Hybrid Slater–Gaussian-type 1s orbitals for the 1∑ ground state of H2 and He

Introduction of noninteger powers of r (or the elliptical coordinate ξ) in the definition of the 1s AO is shown to give better approximate wave-functions for the ground states of H₂ and He than other functions of comparable complexity. This trend is examined for various definitions of hybrid Slater–Gaussian orbitals using a limited CI . The best optimized single-term expansion energy is only 0.000160 a.u. above the “SCF limit” for H₂ at R = 1.4 a.u. and 0.000382 a.u. for He at R = 1.3 a.u.     

Pipek–Mezey localization of occupied and virtual orbitals

Recent advances in orbital localization algorithms are used to minimize the Pipek–Mezey localization function for both occupied and virtual Hartree–Fock orbitals. Virtual Pipek–Mezey orbitals for large molecular systems have previously not been considered in the literature. For this work, the Pipek–Mezey (PM) localization function is implemented for both the Mulliken and a Löwdin population analysis. The results show that the standard PM localization function (using either Mulliken or Löwdin population analyses) may yield local occupied orbitals, although for some systems the occupied orbitals are only semilocal as compared to state‐of‐the‐art localized occupied orbitals. For the virtual orbitals, a Löwdin population analysis shows improvement in locality compared to a Mulliken population analysis, but for both Mulliken and Löwdin population analyses, the virtual orbitals are seen to be considerably less local compared to state‐of‐the‐art localized orbitals. © 2013 Wiley Periodicals, Inc.     

Green's function calculations using non-Hartree–Fock orbitals

The single-particle Green's function is used to generate a new zero-order Hamiltonian. The idea to generate a new zero order from the previous zero order by incorporating perturbative corrections up to certain order is attractive since it allows an iterative procedure to repeatedly improve the results by decreasing the perturbation. In particular, in those cases where the Hartree–Fock Hamiltonian is not a good approximation to the full Hamiltonian and where perturbation theory usually does not produce sufficiently accurate results, one might hope that such a repetitive procedure ultimately yields an improved zero order and accurate perturbative corrections from this newly generated zero order. Two such approaches are investigated: first, one in which the ω-independent part of the self-energy is fully incorporated in the zero order and, second, one in which the correlation energy is incorporated in a one-electron potential in an average way. Numerical calculations are reported.     

MCSCF optimization through combined use of natural orbitals and the brillouin–levy–berthier theorem

A novel approach is developed for optimizing molecular orbitals within the context of a multiconfiguration self-consistent-field problem. The MCSCF wave function is determined through a sequence of eigenvalue problems in the multiconfiguration space and the single-excitation space. They are used to iteratively improve the natural orbitals, which in turn are related, by successively improved transformations, to the MCSCF orbitals. The mathematical problems arising out of this general concept are solved and the computational implementation is discussed. In many applications the method has proven itself as a powerful approach in forcing rapid convergence. Adaptation to spin and spatial symmetry is maintained throughout and the procedure is applicable to excited states as well as to ground states.     

Hybrid molecular orbitals for reacting systems

A method of describing the interactions between two systems in terms of coupled hybrid molecular orbitals of fragments is discussed and is applied to simple interacting systems to provide information on the processes of bond formation.     

Half-projected Hartree–Fock natural orbitals for defining CAS–SCF active spaces

We have extended the range of systems to which the half-projected Hartree–Fock (HPHF ) method has been applied, including the triplet state of the wave function. In our implementation, DIIS overcomes the convergence difficulties reported in earlier studies. HPHF allows generation of a symmetry-broken wave function in regions of the potential energy surface where the RHF wave function is triplet-stable. The fractionally occupied natural orbitals (FONOS ) of the HPHF wave function are good starting vectors for CAS –SCF calculations. A CAS –SCF in the space defined by the HPHF FONOS should be used instead of the unrestricted natural orbital CAS –SCF method in regions of triplet stability and for small active space problems. We draw extensive comparisons between the results of both the UNO –CAS and HPNO –CAS methods and those of full CAS –SCF calculations. © 1993 John Wiley & Sons, Inc.     

Perturbative calculation of the Hartree–Fock interaction energy using orthogonalized orbitals

A many‐body perturbation theory based on the partitioning of the dimer Hamiltonian, formulated in an orthogonalized basis set, is used for the calculation of interaction energies at the Hartree–Fock (HF) level. Numerical results for the (HF)₂ and (H₂O)₂ systems in selected geometries are presented. The interaction‐energy components are compared with the results obtained from the standard supermolecular approach and the intermolecular perturbation theory based on the biorthogonal basis set. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 81–88, 1999     

Variation–iteration method in momentum space: Determination of Hartree–Fock atomic orbitals

A method using the Svartholm iterative procedure to solve atomic Hartree–Fock equations in momentum space is defined and applied to the ground states of Be and B⁺. The calculated atomic orbital properties follow a monotonic and stable convergence, but with rates of convergence depending on each property. The evolution of the orbitals during the iterations is explained by the combined actions of the variational principle, the Svartholm iterative procedure, and the momentum space representation. © 1993 John Wiley & Sons, Inc.     

