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Klaus Ruedenberg - One of the best experts on this subject based on the ideXlab platform.
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quasi atomic bond analyses in the sixth period i relativistic accurate atomic Minimal Basis Sets for the elements cesium to radon
Journal of Physical Chemistry A, 2019Co-Authors: George Schoendorff, Klaus Ruedenberg, Michael W. Schmidt, Aaron C West, Mark S. GordonAbstract:Full-valence relativistic accurate atomic Minimal Basis Set (AAMBS) orbitals are developed for the sixth-row elements from cesium to radon, including the lanthanides. Saturated primitive atomic bas...
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relativistic ab initio accurate atomic Minimal Basis Sets quantitative lumos and oriented quasi atomic orbitals for the elements li xe
Journal of Physical Chemistry A, 2017Co-Authors: George Schoendorff, Klaus Ruedenberg, Michael W. Schmidt, Aaron C West, Angela K Wilson, Mark S. GordonAbstract:Valence virtual orbitals (VVOs) are a quantitative and Basis Set independent method for extracting chemically meaningful lowest unoccupied molecular orbitals (LUMOs). The VVOs are formed based on a singular value decomposition (SVD) with respect to precomputed and internally stored ab initio accurate atomic Minimal Basis Sets (AAMBS) for the atoms. The occupied molecular orbitals and VVOs together form a Minimal Basis Set that can be transformed into orthogonal oriented quasi-atomic orbitals (OQUAOs) that provide a quantitative description of the bonding in a molecular environment. In the present work, relativistic AAMBS are developed that span the full valence orbital space. The impact of using full valence AAMBS for the formation of the VVOs and OQUAOs and the resulting bonding analysis is demonstrated with applications to the cuprous chloride, scandium monofluoride, and nickel silicide diatomic molecules.
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a comprehensive analysis in terms of molecule intrinsic quasi atomic orbitals ii strongly correlated mcscf wave functions
Journal of Physical Chemistry A, 2015Co-Authors: Aaron C West, Mark S. Gordon, Michael W. Schmidt, Klaus RuedenbergAbstract:A methodology is developed for the quantitative identification of the quasi-atomic orbitals that are embedded in a strongly correlated molecular wave function. The wave function is presumed to be generated from configurations in an internal orbital space whose dimension is equal to (or slightly larger) than that of the molecular Minimal Basis Set. The quasi-atomic orbitals are found to have large overlaps with corresponding orbitals on the free atoms. They separate into bonding and nonbonding orbitals. From the bonding quasi-atomic orbitals, localized bonding and antibonding molecular orbitals are formed. The resolution of molecular density matrices in terms of these orbitals furnishes a Basis for analyzing the interatomic bonding patterns in molecules and the changes in these bonding patterns along reaction paths. A new bond strength measure, the kinetic bond order, is introduced.
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a comprehensive analysis of molecule intrinsic quasi atomic bonding and correlating orbitals i hartree fock wave functions
Journal of Chemical Physics, 2013Co-Authors: Aaron C West, Mark S. Gordon, Michael W. Schmidt, Klaus RuedenbergAbstract:Through a Basis-Set-independent web of localizing orbital-transformations, 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 quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic Basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme.
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intrinsic local constituents of molecular electronic wave functions i exact representation of the density matrix in terms of chemically deformed and oriented atomic Minimal Basis Set orbitals
Theoretical Chemistry Accounts, 2008Co-Authors: Gregory J Atchity, Joseph Ivanic, Klaus RuedenbergAbstract:A coherent, intrinsic, Basis-Set-independent analysis is developed for the invariants of the first-order density matrix of an accurate molecular electronic wavefunction. From the hierarchical ordering of the natural orbitals, the zeroth-order orbital space is deduced, which generates the zeroth-order wavefunction, typically an MCSCF function in the full valence space. It is shown that intrinsically embedded in such wavefunctions are elements that are local in bond regions and elements that are local in atomic regions. Basis-Set-independent methods are given that extract and exhibit the intrinsic bond orbitals and the intrinsic Minimal-Basis quasi-atomic orbitals in terms of which the wavefunction can be exactly constructed. The quasi-atomic orbitals are furthermore oriented by a Basis-Set independent method (viz. maximization of the sum of the fourth powers of all off-diagonal density matrix elements) so as to exhibit clearly the chemical interactions. The unbiased nature of the method allows for the adaptation of the localized and directed orbitals to changing geometries.
