SDPA 6.00 by (M. Yamashita, K. Fujisawa, and M. Kojima)

SDPARA 0.90 by (K. Fujisawa, M. Kojima, K. Nakata, and M. Yamashita)

The following set of SDPs are the actual ones solved in [1]. The problem consists of determining the ground state energy of an N-electron system in a given external potential through the so-called Reduced Density Matrix Method. A detailed description on the formulation be found in:

[1] Z. Zhao, B. J. Braams, M. Fukuda, M. L. Overton, and J. K. Percus, "The reduced density matrix method for electronic structure calculations and the role of three-index representability", October, 2003.

The sizes of SDPs depend on the size of the "spin-orbital basis", r, which governs the discretization of the continuous wave function, but do not depend on the number of electrons N of the system. (Accurate electronic structure calculations will have r >= 2N).

The Benchmark SDPs are in SDPA format and are divided according to the basis size r. See sizes of corresponding SDPs.

In our paper [1], we present several SDP calculations for each molecule, but here we only provide the data for the most accurate SDP calculations: those with the P, Q, G, T1 and T2 N-representability conditions. Our results are given in Tables 1 and 2 in [1].

To obtain the energies displayed in Tables 1 and 2 under column $E_{PQGT1T2}$ [1], it is necessary to add the nuclear repulsion energies to the optimal values of each corresponding SDP. The important information we want to extract from solving the SDPs are the optimal value, and the dual vector variable (which provides the One-Reduced Density Matrix and the Two-Reduced Density Matrix). The applications typically require 4 digits of accuracy after the period for the optimal values (which means 6 or 7 digits of accuracy in total). Electronical Structure Calculation Problems (47 problems)

15 SDPs with r=12 (4.1MB)

6 SDPs with r=14 (3.6MB)

2 SDPs with r=16 (2.4MB)

24 SDPs with r=20 (86.2MB)

Sizes of SDPs

r	# equality constraints	Size of block matrices	Size of the diagonal matrix
12	948	6, 6, 6, 6, 15, 15, 36, 15, 15, 36, 72, 36, 36, 20, 90, 90, 20, 306, 306, 90, 90	94
14	1743	7, 7, 7, 7, 21, 21, 49, 21, 21, 49, 98, 49, 49, 35, 147, 147, 35, 490, 490, 147, 147	122
16	2964	8, 8, 8, 8, 28, 28, 64, 28, 28, 64, 128, 64, 64, 56, 224, 224, 56, 736, 736, 224, 224	154
20	7230	10, 10, 10, 10, 45, 45, 100, 45, 45, 100, 200, 100, 100, 120, 450, 450, 120, 1450, 1450, 450, 450	230