Rank Restriction for the Variational Calculation of Two-electron Reduced Density Matrices of Many-electron Atoms and Molecules

Details Rank Restriction for the Variational Calculation of Two-electron Reduced Density Matrices of Many-electron Atoms and Molecules Rank Restriction for the Variational Calculation of Two-electron Reduced Density Matrices of Many-electron Atoms and Molecules

2011-11-08

arxiv.org/abs/1111.1978v1

Phys. Rev. A 84, 052506 (2011)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.84.052506

Variational minimization of the ground-state energy as a function of the two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions, provides a polynomial-scaling approach to studying strongly correlated molecules without computing the many-electron wavefunction. Here we introduce a new route to enhancing necessary conditions for $N$-representability through rank restriction of the 2-RDM. Rather than adding computationally more expensive $N$-representability conditions, we directly enhance the accuracy of two-particle (2-positivity) conditions through rank restriction, which removes degrees of freedom in the 2-RDM that are not sufficiently constrained. We select the rank of the particle-hole 2-RDM by deriving the ranks associated with model wavefunctions including both mean-field and antisymmetrized geminal power (AGP) wave functions. Because the 2-positivity conditions are exact for quantum systems with AGP ground states, the rank of the particle-hole 2-RDM from the AGP ansatz provides a minimum for its value in variational 2-RDM calculations of general quantum systems. To implement the rank-restricted conditions, we extend a first-order algorithm for large-scale semidefinite programming. The rank-restricted conditions significantly improve the accuracy of the energies; for example, the percentages of correlation energies recovered for HF, CO, and N$_{2}$ improve from 115.2%, 121.7%, and 121.5% without rank restriction to 97.8%, 101.1%, and 100.0% with rank restriction. Similar results are found at both equilibrium and non-equilibrium geometries. While more accurate, the rank-restricted $N$-representability conditions are less expensive computationally than the full-rank conditions.

Affiliated with

Also associated with

No associations

Rating

Rank Restriction for the Variational Calculation of Two-electron Reduced Density Matrices of Many-electron Atoms and Molecules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rank Restriction for the Variational Calculation of Two-electron Reduced Density Matrices of Many-electron Atoms and Molecules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rank Restriction for the Variational Calculation of Two-electron Reduced Density Matrices of Many-electron Atoms and Molecules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-54219