Mark S. Gordon - One of the best experts on this subject based on the ideXlab platform.
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quasi atomic bond analyses in the sixth period i relativistic accurate atomic Minimal Basis Sets for the elements cesium to radon
Journal of Physical Chemistry A, 2019Co-Authors: George Schoendorff, Klaus Ruedenberg, Michael W. Schmidt, Aaron C West, Mark S. GordonAbstract:Full-valence relativistic accurate atomic Minimal Basis Set (AAMBS) orbitals are developed for the sixth-row elements from cesium to radon, including the lanthanides. Saturated primitive atomic bas...
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relativistic ab initio accurate atomic Minimal Basis Sets quantitative lumos and oriented quasi atomic orbitals for the elements li xe
Journal of Physical Chemistry A, 2017Co-Authors: George Schoendorff, Klaus Ruedenberg, Michael W. Schmidt, Aaron C West, Angela K Wilson, Mark S. GordonAbstract:Valence virtual orbitals (VVOs) are a quantitative and Basis Set independent method for extracting chemically meaningful lowest unoccupied molecular orbitals (LUMOs). The VVOs are formed based on a singular value decomposition (SVD) with respect to precomputed and internally stored ab initio accurate atomic Minimal Basis Sets (AAMBS) for the atoms. The occupied molecular orbitals and VVOs together form a Minimal Basis Set that can be transformed into orthogonal oriented quasi-atomic orbitals (OQUAOs) that provide a quantitative description of the bonding in a molecular environment. In the present work, relativistic AAMBS are developed that span the full valence orbital space. The impact of using full valence AAMBS for the formation of the VVOs and OQUAOs and the resulting bonding analysis is demonstrated with applications to the cuprous chloride, scandium monofluoride, and nickel silicide diatomic molecules.
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a comprehensive analysis in terms of molecule intrinsic quasi atomic orbitals ii strongly correlated mcscf wave functions
Journal of Physical Chemistry A, 2015Co-Authors: Aaron C West, Mark S. Gordon, Michael W. Schmidt, Klaus RuedenbergAbstract:A methodology is developed for the quantitative identification of the quasi-atomic orbitals that are embedded in a strongly correlated molecular wave function. The wave function is presumed to be generated from configurations in an internal orbital space whose dimension is equal to (or slightly larger) than that of the molecular Minimal Basis Set. The quasi-atomic orbitals are found to have large overlaps with corresponding orbitals on the free atoms. They separate into bonding and nonbonding orbitals. From the bonding quasi-atomic orbitals, localized bonding and antibonding molecular orbitals are formed. The resolution of molecular density matrices in terms of these orbitals furnishes a Basis for analyzing the interatomic bonding patterns in molecules and the changes in these bonding patterns along reaction paths. A new bond strength measure, the kinetic bond order, is introduced.
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a comprehensive analysis of molecule intrinsic quasi atomic bonding and correlating orbitals i hartree fock wave functions
Journal of Chemical Physics, 2013Co-Authors: Aaron C West, Mark S. Gordon, Michael W. Schmidt, Klaus RuedenbergAbstract:Through a Basis-Set-independent web of localizing orbital-transformations, 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 quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic Basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme.
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Charge transfer interaction using quasiatomic Minimal-Basis orbitals in the effective fragment potential method.
Journal of Chemical Physics, 2013Co-Authors: Peng Xu, Mark S. GordonAbstract:The charge transfer (CT) interaction, the most time-consuming term in the general effective fragment potential method, is made much more computationally efficient. This is accomplished by the projection of the quasiatomic Minimal-Basis-Set orbitals (QUAMBOs) as the atomic Basis onto the self-consistent field virtual molecular orbital (MO) space to select a subspace of the full virtual space called the valence virtual space. The diagonalization of the Fock matrix in terms of QUAMBOs recovers the canonical occupied orbitals and, more importantly, gives rise to the valence virtual orbitals (VVOs). The CT energies obtained using VVOs are generally as accurate as those obtained with the full virtual space canonical MOs because the QUAMBOs span the valence part of the virtual space, which can generally be regarded as “chemically important.” The number of QUAMBOs is the same as the number of Minimal-Basis MOs of a molecule. Therefore, the number of VVOs is significantly smaller than the number of canonical virtual MOs, especially for large atomic Basis Sets. This leads to a dramatic decrease in the computational cost.
Michael W. Schmidt - One of the best experts on this subject based on the ideXlab platform.
