The Experts below are selected from a list of 28251 Experts worldwide ranked by ideXlab platform
Gustavo E Scuseria - One of the best experts on this subject based on the ideXlab platform.
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projected hartree Fock Theory as a polynomial of particle hole excitations and its combination with variational coupled cluster Theory
Journal of Chemical Physics, 2017Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Projected Hartree-Fock Theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. Coupled cluster Theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and coupled cluster Theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.
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communication projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
Journal of Chemical Physics, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation th...
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communication projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
Journal of Chemical Physics, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation Theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
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projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
arXiv: Strongly Correlated Electrons, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation Theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
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entanglement and polyradical character of polycyclic aromatic hydrocarbons predicted by projected hartree Fock Theory
Journal of Physical Chemistry B, 2013Co-Authors: Pablo Rivero, Carlos A Jimenezhoyos, Gustavo E ScuseriaAbstract:We study strong correlation effects in a series of fused benzene rings (acenes) of varying length and width using our recently developed projected Hartree-Fock (PHF) method. These molecules, commonly known as polycyclic aromatic hydrocarbons or nanographenes, are very challenging for electronic structure Theory because of their strong multireference character. This challenge is here met by PHF at moderate computational cost optimizing a spin eigenfunction obtained by projection of an unrestricted Hartree-Fock (UHF) trial determinant. The resulting method, known as SUHF, predicts that polyradical behavior and orbital entanglement are enhanced with molecular size, especially in systems whose structural motifs are dominated by zigzag edges, like oligoacenes.
J Meng - One of the best experts on this subject based on the ideXlab platform.
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relativistic brueckner hartree Fock Theory in infinite nuclear matter
Epj Web of Conferences, 2021Co-Authors: Sibo Wang, P Ring, Qiang Zhao, J MengAbstract:On the way of a microscopic derivation of covariant density functionals, the first complete solution of the relativistic Brueckner-Hartree-Fock (RBHF) equations is presented for symmetric nuclear matter. In most of the earlier investigations, the G -matrix is calculated only in the space of positive energy solutions. On the other side, for the solution of the relativistic Hartree-Fock (RHF) equations, also the elements of this matrix connecting positive and negative energy solutions are required. So far, in the literature, these matrix elements are derived in various approximations. We discuss solutions of the Thompson equation for the full Dirac space and compare the resulting equation of state with those of earlier attempts in this direction.
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relativistic brueckner hartree Fock Theory in nuclear matter without the average momentum approximation
Physical Review C, 2018Co-Authors: Hui Tong, Shihang Shen, P Ring, Xiulei Ren, Sibo Wang, J MengAbstract:CITATION: Tong, H., et al. 2018. Relativistic Brueckner-Hartree-Fock Theory in nuclear matter without the average momentum approximation. Physical Review C, 98(5):054302, doi:10.1103/PhysRevC.98.054302.
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relativistic brueckner hartree Fock Theory for neutron drops
Physical Review C, 2018Co-Authors: J Meng, Shihang Shen, Haozhao Liang, P Ring, Shuangquan ZhangAbstract:CITATION: Shen, S., et al. 2018. Relativistic Brueckner-Hartree-Fock Theory for neutron drops. Physical Review C, 97(5):054312, doi:10.1103/PhysRevC.97.054312.
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effects of tensor force in the relativistic scheme a case study of neutron drops
arXiv: Nuclear Theory, 2018Co-Authors: Shihang Shen, J Meng, Haozhao Liang, P Ring, Shuangquan ZhangAbstract:Tensor force is an important component in the nucleon-nucleon interaction, nevertheless, the role of the tensor force in the spin properties in finite nuclei is much less clear. In this report, we mainly focus on our recent progress on this topic about the relativistic Brueckner-Hartree-Fock Theory and the corresponding tensor effects on the spin-orbit splittings in neutron drops. This will serve as an important guide for future microscopic derivations of the relativistic and non-relativistic nuclear energy density functionals.
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effects of tensor forces in nuclear spin orbit splittings from ab initio calculations
Physics Letters B, 2018Co-Authors: Shihang Shen, J Meng, Haozhao Liang, P Ring, Shuangquan ZhangAbstract:Abstract A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin–orbit splittings in neutron drops. This result is obtained from relativistic Brueckner–Hartree–Fock Theory using the bare nucleon–nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.
Yiheng Qiu - One of the best experts on this subject based on the ideXlab platform.
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projected hartree Fock Theory as a polynomial of particle hole excitations and its combination with variational coupled cluster Theory
Journal of Chemical Physics, 2017Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Projected Hartree-Fock Theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. Coupled cluster Theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and coupled cluster Theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.
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communication projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
Journal of Chemical Physics, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation th...
