the electron binding energy that arises from electron correlation is found to be significantly larger for cavity-bound electrons than it is for surface-bound electrons, even for surface states with electron binding energies well above 1 eV. A decomposition of the correlation energy into interactions between pairs of Boys-localized molecular orbitals is used to demonstrate that the larger correlation energy found in the cavity isomers arises from electron-water dispersion interactions, and that the dispersion interaction is larger in cavity-bound isomers because the unpaired electron penetrates well beyond the first solvation shell. In contrast, a surface-bound electron exhibits virtually no penetration into the interior of the cavity. To obtain a qualitatively accurate picture of this phenomenon, one must plot molecular orbitals using isoprobability surfaces rather than arbitrarily-selected isocontours.     

Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory

Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used "average of degenerate states approximation" for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases.