Calculations of molecular ionization energies using a self‐consistent‐charge Hartree–Fock–Slater method

Unified construction of relativistic Hamiltonians

It is shown that the four-component (4C), quasi-four-component (Q4C), and exact two-component (X2C) relativistic Hartree-Fock equations can be implemented in a unified manner by making use of the atomic nature of the small components of molecular 4-spinors. A model density matrix approximation can first be invoked for the small-component charge/current density functions, which gives rise to a static, pre-molecular mean field to be combined with the one-electron term. As a result, only the nonrelativistic-like two-electron term of the 4C/Q4C/X2C Fock matrix needs to be updated during the iterations. A "one-center small-component" approximation can then be invoked in the evaluation of relativistic integrals, that is, all atom-centered small-component basis functions are regarded as extremely localized near the position of the atom to which they belong such that they have vanishing overlaps with all small- or large-component functions centered at other nuclei. Under these approximations, the 4C, Q4C, and X2C mean-field and many-electron Hamiltonians share precisely the same structure and accuracy. Beyond these is the effective quantum electrodynamics Hamiltonian that can be constructed in the same way. Such approximations lead to errors that are orders of magnitude smaller than other sources of errors (e.g., truncation errors in the one- and many-particle bases as well as uncertainties of experimental measurements) and are, hence, safe to use for whatever purposes. The quaternion forms of the 4C, Q4C, and X2C equations are also presented in the most general way, based on which the corresponding Kramers-restricted open-shell variants are formulated for "high-spin" open-shell systems.

Characterization of the charge transfer luminescence of the [WO6]6- octahedron in Ca3WO6 and the [WO5]4- square pyramid in Ca3WO5Cl2

Charge transfer (CT) luminescence of different types of polyhedra, [WO₅]^4- in Ca₃WO₅Cl₂ and [WO₆]^6- in Ca₃WO₆, is characterized by spectroscopic experiments and ab initio calculations. According to the geometry optimization, W⁶⁺ ions form five-fold [WO₅]^4- square pyramids in Ca₃WO₅Cl₂ because of a large interatomic distance between W⁶⁺ and Cl^- of 3.266 Å. The analysis of the density of electronic states reveals the ionic character of Cl^- ions to the W⁶⁺ ions in the Ca₃WO₅Cl₂ lattice, resulting in the observed broad luminescence band peak at 488 nm of the single-crystal Ca₃WO₅Cl₂ sample being assigned to the CT transition in the [WO₅]^4- square pyramid. Compared with the [WO₆]^6- octahedron in Ca₃WO₆, the [WO₅]^4- square pyramid shows an inconsistent CT energy shift: higher CT absorption and lower luminescence energies. The larger bandgap brings about higher absorption energy due to the structural and compositional features of the orthorhombic Ca₃WO₅Cl₂. The redshifted CT luminescence band and small activation energy for the thermal quenching of the Ca₃WO₅Cl₂ sample are explained, assuming that the CT states of the anisotropic [WO₅]^4- square pyramid take a larger offset in the configurational coordinate diagram than the [WO₆]^6- octahedron.

The fractal geometry of Hartree-Fock

The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. In our case, a complex parameter λ controls the strength of the electron-electron interaction. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well.

Electronic Structure of Doped Buckminsterfullerene

Molecular cluster calculations within the local density approximation have been performed in a study of the electronic structure of the C60 molecule - “Buckminsterfullerene” doped with K, B and N. Calculations for the KC60 molecule, with the K atom located at the centre of the cage as well as at different positions inside or outside the cage, show how the valence 4s electron is transferred to the LUMO state of the bare C60 molecule. Doping with a B or N atom located at the centre of the cage creates a molecule with a partly occupied level of 2p character in the HOMO and LUMO gap, similar to donor and acceptor levels in the band gap of traditionally doped semiconductors. Doping by substitution of one or two of the carbon atoms in the cage with X = B or N, as modelled with the C59 X1 or C58X2 clusters, gives a different structure with a splitting of the HOMO and LUMO levels in the pure C60 molecule and with the creation of acceptor and donor levels with the substitution of B and N, respectively.