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communication projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
Journal of Chemical Physics, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation Theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
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projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
arXiv: Strongly Correlated Electrons, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation Theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
Thomas M Henderson - One of the best experts on this subject based on the ideXlab platform.
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projected hartree Fock Theory as a polynomial of particle hole excitations and its combination with variational coupled cluster Theory
Journal of Chemical Physics, 2017Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Projected Hartree-Fock Theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. Coupled cluster Theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and coupled cluster Theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.
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communication projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
Journal of Chemical Physics, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation th...
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communication projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
Journal of Chemical Physics, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation Theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
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projected hartree Fock Theory as a polynomial similarity transformation Theory of single excitations
arXiv: Strongly Correlated Electrons, 2016Co-Authors: Yiheng Qiu, Thomas M Henderson, Gustavo E ScuseriaAbstract:Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style Theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation Theory is an alternative to our recently presented double excitation Theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
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projected hartree Fock Theory
Journal of Chemical Physics, 2012Co-Authors: Carlos A Jimenezhoyos, Thomas M Henderson, Takashi Tsuchimochi, Gustavo E ScuseriaAbstract:Projected Hartree–Fock (PHF) Theory has a long history in quantum chemistry. PHF is here understood as the variational determination of an N-electron broken symmetry Slater determinant that minimizes the energy of a projected state with the correct quantum numbers. The method was actively pursued for several decades but seems to have been abandoned. We here derive and implement a “variation after projection” PHF Theory using techniques different from those previously employed in quantum chemistry. Our PHF methodology has modest mean-field computational cost, yields relatively simple expressions, can be applied to both collinear and non-collinear spin cases, and can be used in conjunction with deliberate symmetry breaking and restoration of other molecular symmetries like complex conjugation and point group. We present several benchmark applications to dissociation curves and singlet-triplet energy splittings, showing that the resulting PHF wavefunctions are of high quality multireference character. We also provide numerical evidence that in the thermodynamic limit, the energy in PHF is not lower than that of broken-symmetry HF, a simple consequence of the lack of size consistency and extensivity of PHF.
Alex J. W. Thom - One of the best experts on this subject based on the ideXlab platform.
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parity time symmetry in hartree Fock Theory
Journal of Chemical Theory and Computation, 2019Co-Authors: Hugh G. A. Burton, Alex J. W. Thom, Pierrefrancois LoosAbstract:PT-symmetry—invariance with respect to combined space reflection P and time reversal T—provides a weaker condition than (Dirac) Hermiticity for ensuring a real energy spectrum of a general non-Herm...
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holomorphic hartree Fock Theory the nature of two electron problems
Journal of Chemical Theory and Computation, 2018Co-Authors: Hugh G. A. Burton, Mark Gross, Alex J. W. ThomAbstract:We explore the existence and behavior of holomorphic restricted Hartree–Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1/2(3n – 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe Theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the π electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the p...
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Holomorphic Hartree-Fock Theory: an inherently multireference approach
arXiv: Chemical Physics, 2015Co-Authors: Hugh G. A. Burton, Alex J. W. ThomAbstract:We investigate the existence of holomorphic Hartree-Fock solutions using a revised SCF algorithm. We use this algorithm to study the Hartree-Fock solutions for H$_{2}$ and H$_{4}^{2+}$ and report the emergence of holomorphic solutions at points of symmetry breaking. Finally, we find these holomorphic solutions for H$_{4}$ and use them as a basis for Non-Orthogonal Configuration Interaction at a range of rectangular geometries and show them to produce energies in good agreement with Full Configuration Interaction.
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holomorphic hartree Fock Theory and configuration interaction
Journal of Chemical Theory and Computation, 2014Co-Authors: Hamish G Hiscock, Alex J. W. ThomAbstract:We investigate the Hartree-Fock solutions to H2 in a minimal basis. We note the properties of the solutions and their disappearance with geometry and propose a new method, called Holomorphic Hartree-Fock Theory, where we modify the self-consistent field (SCF) equations to avoid disappearance of the solutions. We use these solutions as a basis for a nonorthogonal configuration interaction to produce a smooth binding curve over a complete range of geometries.
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holomorphic hartree Fock Theory and configuration interaction
arXiv: Chemical Physics, 2014Co-Authors: Hamish G Hiscock, Alex J. W. ThomAbstract:We investigate the Hartree-Fock solutions to H2 in a minimal basis. We note the properties of the solutions and their disappearance with geometry and propose a new method, Holomorphic Hartree-Fock Theory, where we modify the SCF equations to avoid disappearance of the solutions. We use these solutions as a basis for a non-orthogonal Configuration Interaction to produce a smooth binding curve over a complete range of geometries.