Electron group functions for the analysis of the electronic structures of molecules

The electronic structure of a vast majority of molecular systems can be understood in terms of electron groups and their wave functions. They serve as a natural basis for bringing intuitive chemical and physical concepts into quantum chemical calculations. This article considers the general electron group functions formalism as well as its simple geminal version. We try to characterize the wave function with the group structure and its capabilities in actual calculations. For this purpose we implement a variational method based on the wave function in the form of an antisymmetrized product of strongly orthogonal group functions and perform a series of electronic structure calculations for small molecules and model systems. The most important point studied is the relation between the choice of electron groups and the results obtained. We consider energetic characteristics as well as optimal geometry parameters. In view of practical importance, the structure of variationally optimized local one-electron states is considered in detail as well as intuitive characteristics of chemical bonds.     

Semiempirical implementation of strictly localized geminals for analysis of molecular electronic structure

Approximate electronic trial wave function taken as the antisymmetrized product of strictly localized geminals (APSLG) is implemented for semiempirical analysis of molecular electronic structure of “organic” compounds and for calculations of their heats of formation. This resulted in an O(N)‐scaling method. Using the MINDO/3 form of the semiempirical Hamiltonian with reparameterized β_AB values in combination with the APSLG form of the wave function yields the computational procedure BF'98. Calculations on the heats formation and the equilibrium geometries for a wide range of molecules show that the APSLG‐MINDO/3 approach is more favorable than its self‐consistent field‐based counterpart. Also, the APSLG formalism allows to interpret molecular electronic wave function in chemically sensible terms. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 752–764, 2001     

A study of the ethane internal rotation barrier

In an effort to deduce the source of the ethane internal rotation barrier, we have investigated the contributions of exchange energy and orthogonality: two effects that are required by the Pauli principle. Fully antisymmetrized, partially antisymmetrized and non-antisymmetrized optimized orbital product wavefunctions were determined. Results show that the exchange energy contribution to the barrier is negligible only when it is evaluated from energy-localized orbitals; even in this case the small total results from cancellation of large contributions. The barrier is apparently caused by the orthogonality that is required between CH orbitals on opposite ends of the molecule. The CC bond has insignificant participation in this effect.     

Spin-free quantum chemistry. XIII. Spin waves

We have obtained the Bloch spin wave dispersion formula using the methods of spin-free quantum chemistry. The spin-free eigenvectors are waves in spin-free space. This development makes the point that Bloch spin waves are dynamically spin-free. The neutron diffraction transition moment for spin waves is calculated employing the antisymmetrized projections of vector products of spin-free eigenkets and spin kets and is found to be agreement with results of Moorhouse.     

Spin adaptation of antisymmetrized geminal product wave functions

A spin-free polynomial representation of antisymmetrized geminal products is presented for several cases. In particular, products of identical geminals, which possess different spin multiplicity, are considered. The cases of singlet geminals, singlet geminals with one or two triplet geminals coupled to the lowest possible spin multiplet, and triplet geminals coupled to an arbitrary multiplet are considered in detail, and explicit polynomial representation is given.     

Symmetry adaptation and the relation between the spin-free and space-spin formulations of electronic structure

An information-theoretic degree of symmetry adaptation of a ket with respect to a given group is introduced. Then the general equivalence between spin-free electronic kets and antisymmetrized space-spin kets is obtained so long as our attention is restricted to spin-independent observables. It is noted that there are spin-free kets for which there exists no single antisymmetrized space-spin ket giving all the same expectation values; the converse is also noted.     

Mapping the electronic structure of the blue copper site in plastocyanin by NMR relaxation

The biological function of metalloproteins stems from the electronic and geometric structures of their active sites. Thus, in blue copper proteins such as plastocyanins, an unusual electronic structure of the metal site is believed to contribute to the rapid, long-range electron-transfer reactivity that characterizes these proteins. To clarify this structure-function relationship, numerous quantum chemical calculations of the electronic structure of the blue copper proteins have been made. However, the obtained structures depend strongly on the applied model. Experimental approaches based on ENDOR spectroscopy and X-ray absorption have also been used to elucidate the electronic structure of the blue copper site. Still, the determination of the electronic structure relies on a calibration with quantum chemical calculations, performed on small model complexes. Here we present an approach that allows a direct experimental mapping of the electron spin delocalization in paramagnetic metalloproteins using oxidized plastocyanin from Anabaena variabilis as an example. The approach utilizes the longitudinal paramagnetic relaxation of protons close to the metal site and relies on the dependence of these relaxations on the spatial distribution of the unpaired electron of the metal ion. Surprisingly it is found that the unpaired electron of the copper ion in plastocyanin is less delocalized than predicted by most of the quantum chemical calculations.     

Nonadiabatic theory of electron–vibrational coupling: New basis for microscopic interpretation of superconductivity

A systematic procedure has been developed to construct an electronic energy matrix for diatomics in the basis of antisymmetrized products of atomic wave functions represented as linear combinations of coupled momenta eigenfunctions. The exchange matrix element is expanded in powers of electronic interchange between atoms. General expressions of many-electron angular coefficients have been obtained for all types of products of one- and two-electron and overlap integrals in energy matrix elements. © 1992 John Wiley & Sons, Inc.     

