Direct calculation of excited-state electronic energies and two-electron reduced density matrices from the anti-Hermitian contracted Schrödinger equation

Gidofalvi, Gergely; Mazziotti, David A.

doi:10.1103/physreva.80.022507

Cited by 44 publications

(60 citation statements)

References 73 publications

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“…II C we give the differential equations with which, as demonstrated in Ref. 24, the ACSE can be solved for excited states.…”

Section: Theorymentioning

confidence: 99%

“…Because the ACSE with an initial MCSCF 2-RDM can treat strong multireference correlation effects, [22][23][24] Consider an N-electron, high-spin triplet wave function ⌽͑N͒ represented in a basis of r spatial orbitals ͕ i ͖. The spin properties of the high-spin triplet ⌽͑N͒ are…”

Section: B Solving the Acse For Open-shell Systemsmentioning

confidence: 99%

“…In this paper we study the conical intersection in the triplet excited states of methylene by solving the anti-Hermitian contracted Schrödinger equation ͑ACSE͒ [20][21][22][23][24][25][26][27][28] for 2-RDMs without explicitly computing many-electron wave functions. The work harnesses recent extensions of the ACSE method for the treatment of ͑i͒ excited states 24 and ͑ii͒ arbitrary-spin states. 25 We determine both absolute energies of the 1 3 B 1 , 1 3 A 2 , and 2 3 B 1 states of methylene ͑CH 2 ͒ and the location of the conical intersection along the 1 3 A 2 −2 3 B 1 potential-energy surfaces.…”

Section: Introductionmentioning

confidence: 99%

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Conical intersections in triplet excited states of methylene from the anti-Hermitian contracted Schrödinger equation

Snyder

Rothman

Foley

et al. 2010

The Journal of Chemical Physics

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A conical intersection in triplet excited states of methylene is computed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions of the anti-Hermitian contracted Schrodinger equation (ACSE). The study synthesizes recent extensions of the ACSE method for the treatment of excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary-spin states [A. E. Rothman, J. J. Foley, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]. We compute absolute energies of the 1 (3)B(1), 1 (3)A(2), and 2 (3)B(1) states of methylene (CH(2)) and the location of the conical intersection along the 1 (3)A(2)-2 (3)B(1) potential-energy surfaces. To treat multireference correlation, we seed the ACSE with an initial 2-RDM from a multiconfiguration self-consistent field (MCSCF) calculation. The ACSE produces energies that significantly improve upon those from MCSCF and second-order multireference many-body perturbation theory, and the 2-RDMs from the ACSE nearly satisfy necessary N-representability conditions. Comparison of the results from augmented double-zeta and triple-zeta basis sets demonstrates the importance of augmented (or diffuse) functions for determining the location of the conical intersection.

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“…II C we give the differential equations with which, as demonstrated in Ref. 24, the ACSE can be solved for excited states.…”

Section: Theorymentioning

confidence: 99%

Section: B Solving the Acse For Open-shell Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Conical intersections in triplet excited states of methylene from the anti-Hermitian contracted Schrödinger equation

Snyder

Rothman

Foley

et al. 2010

The Journal of Chemical Physics

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“…[1][2][3][4][5] Recently, two general approaches to the direct calculation of the 2-RDM have emerged: ͑i͒ the minimization of the ground-state energy as a variational functional of a 2-RDM that is constrained by a set of necessary N-representability conditions [6][7][8][9][10][11] and ͑ii͒ the solution of the contracted Schrödinger equation, particularly its antiHermitian part, to determine ground-or excited-state 2-RDMs. [12][13][14][15][16][17][18][19][20] A variant of the variational 2-RDM method has been developed in which 2-RDM is parametrized by single-and double-excitation coefficients; importantly, the parametrization is selected to yield not only energies that scale linearly with system size ͑size extensive͒ but also 2-RDMs that satisfy known N-representability conditions. [21][22][23][24][25][26] Two distinct parametrizations have been designed: ͑i͒ Kollmar 21 proposed a method ͑K͒ that is derived from inspecting the D, Q, and G conditions for N-representability, and ͑ii͒ one of the authors, 25 stressing the balanced treatment of particles and holes, proposed a parametrization ͑M͒ that is derived from the D and Q conditions.…”

Section: Introductionmentioning

confidence: 99%

Exploiting the spatial locality of electron correlation within the parametric two-electron reduced-density-matrix method

