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Klaus Ruedenberg  One of the best experts on this subject based on the ideXlab platform.

a comprehensive analysis of molecule intrinsic quasi atomic bonding and correlating Orbitals i hartree fock wave functions
Journal of Chemical Physics, 2013CoAuthors: Aaron C West, Michael W. Schmidt, Mark S Gordon, Klaus RuedenbergAbstract:Through a basissetindependent web of localizing orbitaltransformations, the electronic wave function of a molecule is expressed in terms of a set of Orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasiatomic Orbitals and splitlocalized molecular Orbitals are determined by new, fast localization methods. The density matrix between the oriented quasiatomic Orbitals as well as the locations of the splitlocalized Orbitals exhibit atomic populations and interatomic bonding patterns. A correlationadapted quasiatomic basis is determined in the external orbital space. The general formulations are specified in detail for HartreeFock wave functions. Applications to specific molecules exemplify the general scheme.

molecule intrinsic minimal basis sets i exact resolution of ab initio optimized molecular Orbitals in terms of deformed atomic minimal basis Orbitals
Journal of Chemical Physics, 2004CoAuthors: W.c. Lu, L Bytautas, Michael W. Schmidt, Cai Zhuang Wang, Kaiming Ho, Klaus RuedenbergAbstract:A method is presented for expressing the occupied selfconsistentfield (SCF) Orbitals of a molecule exactly in terms of chemically deformed atomic minimalbasisset Orbitals that deviate as little as possible from freeatom SCF minimalbasis Orbitals. The molecular Orbitals referred to are the exact SCF Orbitals, the freeatom Orbitals referred to are the exact atomic SCF Orbitals, and the formulation of the deformed “quasiatomic minimalbasissets” is independent of the calculational atomic orbital basis used. The resulting resolution of molecular Orbitals in terms of quasiatomic minimal basis set Orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimalbasis Orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence Orbitals, which are useful for calculati...

molecule intrinsic minimal basis sets i exact resolution of ab initio optimized molecular Orbitals in terms of deformed atomic minimal basis Orbitals
Journal of Chemical Physics, 2004CoAuthors: Cai Zhuang Wang, L Bytautas, Michael W. Schmidt, Klaus RuedenbergAbstract:A method is presented for expressing the occupied selfconsistentfield (SCF) Orbitals of a molecule exactly in terms of chemically deformed atomic minimalbasisset Orbitals that deviate as little as possible from freeatom SCF minimalbasis Orbitals. The molecular Orbitals referred to are the exact SCF Orbitals, the freeatom Orbitals referred to are the exact atomic SCF Orbitals, and the formulation of the deformed “quasiatomic minimalbasissets” is independent of the calculational atomic orbital basis used. The resulting resolution of molecular Orbitals in terms of quasiatomic minimal basis set Orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimalbasis Orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence Orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn–Sham density functional theory Orbitals and is easily generalized to valence MCSCF Orbitals.
Takuro Katsufuji  One of the best experts on this subject based on the ideXlab platform.

electronic states and possible origin of the orbital glass state in a nearly metallic spinel cobalt vanadate an x ray magnetic circular dichroism study
Physical Review B, 2018CoAuthors: Yosuke Nonaka, Goro Shibata, Rui Koborinai, K Ishigami, Shoya Sakamoto, Keisuke Ikeda, Zhendong Chi, T Koide, Arata Tanaka, Takuro KatsufujiAbstract:We have investigated the orbital states of the orbitalglassy (shortrange orbital ordered) spinel vanadate Co$_{1.21}$V$_{1.79}$O$_{4}$ using xray absorption spectroscopy (XAS), xray magnetic circular dichroism (XMCD), and subsequent configurationinteraction clustermodel calculation. From the sign of the XMCD spectra, it was found that the spin magnetic moment of the Co ion is aligned parallel to the applied magnetic field and that of the V ion antiparallel to it, consistent with neutron scattering studies. It was revealed that the excess Co ions at the octahedral site take the trivalent lowspin state, and induce a random potential to the V sublattice. The orbital magnetic moment of the V ion is small although finite, suggesting that the ordered Orbitals mainly consists of realnumber Orbitals.

