The Experts below are selected from a list of 26157 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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spin polynomial Similarity Transformation for repulsive hamiltonians interpolating between coupled cluster and spin projected unrestricted hartree fock
Physical Chemistry Chemical Physics, 2017Co-Authors: John A Gomez, Matthias Degroote, Yiheng Qiu, Jinmo Zhao, Gustavo E ScuseriaAbstract:Our overarching goal is to be able to describe both weak and strong correlation with a single, computationally affordable method without sacrificing important qualities of the wavefunction, e.g. symmetries of the Hamiltonian. We know that coupled cluster theory with low-order excitations is excellent at describing weakly-correlated systems near equilibrium, but breaks down as systems become more strongly correlated. Projected Hartree-Fock on the other hand is inherently capable of describing multireference character, but misses weak correlation. We are thus exploring how best to combine coupled cluster and projected Hartree-Fock in our search for a computationally feasible method that is applicable across a wide range of correlation strengths. In this manuscript, we adapt our earlier work on the pairing Hamiltonian to repulsive Hamiltonians, resulting in the spin polynomial Similarity Transformation (SpinPoST) interpolation. SpinPoST parameterizes the wavefunction in order to interpolate between the coupled cluster and spin-projected unrestricted Hartree-Fock ansatze self consistently, and is a spin-symmetry adapted model which involves only single and double excitations. We employ a unique approach of optimizing the wavefunction by minimizing the effect of connected quadruple excitations, resulting in a method which is spin-symmetry adapted and is comparable energetically to coupled cluster with singles and doubles for weak correlation and spin-projected Hartree-Fock for strong correlation.
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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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polynomial Similarity Transformation theory a smooth interpolation between coupled cluster doubles and projected bcs applied to the reduced bcs hamiltonian
Physical Review B, 2016Co-Authors: Matthias Degroote, Thomas M Henderson, Jinmo Zhao, J Dukelsky, Gustavo E ScuseriaAbstract:We present a Similarity Transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The effective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1\% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.
Yiheng Qiu - One of the best experts on this subject based on the ideXlab platform.
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spin polynomial Similarity Transformation for repulsive hamiltonians interpolating between coupled cluster and spin projected unrestricted hartree fock
Physical Chemistry Chemical Physics, 2017Co-Authors: John A Gomez, Matthias Degroote, Yiheng Qiu, Jinmo Zhao, Gustavo E ScuseriaAbstract:Our overarching goal is to be able to describe both weak and strong correlation with a single, computationally affordable method without sacrificing important qualities of the wavefunction, e.g. symmetries of the Hamiltonian. We know that coupled cluster theory with low-order excitations is excellent at describing weakly-correlated systems near equilibrium, but breaks down as systems become more strongly correlated. Projected Hartree-Fock on the other hand is inherently capable of describing multireference character, but misses weak correlation. We are thus exploring how best to combine coupled cluster and projected Hartree-Fock in our search for a computationally feasible method that is applicable across a wide range of correlation strengths. In this manuscript, we adapt our earlier work on the pairing Hamiltonian to repulsive Hamiltonians, resulting in the spin polynomial Similarity Transformation (SpinPoST) interpolation. SpinPoST parameterizes the wavefunction in order to interpolate between the coupled cluster and spin-projected unrestricted Hartree-Fock ansatze self consistently, and is a spin-symmetry adapted model which involves only single and double excitations. We employ a unique approach of optimizing the wavefunction by minimizing the effect of connected quadruple excitations, resulting in a method which is spin-symmetry adapted and is comparable energetically to coupled cluster with singles and doubles for weak correlation and spin-projected Hartree-Fock for strong correlation.
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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.
Ali Alavi - One of the best experts on this subject based on the ideXlab platform.
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eliminating the wave function singularity for ultracold atoms by a Similarity Transformation
Physical Review Research, 2020Co-Authors: Peter Jeszenszki, Hongjun Luo, Ali Alavi, Ulrich Ebling, Joachim BrandAbstract:The authors propose a Similarity Transformation that removes a singularity in the wave function of many-body systems with contact interactions.
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Similarity Transformation of the electronic Schr\"odinger equation via Jastrow factorisation
The Journal of Chemical Physics, 2019Co-Authors: Aron J. Cohen, Hongjun Luo, Kai Guther, Werner Dobrautz, David P. Tew, Ali AlaviAbstract:By expressing the electronic wavefunction in an explicitly-correlated (Jastrow-factorised) form, a Similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions. The resulting ground-state eigenvalue problem can be solved projectively using a stochastic configuration-interaction formalism. Our approach permits use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets. Results are presented for the total energies and ionisation potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort.
