Simple qualitative rules to study the surface electronic structure of some binary crystals

Based on the use of the important qualitative concept of energy-weighted averages, a few simple rules are formulated that facilitate the analysis of the existence of surface states and enable the estimation of the effect of surface charge self-consistency on the electronic structure of AB-type crystal surfaces. Recent theoretical and experimental investigations of the (001) and (111) surfaces of refractory transition metal compounds TiC and TiN are discussed in detail. The problem of the stability of the polar (111) surface of TiC is mentioned.     

Influence of polarization fluctuations on the electronic structure of molecular solids

Fluctuations in the intermolecular polarization energies of charge states in molecular solids can lead to broad (ΔE ≈ 0.5 eV) distributions of localized states, especially in polymers. Such fluctuations are caused by defects (e.g. surfaces) and thermal vibrations in molecular crystals and also by variations in the local structure in polymers. The resulting energy distributions yield natural interpretations of such diverse observations on the broadening of the photoemission spectra of molecular solids and the contact charge exchange spectra of polymers.     

A theoretical method to determine atomic pseudopotentials for electronic structure calculations of molecules and solids

The characteristic features of model potentials, effective potentials and pseudopotentials are carefully investigated. Then we justify our choice to work only with hermitian pseudopotential operators, and we develop a general non-empirical method to determine atomic pseudopotentials. In view of their numerical use for molecular calculations, these pseudopotentials are cast into semi-local forms, and their parameters are obtained by a least-squares process; tables of parameter values are given for the two first rows of the periodic system.     

Analysis of conformational polymorphism in pharmaceutical solids using solid-state NMR and electronic structure calculations

A detailed analysis of molecular structure in three polymorphic forms of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile is made using a combination of multidimensional solid-state NMR (SSNMR) experiments and molecular modeling via electronic structure calculations. These compounds, collectively referred to as ROY because of their red, orange, and yellow colors, share a similar molecular structure with the exception of the dihedral angle between the phenyl and thiophene rings. The ROY materials make it possible to study the influence of nearly a single degree of freedom on the associated NMR spectra. Using the 2D PASS (Antzutkin et al. J. Magn. Reson. A 1995, 115, 7) experiment, spectral editing techniques, and DFT-based calculations of the local fields, an analysis is made of the sensitivity of all carbon and nitrogen sites to changing molecular conformation. Chemical shift and dipolar coupling information obtained from these experiments vary noticeably between forms and are subsequently used to quantitatively determine aspects of molecular structure in these materials, including the coplanar angle between the phenyl and thiophene rings. The influence of motion on the methyl and nitro chemical shifts is also investigated. The accuracy of the information obtained from local field analysis and the model structure calculation demonstrates the capabilities of SSNMR as a quantitative structural method.     

Influences on the rotated structure of diiron dithiolate complexes: electronic asymmetry vs. secondary coordination sphere interaction

In the pursuit of a "rotated" structure, and exploration of the influence of the aza nitrogen lone pair, the Fe(I)Fe(I) model complexes wherein two Fe(CO)(3-x)P(x) moieties are significantly twisted from the ideal configuration (torsion angle >30°) are reported. [Fe(2)(μ-S(CH(2))(2)N(i)Pr(X)(CH(2))(2)S)(CO)(4)(κ(2)-dppe)](2)(2+) (X = H, 4; Me, 5) prepared from protonation and methylation, respectively, of [Fe(2)(μ-S(CH(2))(2)N(i)Pr(CH(2))(2)S)(CO)(4)(κ(2)-dppe)](2), 1, possess Φ angles of 34.1 and 35.4° (av.), respectively. Such dramatic twist is attributed to asymmetric substitution within the Fe(2) unit in which a dppe ligand is coordinated to one Fe site in the κ(2)-mode. In the presence of the N···C(CO(ap)) interaction, the torsion angle is decreased to 10.8°, suggesting availability of lone pairs of the aza nitrogen sites within 1 is in control of the twist. Backbones of the bridging diphosphine ligands also affect distortion. For a shorter ligand, the more compact structure of [Fe(2)(μ-S(CH(2))(2)N(i)Pr(CH(2))(2)S)(μ-dppm)(CO)(4)](2), 7, is formed. Dppm in a bridging manner allows achievement of the nearly eclipsed configuration. In contrast, dppe in [Fe(2)(μ-S(CH(2))(2)N(i)Pr(CH(2))(2)S)(μ-dppe)(CO)(4)](2), 6, could twist the Fe(CO)(3-x)L(x) fragment to adopt the least strained structure. In addition, the NC(CO(ap)) interaction would direct the twist towards a specific direction for the closer contact. In return, the shorter N···C(CO(ap)) distance of 3.721(7) ? and larger Φ angle of 26.5° are obtained in 6. For comparison, 3.987(7) ? and 3.9° of the corresponding parameters are observed in 7. Conversion of (μ-dppe)[Fe(2)(μ-S(CH(2))(2)N(i)Pr(CH(2))(2)S)(CO)(5)](2), 2, to complex 1 via an associative mechanism is studied.     

