Active-Space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-Representability Constraints for Variational Two-Particle Reduced Density Matrix Calculations

Shenvi, Neil; Izmaylov, Artur F.

doi:10.1103/physrevlett.105.213003

Cited by 54 publications

(63 citation statements)

References 25 publications

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“…25 In this work, we study strong electron correlation in FeMoco using two multireference methods: the configuration interaction complete-active-space self-consistent-field (CI-CASSCF) method 26,27 and the variational two-electron reduced density matrix (V2RDM) method. [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] Strictly speaking, both are complete-active-space methods in which those electrons and orbitals thought to exhibit the greatest entanglement are treated as explicitly correlated. Orbital rotations are performed so as to minimize the energy in a self-consistent fashion.…”

Section: Introductionmentioning

confidence: 99%

Strong Electron Correlation in Nitrogenase Cofactor, FeMoco

Montgomery

Mazziotti

2018

J. Phys. Chem. A

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FeMoco, MoFeSC, has been shown to be the active catalytic site for the reduction of nitrogen to ammonia in the nitrogenase protein. An understanding of its electronic structure including strong electron correlation is key to designing mimic catalysts capable of ambient nitrogen fixation. Active spaces ranging from [54, 54] to [65, 57] have been predicted for a quantitative description of FeMoco's electronic structure. However, a wave function approach for a singlet state using a [54, 54] active space would require 10 variables. In this work, we systematically explore the active-space size necessary to qualitatively capture strong correlation in FeMoco and two related moieties, MoFeS and FeS. Using CASSCF and 2-RDM methods, we consider active-space sizes up to [14, 14] and [30, 30], respectively, with STO-3G, 3-21G, and DZP basis sets and use fractional natural-orbital occupation numbers to assess the level of multireference electron correlation, an examination of which reveals a competition between single-reference and multireference solutions to the electronic Schrödinger equation for smaller active spaces and a consistent multireference solution for larger active spaces.

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Section: Introductionmentioning

confidence: 99%

Strong Electron Correlation in Nitrogenase Cofactor, FeMoco

Montgomery

Mazziotti

2018

J. Phys. Chem. A

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“…Direct calculation of the reduced variables, however, requires that they and their functionals be consistent with a realistic N -electron quantum system; in other words, the reduced variables and functionals must be representable by the integration of an N -electron density matrix. Such consistency relations are known as the N -representability conditions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][20][21][22][23][24]. These conditions are particularly important to 2-RDM methods where they enable the direct calculation of the 2-RDM without the wavefunction, but they are also implicit in the design of realistic approximations to the density functional in density functional theory [31,32].…”

Section: Introductionmentioning

confidence: 99%

Significant conditions for the two-electron reduced density matrix from the constructive solution ofNrepresentability

Mazziotti

2012

Phys. Rev. A

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We recently presented a constructive solution to the N -representability problem of the twoelectron reduced density matrix (2-RDM)-a systematic approach to constructing complete conditions to ensure that the 2-RDM represents a realistic N -electron quantum system [D. A. Mazziotti, Phys. Rev. Lett. 108, 263002 (2012)]. In this paper we provide additional details and derive further N -representability conditions on the 2-RDM that follow from the constructive solution. The resulting conditions can be classified into a hierarchy of constraints, known as the (2, q)-positivity conditions where the q indicates their derivation from the nonnegativity of q-body operators. In addition to the known T1 and T2 conditions, we derive a new class of (2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of (2,6)-positivity conditions. The constraints obtained can be divided into two general types: (i) lifting conditions, that is conditions which arise from lifting lower (2, q)-positivity conditions to higher (2, q + 1)-positivity conditions and (ii) pure conditions, that is conditions which cannot be derived from a simple lifting of the lower conditions. All of the lifting conditions and the pure (2, q)-positivity conditions for q > 3 require tensor decompositions of the coefficients in the model Hamiltonians. Subsets of the new N -representability conditions can be employed with the previously known conditions to achieve polynomially scaling calculations of ground-state energies and 2-RDMs of many-electron quantum systems even in the presence of strong electron correlation.

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“…The definition of the set of pure N ‐representable ‐RDMs by the generalized Pauli conditions may provide new insights into the development of practical 1‐RDM‐based electronic structure methods . The generalized Pauli conditions may also be useful in some cases as further restrictions on the N ‐representability of the 2‐RDM in variational calculations based on the 2‐RDM . As suggested by other authors, pinning of the 1‐RDM to the generalized Pauli conditions provides potentially useful information about the Slater determinants that contribute most significantly to the wave function.…”

Section: Discussionmentioning

confidence: 95%

“…[33,34] The generalized Pauli conditions may also be useful in some cases as further restrictions on the N-representability of the 2-RDM [10,[35][36][37] in variational calculations based on the 2-RDM. [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] As suggested by other authors, [3,4] pinning of the 1-RDM to the generalized Pauli conditions provides potentially useful information about the Slater determinants that contribute most significantly to the wave function. The sufficient condition encoded in the 1-RDM for an open quantum system gives a physical insight through its orbital occupations into the ramifications of environment interactions and openness in quantum mechanics.…”

Section: Discussionmentioning

confidence: 99%

Structure of the one‐electron reduced density matrix from the generalized Pauli exclusion principle

Chakraborty¹,

Mazziotti²

2015

Int J of Quantum Chemistry

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The Pauli exclusion principle requires that the occupations of the orbitals lie between zero and one. These Pauli conditions hold for one-electron reduced density matrices (1-RDMs) from both open and closed quantum systems. More than 40 years ago, it was recognized that there are additional conditions on the 1-RDM for closed quantum systems. In this review, we discuss the structure of the 1-RDM from the generalized Pauli exclusion principle in many-electron atoms and molecules and the violation of the generalized Pauli principle as a sufficient condition for the openness of a many-electron quantum system.

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Active-SpaceN-Representability Constraints for Variational Two-Particle Reduced Density Matrix Calculations

Cited by 54 publications

References 25 publications

Strong Electron Correlation in Nitrogenase Cofactor, FeMoco

Strong Electron Correlation in Nitrogenase Cofactor, FeMoco

Significant conditions for the two-electron reduced density matrix from the constructive solution ofNrepresentability

Structure of the one‐electron reduced density matrix from the generalized Pauli exclusion principle

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