Abstract: Basic mechanisms controlling orbital order and orbital fluctuations in transition metal oxides are discussed. The lattice driven classical orbital picture, e.g. like in manganites LaMnO 3 , is contrasted to the quantum behavior of orbitals in frustrated superexchange models as realised in pseudocubic titanites ATiO 3 and vanadates AVO 3 . In YVO 3 , the lattice and superexchange effects strongly compete - this explains the extreme sensitivity of magnetic states to temperature and doping. Lifting the t 2g orbital degeneracy by a relativistic spin-orbital coupling is considered on example of the layered cobaltates. We find that the spin-orbital mixing of low-energy states leads to unusual magnetic correlations in a triangular lattice of the CoO 2 parent compound. Finally, the magnetism of sodium-rich compounds Na 1-x CoO 2 is discussed in terms of a spin/orbital polaronic liquid.

Abstract: Special care is needed in carrying out combined quantum mechanical and molecular mechanical (QM/MM) calculations if the QM/MM boundary passes through a covalent bond. The present paper discusses the importance of correctly handling the MM partial point charges at the QM/MM boundary, and in particular, it contributes in two aspects: (1) Two schemes, namely, the redistributed charge (RC) scheme and the redistributed charge and dipole (RCD) scheme, are introduced to handle link atoms in QM/MM calculations. In both schemes, the point charge at the MM boundary atom that is replaced by the link atom is redistributed to the midpoint of the bonds that connect the MM boundary atom and its neighboring MM atoms. These redistributed charges serve as classical mimics for the auxiliary orbitals associated with the MM host atom in the generalized hybrid orbital (GHO) method. In the RCD scheme, the dipoles of these bonds are preserved by further adjustment of the values of the redistributed charges. The treatments are j...

Abstract: The fragment molecular orbital (FMO) method was combined with the multiconfiguration self-consistent-field (MCSCF) theory One- and two-layer approaches were developed, the former involving all dimer MCSCF calculations and the latter limiting MCSCF calculations to a small part of the system The accuracy of the two methods was tested using the six electrons in six orbitals complete active space type of MCSCF and singlet spin state for phenol+(H2O)n, n=16,32,64 (6-31G* and 6-311G* basis sets); α helices and β strands of phenylalanine-(alanine)n, n=4,8,16 (6-31G*) Both double-ζ and triple-ζ quality basis sets with polarization were found to have very similar accuracy The error in the correlation energy was at most 0000 88 au, the error in the gradient of the correlation energy was at most 6×10−5 au/bohr and the error in the correlation correction to the dipole moment was at most 0018 D In addition, vertical singlet-triplet electron excitation energies were computed for phenol+(H2O)n, (n=16,32,64),

Abstract: We report magnetic field spectroscopy measurements in carbon nanotube quantum dots exhibiting fourfold shell structure in the energy level spectrum. The magnetic field induces a large splitting between the two orbital states of each shell, demonstrating their opposite magnetic moment and determining transitions in the spin and orbital configuration of the quantum dot ground state. We use inelastic cotunneling spectroscopy to accurately resolve the spin and orbital contributions to the magnetic moment. A small coupling is found between orbitals with opposite magnetic moment leading to anticrossing behavior at zero field.

Abstract: The two-orbital degenerate Hubbard model with distinct hopping integrals is studied by combining dynamical mean-field theory with quantum Monte Carlo simulations. The role of orbital fluctuations for the nature of the Mott transition is elucidated by examining the temperature dependence of spin, charge, and orbital susceptibilities as well as the one-particle spectral function. We also consider the effect of the hybridization between the two orbitals, which is important particularly close to the Mott transition points. The introduction of the hybridization induces orbital fluctuations, resulting in the formation of a Kondo-like heavy-fermion behavior, similarly to $f$-electron systems, but involving electrons in bands of comparable width.

Abstract: For perfectly localized orbitals, the basins of ELF are the domains in which the probability of finding a pair of electrons is maximal.