DePrince

Mazziotti

2010

The Journal of Chemical Physics

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The parametric variational two-electron reduced-density-matrix (2-RDM) method is applied to computing electronic correlation energies of medium-to-large molecular systems by exploiting the spatial locality of electron correlation within the framework of the cluster-in-molecule (CIM) approximation [S. Li et al., J. Comput. Chem. 23, 238 (2002); J. Chem. Phys. 125, 074109 (2006)]. The 2-RDMs of individual molecular fragments within a molecule are determined, and selected portions of these 2-RDMs are recombined to yield an accurate approximation to the correlation energy of the entire molecule. In addition to extending CIM to the parametric 2-RDM method, we (i) suggest a more systematic selection of atomic-orbital domains than that presented in previous CIM studies and (ii) generalize the CIM method for open-shell quantum systems. The resulting method is tested with a series of polyacetylene molecules, water clusters, and diazobenzene derivatives in minimal and nonminimal basis sets. Calculations show that the computational cost of the method scales linearly with system size. We also compute hydrogen-abstraction energies for a series of hydroxyurea derivatives. Abstraction of hydrogen from hydroxyurea is thought to be a key step in its treatment of sickle cell anemia; the design of hydroxyurea derivatives that oxidize more rapidly is one approach to devising more effective treatments.

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“…T he violation, we show, provides a sufficient condition fo r the openness o f any many-electron quantum system that is computable from knowledge o f only the I-RDM. In principle, the 1-RDM can be com puted from experim ent [12], com putation [13][14][15][16][17][18][19][20], or any com bination o f experim ent and com putation. H ere we dem onstrate this condition through calculations o f exciton dynam ics in photosynthetic light harvesting.…”

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confidence: 99%

Sufficient condition for the openness of a many-electron quantum system from the violation of a generalized Pauli exclusion principle

Chakraborty

Mazziotti

2015

Phys. Rev. A

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Information about the interaction of a many-electron quantum system with its environment, we show, is encoded within the one-electron density matrix (1-RDM). While the 1-RDM from an ensemble many-electron quantum system must obey the Pauli exclusion principle, the 1-RDM must obey additional constraints known as generalized Pauli conditions when it corresponds to a closed system describable by a single wave function. By examining the 1-RDM's violation of these generalized Pauli conditions, we obtain a sufficient condition at the level of a single electron for a many-electron quantum system's openness. In an application to exciton dynamics in photosynthetic light harvesting we show that the interaction of the system with the environment (quantum noise) relaxes significant constraints imposed on the exciton dynamics by the generalized Pauli conditions. This relaxation provides a geometric (kinematic) interpretation for the role of noise in enhancing exciton transport in quantum systems. PACS number (s): 03.65.Yz, 31.15.-p T he Pauli exclusion principle requires that the occupations o f the orbitals lie betw een 0 and 1. These Pauli conditions hold for one-electron reduced density m atrices (1-RDM s) from both open and closed quantum system s [1,2], M ore than 40 years ago, it was recognized that there are additional conditions on the 1-RDM for closed quantum system s [3,4], Recently, these additional constraints, know n as generalized Pauli conditions, have been system atically derived for arbitrary num bers o f electrons and orbitals [5,6] and applied to closed, tim e-independent system s such as atom s and m olecules [7-11]. In this R apid Com m unication w e use the violation o f the generalized Pauli conditions to quantify the interaction o f a quantum system with its environm ent. T he violation, we show, provides a sufficient condition fo r the openness o f any many-electron quantum system that is computable from knowledge o f only the I-RDM. In principle, the 1-RDM can be com puted from experim ent [12], com putation [13-20], or any com bination o f experim ent and com putation. H ere we dem onstrate this condition through calculations o f exciton dynam ics in photosynthetic light harvesting. T he results show that environm ental noise relaxes significant constraints im posed on the exciton dynam ics by a closed quantum system , providing a geom etric interpretation for the role o f noise in enhancing exciton transport. T he sufficient condition, com putable from only the 1-RDM, is potentially applicable to a w ide variety o f open m any-electron quantum systems. Integrating the /V-electron density m atrix over all electrons save one generates the 1 -RD M , w hich gives the probability o f finding one electron for all possible configurations o f the other N -1 electrons [1], T he eigenfunctions o f the 1-RDM are know n as the natural orbitals ,-, and its eigenvalues are know n as the natural orbital occupation num bers n, [21]. The generalized Pauli conditions, also know n as pure Nrepresentability conditi...

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Direct calculation of excited-state electronic energies and two-electron reduced density matrices from the anti-Hermitian contracted Schrödinger equation

Cited by 44 publications

References 73 publications

Conical intersections in triplet excited states of methylene from the anti-Hermitian contracted Schrödinger equation

Conical intersections in triplet excited states of methylene from the anti-Hermitian contracted Schrödinger equation

Exploiting the spatial locality of electron correlation within the parametric two-electron reduced-density-matrix method

Sufficient condition for the openness of a many-electron quantum system from the violation of a generalized Pauli exclusion principle

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