Electronic structure of some adenosine receptor antagonists. III. Quantitative investigation of the electronic absorption spectra of alkyl xanthines

Quantitative and comparative investigation of the electronic absorption spectra of theophylline, caffeine and their derivatives is reported. The spectra of theophylline, caffeine and theobromine were compared to establish the predominant tautomeric species in solution. This comparison, analysis of solvent effects and assignments of the observed transitions via MO computations indicate the exits of only one tautomeric species in solution that is the N7 form. A low-lying triplet state was identified which corresponds to a HOMO-LUMO transition. This relatively long-lived T1 state is always less polar than the ground state and may very well underlie the photochemical reactivity of alkyl xanthines. Substituents of different electron donating or withdrawing strengths and solvent effects are investigated and analyzed. The present analysis is facilitated via computer deconvolution of the observed spectra and MO computation.     

Ground-state enthalpies: evaluation of electronic structure approaches with emphasis on the density functional method

Ground-state enthalpies, calculated by various electronic structure methods, are compared with experimentally well-established values across a sizable data base of 577 molecules and 15 atoms. With the diversity of species and bonding types available in this compilation it is possible to detect deficiencies that may escape with smaller test sets. The present analysis relying on DAtEF (Data base optimized Atomic Enthalpies of Formation) yields error statistics which relate to reaction enthalpies among the species much more directly than extrapolations based on atomization enthalpies. The evaluation is applied to methods ranging from high level first principles wavefunction calculations to density functionals and to semiempirical approaches. It is found that computationally efficient and broadly applicable density functional methods with relatively small but adequate numerical basis sets can provide ground-state enthalpies within approximately 20 kJ/mol rms (approximately 4.8 kcal/mol). This must be considered an excellent result, as presently only the heaviest available methods appear to provide about a factor of 2 more accuracy as inferred from a subset of the data base used here.     

The electronic structure of oxo-Mn(salen): single-reference and multireference approaches

Using single- and multireference approaches we have examined many of the low-lying electronic states of oxo-Mn(salen), several of which have not been explored previously. Large complete-active-space self-consistent-field (CASSCF) computations have been performed in pursuit of an accurate ordering for the lowest several electronic states. Basis set and relativistic effects have also been considered. For the geometry considered, our best results indicate the ground spin state to be a closed-shell singlet, followed by a pair of low-lying triplet states, with additional singlet states and the lowest quintet state lying significantly higher in energy. Hartree-Fock and density functional theory (DFT) results are obtained and are compared to the more robust CASSCF results. The Hartree-Fock results are qualitatively incorrect for the relative energies of the states considered. Popular density functionals such as BP86 and B3LYP are superior to Hartree-Fock for this problem, but they give inconsistent answers regarding the ordering of the lowest singlet and triplet states and they greatly underestimate the singlet-quintet gap. We obtained multiple Hartree-Fock and DFT solutions within a given spin multiplicity, and these solutions have been subjected to wave function stability analysis.     

