Abstract: Molecular electronic states energetically below the highest occupied molecular orbital (HOMO) should contribute to laser-driven high harmonic generation (HHG), but this behavior has not been observed previously. Our measurements of the HHG spectrum of N2 molecules aligned perpendicular to the laser polarization showed a maximum at the rotational half-revival. This feature indicates the influence of electrons occupying the orbital just below the N2 HOMO, referred to as the HOMO-1. Such observations of lower-lying orbitals are essential to understanding subfemtosecond/subangstrom electronic motion in laser-excited molecules.

Abstract: New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are inluded as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.

Abstract: We investigate the topological insulating states of the $p$-band systems in optical lattices induced by the on site orbital angular momentum polarization, which exhibit gapless edge modes in the absence of Landau levels. This effect arises from the energy-level splitting between the on site ${p}_{x}+i{p}_{y}$ and ${p}_{x}\ensuremath{-}i{p}_{y}$ orbitals by rotating each optical lattice site around its own center. At large rotation angular velocities, this model naturally reduces to two copies of Haldane's quantum Hall model. The distribution of the Berry curvature in momentum space and the quantized Chern numbers are calculated. The experimental realization of this state is feasible.

Abstract: The frozen natural orbital (FNO) coupled-cluster method increases the speed of coupled-cluster (CC) calculations by an order of magnitude with no consequential error along a potential energy surface. This method allows the virtual space of a correlated calculation to be reduced by about half, significantly reducing the time spent performing the coupled-cluster (CC) calculation. This paper reports the derivation and implementation of analytical gradients for FNO-CC, including all orbital relaxation for both noncanonical and semicanonical perturbed orbitals. These derivatives introduce several new orbital relaxation contributions to the CC density matrices. FNO-CCSD(T) and FNO-ΛCCSD(T) are applied to a test set of equilibrium structures, verifying that these methods are capable of reproducing geometries and vibrational frequencies accurately, as well as energies. Several decomposition pathways of nitroethane are investigated using CCSD(T) and ΛCCSD(T) with 60% of the FNO virtual orbitals in a cc-pVTZ basis,...

Abstract: Based on density functional theory, we have developed a program code to investigate the electron transport characteristics for a variety of nanometer scaled devices in the presence of an external bias voltage. We employed basis sets comprised of linear combinations of numerical type atomic orbitals, particularly focusing on k-point sampling for the realistic modeling of the bulk electrode. The scheme coupled with the matrix version of the nonequilibrium Green's function method enables calculation of the transmission coefficients at a given energy and voltage in a self-consistent manner as well as the corresponding current-voltage (I-V) characteristics. This scheme has advantages because it is applicable to large systems, easily transportable to different types of quantum chemistry packages, and extendable to time-dependent phenomena or inelastic scatterings. It has been applied to diverse types of practical electronic devices such as carbon nanotubes, graphene nanoribbons, metallic nanowires, and molecular electronic devices. The quantum conductance phenomena for systems involving quantum point contacts and I-V curves for a single molecule in contact with metal electrodes using the k-point sampling method are described.

Abstract: We study the hydrogen tunneling problem in a model system that represents the active site of the biological enzyme, soybean lipoxygenase-1. Toward this, we utilize quantum wavepacket dynamics performed on potential surfaces obtained by using hybrid density functional theory under the influence of a dynamical active site. The kinetic isotope effect is computed by using the transmission amplitude of the wavepacket, and the experimental value is reproduced. By computing the hydrogen nuclear orbitals (eigenstates) along the reaction coordinate, we note that tunneling for both hydrogen and deuterium occurs through the existence of distorted, spherical s-type proton wave functions and p-type polarized proton wave functions for transfer along the donor-acceptor axis. In addition, there is also a significant population transfer through distorted p-type proton wave functions directed perpendicular to the donor-acceptor axis (via intervening π-type proton eigenstate interactions) which underlines the three-dimensional nature of the tunneling process. The quantum dynamical evolution indicates a significant contribution from tunneling processes both along the donor-acceptor axis and along directions perpendicular to the donor-acceptor axis. Furthermore, the tunneling process is facilitated by the occurrence of curve crossings and avoided crossings along the proton eigenstate adiabats.

