Abstract: The gauge-including magnetically induced current method for calculating the components of the current-density tensor using gauge-including atomic orbitals has been extended to treating open-shell molecules. The applicability of the method is demonstrated by calculations of first-order induced current densities on cyclobutadiene, Al(3), and B(3) at correlated ab initio levels of theory. For comparison, current-density calculations were also performed on the lowest closed-shell singlet state of cyclobutadiene as well on the closed-shell Al(3)(-) and B(3)(-) anions. The ring-current susceptibilities of the open-shell species are computed at the Hartree-Fock self-consistent-field, second-order Moller-Plesset perturbation theory, and coupled-cluster singles and doubles levels, whereas for the closed-shell systems also density functional theory calculations were employed. Explicit values for the current strengths caused by α and β electrons as well as the difference, representing the spin current, were obtained by numerical integration of the current-density contributions passing a plane perpendicular to the molecular ring. Comparisons of the present results to those recently obtained for the lowest triplet state of biphenyl emphasize that electron correlation effects must be considered for obtaining an accurate description of spin-current densities.

Abstract: Even-tempered Slater-type orbital basis sets were developed in 1973, based on total atomic energy optimization. Here, we revisit ET STOs and propose new sets based on past experience and recent computational studies. From preliminary atomic and molecular tests, these sets are shown to be very well balanced and to perform, at lower cost, almost as well as a very large (close to complete) basis set. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1030–1036, 2004

Abstract: A general definition of orbital contributions, valid for any single-valued distribution of origin of vector potential, is given for the current density induced in a molecule by an external magnetic field. Only for the ipsocentric choice of origin, where current density at each point is calculated with that point as origin, are the orbital contributions free of unphysical occupied–occupied mixing terms, and in this scheme, response of delocalised π systems is restricted to the activity of a small number of frontier electrons, and governed by simple symmetry rules. Localised orbitals can equally well be used in this framework for σ systems. The advantages of the ipsocentric method extend to the integrated properties of magnetisability and nuclear shielding, giving what is, in a well defined sense, the best orbital contributions for interpretation of these properties and their links to aromaticity. The general theory is illustrated by detailed calculations of the magnetic response properties of the benzene molecule.

Abstract: Spin-unrestricted Kohn-Sham (KS) solutions are constructed from accurate ab initio spin densities for the prototype doublet molecules NO(2), ClO(2), and NF(2) with the iterative local updating procedure of van Leeuwen and Baerends (LB). A qualitative justification of the LB procedure is given with a "strong" form of the Hohenberg-Kohn theorem. The calculated energies epsilon(isigma) of the occupied KS spin orbitals provide numerical support to the analogue of Koopmans' theorem in spin-density functional theory. In particular, the energies -epsilon(ibeta) of the minor spin (beta) valence orbitals of the considered doublet molecules correspond fairly well to the experimental vertical ionization potentials (VIPs) I(i) (1) to the triplet cationic states. The energy -epsilon(Halpha) of the highest occupied (spin-unpaired) alpha orbital is equal to the first VIP I(H) (0) to the singlet cationic state. In turn, the energies -epsilon(ialpha) of the major spin (alpha) valence orbitals of the closed subshells correspond to a fifty-fifty average of the experimental VIPs I(i) (1) and I(i) (0) to the triplet and singlet states. For the Li atom we find that the exact spin densities are represented by a spin-polarized Kohn-Sham system which is not in its ground state, i.e., the orbital energy of the lowest unoccupied beta spin orbital is lower than that of the highest occupied alpha spin orbital ("a hole below the Fermi level"). The addition of a magnetic field in the -z direction will shift the beta levels up so as to restore the Aufbau principle. This is an example of the nonuniqueness of the mapping of the spin density on the KS spin-dependent potentials discussed recently in the literature. The KS potentials may no longer go to zero at infinity, and it is in general the differences nu(ssigma)( infinity )-epsilon(isigma) that can be interpreted as (averages of) ionization energies. In total, the present results suggest the spin-unrestricted KS theory as a natural one-electron independent-particle model for interpretation and assignment of the experimental photoelectron spectra of open-shell molecules.