The bond character of rutile type SiO2, GeO2 and SnO2 investigated by molecular orbital calculation

Molecular orbital calculations using descrete-variational Xα method were carried out in order to investigate the bond nature of SiO2, GeO2 and SnO2. The bond overlap populations and the d-orbital populations of cations were decreased with increasing the atomic number. The deformation density maps of electronic charge show the accumulation of electron in interatomic region which is most dominant in SiO2. The calculated density of states indicates that the bond character of SiO2 is more covalent than that of GeO2 and SnO2. From the excited d-electron partial density of states, it is inferred that the Si excited-3d has some connection with the bond nature of SiO2 covalency.

Multiplet calculations of L(2,3) x-ray absorption near-edge structures for 3d transition-metal compounds

The purpose of this work is to compare the two different procedures to calculate the L(2,3) x-ray absorption spectra of transition-metal compounds: (1) the semi-empirical charge transfer multiplet (CTM) approach and (2) the ab initio configuration-interaction (CI) method based on molecular orbitals. We mainly focused on the difference in the treatment of ligand field effects and the charge transfer effects in the two methods. The reduction of multiplet interactions due to the solid state effects has been found by the ab initio CI approach. We have also found that the mixing between the original and the charge transferred configurations obtained by the ab initio CI approach is smaller than that obtained by the CTM approach, since charge transfer through the covalent bonding between metal and ligand atoms has been included by taking the molecular orbitals as the basis functions.

Dynamics of Clusters Initiated by Photon and Surface Impact

Clusters of atoms/molecules show dynamics characteristic of the method of excitation. Two contrasted processes are discussed: (1) electronic excitation via single-photon absorption and (2) impulsive excitation of nuclear motions by surface impact. Process 1 is exemplified by photodissociation dynamics of size-selected metal cluster ions. The electronic energy is converted most likely to vibrational energy of internal modes; dissociation follows via statistical mechanism to produce energetically favored fragments. Exceptionally, a silver cluster ion, Ag4(+), is shown to undergo nonstatistical dissociation along the potential-energy surface of the excited state. Energy partitioning to translational and vibrational modes of fragments is analyzed as well as bond dissociation energies. Furthermore, the spectrum of the photodissociation yield provides electronic and geometrical structures of a cluster with the aid of ab initio calculations; manganese, Mn(N)(+), and chromium, Cr(N)(+), cluster ions are discussed, where the importance of magnetic interactions is manifested. On the other hand, momentum transfer upon surface impact plays a role in process 2. An impulsive mechanical force triggers extraordinary chemical processes distinct from those initiated by atomic collision as well as photoexcitation. Experiments on aluminum, Al(N)(-), silicon, SiN(-), and solvated, I(2)(-)(CO2)(N), cluster anions provide evidence for reactions proceeding under extremely high temperatures, such as pickup of surface atoms, annealing of products, and mechanical splitting of chemical bonds. In addition, a model experiment to visualize and time-resolve the cluster impact process is performed by using a micrometer-sized liquid droplet. Multiphoton absorption initiates superheating of the droplet surface followed by a shock wave and disintegration into a number of small fragments (shattering). These studies further reveal how the nature of chemical bonds influences the dynamics of clusters.

Dipole moments from atomic-number-dependent potentials in analytic density-functional theory

Molecular dipole moments of analytic density-functional theory are investigated. The effect of element-dependent exchange potentials on these moments are examined by comparison with conventional quantum-chemical methods and experiment for the subset of the extended G2 set of molecules that have nonzero dipole moment. Fitting the Kohn-Sham [Phys. Rev. 140, A1133 (1965)] potential itself makes a mean absolute error of less than 0.1 D. Variation of alpha (Slater's [Phys. Rev. 81, 385 (1951)] exchange parameter) values has far less effect on dipole moments than on energies. It is argued that in variable alpha methods one should choose the smaller of the two rather than the geometric mean of the two alpha values for the heteroatomic part of the linear-combination-atomic-orbital density. Calculations on the dipole moment of NH(2)(CH)(24)NO(2) are consistent with earlier calculations and show that varying the differences between alpha values for atoms with different atomic numbers has only short-ranged electrostatic effects.

