Construction of complex STO-NG basis sets by the method of least squares and their applications

The goals of electronic structure theory are to make quantitative predictions of molecular properties and to provide qualitative insight into bonding as well as features of potential energy surfaces. Oftentimes, the two goals are at odds as an accurate treatment requires a complicated wave function that obscures chemical insight. The multifacet graphically contracted function (MFGCF) method offers a new approach that allows both goals to be addressed simultaneously. The recursive product structure of the MFGCF wave function reduces the exponential scaling of the exact wave function and allows the computation of molecular properties with polynomial scaling with respect to system size. Additionally, the graph density concept provides an intuitive tool for visualizing and analyzing the qualitative features of the wave function. In this work, the graph densities for model systems are examined to demonstrate their utility in analyzing the changes in wave function character along potential energy surfaces and near avoided crossings. Finally, we demonstrate that the graph density exposes the structure of the exact wave function for a system of noninteracting molecules as a product of the fragment wave functions.     

How do electron localization functions describe π-electron delocalization?

Scalar fields provide an intuitive picture of chemical bonding. In particular, the electron localization function (ELF) has proven to be highly valuable in interpreting a broad range of bonding patterns. The discrimination between enhanced or reduced electron (de)localization within cyclic π-conjugated systems remains, however, challenging for ELF. In order to clearly distinguish between the local properties of ten highly and weakly π-(de)localized prototype systems, we compare the ELFs of both the canonical wave functions and electron-localized states (diabatic) with those of two closely related scalar fields: the electron localizability indicator (ELI-D) and the localized orbital locator (LOL). The simplest LOL function distinguishes enhanced from weak π-(de)localization in an insightful and reliable manner. LOL offers the finest contrast between annulenes with 4n/4n + 2 π electrons and their inorganic analogues as well as between hyperconjugated cyclopentadiene derivatives. LOL(π) also gives an appealing and intuitive picture of the π-bond. In contrast, the most popular ELF fails to capture subtle contrasting local electronic properties and suffers from the arbitrariness of the σ/π dissection. The orbital separation of the most recent ELI-D is clear-cut but the interpretations sometime less straightforward in the present context.     

Using molecular similarity to construct accurate semiempirical electronic structure theories

Ab initio electronic structure methods give accurate results for small systems, but do not scale well to large systems. Chemical insight tells us that molecular functional groups will behave approximately the same way in all molecules, large or small. This molecular similarity is exploited in semiempirical methods, which couple simple electronic structure theories with parameters for the transferable characteristics of functional groups. We propose that high-level calculations on small molecules provide a rich source of parametrization data. In principle, we can select a functional group, generate a large amount of ab initio data on the group in various small-molecule environments, and "mine" this data to build a sophisticated model for the group's behavior in large environments. This work details such a model for electron correlation: a semiempirical, subsystem-based correlation functional that predicts a subsystem's two-electron density matrix as a functional of its one-electron density matrix. This model is demonstrated on two small systems: chains of linear, minimal-basis (H-H)(5), treated as a sum of four overlapping (H-H)(2) subsystems; and the aldehyde group of a set of HOC-R molecules. The results provide an initial demonstration of the feasibility of the approach.     

Prediction of the Frontier Electronic States in a Finite Single-wall Carbon Nanotube

A theoretical model is summarized into the shorter vector principle. It is used to predict the topological structure of wave function and the oscillation rule of energy gap in various types of finite carbon nanotubes (CNTs). The theoretical model indicates that the characteristics of the electronic states only depend on the nanotube size and its symmetry along the shorter vector direction. In this direction, the wave functions of the original 3m (or 3m/2) periodicity are also suitable for armchair, chiral and zigzag finite CNTs with the C2 (Cs), C1 and Cn point groups, respectively. Energy gaps present the oscillation with 3m (or 3m/2) or odd-even n. The first principle calculations for some prototype systems are performed. The results are consistent with the theoretical model.     

