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Garnet Kin-lic Chan - One of the best experts on this subject based on the ideXlab platform.
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extended implementation of Canonical Transformation theory parallelization and a new level shifted condition
Physical Chemistry Chemical Physics, 2012Co-Authors: Takeshi Yanai, Eric Neuscamman, Yuki Kurashige, Garnet Kin-lic ChanAbstract:The Canonical Transformation (CT) theory has been developed as a multireference electronic structure method to compute high-level dynamic correlation on top of a large active space reference treated with the ab initio density matrix renormalization group method. This article describes a parallelized algorithm and implementation of the CT theory to handle large computational demands of the CT calculation, which has the same scaling as the coupled cluster singles and doubles theory. To stabilize the iterative solution of the CT method, a modification to the CT amplitude equation is introduced with the inclusion of a level shift parameter. The level-shifted condition has been found to effectively remove a type of intruder state that arises in the linear equations of CT and to address the discontinuity problems in the potential energy curves observed in the previous CT studies.
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a review of Canonical Transformation theory
International Reviews in Physical Chemistry, 2010Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory targets the description of dynamic correlation in multireference quantum chemistry problems. When combined with a static correlation quantum chemistry method, it enables the quantitative description of chemical processes involving electronic structure not described by a single electronic configuration. We argue that many multireference dynamic correlation methods display unsatisfactory characteristics, including lack of size-consistency, a low-order treatment of correlation, and a poor computational scaling. By contrast, CT theory is based on an exponential ansatz that is rigorously size-consistent, reduces in a single-reference limit to a coupled cluster theory, and has an n^6 computational scaling with system and active space size. The efficient formulation of CT theory has allowed it to be applied to difficult systems in conjunction with active spaces with more than 30 orbitals, beyond the reach of traditional methods, with an accuracy that far exceeds multireference perturbation theories. Here we review the basic motivation, formulation, and implementation of CT theory, as well as survey some of our recent applications and possible future directions.
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strongly contracted Canonical Transformation theory
Journal of Chemical Physics, 2010Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory describes dynamic correlation in multireference systems with large active spaces. Here we discuss CT theory’s intruder state problem and why our previous approach of overlap matrix truncation becomes infeasible for sufficiently large active spaces. We propose the use of strongly and weakly contracted excitation operators as alternatives for dealing with intruder states in CT theory. The performance of these operators is evaluated for the H2O, N2, and NiO molecules, with comparisons made to complete active space second order perturbation theory and Davidson-corrected multireference configuration interaction theory. Finally, using a combination of strongly contracted CT theory and orbital-optimized density matrix renormalization group theory, we evaluate the singlet-triplet gap of free base porphin using an active space containing all 24 out-of-plane 2p orbitals. Modeling dynamic correlation with an active space of this size is currently only possible using CT theory.
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multireference quantum chemistry through a joint density matrix renormalization group and Canonical Transformation theory
Journal of Chemical Physics, 2010Co-Authors: Takeshi Yanai, Eric Neuscamman, Yuki Kurashige, Garnet Kin-lic ChanAbstract:We describe the joint application of the density matrix renormalization group and Canonical Transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the Canonical Transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]^(2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]^(2+).
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quadratic Canonical Transformation theory and higher order density matrices
Journal of Chemical Physics, 2009Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT’s accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H2OH2O and N2N2 binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.
Takeshi Yanai - One of the best experts on this subject based on the ideXlab platform.
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extended implementation of Canonical Transformation theory parallelization and a new level shifted condition
Physical Chemistry Chemical Physics, 2012Co-Authors: Takeshi Yanai, Eric Neuscamman, Yuki Kurashige, Garnet Kin-lic ChanAbstract:The Canonical Transformation (CT) theory has been developed as a multireference electronic structure method to compute high-level dynamic correlation on top of a large active space reference treated with the ab initio density matrix renormalization group method. This article describes a parallelized algorithm and implementation of the CT theory to handle large computational demands of the CT calculation, which has the same scaling as the coupled cluster singles and doubles theory. To stabilize the iterative solution of the CT method, a modification to the CT amplitude equation is introduced with the inclusion of a level shift parameter. The level-shifted condition has been found to effectively remove a type of intruder state that arises in the linear equations of CT and to address the discontinuity problems in the potential energy curves observed in the previous CT studies.
