On the size-consistency of the reduced-density-matrix method and the unitary invariant diagonal N-representability conditions

  title={On the size-consistency of the reduced-density-matrix method and the unitary invariant diagonal N-representability conditions},
  author={Maho Nakata},
  journal={AIP Advances},
  • Maho Nakata
  • Published 29 August 2011
  • Mathematics
  • AIP Advances
A promising variational approach for determining the ground state energy and its properties is by using the second-order reduced density matrix (2-RDM). However, the leading obstacle with this approach is the N-representability problem. By employing a subset of conditions (typically the P, Q, G, T1 and T2′ conditions) results comparable to those of CCSD(T) can be achieved. However, these conditions do not guarantee size-consistency. In this work, we show that size-consistency can be satisfied… 

Method for making 2-electron response reduced density matrices approximately N-representable.

A new algorithm is presented for making non-N-representable 2-RDMs which are close to being N-Representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions.

Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods.

A large-scale implementation of the complete active space self-consistent field (CASSCF) method using the variational two-electron reduced-density-matrix approach is presented and the quality of the results is still far superior to those obtained from standard single-reference approaches.

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

ABSTRACT Variational two-electron reduced-density-matrix (2-RDM) methods can provide a reference-independent description of the electronic structure of strongly correlated molecules and materials.

Rigorous Lower Bounds for the Ground State Energy of Molecules by Employing Necessary N-Representability Conditions.

The software VSDP, which takes all numerical errors due to floating-point arithmetic operations into consideration, provides tight rigorous error bounds lower than full CI energies reported with an accuracy of 0.1 to 0.01 mhartree, is applied.

Variational optimization of the 2DM: approaching three-index accuracy using extended cluster constraints

This work derives new constraints which extend these cluster constraints to incorporate the open-system nature of a cluster on a larger lattice, at a fraction of the computational cost.

Geometric constraints on two-electron reduced density matrices

For many-electron systems, the second-order reduced density matrix (2-RDM) provides sufficient information for characterizing their properties of interests in physics and chemistry, ranging from

Assessing the orbital-optimized unitary Ansatz for density cumulant theory.

It is found that methods derived from the Ansatz beyond the previously known ODC-12 method tend to be less accurate for equilibrium properties and less reliable when attempting to describe H2 dissociation.

Trends in non-metal doping of the SrTiO₃ surface: a hybrid density functional study.

The results indicate that the band alignments of N-doping, Br-doped and I-dope SrTiO3(001) surfaces are well positioned for the feasibility of photo-oxidation and photo-reduction of water, which are promising for water splitting in the visible light region.



Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver.

This work explores the well-known N-representability conditions (P, Q, and G) together with the more recent and much stronger T1 and T2(') conditions and provides physically meaningful results for the Hubbard model in the high correlation limit.

Variational minimization of atomic and molecular ground-state energies via the two-particle reduced density matrix

Atomic and molecular ground-state energies are variationally determined by constraining the two-particle reduced density matrix (2-RDM) to satisfy positivity conditions. Because each positivity

Variational reduced-density-matrix method using three-particle N-representability conditions with application to many-electron molecules

Molecular two-electron reduced density matrices (2-RDMs) are computed variationally without the many-electron wave function by constraining the 2-RDM with a set of three-particle N-representability

Chemical verification of variational second-order density matrix based potential energy surfaces for the N2 isoelectronic series.

A novel constraint is introduced that imposes the correct dissociation and enforces size consistency on diatomic 14-electron molecules and is illustrated with calculations on NO(+), CO, CN(-), N(2), and O(2)(2+).

The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions.

The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q, and G conditions, and it is found that the use of the T1 and T2 conditions gives a significant improvement over just the P,Q, andG conditions.

Density matrix variational theory: Application to the potential energy surfaces and strongly correlated systems

The density matrix variational theory (DMVT) algorithm developed previously [J. Chem. Phys. 114, 8282 (2001)] was utilized for calculations of the potential energy surfaces of molecules, H4, H2O,

Reduced Density Matrices of Atoms and Molecules. II. On the N‐Representability Problem

For the 2‐matrix of the ``double occupancy configuration interaction'' (DOCI) wavefunction described in a previous paper, the N‐representability problem is stated in terms of algebraic equations

On the Diagonal N-Representability Problem

The removal of the N-electron wave function from many-body theory requires solution of the N-representability problem for the second-order reduced density matrix (RDM-2). This difficult problem,

Size extensivity of the variational reduced-density-matrix method

With the density-matrix variational method, the ground-state energy of a many-electron system is calculated by minimizing the energy expectation value subject to the selected representability

Subsystem constraints in variational second order density matrix optimization: curing the dissociative behavior.

This paper introduces a general class of N-representability conditions, called subsystem constraints, and shows that they cure the dissociation problem at little additional computational cost.