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules

We pursue the development and application of the recently introduced linear optimization method for determining the optimal linear and nonlinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a linear combination of the energy and the energy variance. We apply the linear optimization method to obtain the complete ground-state potential energy curve of the C(2) molecule up to the dissociation limit and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform calculations for the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.     

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems.     

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.     

Core molecular orbital contribution to N2O isomerization as studied using theoretical electron momentum spectroscopy

Core molecular orbital contribution to the electronic structure of N2O isomers has been studied using quantum mechanical density functional theory combined with a plane wave impulse approximation method. Momentum distributions of wave functions for inner shell molecular orbitals of the linear NNO, cyclic and linear NON isomers of N2O are calculated through the (e, 2e) differential cross sections in momentum space. This is possible because this momentum distribution is directly proportional to the modulus squared of the momentum space wave function for the molecular orbital in question. While the momentum distributions of the NNO and cyclic N2O isomers demonstrate strong atomic orbital characteristics in their core space, the outer core molecular orbitals of the linear NON isomer exhibit configuration interactions between them and the valence molecular orbitals. It is suggested that the frozen core approximation breaks down in the prediction of the electronic structure of such an isomer. Core molecular orbital contributions to the electronic structure can alter the order of total energies of the isomers and lead to incorrect conclusions of the stability among the isomers. As a result, full electron calculations should be employed in the study of N2O isomerization.     

Ab initio electron propagators in molecules with strong electron-phonon interaction. I. Phonon averages

Ab initio electron propagators in molecular systems with strong electron-electron and electron-phonon interactions are considered to study molecular electronic properties. This research is important in electron transfer reactions where the electron transition is not considered any longer as a single electron transfer process or in temperature dependences of current-voltage characteristics in molecular wires or aggregates. To calculate electron Green's functions, the authors apply a small polaron canonical transformation that intrinsically contains strong electron-phonon effects. According to this transformation, the excitation energies of the noninteracting Hamiltonian are shifted down by the relaxation (solvation) energy for each state. The electron-electron interaction is also renormalized by the electron-phonon coupling. For some values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative resulting in the attraction between two electrons. Within this transformation, they develop a diagrammatic expansion for electron Green's function in which the electron-phonon interaction is included into the multiple phonon correlation functions. The multiple phonon correlation functions are exactly found. It is pointed out that Wick's theorem for such correlation functions is invalid. Consequently, there is no Dyson equation for electron Green's functions. The proposed approach can be considered for future method developments for quantum chemical calculations that include strong nonadiabatic (non-Born-Oppenheimer) effects.     

Ab initio study of molecular structures and excited states in anthocyanidins

The structural and electronic characters of four types of hydroxyl group-substituted anthocyanidins (pelargonidin, cyanidin, delphinidin, and aurantinidin) were examined using quantum chemical calculations. For these cationic molecules, both the planar and non-planar structures in the electronic ground state were determined at the B3LYP/D95 level of theory. We revealed that the planar structure is slightly more stable than the non-planar structure for each molecule. For the optimized planar structures, single excitation-configuration interaction (SE-CI) based on the restricted Hartree-Fock (RHF) wave function was evaluated and the electronic character in the low-excited states was discussed in terms of the MO theory. Symmetry adapted cluster (SAC)/SAC-CI calculations were also carried out to estimate the excitation energies precisely. The results showed that hydroxylation of the phenyl group causes a change in the excitation energies without taking the solvent effects into account. The results are in agreement with spectral experiments and previous MO calculations.     

The electronic mean-field configuration interaction method. I. Theory and integral formulas

In this article, we introduce a new method for solving the electronic Schrodinger equation. This new method follows the same idea followed by the mean-field configuration interaction method already developed for molecular vibrations; i.e., groups of electronic degrees of freedom are contracted together in the mean field of the other degrees. If the same partition of electronic degrees of freedom is iterated, a self-consistent field method is obtained. Making coarser partitions (i.e., including more degrees in the same groups) and discarding the high energy states, the full configuration interaction limit can be approached. In contrast with the usual group function theory, no strong orthogonality condition is enforced. We have made use of a generalized version of the fundamental formula defining a Hopf algebra structure to derive Hamiltonian and overlap matrix element expressions which respect the group structure of the wave function as well as its fermionic symmetry. These expressions are amenable to a recursive computation.     