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a review of Canonical Transformation theory
International Reviews in Physical Chemistry, 2010Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory targets the description of dynamic correlation in multireference quantum chemistry problems. When combined with a static correlation quantum chemistry method, it enables the quantitative description of chemical processes involving electronic structure not described by a single electronic configuration. We argue that many multireference dynamic correlation methods display unsatisfactory characteristics, including lack of size-consistency, a low-order treatment of correlation, and a poor computational scaling. By contrast, CT theory is based on an exponential ansatz that is rigorously size-consistent, reduces in a single-reference limit to a coupled cluster theory, and has an n^6 computational scaling with system and active space size. The efficient formulation of CT theory has allowed it to be applied to difficult systems in conjunction with active spaces with more than 30 orbitals, beyond the reach of traditional methods, with an accuracy that far exceeds multireference perturbation theories. Here we review the basic motivation, formulation, and implementation of CT theory, as well as survey some of our recent applications and possible future directions.
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strongly contracted Canonical Transformation theory
Journal of Chemical Physics, 2010Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory describes dynamic correlation in multireference systems with large active spaces. Here we discuss CT theory’s intruder state problem and why our previous approach of overlap matrix truncation becomes infeasible for sufficiently large active spaces. We propose the use of strongly and weakly contracted excitation operators as alternatives for dealing with intruder states in CT theory. The performance of these operators is evaluated for the H2O, N2, and NiO molecules, with comparisons made to complete active space second order perturbation theory and Davidson-corrected multireference configuration interaction theory. Finally, using a combination of strongly contracted CT theory and orbital-optimized density matrix renormalization group theory, we evaluate the singlet-triplet gap of free base porphin using an active space containing all 24 out-of-plane 2p orbitals. Modeling dynamic correlation with an active space of this size is currently only possible using CT theory.
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multireference quantum chemistry through a joint density matrix renormalization group and Canonical Transformation theory
Journal of Chemical Physics, 2010Co-Authors: Takeshi Yanai, Eric Neuscamman, Yuki Kurashige, Garnet Kin-lic ChanAbstract:We describe the joint application of the density matrix renormalization group and Canonical Transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the Canonical Transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]^(2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]^(2+).
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quadratic Canonical Transformation theory and higher order density matrices
Journal of Chemical Physics, 2009Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT’s accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H2OH2O and N2N2 binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.
Eric Neuscamman - One of the best experts on this subject based on the ideXlab platform.
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extended implementation of Canonical Transformation theory parallelization and a new level shifted condition
Physical Chemistry Chemical Physics, 2012Co-Authors: Takeshi Yanai, Eric Neuscamman, Yuki Kurashige, Garnet Kin-lic ChanAbstract:The Canonical Transformation (CT) theory has been developed as a multireference electronic structure method to compute high-level dynamic correlation on top of a large active space reference treated with the ab initio density matrix renormalization group method. This article describes a parallelized algorithm and implementation of the CT theory to handle large computational demands of the CT calculation, which has the same scaling as the coupled cluster singles and doubles theory. To stabilize the iterative solution of the CT method, a modification to the CT amplitude equation is introduced with the inclusion of a level shift parameter. The level-shifted condition has been found to effectively remove a type of intruder state that arises in the linear equations of CT and to address the discontinuity problems in the potential energy curves observed in the previous CT studies.
-
a review of Canonical Transformation theory
International Reviews in Physical Chemistry, 2010Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory targets the description of dynamic correlation in multireference quantum chemistry problems. When combined with a static correlation quantum chemistry method, it enables the quantitative description of chemical processes involving electronic structure not described by a single electronic configuration. We argue that many multireference dynamic correlation methods display unsatisfactory characteristics, including lack of size-consistency, a low-order treatment of correlation, and a poor computational scaling. By contrast, CT theory is based on an exponential ansatz that is rigorously size-consistent, reduces in a single-reference limit to a coupled cluster theory, and has an n^6 computational scaling with system and active space size. The efficient formulation of CT theory has allowed it to be applied to difficult systems in conjunction with active spaces with more than 30 orbitals, beyond the reach of traditional methods, with an accuracy that far exceeds multireference perturbation theories. Here we review the basic motivation, formulation, and implementation of CT theory, as well as survey some of our recent applications and possible future directions.