Abstract: In this paper we present a detailed and unified theoretical treatment of secondary electron cascades that follow the absorption of an X-ray photon. A Monte Carlo model has been constructed that treats in detail the evolution of electron cascades induced by photoelectrons and by Auger electrons following inner shell ionizations. Detailed calculations are presented for cascades initiated by electron energies between 0.1-10 keV. The present paper expands our earlier work by extending the primary energy range, by improving the treatment of secondary electrons, especially at low electron energies, by including ionization by holes, and by taking into account their coupling to the crystal lattice. The calculations describe the three-dimensional evolution of the electron cloud, and monitor the equivalent instantaneous temperature of the free-electron gas as the system cools. The dissipation of the impact energy proceeds predominantly through the production of secondary electrons whose energies are comparable to the binding energies of the valence (40-50 eV) and of the core electrons (300 eV). The electron cloud generated by a 10 keV electron is strongly anisotropic in the early phases of the cascade (t {le} 1 fs). At later times, the sample is dominated by low energy electrons, and these are scattered more » more isotropically by atoms in the sample. Our results for the total late time number of secondary electrons agree with available experimental data, and show that the emission of secondary electrons approaches saturation within about 100 fs, following the primary impact. « less

Abstract: Using a combination of first principles calculations and empirical potentials we have undertaken a systematic study of the low energy structures of gold nanoclusters containing from 3 to 38 atoms. A Lennard-Jones and many-body potential have been used in the empirical calculations, while the first principles calculations employ an atomic orbital, density functional technique. For the smaller clusters ( n =3–5) the potential energy surface has been mapped at the ab initio level and for larger clusters an empirical potential was first used to identify low energy candidates which were then optimised with full ab initio calculations. At the DFT-LDA level, planar structures persist up to six atoms and are considerably more stable than the cage structures by more than 0.1 eV/atom. The difference in ab initio energy between the most stable planar and cage structures for seven atoms is only 0.04 eV/atom. For larger clusters there are generally a number of minima in the potential energy surface lying very close in energy. Furthermore our calculations do not predict ordered structures for the magic numbers n =13 and 38. They do predict the ordered tetrahedral structure for n =20. The results of the calculations show that gold nanoclusters in this size range are mainly disordered and will likely exist in a range of structures at room temperature.

Abstract: DFT calculations were driven for a set of differently charged polyoxoanions in the gas phase and in solution. We have calculated and analyzed their geometries and orbital energies to trace simple rules of behavior regarding the modeling of anions in isolated form. We discuss the quality of the results depending on the molecular charge, q, and the size of the cluster in terms of the number of metal centers, m. When the q/m ratio reaches a value of ∼0.8, DFT calculations for the isolated anion fail to describe the gap between the band of occupied oxo orbitals and the set of unoccupied orbitals delocalized among the metal atoms. In these cases the incorporation of the stabilizing external fields generated by the solvent through continuum models improves the geometries and orbital energies. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1542–1549, 2004

Abstract: We have studied the interaction of atomic hydrogen with (5,5) and (10,0) single-walled carbon nanotubes (SWNT) using density functional theory. These calculations use Gaussian orbitals and periodic boundary conditions. We compare results from the local spin density approximation, generalized gradient approximation (GGA), and hybrid density functionals. We have first kept the SWNT geometric structure fixed while a single H atom approaches the tube on top of a carbon atom. In that case, a weakly bound state with binding energies from -0.8 to -0.4 eV was found. Full geometry relaxation leads to a strong SWNT deformation, weakening the nearest C-C bonds and increasing the binding energy by about 1 eV. Full hydrogen coverage of the (5,5) SWNT converts this metallic nanotube into an insulator with a band gap of 3.4 eV for the GGA functional and 4.8 eV for the hybrid functional. Hybrid functionals perform similar to pure density functional theory functionals for the calculation of binding energies while band gaps critically depend on the functional choice.