Abstract: The hydrogen adsorption in porous Prussian blue analogues shows the highest value for copper, suggesting the possibility that a direct interaction between the copper atom and the hydrogen molecule is established. The bonding of copper (2+) to the CN group of cyanometallates shows a unique behavior. The trend of copper to receive electrons in its 3d hole to adopt an electronic configuration close to 3d10 is complemented by the ability of the CN group to donate electrons from its 5σ orbital, which has certain antibonding character. Because of this cooperative effect, the electronic configuration of the copper atom at the cavity surface is close to Cu(+). The resulting large availability of electron density on the copper atom favors its interaction with the antibonding σ* orbital of the hydrogen molecule. The charge removed from the metal t2g orbitals is compensated (donated) by H2 through a side-on σ interaction. From these combined mechanisms, where H2 behaves as an acceptor−donor ligand for the copper ato...

Abstract: A fully atomic orbital (AO)-based reformulation of second-order Moller–Plesset perturbation theory (MP2) energy gradients is introduced, which provides the basis for reducing the computational scaling with the molecular size from the fifth power to linear Our formulation avoids any transformation between the AO and the molecular orbital (MO) basis and employs pseudodensity matrices similar to the AO-MP2 energy expressions within the Laplace scheme for energies The explicit computation of perturbed one-particle density matrices emerging in the new AO-based gradient expression is avoided by reformulating the Z-vector method of Handy and Schaefer [J Chem Phys 81, 5031 (1984)] within a density matrix-based scheme

Abstract: The temporary anion states of trimethyl phosphate and several compounds bearing the PO group were explored using electron transmission spectroscopy and ab initio calculations to determine if these states have the characteristics of the π* resonances usually associated with multiple bonds. No evidence was found for this in (CH3O)3PO and, by extension, we do not expect them to appear in the phosphate group of DNA. Cl3PO, however, does display such characteristics to some extent, and we show that they arise from the spatial properties of the σ* (P−Cl) orbitals rather than from multiple PO bonding. A novel computational means to explore effects due to the relative size of a molecular orbital and that of the angular momentum barrier responsible for confining the additional electron is presented.

Abstract: We determine the equation of state of stoichiometric FeO by employing the diffusion Monte Carlo method. The fermionic nodes are fixed by a single Slater determinant of spin-unrestricted orbitals. The calculated ambient-pressure properties (lattice constant, bulk modulus, and cohesive energy) agree very well with available experimental data. At approximately 65 GPa, the atomic lattice changes from the rocksalt B1 to the NiAs-type inverse B8 structure.

Abstract: National Science Foundation of China [20673104, 50121202]; National Basic Research Program of China [2004CB719901, 2006CB922004]

Abstract: We extend the shell model Monte Carlo approach to heavy deformed nuclei using a new proton-neutron formalism. The low excitation energies of such nuclei necessitate low-temperature calculations, for which a stabilization method is implemented in the canonical ensemble. We apply the method to study a well-deformed rare-earth nucleus, {sup 162}Dy. The single-particle model space includes the 50-82 shell plus 1f{sub 7/2} orbital for protons and the 82-126 shell plus 0h{sub 11/2}, 1g{sub 9/2} orbitals for neutrons. We show that the spherical shell model reproduces well the rotational character of {sup 162}Dy within this model space. We also calculate the level density of {sup 162}Dy and find it to be in excellent agreement with the experimental level density, which we extract from several experiments.

Abstract: The mathematical apparatus of quantum-mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU(2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, nowadays plays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory—and of its extension to other Lie and quantum groups—by using the collective term of 'spin networks'. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper, we list and discuss some aspects of these developments—such as for instance the hyperquantization algorithm—as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.

