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Hiromi Nakai  One of the best experts on this subject based on the ideXlab platform.

database assisted local Unitary Transformation method for two electron integrals in two component relativistic calculations
2021CoAuthors: Chinami Takashima, Junji Seino, Hiromi NakaiAbstract:Abstract This letter presents an efficient algorithm for local Unitary Transformation based on the spinfree infiniteorder twocomponent relativistic method for the twoelectron interaction, which is assisted by onecenter relativistic twoelectron integral (TEI) database. The database stores a set of TEIs, one for each element–basis set combination. The algorithm is numerically assessed for hydrogen halide chains, (HX)n (X = Cl and At), Aun, Ir(ppy)3, Pt3(C7H7)2(HCN)3, and PtCl2(NH3)2. The computational cost (time and memory size) at the Hartree–Fock level is lower than that of the conventional method, especially for small and mediumsized molecules.

gauge origin independent formalism of two component relativistic framework based on Unitary Transformation in nuclear magnetic shielding constant
2018CoAuthors: Masao Hayami, Junji Seino, Hiromi NakaiAbstract:This article proposes a gaugeorigin independent formalism of the nuclear magnetic shielding constant in the twocomponent relativistic framework based on the Unitary Transformation. The proposed scheme introduces the gauge factor and the Unitary Transformation into the atomic orbitals. The twocomponent relativistic equation is formulated by blockdiagonalizing the Dirac Hamiltonian together with gauge factors. This formulation is available for arbitrary relativistic Unitary Transformations. Then, the infiniteorder DouglasKrollHess (IODKH) Transformation is applied to the present formulation. Next, the analytical derivatives of the IODKH Hamiltonian for the evaluation of the nuclear magnetic shielding constant are derived. Results obtained from the numerical assessments demonstrate that the present formulation removes the gaugeorigin dependence completely. Furthermore, the formulation with the IODKH Transformation gives results that are close to those in fourcomponent and other twocomponent relativistic schemes.

implementation of analytical energy gradient of spin dependent general hartree fock method based on the infinite order douglas kroll hess relativistic hamiltonian with local Unitary Transformation
2016CoAuthors: Yuya Nakajima, Junji Seino, Hiromi NakaiAbstract:An analytical energy gradient for the spindependent general Hartree–Fock method based on the infiniteorder Douglas–Kroll–Hess (IODKH) method was developed. To treat realistic systems, the local Unitary Transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth and sixthperiod elements and to examine the efficiency in one, two, and threedimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of factris(2phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavyelement atoms.

large scale two component relativistic quantum chemical theory combination of the infinite order douglas kroll hess method with the local Unitary Transformation scheme and the divide and conquer method
2015CoAuthors: Junji Seino, Hiromi NakaiAbstract:Largescale twocomponent (2c) relativistic quantumchemical (RQC) theory is reviewed. We briefly discuss the theories, advantages, and extensibilities of an overall linearscaling scheme in 2c relativistic theory. The theory is based on the infiniteorder Douglas–Kroll–Hess method, with the local Unitary Transformation scheme to produce the 2c relativistic Hamiltonian, and the divideandconquer method to achieve linearscaling of Hartree–Fock and electron correlation methods. Furthermore, perspectives for largescale RQC are explained to bring the practical usage and treatment of light and heavy elements in 2c relativistic calculations close to those in nonrelativistic methods. © 2014 Wiley Periodicals, Inc.

Analytical energy gradient based on spinfree infiniteorder DouglasKrollHess method with local Unitary Transformation
2013CoAuthors: Yuya Nakajima, Junji Seino, Hiromi NakaiAbstract:In this study, the analytical energy gradient for the spinfree infiniteorder DouglasKrollHess (IODKH) method at the levels of the HartreeFock (HF), density functional theory (DFT), and secondorder MollerPlesset perturbation theory (MP2) is developed. Furthermore, adopting the local Unitary Transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides, and coinage metal dimers, and 20 metal complexes, including the fourth–sixth row transition metals. In addition, the efficiencies are investigated for one, two, and threedimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.
Junji Seino  One of the best experts on this subject based on the ideXlab platform.

database assisted local Unitary Transformation method for two electron integrals in two component relativistic calculations
2021CoAuthors: Chinami Takashima, Junji Seino, Hiromi NakaiAbstract:Abstract This letter presents an efficient algorithm for local Unitary Transformation based on the spinfree infiniteorder twocomponent relativistic method for the twoelectron interaction, which is assisted by onecenter relativistic twoelectron integral (TEI) database. The database stores a set of TEIs, one for each element–basis set combination. The algorithm is numerically assessed for hydrogen halide chains, (HX)n (X = Cl and At), Aun, Ir(ppy)3, Pt3(C7H7)2(HCN)3, and PtCl2(NH3)2. The computational cost (time and memory size) at the Hartree–Fock level is lower than that of the conventional method, especially for small and mediumsized molecules.