Comparison of vertical and adiabatic harmonic approaches for the calculation of the vibrational structure of electronic spectra

The calculation of the vibrational structure associated to electronic spectra in large molecules requires a Taylor expansion of the initial and final state potential energy surface (PES) around some reference nuclear structure. Vertical (V) and adiabatic (A) approaches expand the final state PES around the initial-state (V) or final-state (A) equilibrium structure. Simplest models only take into account displacements of initial- and final-state minima, intermediate ones also allow for difference in frequencies and more accurate models introduce the Dushinsky effect through the computation of the Hessians of both the initial and final state. In this contribution we summarize and compare the mathematical expressions of the complete hierarchy of V and A harmonic models and we implement them in a numerical code, presenting a detailed comparison of their performance on a number of prototypical systems. We also address non-Condon effects through linear expansions of the transition dipole as a function of nuclear coordinates (Herzberg-Teller effect) and compare the results of expansions around initial and final state equilibrium geometries. By a throughout analysis of our results we highlight a number of general trends in the relative performance of the models that can provide hints for their proper choice. Moreover we show that A and V models including final state PES Hessian outperform the simpler ones and that discrepancies in their predictions are diagnostic for failure of harmonic approximation and/or of Born-Oppenheimer approximation (existence of remarkable geometry-dependent mixing of electronic states).     

The symmetry-broken formalism applied to the electronic structure of an iminosemiquinone copper(II) catalyst: a key to the qualitative understanding of its reactivity

A concise outline of the known derivation of the singlet-triplet energy-gap equations within the symmetry-broken wavefunction framework is given. They allow a computation of the singlet-triplet energy gap for molecules that exhibit a weak antiferromagnetic coupling of electrons. The accuracy of the equations is assessed by computation of the singlet-triplet gaps in model Na2 molecules. Various antiferromagnetic coupling strengths are simulated by the use of different Na-Na bond lengths in the computations. The singlet-triplet energy gaps obtained with the different equations are compared with the gaps computed with the more accurate coupled-cluster methods. Subsequently, the equations are applied to an iminosemiquinone copper(II) complex found previously to have remarkable catalytic properties. The application is performed by employing wave-function equations but with quantities computed within the density functional framework. The electronic ground state of this complex is computed to be a singlet state, which is also the experimental finding. Moreover, the experimental geometry and the singlet-triplet gap are reasonably reproduced by the computation. A straightforward method to determine the magnetic orbitals is suggested and applied. We illustrate that the form of the magnetic orbitals indicates in a qualitative manner that hydrogen-atom abstraction should be a major reaction pathway of the iminosemiquinone copper(II) complex. Hydrogen-atom abstraction has been suggested previously to be the rate-determining step in a catalytic process initiated by the iminosemiquinone copper(II) complex. The results support the notion that the form of the magnetic orbitals might be a qualitative indicator for the reactivity of molecules that exhibit weak antiferromagnetic coupling.     

Geometric and electronic approaches to size effects in heterogeneous catalysis

The influence of electronic and geometric factors is considered in the context of the manifestation of size effects in heterogeneous catalytic oxidation and hydrogenation reactions. Both of the factors are interdependent; however, the electronic factor predominates with regard to small metal and metal oxide particles (smaller than 10 nm), for which the energies of electron transitions in an activated complex are size-dependent. Only the geometry of active component nanoparticles exerts the main effect on the catalytic properties of coarser particles. In this case, the geometric factor depends on the accessibility of the active surface to reactants. The probability of the occurrence of complex active centers including several surface atoms increases as the active component particles of a catalyst become larger. The efficiency of the approach proposed to study the activating effect of nanophase catalysts is demonstrated using the oxidation and hydrogenation reactions of carbon oxides and the hydrogenation of acetonitrile and acetone as examples.     

A CNDO/S study of trans-indanylideneindane. Implications to the trans-stilbene electronic structure

CNDO calculations have been performed on chiral derivatives of trans-1-(indan-1-ylidene)-indane, a stiff trans-stilbene analogue. The results are in complete agreement with the recently published UV and CD spectra of these compounds and allow state assignments down to 225 nm. The calculations are relevant to the trans-stilbene electronic structure which is under current dispute.     