electronic states and possible origin of the orbital glass state in a nearly metallic spinel cobalt vanadate an x ray magnetic circular dichroism study
Physical Review B, 2018CoAuthors: Yosuke Nonaka, Goro Shibata, Rui Koborinai, K Ishigami, Shoya Sakamoto, Keisuke Ikeda, Zhendong Chi, T Koide, Arata Tanaka, Takuro KatsufujiAbstract:We have investigated the orbital states of the orbitalglassy (shortrange orbital ordered) spinel vanadate ${\mathrm{Co}}_{1.21}{\mathrm{V}}_{1.79}{\mathrm{O}}_{4}$ using xray absorption spectroscopy (XAS), xray magnetic circular dichroism (XMCD), and subsequent configurationinteraction clustermodel calculation. From the sign of the XMCD spectra, it was found that the spin magnetic moment of the Co ion is aligned parallel to the applied magnetic field and that of the V ion antiparallel to it, consistent with neutron scattering studies. It was revealed that the excess Co ions at the octahedral site take the trivalent lowspin state and induce a random potential to the V sublattice. The orbital magnetic moment of the V ion is small, suggesting that the ordered Orbitals mainly consist of realnumber Orbitals.
Akira Imamura  One of the best experts on this subject based on the ideXlab platform.

extraction of one handed helical frontier orbital in even n cumulenes by breaking mirror images of right and left handed helical Orbitals theoretical study
Journal of Physical Chemistry C, 2019CoAuthors: Yuuichi Orimoto, Yuriko Aoki, Akira ImamuraAbstract:Even [n]cumulenes with an even number n of double bonds are known to have degenerate helical frontier Orbitals even in linearchain structures. Theoretical analysis was conducted to separate onehanded helical Orbitals from the others in cumulenes to determine their enantioselective chemical/physical properties. Donor ((NH2)3C−) and acceptor ((NO2)3C−) substituents separate the degenerate energy levels of right and lefthanded helical frontier Orbitals in even [n]cumulenes. Lone pairs (LPs) in the donor group can interact with helical Orbitals on the cumulene backbone, leading to “LP–helical orbital” interactions. A difference in the manner of interaction between left and righthanded Orbitals, depending on the LP direction, breaks the mirror symmetry between them. Consequent energy splitting between left and righthanded Orbitals results in extraction of a onehanded helical frontier orbital only. This is the first example of extracting a onehanded helical frontier orbital while maintaining sufficien...

Extraction of OneHanded Helical Frontier Orbital in Even [n]Cumulenes by Breaking Mirror Images of Right and LeftHanded Helical Orbitals: Theoretical Study
2019CoAuthors: Yuuichi Orimoto, Yuriko Aoki, Akira ImamuraAbstract:Even [n]cumulenes with an even number n of double bonds are known to have degenerate helical frontier Orbitals even in linearchain structures. Theoretical analysis was conducted to separate onehanded helical Orbitals from the others in cumulenes to determine their enantioselective chemical/physical properties. Donor ((NH2)3C−) and acceptor ((NO2)3C−) substituents separate the degenerate energy levels of right and lefthanded helical frontier Orbitals in even [n]cumulenes. Lone pairs (LPs) in the donor group can interact with helical Orbitals on the cumulene backbone, leading to “LP–helical orbital” interactions. A difference in the manner of interaction between left and righthanded Orbitals, depending on the LP direction, breaks the mirror symmetry between them. Consequent energy splitting between left and righthanded Orbitals results in extraction of a onehanded helical frontier orbital only. This is the first example of extracting a onehanded helical frontier orbital while maintaining sufficiently large energy splitting in even [n]cumulene in the framework of C1 molecular symmetry by donor–acceptor substitutions
Zoila Barandiaran  One of the best experts on this subject based on the ideXlab platform.