Abstract: Electron transport properties of a $\mathrm{Si}/\mathrm{\text{organic-molecule}}/\mathrm{Si}$ junction are investigated by large-scale nonequilibrium Green function calculations The results provide a qualitative picture and quantitative understanding of the importance of self-consistent screening, broadening of quasimolecular orbitals under large bias, and enhancement of transmission, which occurs when the broadened lowest unoccupied molecular orbital aligns with the conduction band edge of the negative lead The varying coupling can lead to negative differential resistance for a large class of small molecules

Abstract: The generalized hybrid orbital (GHO) method has previously been formulated for combining molecular mechanics with various levels of quantum mechanics, in particular semiempirical neglect of diatomic differential overlap theory, ab initio Hartree-Fock theory, and self-consistent charge density functional tight-binding theory. To include electron-correlation effects accurately and efficiently in GHO calculations, we extend the GHO method to density functional theory in the generalized-gradient approximation and hybrid density functional theory (denoted by GHO-DFT and GHO-HDFT, respectively) using Gaussian-type orbitals as basis functions. In the proposed GHO-(H)DFT formalism, charge densities in auxiliary hybrid orbitals are included to calculate the total electron density. The orthonormality constraints involving the auxiliary Kohn-Sham orbitals are satisfied by carrying out the hybridization in terms of a set of Lowdin symmetrically orthogonalized atomic basis functions. Analytical gradients are formulated for GHO-(H)DFT by incorporating additional forces associated with GHO basis transformations. Scaling parameters are introduced for some of the one-electron integrals and are optimized to obtain the correct charges and geometry near the QM/MM boundary region. The GHO-(H)DFT method based on the generalized gradient approach (GGA) (BLYP and mPWPW91) and HDFT methods (B3 LYP, mPW1PW91, and MPW1 K) is tested-for geometries and atomic charges-against a set of small molecules. The following quantities are tested: 1) the C--C stretch potential in ethane, 2) the torsional barrier for internal rotation around the central C--C bond in n-butane, 3) proton affinities for a set of alcohols, amines, thiols, and acids, 4) the conformational energies of alanine dipeptide, and 5) the barrier height of the hydrogen-atom transfer between n-C4H10 and n-C4H9, where the reaction center is described at the MPW1 K/6-31G(d) level of theory.

Abstract: Publisher Summary This chapter summarizes the results of quantum chemical calculations where it has investigated the nature of the chemical bond in main-group and transition metal compounds with an energy decomposition analysis (EDA). The EDA decomposes the instantaneous interaction energy A –B between two fragments A and B into three terms that can be interpreted in a chemically meaningful way. The three terms are the quasi-classical electrostatic interaction between the frozen charges of the fragments ΔE elstat , the exchange (Pauli) repulsion between electrons possessing the same spin ΔE Pauli, , and the orbital interaction term ΔE orb . The latter term can be divided into contributions of orbitals having different symmetry, which allows an estimate of the strength of s, p, and d bonding. The results show that the quasi-classical electrostatic interaction significantly contributes to the bonding interactions in all molecules. The trend of the bond strength is in most cases correctly predicted by the orbital term ΔE orb but there are cases where the electrostatic attraction or the Pauli repulsion is more important for an understanding of the bonding interactions. The EDA is an unambiguously defined partitioning scheme that considers all terms yielding a chemical bond. The EDA can be considered as a bridge between the classical heuristic bonding models of chemistry and the physical mechanism of chemical bond formation.

Abstract: We derive a spin-orbital Hamiltonian for a triangular lattice of e_g orbital degenerate (Ni^{3+}) transition metal ions interacting via 90 degree superexchange involving (O^{2-}) anions, taking into account the on-site Coulomb interactions on both the anions and the transition metal ions. The derived interactions in the spin-orbital model are strongly frustrated, with the strongest orbital interactions selecting different orbitals for pairs of Ni ions along the three different lattice directions. In the orbital ordered phase, favoured in mean field theory, the spin-orbital interaction can play an important role by breaking the U(1) symmetry generated by the much stronger orbital interaction and restoring the threefold symmetry of the lattice. As a result the effective magnetic exchange is non-uniform and includes both ferromagnetic and antiferromagnetic spin interactions. Since ferromagnetic interactions still dominate, this offers yet insufficient explanation for the absence of magnetic order and the low-temperature behaviour of the magnetic susceptibility of stoichiometric LiNiO_2. The scenario proposed to explain the observed difference in the physical properties of LiNiO_2 and NaNiO_2 includes small covalency of Ni-O-Li-O-Ni bonds inducing weaker interplane superexchange in LiNiO_2, insufficient to stabilize orbital long-range order in the presence of stronger intraplane competition between superexchange and Jahn-Teller coupling.