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Similarity Transformation of the electronic schrodinger equation via jastrow factorization
Journal of Chemical Physics, 2019Co-Authors: Aron J. Cohen, Hongjun Luo, Kai Guther, Werner Dobrautz, David P. Tew, Ali AlaviAbstract:By expressing the electronic wavefunction in an explicitly correlated (Jastrow-factorized) form, a Similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions. The resulting ground-state eigenvalue problem can be solved projectively using a stochastic configuration-interaction formalism. Our approach permits the use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets. Results are presented for the total energies and ionization potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort.
Thomas M Henderson - One of the best experts on this subject based on the ideXlab platform.
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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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polynomial Similarity Transformation theory a smooth interpolation between coupled cluster doubles and projected bcs applied to the reduced bcs hamiltonian
Physical Review B, 2016Co-Authors: Matthias Degroote, Thomas M Henderson, Jinmo Zhao, J Dukelsky, Gustavo E ScuseriaAbstract:We present a Similarity Transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The effective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1\% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.
Liang-cai Zhong - One of the best experts on this subject based on the ideXlab platform.
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a Similarity Transformation of velocity field and its application for an in depth study on laminar free convection heat transfer of gases
International Journal of Thermal Sciences, 2016Co-Authors: De-yi Shang, Liang-cai ZhongAbstract:Abstract An innovative Similarity Transformation of velocity field is reported for equivalent Transformation of governing partial differential equations of laminar free convection. To demonstrate its rationality theoretically, its rigorous theoretical derivation is presented firstly in this work. On this basis, an example is presented with successful application for demonstration of its advantages in in-depth study on free convection heat transfer. The governing ordinary differential equations of laminar free convection equivalently transformed by the innovative Similarity Transformation are presented. It is seen that by the innovative Similarity Transformation the variable physical properties are transformed into the forms of the related physical property factors, which are organically coupled in the transformed governing ordinary differential equations. It proves that the innovative Similarity Transformation is very well suitable for consideration of variable physical properties. Then, a new algorithm is presented to calculate fluids flow and heat transfer of laminar free convection. It contains the theoretical and numerical models on laminar free convection, to consider the variable physical properties, to obtain the system of numerical solutions, and then, to create formalization equations for the convection heat transfer coefficient by means of an optimal curve-fitting approach based on the system of numerical solutions. A system of numerical calculations of the governing ordinary differential equations is presented for the gaseous laminar free convection. A temperature parameter model is induced for convenient and reliable treatment of variable physical properties of gases. The delivered formalization equations of heat transfer coefficient on gaseous free convection have strong theoretical and practical value for heat transfer applications because they are created based on the theoretically reasonable Similarity Transformation model combined with a better model of consideration of fluid's variable physical properties, accurate numerical solutions, and rigorous formalization equations combined with rigorous theoretical derivation. All these prove that the reported innovative Similarity Transformation is a better alternative applied for in-depth study on free convection heat transfer.
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heat transfer of laminar mixed convection of liquid
2016Co-Authors: De-yi Shang, Liang-cai ZhongAbstract:Introduction.- Conservation Equations for Laminar Mixed Convection.- An Innovative Similarity Transformation.- Similarity Transformation of Governing Partial Differential Equations.- Hydrodynamics.- Heat Transfer.- Similarity Transformation of Governing Partial Differential Equations.- Velocity Fields.- Skin-Friction Coefficient.- Temperature Fields.- Theoretical Heat Transfer Equation and Wall Temperature Gradient.- Effect of Local Prandtl Number on Wall Temperature Gradient.- Formulization Equations of Wall Temperature Gradient.- Verification of Formulated Correlation Equations on Wall Temperature Gradient.
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an innovative Similarity Transformation for in depth research of convection heat and mass transfer
Science Journal of Energy Engineering, 2015Co-Authors: De-yi Shang, Buxuan Wang, Liang-cai ZhongAbstract:Our innovative Similarity Transformation for in-depth research of convection heat and mass transfer is presented. For solving convection heat and mass transfer issues, the boundary layer analysis method is used, and meanwhile, the Falkner-Skan Transformation is currently popular to treat the core Similarity variables for velocity field Similarity. But this type of Transformation is inconvenient to do this core work, for Similarity Transformation of velocity field, because it is necessary to first induce flow function and group theory to derive an intermediate function for an indirect Similarity Transformation of the velocity field. This case also allows a difficult situation on consideration of variable physical properties. With our innovative Similarity Transformation, the above inconvenient and difficult situations are avoided, and the velocity components can be directly transformed to the related dimensionless ones. Then, the Similarity analysis and Transformation of the governing partial differential equations can be simplified greatly. Furthermore, our innovative Similarity Transformation can conveniently treat variable physical properties and their coupled effect on heat and mass transfer for enhancement of the practical value of convection heat and mass transfer, and so is a better alternative Transformation method to the traditional Falkner-Skan Transformation. It was proved that the above two innovative methods have a wide practical application in industry.