Abstract: Measurements of magnetization M(T, H), heat capacity C(T), NMR lineshift K(T) and linewidth Δ(T), neutron scattering S(Q, ω, T) and broadband dielectric spectroscopy (ω, T) provide experimental evidence of the different orbital ground states in the cubic sulfur spinels under investigation. In all compounds, the tetrahedrally coordinated Jahn–Teller ions Fe2+ are characterized by a degeneracy of the orbital degrees of freedom. Particularly, we found a long-range orbital ordering in polycrystalline (PC) FeCr2S4, and a glassy freezing of the orbital degrees of freedom in FeCr2S4 (single crystals) (SCs). In contrast, FeSc2S4 belongs to the rare class of spin–orbital liquids, where quantum fluctuations accompanying the glassy freezing of the orbitals suppress long-range magnetic order.

Abstract: Second-row dicarbides C2X (X = Na−Cl) are investigated with quantum mechanical techniques. The cyclic−linear competition in these systems is studied, and the bonding scheme for these compounds is discussed in terms of the topological analysis of the electronic density. C2Na, C2Mg, C2Al, and C2Si are found to prefer a C2v-symmetric arrangement corresponding to a T-shape structure. On the other hand, for C2P, C2S, and C2Cl the linear isomer is predicted to be the ground state. A detailed analysis of the variation of the electronic energy and orbital energies with the geometry has been carried out. A simple theoretical model, taking into account the main interactions between the valence orbitals of both fragments, the X atom and the C2 molecule, allows an interpretation of the main features of these compounds.

Abstract: We report on the results of an exhaustive study of the valence electronic structure of norbornane (C7H12), up to binding energies of 29 eV. Experimental electron momentum spectroscopy and theoretical Green's function and density functional theory approaches were all utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among all the tested models, the combination of the Becke-Perdew functional and a polarized valence basis set of triple-zeta quality provides the best representation of the electron momentum distributions for all of the 20 valence orbitals of norbornane. This experimentally validated quantum chemistry model was then used to extract some chemically important properties of norbornane. When these calculated properties are compared to corresponding results from other independent measurements, generally good agreement is found. Green's function calculations with the aid of the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than 22.5 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet photoemission and newly presented (e,2e) ionization spectra, except for the band associated with the 1a(2)(-1) one-hole state, which is probably subject to rather significant vibronic coupling effects, and a band at similar to25 eV characterized by a momentum distribution of "s-type" symmetry, which Green's function calculations fail to reproduce. We note the vicinity of the vertical double ionization threshold at similar to26 eV. (C) 2004 American Institute of Physics.

Abstract: In this paper, we present a theoretical approach to calculate differential and total ionization cross sections of polyatomic molecules by fast electron impact. More exactly, we have studied the ionization of ammonia (NH3) and methane (CH4) molecules, and previous results concerning the H2O molecule ionization are reported for comparison. The calculations are performed in the distorted wave Born approximation without exchange by employing the independent electron model. The molecular target wave functions are described by linear combinations of atomic orbitals. To describe the interaction between the inactive target electrons and the slow ejected electron, we have introduced a distortion via an effective potential calculated for each molecular orbital. The present theoretical calculations agree well with a large set of existing experimental data in terms of multiple differential and total cross sections.

Abstract: We use frequency-dependent capacitance-voltage spectroscopy to measure the tunneling probability into self-assembled InAs quantum dots. Using an in-plane magnetic field of variable strength and orientation, we are able to obtain information on the quasi-particle wave functions in momentum space for 1 to 6 electrons per dot. For the lowest two energy states, we find a good agreement with Gaussian functions for a harmonic potential. The high energy orbitals exhibit signatures of anisotropic confinement and correlation effects.