Abstract: The orbital excitations of a series of transition-metal compounds are studied by means of optical spectroscopy. Our aim was to identify signatures of collective orbital excitations by comparison with experimental and theoretical results for predominantly local crystal-field excitations. To this end, we have studied TiOCl, RTiO3 (R = La, Sm and Y), LaMnO3, Y2BaNiO5, CaCu2O3 and K4Cu4OCl10, ranging from early to late transition-metal ions, from t2g to eg systems, and including systems in which the exchange coupling is predominantly three-dimensional, one-dimensional or zero-dimensional. With the exception of LaMnO3, we find orbital excitations in all compounds. We discuss the competition between orbital fluctuations (for dominant exchange coupling) and crystal-field splitting (for dominant coupling to the lattice). Comparison of our experimental results with configuration-interaction cluster calculations in general yields good agreement, demonstrating that the coupling to the lattice is important for a quantitative description of the orbital excitations in these compounds. However, detailed theoretical predictions for the contribution of collective orbital modes to the optical conductivity (e.g. the line shape or the polarization dependence) are required to decide on a possible contribution of orbital fluctuations at low energies, in particular, in case of the orbital excitations at ≈0.25 eV in RTiO3. Further calculations are called for which take into account the exchange interactions between the orbitals and the coupling to the lattice on an equal footing.

Abstract: The minimum-energy structures on the torsional potential-energy surface of 1,3-butadiene have been studied quantum mechanically using a range of models including ab initio Hartree-Fock and second-order Moller-Plesset theories, outer valence Green’s function, and density-functional theory with a hybrid functional and statistical average orbital potential model in order to understand the binding-energy (ionization energy) spectra and orbital cross sections observed by experiments. The unique full geometry optimization process locates the s-trans-1,3-butadiene as the global minimum structure and the s-gauche-1,3-butadiene as the local minimum structure. The latter possesses the dihedral angle of the central carbon bond of 32.81° in agreement with the range of 30°–41° obtained by other theoretical models. Ionization energies in the outer valence space of the conformer pair have been obtained using Hartree-Fock, outer valence Green’s function, and density-functional (statistical average orbital potentials) mod...

Abstract: A method for atomic-orbital orientation determination at each $k$ point has been developed. The three-dimensional Cu Fermi surface (FS) structure was measured and visualized by stacking a series of photoelectron intensity angular distribution (PIAD) at different photon energies. PIADs from the Cu(001) surface were obtained using a display-type analyzer and linearly polarized synchrotron radiation. The atomic orbitals composing the FS were determined to be mainly $4p$ orbitals with their axes pointing outward. Atomic orbital orientations at different $k$ coordinates on FS as well as the FS cross-section structures were revealed directly from experiment and were confirmed by ab initio calculation.

Abstract: The orbital excitations of a series of transition-metal compounds are studied by means of optical spectroscopy. Our aim was to identify signatures of collective orbital excitations by comparison with experimental and theoretical results for predominantly local crystal-field excitations. To this end, we have studied TiOCl, RTiO3 (R=La, Sm, Y), LaMnO3, Y2BaNiO5, CaCu2O3, and K4Cu4OCl10, ranging from early to late transition-metal ions, from t_2g to e_g systems, and including systems in which the exchange coupling is predominantly three-dimensional, one-dimensional or zero-dimensional. With the exception of LaMnO3, we find orbital excitations in all compounds. We discuss the competition between orbital fluctuations (for dominant exchange coupling) and crystal-field splitting (for dominant coupling to the lattice). Comparison of our experimental results with configuration-interaction cluster calculations in general yield good agreement, demonstrating that the coupling to the lattice is important for a quantitative description of the orbital excitations in these compounds. However, detailed theoretical predictions for the contribution of collective orbital modes to the optical conductivity (e.g., the line shape or the polarization dependence) are required to decide on a possible contribution of orbital fluctuations at low energies, in particular in case of the orbital excitations at about 0.25 eV in RTiO3. Further calculations are called for which take into account the exchange interactions between the orbitals and the coupling to the lattice on an equal footing.