Abstract: The total electron density distribution of an isolated atom or an atom in a molecule does not reveal an atomic shell structure. Many localization functions, such as the radial averaged electron density, the Laplacian of the electron density, or the electron localization function have been proposed to visualize and analyze the shell structure of atoms. It was found that for light main group elements the correct number of shells is revealed by such functions. Later it was recognized that for heavy main group elements and for transition metals many of these diagnostic tools fail to reveal the full set of electronic shells as expected from the periodic table. In this work we focus on the radial structure of isolated atoms as revealed by the Laplacian of the electron density. We will demonstrate that it is the nodal structure of the orbitals of the inner shells which is responsible for the diminishing of at least one valence shell of third row transition metal atoms. Particular attention is paid to the effect of different electronic configurations on the shell structure of atoms and the question if the changes observed in the Laplacian of the radial density are sufficiently large for experimental studies on the topology of the electron density. Our presentation is as general as possible and, hence, employs a fully relativistic, i.e., four-component picture and a multiconfigurational ansatz for the wave function, which is thus valid for the whole periodic table of elements.

Abstract: The valence-shell electron momentum distributions for 1-butene are measured by electron momentum spectroscopy (EMS) employing non-coplanar symmetric geometry. The experimental electron momentum distributions are compared with the density functional theory (DFT) calculations using different-sized basis sets. Although the two conformers of 1-butene in the gas phase, namely the skew and syn, have very close ionization potentials, the electron momentum distributions, especially in the low momentum region, can show prominent differences for some of the valence orbitals. By comparing the experimental electron momentum profiles with the theoretical ones, the skew conformer is found to be more stable than the syn and their relative abundances at room temperature are estimated to be (69 ± 6)% and (31 ± 6)%, respectively. It demonstrates that EMS has the latent potential to study the relative stability of conformers.

Abstract: We use group theory to classify the superconducting states of systems with two orbitals on a tetragonal lattice. The orbital part of the superconducting gap function can be either symmetric or antisymmetric. For the orbital symmetric state, the parity is even for spin singlet and odd for spin triplet; for the orbital antisymmetric state, the parity is odd for spin singlet and even for spin triplet. The gap basis functions are obtained with the use of the group chain scheme by taking into account the spin-orbit coupling. In the weak pairing limit, the orbital antisymmetric state is only stable for the degenerate orbitals. Possible application to iron-based superconductivity is discussed.

Abstract: The Fisher–Shannon information and a statistical measure of complexity are calculated in position and momentum spaces for the wavefunctions of the quantum isotropic harmonic oscillator. We show that these quantities are independent of the strength of the harmonic potential. Moreover, for each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the classical (circular) orbits in the Bohr-like quantum image, just those with the highest orbital angular momentum.

Abstract: Acetonitrile molecules are known for their intriguing ability to accommodate an excess electron in either a diffuse dipole-bound orbital, away from the valence electrons, or in its valence orbitals, depending on the environment. In this work, we report a computational investigation of the monomer and dimer acetonitrile anions, with the main goal of gaining further insight into the unusual electronic structure of these species. To this end, the topology of the electron density distribution has been examined in detail with the quantum theory of atoms in molecules (AIM). The excess electron is found to affect the topology of the electron density very differently for two dipole-bound-electron isomers of the acetonitrile dimer anion: for the head-to-tail isomer, the electron density simply decays away from the atomic nuclei, and the presence of the excess electron only manifests itself in the Laplacian of the electron density as a very diffuse region of “dipole-bound” charge concentration; in contrast, for th...

Abstract: We have performed a joint experimental and theoretical study of the unoccupied electronic structure of alkali adsorbates on the (111) surfaces of Cu and Ag. Combining angle- and time-resolved two-photon photoemission spectroscopy with wave packet propagation calculations we show that, along with the well known sigma resonance oriented along the surface normal, there exist long-lived alkali-localized resonances oriented parallel to the surface (pi symmetry). These new resonances are stabilized by the projected band gap of the substrate and emerge primarily from the mixing of the p and d Rydberg orbitals of the free alkali atom modified by the interaction with the surface.