-
strongly contracted Canonical Transformation theory
Journal of Chemical Physics, 2010Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory describes dynamic correlation in multireference systems with large active spaces. Here we discuss CT theory’s intruder state problem and why our previous approach of overlap matrix truncation becomes infeasible for sufficiently large active spaces. We propose the use of strongly and weakly contracted excitation operators as alternatives for dealing with intruder states in CT theory. The performance of these operators is evaluated for the H2O, N2, and NiO molecules, with comparisons made to complete active space second order perturbation theory and Davidson-corrected multireference configuration interaction theory. Finally, using a combination of strongly contracted CT theory and orbital-optimized density matrix renormalization group theory, we evaluate the singlet-triplet gap of free base porphin using an active space containing all 24 out-of-plane 2p orbitals. Modeling dynamic correlation with an active space of this size is currently only possible using CT theory.
-
multireference quantum chemistry through a joint density matrix renormalization group and Canonical Transformation theory
Journal of Chemical Physics, 2010Co-Authors: Takeshi Yanai, Eric Neuscamman, Yuki Kurashige, Garnet Kin-lic ChanAbstract:We describe the joint application of the density matrix renormalization group and Canonical Transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the Canonical Transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]^(2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]^(2+).
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quadratic Canonical Transformation theory and higher order density matrices
Journal of Chemical Physics, 2009Co-Authors: Eric Neuscamman, Takeshi Yanai, Garnet Kin-lic ChanAbstract:Canonical Transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT’s accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H2OH2O and N2N2 binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.
Klaus Richter - One of the best experts on this subject based on the ideXlab platform.
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complex scattering as Canonical Transformation a semiclassical approach in fock space
Annalen der Physik, 2015Co-Authors: Thomas Engl, Juan Diego Urbina, Quirin Hummel, Klaus RichterAbstract:We show that a theory of com plex scattering between many-body (Fock) states can be constructed such that its classical limit is a Canonical Transformation thus encoding quantum interference in the semiclassical form of the associated unitary operator. Based on this idea, we study the different coherent effects expected under different choices of the many-body states and provide different representations of the associated transition probabilities. In this way, we derive exact relations and representations of the scattering process that can be used to attack timely problems related with Boson Sampling.
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boson sampling as Canonical Transformation a semiclassical approach in fock space
arXiv: Quantum Physics, 2015Co-Authors: Thomas Engl, Juan Diego Urbina, Quirin Hummel, Klaus RichterAbstract:We show that a theory of complex scattering between many-body (Fock) states can be constructed such that its classical limit is a Canonical Transformation thus encoding quantum interference in the semiclassical form of the associated unitary operator. Based on this idea, we study the different coherent effects expected under different choices of the many-body states and provide different representations of the associated transition probabilities. In this way, we derive exact relations and representations of the scattering process that can be used to attack timely problems related with Boson Sampling.
R F Alvarezestrada - One of the best experts on this subject based on the ideXlab platform.
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third order equation for harmonic generation complex Canonical Transformation and jwkb solution
Journal of Physics A, 2004Co-Authors: Gabriel Alvarez, R F AlvarezestradaAbstract:The quantum description of third harmonic generation can be formulated as an eigenvalue problem for a third-order linear differential equation. We perform a semiclassical study of this third-order equation, generalizing the familiar JWKB theory for the second-order Schrodinger equation, and deriving explicit (albeit approximate) formulas for the eigenvalues within this semiclassical context. A central role in this analysis is played by a nonlinear complex Canonical Transformation which permits a complete description of the classical motion (generated by a complex polynomial Hamiltonian function) in the complexified position and momentum planes.