Abstract: Ionization differential cross sections are presented for low energy electron scattering from the 1πg and 4σg orbitals of the tri-atomic molecule CO2, at incident electron energies ranging from 10 eV to 80 eV above the ionization threshold. The (e, 2e) experiments were conducted in a coplanar symmetric geometry, the outgoing electrons sharing the excess energy from the interaction equally. The results are compared to experiments previously conducted in the same geometry and over the same energy range from the 1πu and 3σg orbitals of N2. An unusual feature has been discovered ionizing from the 1πg orbital at a scattered and ejected electron energy of 10 eV, where a second forward scattering peak is found at low angles.

Abstract: The molecular dynamics with quantum transitions (MDQT) method is applied to study the fragmentation dynamics of neon clusters following vertical ionization of neutral clusters with 3 to 14 atoms. The motion of the neon atoms is treated classically, while transitions between the adiabatic electronic states of the ionic clusters are treated quantum mechanically. The potential energy surfaces are described by the diatomics-in-molecules model in a minimal basis set consisting of the effective 2p orbitals on each neon atom for the missing electron. The fragmentation mechanism is found to be rather explosive, with a large number of events where several atoms simultaneously dissociate. This is in contrast with evaporative atom by atom fragmentation. The dynamics are highly nonadiabatic, especially at shorter times and for the larger clusters. Initial excitation of the neutral clusters does not affect the fragmentation pattern. The influence of spin-orbit coupling is also examined and found to be small, except for the smaller size systems for which the proportion of the Ne+ fragment is increased up to 43%. From the methodological point of view, most of the usual momentum adjustment methods at hopping events are shown to induce nonconservation of the total nuclear angular momentum because of the nonzero electronic to rotation coupling in these systems. A new method for separating out this coupling and enforcing the conservation of the total nuclear momentum is proposed. It is applied here to the MDQT method of Tully but it is very general and can be applied to other surface hopping methods.

Abstract: Results of a study of the valence electronic structure of norbornene (C7H10), up to binding energies of 30 eV, are reported. Experimental electron momentum spectroscopy (EMS) and theoretical Green's function and density functional theory approaches were utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among the tested models, the combination of the Becke−Perdew functional and a polarized valence basis set of triple-ζ quality provides the best representation of the electron momentum distributions for all 19 valence orbitals of norbornene. This experimentally validated model was then used to extract other molecular properties of norbornene (geometry, infrared spectrum). When these calculated properties are compared to corresponding results from independent measurements, reasonable agreement is typically found. Due to the improved energy resolution, EMS is now at a stage to very finely image the effect...