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quasi atomic bond analyses in the sixth period i relativistic accurate atomic Minimal Basis Sets for the elements cesium to radon
Journal of Physical Chemistry A, 2019Co-Authors: George Schoendorff, Klaus Ruedenberg, Michael W. Schmidt, Aaron C West, Mark S. GordonAbstract:Full-valence relativistic accurate atomic Minimal Basis Set (AAMBS) orbitals are developed for the sixth-row elements from cesium to radon, including the lanthanides. Saturated primitive atomic bas...
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relativistic ab initio accurate atomic Minimal Basis Sets quantitative lumos and oriented quasi atomic orbitals for the elements li xe
Journal of Physical Chemistry A, 2017Co-Authors: George Schoendorff, Klaus Ruedenberg, Michael W. Schmidt, Aaron C West, Angela K Wilson, Mark S. GordonAbstract:Valence virtual orbitals (VVOs) are a quantitative and Basis Set independent method for extracting chemically meaningful lowest unoccupied molecular orbitals (LUMOs). The VVOs are formed based on a singular value decomposition (SVD) with respect to precomputed and internally stored ab initio accurate atomic Minimal Basis Sets (AAMBS) for the atoms. The occupied molecular orbitals and VVOs together form a Minimal Basis Set that can be transformed into orthogonal oriented quasi-atomic orbitals (OQUAOs) that provide a quantitative description of the bonding in a molecular environment. In the present work, relativistic AAMBS are developed that span the full valence orbital space. The impact of using full valence AAMBS for the formation of the VVOs and OQUAOs and the resulting bonding analysis is demonstrated with applications to the cuprous chloride, scandium monofluoride, and nickel silicide diatomic molecules.
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a comprehensive analysis in terms of molecule intrinsic quasi atomic orbitals ii strongly correlated mcscf wave functions
Journal of Physical Chemistry A, 2015Co-Authors: Aaron C West, Mark S. Gordon, Michael W. Schmidt, Klaus RuedenbergAbstract:A methodology is developed for the quantitative identification of the quasi-atomic orbitals that are embedded in a strongly correlated molecular wave function. The wave function is presumed to be generated from configurations in an internal orbital space whose dimension is equal to (or slightly larger) than that of the molecular Minimal Basis Set. The quasi-atomic orbitals are found to have large overlaps with corresponding orbitals on the free atoms. They separate into bonding and nonbonding orbitals. From the bonding quasi-atomic orbitals, localized bonding and antibonding molecular orbitals are formed. The resolution of molecular density matrices in terms of these orbitals furnishes a Basis for analyzing the interatomic bonding patterns in molecules and the changes in these bonding patterns along reaction paths. A new bond strength measure, the kinetic bond order, is introduced.
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a comprehensive analysis of molecule intrinsic quasi atomic bonding and correlating orbitals i hartree fock wave functions
Journal of Chemical Physics, 2013Co-Authors: Aaron C West, Mark S. Gordon, Michael W. Schmidt, Klaus RuedenbergAbstract:Through a Basis-Set-independent web of localizing orbital-transformations, 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 quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic Basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme.
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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, 2004Co-Authors: W.c. Lu, L Bytautas, Michael W. Schmidt, Cai Zhuang Wang, Kaiming Ho, Klaus RuedenbergAbstract:A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic Minimal-Basis-Set orbitals that deviate as little as possible from free-atom SCF Minimal-Basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed “quasiatomic Minimal-Basis-Sets” 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 Minimal-Basis 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...
Cai Zhuang Wang - One of the best experts on this subject based on the ideXlab platform.
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benchmark of correlation matrix renormalization method in molecule calculations
Journal of Physics: Condensed Matter, 2019Co-Authors: Han Zhang, Yongxin Yao, Cai Zhuang WangAbstract:We report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule Set. This subSet represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic Minimal Basis-Set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. The CMR benchmark calculations yield a standard deviation of 0.09 A for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree-Fock method.