gauge origin independent formalism of two component relativistic framework based on Unitary Transformation in nuclear magnetic shielding constant
2018CoAuthors: Masao Hayami, Junji Seino, Hiromi NakaiAbstract:This article proposes a gaugeorigin independent formalism of the nuclear magnetic shielding constant in the twocomponent relativistic framework based on the Unitary Transformation. The proposed scheme introduces the gauge factor and the Unitary Transformation into the atomic orbitals. The twocomponent relativistic equation is formulated by blockdiagonalizing the Dirac Hamiltonian together with gauge factors. This formulation is available for arbitrary relativistic Unitary Transformations. Then, the infiniteorder DouglasKrollHess (IODKH) Transformation is applied to the present formulation. Next, the analytical derivatives of the IODKH Hamiltonian for the evaluation of the nuclear magnetic shielding constant are derived. Results obtained from the numerical assessments demonstrate that the present formulation removes the gaugeorigin dependence completely. Furthermore, the formulation with the IODKH Transformation gives results that are close to those in fourcomponent and other twocomponent relativistic schemes.

implementation of analytical energy gradient of spin dependent general hartree fock method based on the infinite order douglas kroll hess relativistic hamiltonian with local Unitary Transformation
2016CoAuthors: Yuya Nakajima, Junji Seino, Hiromi NakaiAbstract:An analytical energy gradient for the spindependent general Hartree–Fock method based on the infiniteorder Douglas–Kroll–Hess (IODKH) method was developed. To treat realistic systems, the local Unitary Transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth and sixthperiod elements and to examine the efficiency in one, two, and threedimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of factris(2phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavyelement atoms.

large scale two component relativistic quantum chemical theory combination of the infinite order douglas kroll hess method with the local Unitary Transformation scheme and the divide and conquer method
2015CoAuthors: Junji Seino, Hiromi NakaiAbstract:Largescale twocomponent (2c) relativistic quantumchemical (RQC) theory is reviewed. We briefly discuss the theories, advantages, and extensibilities of an overall linearscaling scheme in 2c relativistic theory. The theory is based on the infiniteorder Douglas–Kroll–Hess method, with the local Unitary Transformation scheme to produce the 2c relativistic Hamiltonian, and the divideandconquer method to achieve linearscaling of Hartree–Fock and electron correlation methods. Furthermore, perspectives for largescale RQC are explained to bring the practical usage and treatment of light and heavy elements in 2c relativistic calculations close to those in nonrelativistic methods. © 2014 Wiley Periodicals, Inc.

Analytical energy gradient based on spinfree infiniteorder DouglasKrollHess method with local Unitary Transformation
2013CoAuthors: Yuya Nakajima, Junji Seino, Hiromi NakaiAbstract:In this study, the analytical energy gradient for the spinfree infiniteorder DouglasKrollHess (IODKH) method at the levels of the HartreeFock (HF), density functional theory (DFT), and secondorder MollerPlesset perturbation theory (MP2) is developed. Furthermore, adopting the local Unitary Transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides, and coinage metal dimers, and 20 metal complexes, including the fourth–sixth row transition metals. In addition, the efficiencies are investigated for one, two, and threedimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.
Xiao Gang Wen  One of the best experts on this subject based on the ideXlab platform.

local Unitary Transformation long range quantum entanglement wave function renormalization and topological order
2010CoAuthors: Xie Chen, Xiao Gang WenAbstract:Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local Unitary Transformation that maps between the states. On the other hand, gapped ground states remain within the same phase under local Unitary Transformations. Therefore, local Unitary Transformations define an equivalence relation and the equivalence classes are the universality classes that define the different phases for gapped quantum systems. Since local Unitary Transformations can remove local entanglement, the above equivalence/universality classes correspond to pattern of long range entanglement, which is the essence of topological order. The local Unitary Transformation also allows us to define a wave function renormalization scheme, under which a wave function can flow to a simpler one within the same equivalence/universality class. Using such a setup, we find conditions on the possible fixedpoint wave functions where the local Unitary Transformations have finite dimensions. The solutions of the conditions allow us to classify this type of topological orders, which generalize the stringnet classification of topological orders. We also describe an algorithm of wave function renormalization induced by local Unitary Transformations. The algorithm allows us to calculate the flow of tensorproduct wave functions which are not at the fixed points. This will allow us to calculate topological orders as well as symmetry breaking orders in a generic tensorproduct state.