Abstract: The density matrix formulation of the nuclear-electronic orbital explicitly correlated Hartree–Fock (NEO-XCHF) approach for including electron-proton correlation in mixed nuclear-electronic wave functions is presented. This approach is based on a general ansatz for the nuclear-electronic wave function that includes explicit dependence on the nuclear-electronic distances with Gaussian-type geminal functions. The NEO-XCHF approach is extended to treat multielectron, multiproton systems and to describe a broader class of systems that require a more general form of the wave function, such as open-shell and multireference wave functions. General expressions are derived for the one-particle and two-particle densities, as well as the total energy. In addition, expressions for the total energy and Fock matrices in an atomic orbital basis are derived for the special case of a closed-shell electronic system. The resulting Hartree–Fock–Roothaan equations can be solved iteratively to self consistency. An advantage of the density matrix representation is that it facilitates the development of approximate NEO-XCHF methods in which specified high-order density terms are neglected to decrease the computational expense. Another advantage of the density matrix representation is that it provides the foundation for the development of electron-proton functionals within the framework of density functional theory, thereby enabling a consistent treatment of both electron-electron and electron-proton correlation in a computationally practical manner.

Abstract: The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the quantum isotropic harmonic oscillator. We show that these magnitudes are independent of the strength of the harmonic potential. Moreover, for each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the classical (circular) orbits in the Bohr-like quantum image, just those with the highest orbital angular momentum.

Abstract: We report all-electron and pseudopotential calculations of the ground-stateenergies of the neutral Ne atom and the Ne+ ion using the variational and diffusion quantum Monte Carlo (DMC) methods. We investigate different levels of Slater-Jastrow trial wave function: (i) using Hartree-Fock orbitals, (ii) using orbitals optimized within a Monte Carlo procedure in the presence of a Jastrow factor, and (iii) including backflow correlations in the wave function. Small reductions in the total energy are obtained by optimizing the orbitals, while more significant reductions are obtained by incorporating backflow correlations. We study the finite-time-step and fixed-node biases in the DMC energy and show that there is a strong tendency for these errors to cancel when the first ionization potential (IP) is calculated. DMC gives highly accurate values for the IP of Ne at all the levels of trial wave function that we have considered.

Abstract: We present an analytic scheme for the calculation of pure vibrational contributions to linear and nonlinear optical properties such as the polarizability and the first and second hyperpolarizabilities. The formalism is fully expressed in terms of a perturbation- and time-dependent atomic orbital basis, using the elements of the density matrix in the atomic orbital basis as the basic variables. We calculate perturbed densities up to third order with respect to the electric field in accordance with the n + 1 rule, and the approach is therefore applicable for the calculation of pure vibrational contributions involving all vibrational coordinates in large molecular complexes. In the case of static electric fields, we therefore only need to calculate 19 response equations, independent of the size of the molecule. If we can determine the molecular energy and force field, the calculation of pure vibrational contributions to the nonlinear optical properties of the molecule is therefore a rather straightforward task. We illustrate the implementation by calculating pure vibrational contributions to the first and second hyperpolarizabilities of molecules containing up to 66 atoms using basis sets of good quality.

Abstract: The pseudorotation of tetrahydrofuran (THF) (C4H8O) has been studied using density functional theory, with respect to the valence orbital responses to the ionization potentials and to orbital electron and momentum distributions. Three conformations of THF, the global minimumstructure Cs, local minimum structure C2, and a transition state structure C1, which arecharacteristic configurations on the potential energy surface, are examined using the SAOP∕et-pVQZ//B3LYP∕6-311++G** models with the aforementioned dual space analysis. It is noted in the ionization energy spectra that the minimum structures Cs and C2 are not directly connected by pseudorotation, but through the transition state structure C1. As a result, some orbitals of the Cs conformer are able to “correlate” to orbitals of the C2 conformer without a strict symmetry constraint, i.e., orbital 7a′ of the Cs conformer is correlated to orbital 5b of the C2 conformer. It is also noted that although the valence orbital ionization potentials are not significantly altered by the pseudorotation of THF, their spectra (mainly due to excitation) are quite different indeed. Detailed orbital analysis based on dual space analysis is given. The valence orbital behavior of the conformations is orbital dependent. It can be approximately divided into three groups: the “signature group” is associated with orbitals experiencing significant changes. The frontier orbitals are in this group. The “nearly identical group” includes orbitals without apparent changes across the conformations. Most of the orbitals showing a certain degree of distortion during the pseudorotation process belong to the third group. The present study demonstrates that a comprehensive understanding of the pseudorotation of THF and its dynamics requires multidimensional information and that the information gained from momentum space is complementary to that from the more familiar coordinate space.