Abstract: Important chemical reactions for life often require multistep electron transfers (ET) and strong reducing forces. In these reactions, electron transfer proteins as ferredoxins (Fds) play a key role. For elucidation of the core electronic states in these electron transfer processes, an inorganic model compound [Fe2S2(S2-o-xyl)2] is used as our first study. It was experimentally characterized that the model compound is in a similar electronic state to the active site core in Fds. On the reduced form, the diiron core exists in a characteristic mixed-valence state that has mobile electron (spin). Hybrid density functional theory (HDFT) calculations are performed to investigate the chemical bond nature, electronic structures, and magnetic interactions. The spin states and energy levels are further discussed with spin Hamiltonians, which contain Heisenberg exchange term and double exchange term to describe the mixed-valence state. We have determined their effective exchange integrals (J) and resonance parameters (B) from (HDFT) calculations in several procedures. These magnetic interactions are in good agreement with experiments. To estimate B values, we propose a new procedure using molecular orbital energies. The B values are properly evaluated compared with other procedures, using total energies. The chemical bond natures and the ground electronic structures are elucidated in terms of chemical indices defined by the occupation number of natural orbitals. Finally, implications of the computational results are discussed in relation to rational design of biomolecular devices. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Abstract: A quantum spin-correction scheme based on spin-correlation functions is proposed for multiple bond-breaking processes described by the unrestricted single determinant (USD) approaches, such as unrestricted Hartree–Fock (UHF) and unrestricted Kohn–Sham (UKS) density functional theory (DFT). It is known that natural orbitals (NOs) and occupation numbers (ONs) contain full information of USD solutions. We introduce a bond-operator representation of UHF and UKS wave functions to exploit information about those NOs, enabling us not only to facilitate the calculus, but also to understand the essential feature of the USD and those quantum spin-corrected solutions. We found that usual spin-projected solutions do not work for multiple bonds in the Heisenberg model mapping scheme. We propose quantum spin-correction schemes to obtain the spin-symmetry allowed solutions from the spin-unrestricted KS-DFT solutions. We examine these schemes for a chromium dimer, which is a typical example exhibiting multiple bonds. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Abstract: We present an extension of density matrix based linear scaling electronic structure theory to incorporate spin degrees of freedom. When the spin multiplicity of the system can be predetermined, the generalization of the existing linear scaling methods to spin unrestricted cases is straightforward. However, without calculations it is hard to determine the spin multiplicity of some complex systems, such as, many magnetic nanostuctures, some inorganic or bioinorganic molecules. Here we give a general prescription to obtain the spin-unrestricted ground state of open shell systems. Our methods are implemented into the linear scaling trace-correcting density matrix purification algorithm. The numerical atomic orbital basis, rather than the commonly adopted Gaussian basis functions is used. The test systems include O2 molecule, and magnetic carbon doped BN(5,5) and BN(7,6) nanotubes. Using the newly developed method, we find the magnetic moments in carbon doped BN nanotubes couple antiferromagnetically with each other. Our results suggest that the linear scaling spin-unrestricted trace-correcting purification method is very powerful to treat large magnetic systems.

Abstract: Publisher Summary This chapter describes the different aspects of bond breaking in quantum chemistry. Ab initio quantum chemical methods can predict the equilibrium properties of small molecules in the gas phase to near-spectroscopic accuracy. A detailed understanding of a chemical reaction often requires the knowledge of its dynamics, which in turn requires the knowledge of the potential energy surface. By allowing the alpha and beta electrons to occupy different orbitals, the wave function can avoid the unphysical ionic terms. This approach is called unrestricted “Hartree–Fock (UHF),” as opposed to the usual, restricted Hartree–Fock (RHF) method. The UHF potential energy curve is qualitatively correct, but often quantitatively poor. It also has the rather undesirable property that it is not an Eigen function of the electronic spin operator. CASSCF is the most widely used quantum chemical method for bond-breaking reactions. CASSCF wave functions are usually easier to converge than general multiconfigurational self-consistent-field (MCSCF) wave functions and the ambiguity of selecting individual configurations is removed. The problematic ionic terms that make the RHF energy too high for large separations can also be avoided by using nonorthogonal orbitals in the valence bond approach.

Abstract: Core molecular orbital (MO) topology and influence on the electronic structures of norbornadiene (NBD, C7H8, ,X 1 A1), norbornene (NBN, C7H10, , X 1 A 0 ) and norbornane (NBA, C7H12, ,X 1 A2) in their ground electronic states are studied using both RHF/TZVP and B3LYP/TZVP models quantum mechanically. The present work focuses on the analysis of the topology, symmetry and implication on the electronic structures of the three structurally similar bicyclic hydrocarbons. The present work analyzes the changes in core orbitals of the molecules as a result of the CaC double bond saturation. It has been demonstrated that the core orbital energy shift and wavefunction distortion of the strained molecular species are not subtle, even though they have similarities in geometries and bicyclic carbon frames. It is revealed in this work that the carbon atoms of the methano bridge bear large orbital energy changes (chemical shifts), due to the relaxation of the strained bridge angle :C(1)C(7)C(4), but remain inactive in momentum space, in the hydrogenation process of NBD and NBN. The core MOs in the ethano-ring experience obvious changes in both orbital energies (chemical shifts) and in particular, orbital momentum distributions (MDs), which is a direct indicator of electronic structural variation of the species. The distortion of molecular orbital MDs of NBD, NBN and NBA with respect to the corresponding carbon atomic orbital MDs can be considered as indicators of orbital polarization, imposed symmetry and chemical shifts within the individual molecular framework. The combination of electronic structural information in both configuration space and momentum space is capable of providing a comprehensive understanding of the electronic structural changes in the hydrocarbons. q 2005 Elsevier B.V. All rights reserved.