Hybrid Organic–Inorganic Antiperovskites

Substitution of A‐site and/or X‐site ions of ABX₃‐type perovskites with organic groups can give rise to hybrid perovskites, many of which display intriguing properties beyond their parent compounds. However, this method cannot be extended effectively to hybrid antiperovskites. Now, the design of hybrid antiperovskites under the guidance of the concept of Goldschmidt's tolerance factor is presented. Spherical anions were chosen for the A and B sites and spherical organic cations for the X site, and seven hybrid antiperovskites were obtained, including (F₃(H₂O)_x)(AlF₆)(H₂dabco)₃, ((Co(CN)₆)(H₂O)₅)(MF₆)(H₂dabco)₃ (M=Al³⁺, Cr³⁺, or In³⁺), (Co(CN)₆)(MF₆)(H₂pip)₃ (M=Al³⁺ or Cr³⁺), and (SbI₆)(AlF₆)(H₂dabco)₃. These new structures reveal that all ions at A, B, and X sites of inorganic antiperovskites can be replaced by molecular ions to form hybrid antiperovskites. This work will lead to the synthesis of a large family of hybrid antiperovskites.     

Local Hartree–Fock orbitals using a three‐level optimization strategy for the energy

Using the three‐level energy optimization procedure combined with a refined version of the least‐change strategy for the orbitals—where an explicit localization is performed at the valence basis level—it is shown how to more efficiently determine a set of local Hartree–Fock orbitals. Further, a core–valence separation of the least‐change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree–Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. © 2013 Wiley Periodicals, Inc.     

Representation of Kohn–Sham free atom eigenfunctions by Slater‐type orbitals

Slater‐type orbitals are applied to represent the numerically obtained Kohn–Sham eigenfunction of free atom. The algorithm evaluating the nonlinear expansion coefficients of this approximation is described. Standard iterative solution of Kohn–Sham equation to obtain the nonlinear expansion coefficients is avoided and replaced by the projection method. First, the eigenfunction is obtained in the B‐spline space based on the Galerkin formulation of the finite element method. Then, based on the density functional theory, the conditions are formulated, which leads to the set of nonlinear equations. The proposed algorithm is general and can be applied for any atomic Kohn–Sham eigenfunction. As an examplary application of the proposed algorithm, the set of nonlinear equations is derived for occupied states of N, Al, Ga, and In atoms. The expansion coefficients, obtained for these atoms, are evaluated numerically by Newton procedure and listed in the tables. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Hybrid Organic–Inorganic Thermoelectric Materials and Devices

Hybrid organic–inorganic materials have been considered as a new candidate in the field of thermoelectric materials since the last decade owing to their great potential to enhance the thermoelectric performance by utilizing the low thermal conductivity of organic materials and the high Seebeck coefficient, and high electrical conductivity of inorganic materials. Herein, we provide an overview of interfacial engineering in the synthesis of various organic–inorganic thermoelectric hybrid materials, along with the dimensional design for tuning their thermoelectric properties. Interfacial effects are examined in terms of nanostructures, physical properties, and chemical doping between the inorganic and organic components. Several key factors which dictate the thermoelectric efficiency and performance of various electronic devices are also discussed, such as the thermal conductivity, electric transportation, electronic band structures, and band convergence of the hybrid materials.     

Hybrid molecular orbitals for interacting systems. reactive region and reaction sites

It is shown how the reactive region is determined in a molecule and how the reaction sites are specified in the reactive region by the use of hybrid molecular orbitals.     

Selected‐Control Fabrication of Multifunctional Fluorescent–Magnetic Core–Shell and Yolk–Shell Hybrid Nanostructures

The selected‐control preparation of uniform core–shell and yolk–shell architectures, which combine the multiple functions of a superparamagnetic iron oxide (SPIO) core and europium‐doped yttrium oxide (Y₂O₃:Eu) shell in a single material with tunable fluorescence and magnetic properties, has been successfully achieved by controlling the heat‐treatment conditions. Furthermore, the shell thickness and interior cavity of SPIO@Y₂O₃:Eu core–shell and yolk–shell nanostructures can be precisely tuned. Importantly, as‐prepared SPIO@Y₂O₃:Eu yolk–shell nanocapsules (NCs) modified with amino groups as cancer‐cell fluorescence imaging agents are also demonstrated. To the best of our knowledge, this is the first report on the selected‐control fabrication of uniform SPIO@Y₂O₃:Eu core–shell nanoparticles and yolk–shell NCs. The combined magnetic manipulation and optical monitoring of magnetic–fluorescent SPIO@Y₂O₃:Eu yolk–shell NCs will open up many exciting opportunities in dual imaging for targeted delivery and thermal therapy.     

Calculation of the brueckner orbitals and generalized natural orbitals

The diagrammatic-perturbation approach for the construction of the one-particle Hermitian pseudoeigenvalue problem determining the Brueckner orbitals and/or generalized natural orbitals is elaborated.     

Momentum–space electron densities—localized orbitals in hydrocarbons,boranes, and transition metal complexes

Position and momentum space plots are presented for localized molecular orbitals in hydrocarbons, boranes, a carborane, and two octahedral transition metal complexes. The p-space representation proves to be valuable for visualizing such orbitals since it highlights the differences in their character from one molecule to another. Factors influencing the form of the orbitals in p space, including the oscillatory behavior caused by contributions to an orbital from more than one center, are examined in detail. © 1996 John Wiley & Sons, Inc.     

Hybrid molecular orbitals for reacting systems. Elucidation of reactive domains

A pair of orbital transformations Is suggested to provide a simple criterion to interpret the pathway of nonpolar reactions and to elucidate the reactive domains for competitive reactions.