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correlation matrix renormalization approximation for total energy calculations of correlated electron systems
Physical Review B, 2014Co-Authors: Yongxin Yao, Jun Liu, Cai Zhuang WangAbstract:We generalized the commonly used Gutzwiller approximation for calculating the electronic structure and total energy of strongly correlated electron systems. In our method, the evaluation of one-body and two-body density matrix elements of the Hamiltonian is simplified using a renormalization approximation to achieve better scaling of the computational effort as a function of system size. To achieve a clear presentation of the concept and methodology, we describe the detailed formalism for a finite hydrogen system with Minimal Basis Set. We applied the correlation matrix renormalization approximation approach to a H${}_{2}$ dimer and H${}_{8}$ cubic fragment with Minimal Basis Sets, as well as a H${}_{2}$ molecule with a large Basis Set. The results compare favorably with sophisticated quantum chemical calculations. We believe our approach can serve as an alternative way to build up the exchange-correlation energy functional for an improved density functional theory description of systems with strong electron correlations.
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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, 2004Co-Authors: W.c. Lu, L Bytautas, Michael W. Schmidt, Cai Zhuang Wang, Kaiming Ho, Klaus RuedenbergAbstract:A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic Minimal-Basis-Set orbitals that deviate as little as possible from free-atom SCF Minimal-Basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed “quasiatomic Minimal-Basis-Sets” 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 Minimal-Basis 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...
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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, 2004Co-Authors: Cai Zhuang Wang, L Bytautas, Michael W. Schmidt, Klaus RuedenbergAbstract:A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic Minimal-Basis-Set orbitals that deviate as little as possible from free-atom SCF Minimal-Basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed “quasiatomic Minimal-Basis-Sets” 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 Minimal-Basis 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.
Aaron C West - One of the best experts on this subject based on the ideXlab platform.
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quasi atomic bond analyses in the sixth period i relativistic accurate atomic Minimal Basis Sets for the elements cesium to radon
Journal of Physical Chemistry A, 2019Co-Authors: George Schoendorff, Klaus Ruedenberg, Michael W. Schmidt, Aaron C West, Mark S. GordonAbstract:Full-valence relativistic accurate atomic Minimal Basis Set (AAMBS) orbitals are developed for the sixth-row elements from cesium to radon, including the lanthanides. Saturated primitive atomic bas...
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relativistic ab initio accurate atomic Minimal Basis Sets quantitative lumos and oriented quasi atomic orbitals for the elements li xe
Journal of Physical Chemistry A, 2017Co-Authors: George Schoendorff, Klaus Ruedenberg, Michael W. Schmidt, Aaron C West, Angela K Wilson, Mark S. GordonAbstract:Valence virtual orbitals (VVOs) are a quantitative and Basis Set independent method for extracting chemically meaningful lowest unoccupied molecular orbitals (LUMOs). The VVOs are formed based on a singular value decomposition (SVD) with respect to precomputed and internally stored ab initio accurate atomic Minimal Basis Sets (AAMBS) for the atoms. The occupied molecular orbitals and VVOs together form a Minimal Basis Set that can be transformed into orthogonal oriented quasi-atomic orbitals (OQUAOs) that provide a quantitative description of the bonding in a molecular environment. In the present work, relativistic AAMBS are developed that span the full valence orbital space. The impact of using full valence AAMBS for the formation of the VVOs and OQUAOs and the resulting bonding analysis is demonstrated with applications to the cuprous chloride, scandium monofluoride, and nickel silicide diatomic molecules.
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a comprehensive analysis in terms of molecule intrinsic quasi atomic orbitals ii strongly correlated mcscf wave functions
Journal of Physical Chemistry A, 2015Co-Authors: Aaron C West, Mark S. Gordon, Michael W. Schmidt, Klaus RuedenbergAbstract:A methodology is developed for the quantitative identification of the quasi-atomic orbitals that are embedded in a strongly correlated molecular wave function. The wave function is presumed to be generated from configurations in an internal orbital space whose dimension is equal to (or slightly larger) than that of the molecular Minimal Basis Set. The quasi-atomic orbitals are found to have large overlaps with corresponding orbitals on the free atoms. They separate into bonding and nonbonding orbitals. From the bonding quasi-atomic orbitals, localized bonding and antibonding molecular orbitals are formed. The resolution of molecular density matrices in terms of these orbitals furnishes a Basis for analyzing the interatomic bonding patterns in molecules and the changes in these bonding patterns along reaction paths. A new bond strength measure, the kinetic bond order, is introduced.
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a comprehensive analysis of molecule intrinsic quasi atomic bonding and correlating orbitals i hartree fock wave functions
Journal of Chemical Physics, 2013Co-Authors: Aaron C West, Mark S. Gordon, Michael W. Schmidt, Klaus RuedenbergAbstract:Through a Basis-Set-independent web of localizing orbital-transformations, 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 quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic Basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme.