Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Chemistry

Contraction algorithms for third-order reduced density matrices: Symmetric group approach

A. Tone, Luis Laín, Judith Millán

Published Jan 1, 1993• 0 citations
Publisher
DOI
10.1007/bf01165563

Related papers

Unitary group approach to reduced density matrices

Josef Paldus, M. D. Gould

Theoretical Chemistry Accounts•Jul 1, 1993•12 citations

Traces ofpth-order reduced density matrices: symmetric group approach

Alicia Torre, Luis Laín

This paper describes a general procedure for calculating the traces of reduced density matrices of any order p of an N -electron system, in the basis of the irreducible representations of the symmetric group , in a spin-free formalism. The numerical values of these traces are determined by useful formulae. This approach provides a suitable study of the N - and S -representability of the reduced density matrices.

Journal of Physics A Mathematical and General•Jul 10, 1998•1 citation

Theory of reduced density matrices

Eugene S. Kryachko

Theoretical and Mathematical Physics•Sep 1, 1975•1 citation

Family of modified-contracted Schrödinger equations

Diego R. Alcoba, Carmela Valdemoro

A family of equations that combines contracted Schr\"odinger equations of different orders is reported here. Attention is focussed on the resulting second order, third order, and fourth order of these modified-contracted Schr\"odinger equations. Some of these equations are self-contained and have as fixed points those corresponding to the full-configuration interaction eigenstates. The indeterminacy, which hindered initially the use of the contracted Schr\"odinger equations, does not formally exist in these equations. Relations linking the lower-order reduced density matrices with the higher-order matrices are exactly incorporated into the modified-contracted Schr\"odinger-equations structure. The cancellation of high-order correlation terms, which is hidden in the contracted Schr\"odinger equations, now takes an explicit form.

Physical Review A•Nov 13, 2001•32 citations

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory

Sandeep Sharma, Gerald Knizia, Sheng Guo +1 more

We present two efficient and intruder-free methods for treating dynamic correlation on top of general multiconfiguration reference wave functions — including such as obtained by the density matrix renormalization group (DMRG) with large active spaces. The new methods are the second order variant of the recently proposed multireference linearized coupled cluster method (MRLCC) [Sharma, S.; Alavi, A. J. Chem. Phys. 2015, 143, 102815] and of N-electron valence perturbation theory (NEVPT2), with expected accuracies similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains are realized by representing the first order wave function with a combination of internal contraction (IC) and matrix product state perturbation theory (MPSPT). With this combination, only third order reduced density matrices (RDMs) are required. Thus, we obviate the need for calculating (or estimating) RDMs of fourth or higher order; these had so far posed a severe bottleneck for dynamic correlation treatments involving the large active spaces accessible to DMRG. Using several benchmark systems, including first and second row containing small molecules, Cr 2, pentacene, and oxo-Mn(Salen), we show that active spaces containing at least 30 orbitals can be treated using this method. On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550 and 1100 virtual orbitals, respectively. We also critically examine the errors incurred due to the three sources of errors introduced in the present implementation – calculating second order instead of third order energy corrections, use of internal contraction, and approximations made in the reference wave function due to DMRG.

arXiv:1609.03496•Journal of Chemical Theory and Computation•Jan 7, 2017•67 citations

Properties of Reduced Density Matrices

Theoretical chemistry•Jan 1, 1976•0 citations
A family of equations that combines contracted Schr\"odinger equations of different orders is reported here. Attention is focussed on the resulting second order, third order, and fourth order of these modified-contracted Schr\"odinger equations. Some of these equations are self-contained and have as fixed points those corresponding to the full-configuration interaction eigenstates. The indeterminacy, which hindered initially the use of the contracted Schr\"odinger equations, does not formally exist in these equations. Relations linking the lower-order reduced density matrices with the higher-order matrices are exactly incorporated into the modified-contracted Schr\"odinger-equations structure. The cancellation of high-order correlation terms, which is hidden in the contracted Schr\"odinger equations, now takes an explicit form.
We present two efficient and intruder-free methods for treating dynamic correlation on top of general multiconfiguration reference wave functions — including such as obtained by the density matrix renormalization group (DMRG) with large active spaces. The new methods are the second order variant of the recently proposed multireference linearized coupled cluster method (MRLCC) [Sharma, S.; Alavi, A. J. Chem. Phys. 2015, 143, 102815] and of N-electron valence perturbation theory (NEVPT2), with expected accuracies similar to MRCI+Q and (at least) CASPT2, respectively. Great efficiency gains are realized by representing the first order wave function with a combination of internal contraction (IC) and matrix product state perturbation theory (MPSPT). With this combination, only third order reduced density matrices (RDMs) are required. Thus, we obviate the need for calculating (or estimating) RDMs of fourth or higher order; these had so far posed a severe bottleneck for dynamic correlation treatments involving the large active spaces accessible to DMRG. Using several benchmark systems, including first and second row containing small molecules, Cr 2, pentacene, and oxo-Mn(Salen), we show that active spaces containing at least 30 orbitals can be treated using this method. On a single node, MRLCC2 and NEVPT2 calculations can be performed with over 550 and 1100 virtual orbitals, respectively. We also critically examine the errors incurred due to the three sources of errors introduced in the present implementation – calculating second order instead of third order energy corrections, use of internal contraction, and approximations made in the reference wave function due to DMRG.