First-principles multi-electron calculations for L2,3 ELNES/XANES of 3d transition metal monoxides

A computational method having quantitatively predictive performance of L(2,3) ELNES/XANES of 3d transition metal (TM) compounds without any empirical parameter is given. Calculations are made on three TM monoxides with rock salt structures, MnO, FeO and CoO using model clusters composed of a TM ion with six coordinating oxide ions. Multi-electron wavefunctions are expressed by a linear combination of Slater determinants made by fully relativistic molecular orbitals for TM-2p, 3d and O-2p. Relative intensity and positions of subpeaks are in excellent agreement to experimental spectra. Our analyses of multi-electron eigenstates found that these subpeaks originate not from different one electron configurations but entirely from the multiplet effects. The dependence of the branching ratio on the formal number of 3d electrons agrees with that of an empirical atomic multiplet theory reported in literature.

Ab initio modeling of the interaction of electron beams and single-walled carbon nanotubes

Single-walled carbon nanotubes are readily observable in a scanning electron microscope, which traditional models fail to explain. We present an ab initio model to explain how the electron beam can interact with these structures despite the very small, nanoscale, interaction volume. In particular, we show how the electron beam can generate very strong secondary electron emission from the tip of a nanotube under external electric field. The approach may also be used in modeling the interaction of charged particles with nanostructures in other applications such as electron detection.

First-principles calculations for the cooperative transitions of Yb3+ dimer clusters in Y3Al5O12 and Y2O3 crystals

A first-principles multielectron method is applied to the calculations for the cooperative transitions of trivalent ytterbium ions (Yb3+) in yttrium aluminum garnet (Y3Al5O12; YAG) and yttrium sesquioxide (Y2O3) crystals. The method is based on a molecular-orbital method, in which the overlap between the Yb 4f and the oxygen 2p orbitals is directly considered through a self-consistent procedure. A Yb2(3+) two-ion model and a (Yb2O14)22- dimer cluster embedded in the point charges of the YAG lattice are compared. The 4f-2p overlaps in the cluster model is needed to explain the cooperative transition probability originating from electric dipole transitions. A (Yb2O10)14- dimer molecule in Y2O3 lattice produces larger electric dipole transition probabilities than the case of YAG. The smaller coordination number in Y2O3 produces the larger 4f-2p overlaps, which result in the larger transition probabilities.

Newly developed basis sets for density functional calculations

Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculated and compared with the experimental ones. The calculated values were also compared with those obtained using the previously available DZVP basis sets developed at the local-density functional level. Because the new basis sets work better than the previous ones, possible reasons of this behavior are analyzed. The newly developed basis sets also provide a good estimation of other atomic properties such as ionization energies.

Surface structures of SrTiO3 (001): a TiO2-rich reconstruction with a c(4 x 2) unit cell

We report the solution of the c(4 x 2) reconstruction of SrTiO(3) (001), obtained through a combination of high-resolution transmission electron microscopy, direct methods analysis, and density functional theory. The structure is characterized by a single overlayer of TiO(2) stoichiometry in which TiO(5) polyhedra are arranged into edge-shared structures, in contrast to the corner-shared TiO(6) polyhedra in bulk. This structural pattern is similar to that reported by us earlier for the (2 x 1) reconstruction of the same crystal face formed at higher temperature. We discuss probable mechanisms of surface stabilization as revealed by these two solutions which are likely to apply to other reconstructions of SrTiO(3) (001) and, possibly, other perovskites in general.