Mechanism of linear and nonlinear optical properties of the urea crystal family

First-principles calculations of the second-order optical response functions and the dielectric functions of urea [CO(NH(2))(2)] and some of its derivatives such as monomethylurea (H(2)NCONHCH(3), MMU), and N,N'-dimethylurea (H(3)CHNCONHCH(3), DMU) crystals are performed. On the basis of the density functional theory (DFT) in the local-density approximation (LDA), the highly accurate full-potential projected augmented wave (FP-PAW) method was used to obtain the electronic structure. Over a wide frequency range (0.0-10.0 eV), the dielectric constants and second-harmonic generation (SHG) susceptibilities of the urea crystal family have been obtained, and the results are in good agreement with the experimental values. The origin of the linear and nonlinear optical (NLO) properties of the urea crystal family has been analyzed by coupling the calculated electronic structure and optical spectrum. The prominent spectra of χ((2)) are successfully correlated with the dielectric function ε(ω) in terms of single-photon and double-photon resonances. The virtual electron (VE) and virtual hole (VH) processes have also been performed for the urea crystal family. From the research into the electron deformation density, crystal configuration, substitutional group, and so forth, it is found that the origin of the SHG of the urea crystal family is the charge transfer due to the strong "(?)push-pull" effect along the hydrogen bond, which favors a head-to-tail arrangement of the molecules and enhances the SHG response. The electron-donating substitutional group supplies more electrons to the electron-accepting group, and helps to form large dipoles in molecules. The influence on the NLO properties of the local symmetry of the substitutional group is also discussed in detail.     

Projection between basis sets: A means of defining the electronic structure of functional subunits

The general problem of the transfer of the representation of a set of orthonormal functions from one basis to a different, nonequivalent one is considered and specialized to a matrix formulation convenient for use in molecular electronic structure calculations. A procedure is suggested for treating problems where the transfer of representation breaks into a subset of most interest and one of less interest as for example the occupied and virtual orbitals of a Hartree-Fock SCF calculation. These techniques are then applied to obtain a representation of a methyl group from an SCF wave function for methane.     

Chemical trends in adsorption on semiconductor surfaces: Results from local density theory

In this paper we briefly review some chemical trends in structural and electronic properties of monolayers of group IV to group VII adatoms adsorbed on (001) surfaces of homopolar semiconductors. Particular emphasis is put on adsorption of Si, As, Se and Cl at the Si (001) surface. We discuss results from our local density Green function calculations for semi-infinite adsorption systems. The calculated optimal structures can be interpreted in a simple picture of the surface chemical bond and they are in excellent agreement with experimental data where they are available. The calculated electronic structure agrees very good with ARPES data for those systems for which well-ordered monolayer adsorption on the substrate surface has been observed experimentally.     

Electronic coupling matrix elements from charge constrained density functional theory calculations using a plane wave basis set

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q(-)) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, (<|H(ab)|(2)>)(1/2)=6.7 mH, is significantly higher than the value obtained for the minimum energy structure, |H(ab)|=3.8 mH. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q(-) in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.     

Hydrogen bonding in the LaNi3BH3 hydride

The electronic structure of the intermetallic LaNi3B as well as the novel hydride LaNi3BH3 have been theoretically investigated by means of quantum chemistry methods. We employed a mixed approach to investigate the electronic structure of these compounds: state-of-the-art energy band calculations and molecular cluster computations. We computed the energy bands and the total and partial density of states using both the linear-augmented plane waves and projector-augmented wave methods. In addition the electronic structure of three representative clusters of the local environment of Ni atoms was investigated by quantum chemistry ab initio molecular calculations. In this report, we discuss the chemical bonding and we investigated the H site occupancy energies and correlate this estimate with the occupancy fraction and metal-hydrogen distances experimentally observed.