Abstract: The magnetic interaction and spin transfer via phosphorus have been investigated for the tri-tert-butylaminoxyl para-substituted triphenylphosphine oxide. For this radical unit, the conjugation existing between the * orbital of the NO group and the phenyl orbitals leads to an efficient delocalization of the spin from the radical to the neighboring aromatic ring. This has been confirmed by using fluid solution high-resolution EPR and solid state MAS NMR spectroscopy. The spin densities located on the atoms of the molecule could be probed since 1H, 13C, 14N, and 31P are nuclei active in NMR and EPR, and lead to a precise spin distribution map for the triradical. The experimental investigations were completed by a DFT computational study. These techniques established in particular that spin density is located at the phosphorus (=-15×10-3 au), that its sign is in line with the sign alternation principle and that its magnitude is in the order of that found on the aromatic C atoms of the molecule. Surprisingly, whereas the spin distribution scheme supports ferromagnetic interactions among the radical units, the magnetic behavior found for this molecule revealed a low-spin ground state characterized by an intramolecular exchange parameter of J=-7.55 cm-1 as revealed by solid state susceptibility studies and low temperature EPR. The X-ray crystal structures solved at 293 and 30 K show the occurrence of a crystallographic transition resulting in an ordering of the molecular units at low temperature.

Abstract: We present a theoretical study on the effects of electron-LO-phonon interaction in two coupled stacked $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{Al}\mathrm{As}$ quantum dots. The resonant and nonresonant electron-phonon coupling contributions to the polaron states are obtained in the framework of the Green function formalism and perturbation approaches at zero and finite temperatures. Ground state renormalization is achieved due to phonon virtual absorption at $Tg0$. Tunneling effects between dots have been addressed and their influence on the electronic properties and optical absorption are analyzed. Topological modifications of electronic orbitals are found as a result of phonon-assisted tunneling.

Abstract: The J-OC-PSP (decomposition of J into Orbital Contributions using Orbital Currents and Partial Spin Polarization) method is applied to analyze NMR spin–spin coupling constants in polyenes, which were calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set. The analysis revealed that the π-mechanism for Fermi contact (FC) spin coupling is based on passive π-orbital contributions. The π-orbitals transfer spin information between σ orbitals (spin-transport mechanism) or increase the spin information of a σ orbital by an echo effect. The calculated FC(π) values are rather constant for small polyenes ranging between 3.5–5.5 Hz for a double bond. They decay more slowly with the distance between perturbing and responding nucleus than the σ contributions to the FC term. The sign of the passive FC(π) contribution can be assessed from a Dirac vector model. The limits for long-range coupling in a polyene were determined and their practical implications discussed.

Abstract: The potential energy surface of benzene (C(6)H(6)) with a He*(2(3)S) atom was obtained by comparison of experimental data in collision-energy-resolved two-dimensional Penning ionization electron spectroscopy with classical trajectory calculations. The ab initio model interaction potentials for C(6)H(6)+He*(2(3)S) were successfully optimized by the overlap expansion method; the model potentials were effectively modified by correction terms proportional to the overlap integrals between orbitals of the interacting system, C(6)H(6) and He*(2(3)S). Classical trajectory calculations with optimized potentials gave excellent agreement with the observed collision-energy dependence of partial ionization cross sections. Important contributions to corrections were found to be due to interactions between unoccupied molecular orbitals and the He*2s orbital. A C(6)H(6) molecule attracts a He*(2(3)S) atom widely at the region where pi electrons distribute, and the interaction of -80 meV (ca. -1.8 kcal/mol) just cover the carbon hexagon. The binding energy of a C(6)H(6) molecule and a He* atom was 107 meV at a distance of 2.40 A on the sixfold axis from the center of a C(6)H(6) molecule, which is similar to that of C(6)H(6)+Li and is much larger than those of the C(6)H(6)+[He,Ne,Ar] systems.