Spin and symmetry adaptation of the variational two-electron reduced-density-matrix method

Gidofalvi, Gergely; Mazziotti, David A.

doi:10.1103/physreva.72.052505

Cited by 71 publications

(62 citation statements)

References 60 publications

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“…As discussed in Ref. [36], when considering singlet states, the use of spin adapted basis functions reduces the dimension of the large block of the 2 G matrix by a factor of 2, leading to substantial computational savings. However, one must be careful when considering non-singlet states, as the spin-block structure of 2 G (and the other spinadapted 2-RDMs) changes in this case [35].…”

Section: Theorymentioning

confidence: 99%

Accuracy of two-particleN-representability conditions for describing different spin states and the singlet–triplet gap in the linear acene series

2015

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Variational two-electron reduced-density-matrix (2-RDM) methods can provide a referenceindependent description of the electronic structure of strongly correlated molecules and materials. These methods represent one of few ways of performing large active-space-based computations that are beyond the scope of conventional configuration-interaction-based approaches. However, implementations of the method are quite rare, making it difficult for the quantum chemistry community to assess the utility of the approach. Here, we discuss an open-shell implementation of the variational 2-RDM method and explore its ability to describe different spin states in several model systems, including linear hydrogen chains and linear acenes. The largest calculations considered are comparable to complete-active-space computations with 50 electrons in 50 orbitals..

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Section: Theorymentioning

confidence: 99%

Accuracy of two-particleN-representability conditions for describing different spin states and the singlet–triplet gap in the linear acene series

2015

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“…We illustrate the method briefly here by reviewing a calculation of the potential energy curve of the hydrogen fluoride molecule [44]. The 2-RDM method with 2-positivity plus the T 2 condition produces a semidefinite program for hydrogen fluoride (after applying spin and symmetry adaptation [23]) with 336 664 variables, 168 432 constraints, 650 583 non-zero elements in the constraint matrix A, and 38 blocks in the solution matrix M . Semidefinite programs with several million variables and constraints have been solved with the method [24,27,28,44,45].…”

Section: Applications Of the 2-rdmmentioning

confidence: 99%

“…Semidefinite programs with several million variables and constraints have been solved with the method [24,27,28,44,45]. Comparisons of the first-order algorithm with second-order primal-dual interior-point algorithms have been reported in the literature [23,42].…”

Section: Applications Of the 2-rdmmentioning

confidence: 99%

First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules

Mazziotti¹

2007

ESAIM: M2AN

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Abstract. The ground-state energy and properties of any many-electron atom or molecule may be rigorously computed by variationally computing the two-electron reduced density matrix rather than the many-electron wavefunction. While early attempts fifty years ago to compute the ground-state 2-RDM directly were stymied because the 2-RDM must be constrained to represent an N -electron wavefunction, recent advances in theory and optimization have made direct computation of the 2-RDM possible. The constraints in the variational calculation of the 2-RDM require a special optimization known as a semidefinite programming. Development of first-order semidefinite programming for the 2-RDM method has reduced the computational costs of the calculation by orders of magnitude [Mazziotti, Phys. Rev. Lett. 93 (2004) 213001]. The variational 2-RDM approach is effective at capturing multireference correlation effects that are especially important at non-equilibrium molecular geometries. Recent work on 2-RDM methods will be reviewed and illustrated with particular emphasis on the importance of advances in large-scale semidefinite programming.Mathematics Subject Classification. 90C22, 81Q05, 52A40.

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“…16 and 17 by means of formalisms related to the particle-hole reduced density matrix framework. [18][19][20][21][22][23][24] In those references, it has also been suggested that the numerical value of the i ( 1 D i i − 2 2 D ii ii ) quantity could constitute an alternative measure of the number of effectively unpaired electrons corresponding to the wave function (N, S) and this result could be compared with those reported using other methods. [25][26][27][28][29][30][31][32][33] According to Eq.…”

Section: A the Seniority Number For A Spin-adapted Wave Functionmentioning

confidence: 99%

Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions

Alcoba

Torre

Laín

et al. 2013

The Journal of Chemical Physics

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This work extends the concept of seniority number, which has been widely used for classifying N-electron Slater determinants, to wave functions of N electrons and spin S, as well as to N-electron spin-adapted Hilbert spaces. We propose a spin-free formulation of the seniority number operator and perform a study on the behavior of the expectation values of this operator under transformations of the molecular basis sets. This study leads to propose a quantitative evaluation for the convergence of the expansions of the wave functions in terms of Slater determinants. The non-invariant character of the seniority number operator expectation value of a wave function with respect to a unitary transformation of the molecular orbital basis set, allows us to search for a change of basis which minimizes that expectation value. The results found in the description of wave functions of selected atoms and molecules show that the expansions expressed in these bases exhibit a more rapid convergence than those formulated in the canonical molecular orbital bases and even in the natural orbital ones.

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Spin and symmetry adaptation of the variational two-electron reduced-density-matrix method

Cited by 71 publications

References 60 publications

Accuracy of two-particleN-representability conditions for describing different spin states and the singlet–triplet gap in the linear acene series

Accuracy of two-particleN-representability conditions for describing different spin states and the singlet–triplet gap in the linear acene series

First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules

Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions

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