Abstract: The application of combined quantum mechanical (QM) and molecular mechanical methods to large molecular systems requires an adequate treatment of the boundary between the two approaches. In this article, we extend the generalized hybrid orbital (GHO) method to the semiempirical parameterized model 3 (PM3) Hamiltonian combined with the CHARMM force field. The GHO method makes use of four hybrid orbitals, one of which is included in the QM region in self-consistent field optimization and three are treated as auxiliary orbitals that do not participate in the QM optimization, but they provide an effective electric field for interactions. An important feature of the GHO method is that the semiempirical parameters for the boundary atom are transferable, and these parameters have been developed for a carbon boundary atom consistent with the PM3 model. The combined GHO-PM3/CHARMM model has been tested on molecular geometry and proton affinity for a series of organic compounds.

Abstract: We formulate an effective independent particle model where the effective Hamiltonian is composed of the Fock operator and a correlation potential. Within the model the kinetic energy and the exchange energy can be expressed exactly leaving the correlation energy functional as the remaining unknown. Our efforts concentrate on finding a correlation potential such that exact ionization potentials and electron affinities can be reproduced as orbital energies. The equation-of-motion coupled-cluster approach enables us to define an effective Hamiltonian from which a correlation potential can be extracted. We also make the connection to electron propagator theory. The disadvantage of the latter is the inherit energy dependence of the potential resulting in a different Hamiltonian for each orbital. Alternatively, the Fock space coupled-cluster approach employs an effective Hamiltonian which is energy independent and universal for all orbitals. A correlation potential is extracted which yields the exact ionization potentials and electron affinities and a set of associated molecular orbitals. We also describe the close relationship to Brueckner theory.

Abstract: We have reformulated the quantum Monte Carlo (QMC) technique so that a large part of the calculation scales linearly with the number of atoms. The reformulation is related to a recent alternative proposal for achieving linear-scaling QMC, based on maximally localized Wannier orbitals (MLWO), but has the advantage of greater simplicity. The technique we propose draws on methods recently developed for linear-scaling density functional theory. We report tests of the new technique on the insulator MgO, and show that its linear-scaling performance is somewhat better than that achieved by the MLWO approach. Implications for the application of QMC to large complex systems are pointed out.

Abstract: Electron-conducting quantum-dot solids can be prepared on the basis of assemblies of colloidal insulating nanocrystals if electrons can be injected in the delocalized conduction orbitals. We discuss the energetics of electron injection in such an artificial solid consisting of weakly coupled quantum dots. We show that quantum confinement and electron–electron repulsion determine the charging characteristics. The electron–electron repulsion energy can be screened by three-dimensional charge compensation from trapped holes or positive inert ions inserted in the assembly. We present experimental results on the electron storage and long-range transport in assemblies of ZnO nanocrystals in which the electron charge is compensated by positive ions. The electron–electron repulsion energy in assemblies permeated with an aqueous electrolyte solution is strongly screened. In contrast, the repulsion energy is about 100 meV in aprotic solvents; the repulsion energy strongly influences electron storage and the characteristics of long-range electron transport.

Abstract: We present a new linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any localization method of choice and on the use of orbital-specific basis sets. The full set of localized orbitals of a large molecule is seen as an orbital mosaic where each tessera is made of only a few of them. The orbital tesserae are computed out of a set of embedded cluster pseudoeigenvalue coupled equations which are solved in a building-block self-consistent fashion. In each iteration, the embedded cluster equations are solved independently of each other and, as a result, the method is parallel at a high level of the calculation. In addition to full system calculations, the method enables to perform simpler, much less demanding embedded cluster calculations, where only a fraction of the localized molecular orbitals are variational while the rest are frozen, taking advantage of the transferability of the localized orbitals of a given localization method between similar molecules. Monitoring single point energy calculations of large poly(ethylene oxide) molecules and three dimensional carbon monoxide clusters using an extended Huckel Hamiltonian are presented.