Pi topology and spin alignment in unique photoexcited triplet and quintet states arising from four unpaired electrons of an organic spin system

Syntheses, electronic structures in the ground state, unique photoexcited states, and spin alignment are reported for novel biradical 1, which was designed as an ideal model compound to investigate photoinduced spin alignment in the excited state. Electron spin resonance (ESR), time-resolved ESR (TRESR), and laser-excitation pulsed ESR experiments were carried out. The magnetic properties were examined with a SQUID magnetometer. In the electronic ground state, two radical moieties interact very weakly (almost no interaction) with each other through the closed-shell diphenylanthracene spin coupler. On photoirradiation, a novel lowest photoexcited state with the intermediate spin (S = 1) arising from four unpaired electrons with low-lying quintet (S = 2) photoexcited state was detected. The unique triplet state has an interesting electronic structure, the D value of which is reduced by antiferromagnetic spin alignment between two radical spins through the excited triplet spin coupler. The general theoretical predictions of the spin alignment and the reduction of the fine-structure splitting of the triplet bis(radical) systems are presented. The fine-structure splitting of the unique photoexcited triplet state of 1, as well as the existence of the low-lying quintet state, is interpreted well on the basis of theoretical predictions. Details of the spin alignment in the photoexcited states are discussed.     

Coupled perturbation theory within the antisymmetrized product of separated geminals (APSG) framework

A coupled perturbation theory for the antisymmetrized product of separated geminals (APSG ) approximation is derived. The variational principle for the APSG wave function in an external oscillating field is employed and a set of equations of the form analogous to the normal RPA is obtained. At this level the reduced resolvent in the form of a spectral expansion is written and it is used for the evaluation of the second-order properties.     

Characterization of electronic structure and properties of a Bis(histidine) heme model complex

Ferric and ferrous hemes, such as those present in electron transfer proteins, often have low-lying spin states that are very close in energy. To explore the relationship between spin state, geometry, and cytochrome electron transfer, we investigate, using density functional theory, the relative energies, electronic structure, and optimized geometries for a high- and low-spin ferric and ferrous heme model complex. Our model consists of an iron-porphyrin axially ligated by two imidazoles, which model the interaction of a heme with histidine residues. Using the B3LYP hybrid functional, we found that, in the ferric model heme complex, the doublet is lower in energy than the sextet by 8.4 kcal/mol and the singlet ferrous heme is 6.7 kcal/mol more stable than the quintet. The difference between the high-spin ferric and ferrous model heme energies yields an adiabatic electron affinity (AEA) of 5.24 eV, and the low-spin AEA is 5.17 eV. Both values are large enough to ensure electron trapping, and electronic structure analysis indicates that the iron d(pi) orbital is involved in the electron transfer between hemes. M?ssbauer parameters calculated to verify the B3LYP electronic structure correlate very well with experimental values. Isotropic hyperfine coupling constants for the ligand nitrogen atoms were also evaluated. The optimized geometries of the ferric and ferrous hemes are consistent with structures from X-ray crystallography and reveal that the iron-imidazole distances are significantly longer in the high-spin hemes, which suggests that the protein environment, modeled here by the imidazoles, plays an important role in regulating the spin state. Iron-imidazole dissociation energies, force constants, and harmonic frequencies were calculated for the ferric and ferrous low-spin and high-spin hemes. In both the ferric and the ferrous cases, a single imidazole ligand is more easily dissociated from the high-spin hemes.     

Die horizontale Korrelation in π-Elektronensystemen und ihre Beschreibung durch Elektronenpaarfunktionen

Different types of pair functions (geminal products and their linear combinations) are tested with respect to their ability to describe the “horizontal correlation” of the π-electrons of butadiene. The validity of the π-electron approximation is not discussed and “full configuration interaction” within the limited LCAO basis is used as the standard to which the model calculations are referred. An APSG-function (APSG = antisymmetrized product of strongly orthogonal geminals) built up from equivalent (localized) geminals, which contains only one variational parameter is able to account for about 90% of the “horizontal correlation energy”. Both APSG and APIG functions constructed from delocalized geminals, are much less favorable. Criteria of the goodness of an approximate wave function are a) the energy b) comparison of its one- and two-particle density matrices with those obtained from “full CI”. The good results with the localized APSG function are related to the fact that electron correlation between electrons of opposite spin is (in this molecule) essential only within either of the “double bonds” of the “canonical structure”. The pertinent results are quite insensitive to different parametrization of the integrals.     

High harmonic generation and molecular orbital tomography in multielectron systems

High harmonic radiation is produced when atoms or molecules are ionized by an intense femtosecond laser pulse. The radiated spectrum has been shown experimentally to contain information on the electronic structure of the molecule, which can be interpreted as an image of a single molecular orbital. Previous theory for high harmonic generation has been limited to the single-active-electron approximation. Utilizing semisudden approximation, the authors develop a theory of the recombination step in high harmonic generation and tomographic reconstruction in multielectron systems, taking into account electron spin statistics and electron-electron correlations within the parent molecule and the ion. They show that the resulting corrections significantly modify the theoretical predictions, and bring them in a better agreement with experiment. They further show that exchange contributions to harmonic radiation can be used to extract additional information on the electronic wave function.     

Electron correlation studies: Rumer basis approach

A technique for the configuration interaction (CI) study of many-electron systems is developed based on Rumer spin-coupling scheme for the antisymmetrized configuration state functions (CSF). Incorporating a new graphical approach, the primitive configurations have been generated in blocks of definite ionocities to permit ready association of possible spin functions with each of the primitive configurations. Simple as well as extended Hubard model Hamiltonians have been studied to test the efficiency of the method. Procedures have been incorporated to calculate various correlation functions using the spin-adapted CSFs without invoking explicit expansions in terms of slater determinants. © 1996 John Wiley & Sons, Inc.     

Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.