Intramolecular and intermolecular contributions to the barriers for rotation of methyl groups in crystalline solids: electronic structure calculations and solid-state NMR relaxation measurements

The rotation barriers for 10 different methyl groups in five methyl-substituted phenanthrenes and three methyl-substituted naphthalenes were determined by ab initio electronic structure calculations, both for the isolated molecules and for the central molecules in clusters containing 8-13 molecules. These clusters were constructed computationally using the carbon positions obtained from the crystal structures of the eight compounds and the hydrogen positions obtained from electronic structure calculations. The calculated methyl rotation barriers in the clusters (E(clust)) range from 0.6 to 3.4 kcal/mol. Solid-state (1)H NMR spin-lattice relaxation rate measurements on the polycrystalline solids gave experimental activation energies (E(NMR)) for methyl rotation in the range from 0.4 to 3.2 kcal/mol. The energy differences E(clust) - E(NMR) for each of the ten methyl groups range from -0.2 kcal/mol to +0.7 kcal/mol, with a mean value of +0.2 kcal/mol and a standard deviation of 0.3 kcal/mol. The differences between each of the computed barriers in the clusters (E(clust)) and the corresponding computed barriers in the isolated molecules (E(isol)) provide an estimate of the intermolecular contributions to the rotation barriers in the clusters. The values of E(clust) - E(isol) range from 0.0 to 1.0 kcal/mol.     

On the electronic structure of giant polyoxometalates: Mo(132)vs. W(72)Mo(60)

The molecular and electronic structure of the spherical Keplerates [{(Mo(VI))Mo(VI)(5)O(21)}(12)(Mo(V)(2)O(4))(30)](12-) (Mo(132)) and [{(W(VI))W(VI)(5)O(21)}(12)(Mo(V)(2)O(4))(30)](12-) (W(72)Mo(60)) has been determined, for the first time, using first-principles density functional theory (DFT) based methods including solvent effects. Computed geometric parameters are in very good agreement with X-ray data, whereas the electronic structure reveals the archetypal nature of polyoxometalates.     

An algebraic operator approach to electronic structure

In this paper, we introduce an algebraic approach to electronic structure calculations. Our approach constructs a Jordan algebra based on the second-quantized electronic Hamiltonian. From the structure factor of this algebra, we show that we can calculate the energy of the ground electronic state of the Hamiltonian operator. We apply our method to several generalized Hubbard models and show that we can usually obtain a significant fraction of the correlation energy for low-to-moderate values of the electronic repulsion parameter while still retaining the O(L(3)) scaling of the Hartree-Fock algorithm. This surprising result, along with several other observations, suggests that our algebraic approach represents a new paradigm for electronic structure calculations which opens up many new directions for research.     

Dynamical variational approach to non-adiabatic electronic structure

Studying non-adiabatic effects in molecular dynamics simulations and modeling their optical signatures in linear and non-linear spectroscopies calls for electronic structure calculations in a situation when the ground state is degenerate or almost degenerate. Such degeneracy causes serious problems in invoking single Slater determinant Hartree–Fock (HF) and density functional theory (DFT) methods. To resolve this problem, we develop a generalization of time-dependent (dynamical) variational approach which accounts for the degenerate or almost degenerate ground state structure. Specifically, we propose a ground state ansatz for the subspace of generalized electronic configurations spanned on the degenerate grounds state multi-electron wavefunctions. Further employing the invariant form of Hamilton dynamics we arrive with the classical equations of motion describing the time-evolution of this subspace in the vicinity of the stationary point. The developed approach can be used for accurate calculations of molecular excited states and electronic spectra in the degenerate case.     

On the electronic structure of ethidium

The electronic structure of the common intercalating agent ethidium bromide (3,8-diamino-5-ethyl-6-phenylphenanthridinium bromide) is dominated by an interplay of electron donating and withdrawing effects mediated by its nitrogen atoms. X-ray crystallography, UV/Vis and IR absorption, fluorescence emission, and NMR spectroscopy are used to probe the electronic properties of the phenanthridinium "core" of ethidium as well as its exocyclic amines and 6-phenyl groups. Interestingly, despite its positive charge, most of ethidium's aromatic carbon and hydrogen atoms have high electron densities (compared to both 6-phenylphenanthridine and benzene). The data suggest that electron donation by ethidium's exocyclic amines dominates over the electron withdrawing effects of its endocyclic iminium in their combined influence on the electron densities of these atoms. Ethidium's nitrogen atoms are, conversely, electron deficient where the 5-position is the most electropositive, followed by the 3-amino, and lastly the 8-amino group. These results have been used to generate an empirically-based pi-electron density map of ethidium that may prove useful to understanding its nucleic acid binding specificity.