Abstract: The communication channels of information theory are generated for simple orbital models, in which each atom contributes a single atomic orbital (AO) to form the chemical bonds in the molecule. The 2- and 3-AO models represent the prototype chemical bonds in a diatomic molecule and in a symmetrical transition-state complex, respectively. The representative conjugated π bond systems (butadiene and benzene) in the Huckel approximation are also examined. Several entropy/information concepts introduced in Part I of this series (preceding article of this issue), including the conditional entropy, mutual information and information distance (entropy deficiency) quantities involving the input and output probability distributions of molecular communication systems in the atomic/orbital resolution, are used to characterize the chemical bond and its covalent and ionic components. The two-orbital model is used to generate representative atoms-in-molecules (AIM) information networks for both the orbital and spin prob...

Abstract: The influence of relaxations of atoms making up the DNA and atoms attached to it on radiation-induced cellular DNA damage by photons was studied by very detailed Monte Carlo track structure calculations, as an unusually high importance of inner shell ionizations for biological action was suspected from reports in the literature. For our calculations cross sections for photons and electrons for inner shell orbitals were newly derived and integrated into the biophysical track structure simulation programme PARTRAC. Both the local energy deposition in a small sphere around the interacting relaxed atom, and the number of relaxations per Gy and Gbp were calculated for several target geometries and many monoenergetic photon irradiations. Elements with the highest order number yielded the largest local energy deposition after interaction. The atomic relaxation after ionization of the L1 shell was found to be more biologically efficient than that of the K shell for high Z atoms. Generally, the number of inner shell relaxations produced by photon irradiation was small in comparison to the total number of double strand breaks generated by such radiation. Furthermore, the energy dependence of the total number of photon-induced and electron-induced relaxations at the DNA atoms does not agree with observed RBE values for different biological endpoints. This suggests that the influence of inner shell relaxations of DNA atoms on radiation-induced DNA damage is in general rather small.

Abstract: The characteristic features of molecules like polyhedra and fullerenes, which follow the 2(N+1)(2) rule of spherical aromaticity, can be related to energetically stable closed-shell configurations of (pseudo-)atoms. This unifying view relies on a thought experiment, which produces a polyhedron in a two-step process and which can, in turn, relate the electronic configuration of any spherical polyhedron to the one of a corresponding closed-shell atom. In the first step, the electronic ground-state configuration is identified. In the second step, a group theoretical analysis can be carried out; this relates the spherically symmetric atomic orbitals to the molecular orbitals classified according to the irreducible representations of the point group of the polyhedron under consideration. This procedure explains and justifies the pseudo-l classification of molecular orbitals, which is the basis of the 2(N+1)(2) rule. For the transition from the electronic configuration of the rare gas Eka-Rn (Uuo) to the icosahedral fullerene C(20) (2+), we show how a change in the ground-state configuration leads to the phenomenologically found 2(N+1)(2) rule for spherically aromatic fullerenes.

Abstract: The analysis of the orbital interaction between an alkali metal ion and the surrounding solvent molecules is performed for aqueous solutions of Li+, Na+, and K+, by means of the ab initio MO method with the aid of the quantum mechanical (QM)/molecular mechanics (MM) method. A total of 171 water molecules are included for each system. The effect of Li+ orbitals reaches as far as 6 A 7 A for Na+; and 9 A for K+. This effect is caused by the orbital interactions between the valence orbitals of an alkali metal ion and of the surrounding water molecules. The electrostatic interaction and the orbital interaction must not be neglected. The difference in the effect between the alkali metal ions originates from the difference in the valence orbital extensions of the alkali metal ions.

Abstract: Calculations of formation energies of the ionized water clusters and energies of reactions between small (including less than eight water molecules) neutral and positively ionized water chisters are presented. Moreover, we discuss some reaction paths between neutral and positively charged dimers, trimers and tetramers and proton transfer reactions (PTR) between cyclic clusters and H3O+ ions which can appear in beam, experiments on formation and ionization of water clusters. Calculations were made using ab initio Hartree-Fock method for 4–31G and 6–311G** atomic orbitals basis sets.