parallel linear scaling building block and embedding method based on localized Orbitals and orbital specific basis sets
Journal of Chemical Physics, 2004CoAuthors: Luis Seijo, Zoila BarandiaranAbstract:We present a linear scaling method for the energy minimization step of semiempirical and firstprinciples Hartree–Fock and Kohn–Sham calculations. It is based on the selfconsistent calculation of the optimum localized Orbitals of any localization method of choice and on the use of orbitalspecific 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 buildingblock selfconsistent 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 is 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.

parallel linear scaling building block and embedding method based on localized Orbitals and orbital specific basis sets
arXiv: Materials Science, 2004CoAuthors: Luis Seijo, Zoila BarandiaranAbstract:We present a new linear scaling method for the energy minimization step of semiempirical and firstprinciples HartreeFock and KohnSham calculations. It is based on the selfconsistent calculation of the optimum localized Orbitals of any localization method of choice and on the use of orbitalspecific 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 buildingblock selfconsistent 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.
Michael W. Schmidt  One of the best experts on this subject based on the ideXlab platform.

a comprehensive analysis of molecule intrinsic quasi atomic bonding and correlating Orbitals i hartree fock wave functions
Journal of Chemical Physics, 2013CoAuthors: Aaron C West, Michael W. Schmidt, Mark S Gordon, Klaus RuedenbergAbstract:Through a basissetindependent web of localizing orbitaltransformations, the electronic wave function of a molecule is expressed in terms of a set of Orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasiatomic Orbitals and splitlocalized molecular Orbitals are determined by new, fast localization methods. The density matrix between the oriented quasiatomic Orbitals as well as the locations of the splitlocalized Orbitals exhibit atomic populations and interatomic bonding patterns. A correlationadapted quasiatomic basis is determined in the external orbital space. The general formulations are specified in detail for HartreeFock wave functions. Applications to specific molecules exemplify the general scheme.

molecule intrinsic minimal basis sets i exact resolution of ab initio optimized molecular Orbitals in terms of deformed atomic minimal basis Orbitals
Journal of Chemical Physics, 2004CoAuthors: W.c. Lu, L Bytautas, Michael W. Schmidt, Cai Zhuang Wang, Kaiming Ho, Klaus RuedenbergAbstract:A method is presented for expressing the occupied selfconsistentfield (SCF) Orbitals of a molecule exactly in terms of chemically deformed atomic minimalbasisset Orbitals that deviate as little as possible from freeatom SCF minimalbasis Orbitals. The molecular Orbitals referred to are the exact SCF Orbitals, the freeatom Orbitals referred to are the exact atomic SCF Orbitals, and the formulation of the deformed “quasiatomic minimalbasissets” is independent of the calculational atomic orbital basis used. The resulting resolution of molecular Orbitals in terms of quasiatomic minimal basis set Orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimalbasis Orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence Orbitals, which are useful for calculati...

molecule intrinsic minimal basis sets i exact resolution of ab initio optimized molecular Orbitals in terms of deformed atomic minimal basis Orbitals
Journal of Chemical Physics, 2004CoAuthors: Cai Zhuang Wang, L Bytautas, Michael W. Schmidt, Klaus RuedenbergAbstract:A method is presented for expressing the occupied selfconsistentfield (SCF) Orbitals of a molecule exactly in terms of chemically deformed atomic minimalbasisset Orbitals that deviate as little as possible from freeatom SCF minimalbasis Orbitals. The molecular Orbitals referred to are the exact SCF Orbitals, the freeatom Orbitals referred to are the exact atomic SCF Orbitals, and the formulation of the deformed “quasiatomic minimalbasissets” is independent of the calculational atomic orbital basis used. The resulting resolution of molecular Orbitals in terms of quasiatomic minimal basis set Orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimalbasis Orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence Orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn–Sham density functional theory Orbitals and is easily generalized to valence MCSCF Orbitals.