Local Unitary Transformation, longrange quantum entanglement, wave function renormalization, and topological order
2010CoAuthors: Xie Chen, Zheng Cheng Gu, Xiao Gang WenAbstract:Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local Unitary Transformation that maps between the states. On the other hand, gapped ground states remain within the same phase under local Unitary Transformations. Therefore, local Unitary Transformations define an equivalence relation and the equivalence classes are the universality classes that define the different phases for gapped quantum systems. Since local Unitary Transformations can remove local entanglement, the above equivalence/universality classes correspond to pattern of long range entanglement, which is the essence of topological order. The local Unitary Transformation also allows us to define a wave function renormalization scheme, under which a wave function can flow to a simpler one within the same equivalence/universality class. Using such a setup, we find conditions on the possible fixedpoint wave functions where the local Unitary Transformations have \emph{finite} dimensions. The solutions of the conditions allow us to classify this type of topological orders, which generalize the stringnet classification of topological orders. We also describe an algorithm of wave function renormalization induced by local Unitary Transformations. The algorithm allows us to calculate the flow of tensorproduct wave functions which are not at the fixed points. This will allow us to calculate topological orders as well as symmetry breaking orders in a generic tensorproduct state.
Xie Chen  One of the best experts on this subject based on the ideXlab platform.

local Unitary Transformation long range quantum entanglement wave function renormalization and topological order
2010CoAuthors: Xie Chen, Xiao Gang WenAbstract:Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local Unitary Transformation that maps between the states. On the other hand, gapped ground states remain within the same phase under local Unitary Transformations. Therefore, local Unitary Transformations define an equivalence relation and the equivalence classes are the universality classes that define the different phases for gapped quantum systems. Since local Unitary Transformations can remove local entanglement, the above equivalence/universality classes correspond to pattern of long range entanglement, which is the essence of topological order. The local Unitary Transformation also allows us to define a wave function renormalization scheme, under which a wave function can flow to a simpler one within the same equivalence/universality class. Using such a setup, we find conditions on the possible fixedpoint wave functions where the local Unitary Transformations have finite dimensions. The solutions of the conditions allow us to classify this type of topological orders, which generalize the stringnet classification of topological orders. We also describe an algorithm of wave function renormalization induced by local Unitary Transformations. The algorithm allows us to calculate the flow of tensorproduct wave functions which are not at the fixed points. This will allow us to calculate topological orders as well as symmetry breaking orders in a generic tensorproduct state.

Local Unitary Transformation, longrange quantum entanglement, wave function renormalization, and topological order
2010CoAuthors: Xie Chen, Zheng Cheng Gu, Xiao Gang WenAbstract:Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local Unitary Transformation that maps between the states. On the other hand, gapped ground states remain within the same phase under local Unitary Transformations. Therefore, local Unitary Transformations define an equivalence relation and the equivalence classes are the universality classes that define the different phases for gapped quantum systems. Since local Unitary Transformations can remove local entanglement, the above equivalence/universality classes correspond to pattern of long range entanglement, which is the essence of topological order. The local Unitary Transformation also allows us to define a wave function renormalization scheme, under which a wave function can flow to a simpler one within the same equivalence/universality class. Using such a setup, we find conditions on the possible fixedpoint wave functions where the local Unitary Transformations have \emph{finite} dimensions. The solutions of the conditions allow us to classify this type of topological orders, which generalize the stringnet classification of topological orders. We also describe an algorithm of wave function renormalization induced by local Unitary Transformations. The algorithm allows us to calculate the flow of tensorproduct wave functions which are not at the fixed points. This will allow us to calculate topological orders as well as symmetry breaking orders in a generic tensorproduct state.
Yuya Nakajima  One of the best experts on this subject based on the ideXlab platform.

implementation of analytical energy gradient of spin dependent general hartree fock method based on the infinite order douglas kroll hess relativistic hamiltonian with local Unitary Transformation
2016CoAuthors: Yuya Nakajima, Junji Seino, Hiromi NakaiAbstract:An analytical energy gradient for the spindependent general Hartree–Fock method based on the infiniteorder Douglas–Kroll–Hess (IODKH) method was developed. To treat realistic systems, the local Unitary Transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth and sixthperiod elements and to examine the efficiency in one, two, and threedimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of factris(2phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavyelement atoms.

Analytical energy gradient based on spinfree infiniteorder DouglasKrollHess method with local Unitary Transformation
2013CoAuthors: Yuya Nakajima, Junji Seino, Hiromi NakaiAbstract:In this study, the analytical energy gradient for the spinfree infiniteorder DouglasKrollHess (IODKH) method at the levels of the HartreeFock (HF), density functional theory (DFT), and secondorder MollerPlesset perturbation theory (MP2) is developed. Furthermore, adopting the local Unitary Transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides, and coinage metal dimers, and 20 metal complexes, including the fourth–sixth row transition metals. In addition, the efficiencies are investigated for one, two, and threedimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.