Abstract: The molecular communication channels of Information Theory (IT) are constructed within the orbital description of molecular electronic structure using the superposition principle of quantum mechanics. Two types of such information systems are introduced, called the “geometric” and “physical” channels. The communication network of the former is determined by all molecular orbitals (MO), occupied and virtual, which result from the specified set of atomic orbitals (AO). The geometric channel thus reflects the relative “rotation” of MO relative to AO in the molecular Hilbert space, and the associated “promotion” of AO in the molecule due to the probability scattering via the communication network generated by the complete set of MO. They are devoid of the physical content embodied in the MO-occupations, which distinguish one electron configuration of the molecule from another. The latter information is included in the physical AO-promotion channels, which involve the probability scattering via the occupied MO alone. The probability conditioning is shown to be related to the appropriate projection in the orbital Hilbert space. The geometric and the physical (ground-state) bond indices of the conditional-entropy (IT-covalency) and mutual-information (IT-ionicity) are generated for the 2-AO model and selected π-electron systems (ethylene, allyl, butadiene, and benzene) in the Huckel approximation. They are shown to compare favorably with the previously reported IT bond-orders obtained from the two-electron molecular information channels in atomic resolution.

Abstract: The scattering unit of X-ray crystal structure analysis is changed from atoms to the subshell electrons by X-ray atomic orbital analysis (XAO). All the atoms in the unit cell are divided into groups of subshell electrons in the XAO analysis. Each subshell is treated as an independent pseudo-atom, which enables the atomic orbitals (AO's) and the electron population of each AO expressed as a linear combination of s/p/d/f orbitals in each subshell to be determined. When the environmental condition of the sample is varied, the electron transfer among the AO's in the crystal can be traced with XAO. It is applicable mainly to analyses of the electron-density distribution in ionic solids including those with a nonstoichiometric structure. The expansion coefficients of each AO are calculated with the perturbation theory putting a point charge on each atom in the unit cell. This automatically makes the perturbation potential have the point-group symmetry of the atom in the crystal field. Then the coefficients of each AO are refined to fit to the observed structure factors keeping the orthonormal relationships among the AO's. Complex basis functions with α or β spin as well as real ones are employed for heavy atoms and the relationships among the coefficients for the AO's of an electron in the crystal fields of the 32 point-group symmetries are derived for p, d and f orbitals. The AO's thus derived can be applicable to an anti-symmetrized multi-electron system, although X-ray diffraction cannot specify the atomic terms occupied when the crystal symmetry permits the atom to have many terms.

Abstract: For 12 alkali and alkaline earth metal atoms from Li to Ra, contracted Gaussian-type function sets are developed for the description of correlations among the (n−1)s, (n−1)p, and ns electrons, where n is the principal quantum number of the outermost shell. A segmented contraction scheme is employed for the compactness and efficiency. Contraction coefficients and exponents are determined so that the deviation from accurate natural orbitals of the ground states is minimized. For heavy atoms from Cs to Ra, the spin-free relativistic effects are considered through the third-order Douglas–Kroll approximation. To test the present correlating sets, all-electron calculations are performed for the ground state of 12 diatomic hydrides, 6 alkali metal dimers, 4 alkaline earth metal oxides, and 12 diatomic fluorides. The calculated spectroscopic constants are in excellent agreement with the experimental values.