New

Please refer to the new problem sets available from here, since the data below is obsolete.


SDP Benchmark Problems from Electronic Structure Calculations

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 conditions," The Journal of Chemical Physics, 120 (2004), pp. 2095-2104.

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).

Electronic Structure Calculation Problems (47 problems)

15 SDPs with r=12 (4.6MB)

6 SDPs with r=14 (4.0MB)

2 SDPs with r=16 (2.6MB)

24 SDPs with r=20 (94.2MB)

(Note: The above set of problems were replaced on December 26, 2003 because the function "fromsdpa" from SeDuMi 1.05 (currently, version 1.3) assumes that the data matrices in SDPA format are ordered. We thank Hans D. Mittelmann for providing the new set of problems readable from all the SDP codes).

Sizes of SDPs
r# equality constraintsSize of block matricesSize of the diagonal matrix
129486, 6, 6, 6, 15, 15, 36, 15, 15, 36, 72, 36, 36, 20, 90, 90, 20, 306, 306, 90, 9094
1417437, 7, 7, 7, 21, 21, 49, 21, 21, 49, 98, 49, 49, 35, 147, 147, 35, 490, 490, 147, 147122
1629648, 8, 8, 8, 28, 28, 64, 28, 28, 64, 128, 64, 64, 56, 224, 224, 56, 736, 736, 224, 224154
20723010, 10, 10, 10, 45, 45, 100, 45, 45, 100, 200, 100, 100, 120, 450, 450, 120, 1450, 1450, 450, 450230

Repulsion Energies (in Hartree units)
SystemNrRepulsion Energy
LiH4120.9948810848
BeH5121.5772794307
BH+5122.1782219849
BH6122.1469378814
CH+6122.8075545972
CH7122.8351312564
CH-8122.9398736056
NH+7123.4619072364
NH8123.5748318307
NH-9123.5379567746
OH+8124.1145086908
OH9124.3656986614
OH-10124.3643484454
HF+9124.7578374036
HF10125.1948028370
BH27144.7269615539
CH2(1A1)8146.0430274001
CH2(3B1)8146.1757874267
NH29147.5640948299
H2O+9148.7976559250
H2O10149.1949655162
NH3101611.9103794143
H3O+101614.0016864732
Li26201.7818082386
B210208.3203969969
C2+1120 13.5783185773
C2122015.3322985626
C2-132015.0239597508
LiF12209.1359970094
BeO122012.7234743166
NaH12203.0841102782
BeF132013.9973408993
BO132017.5733416023
N2+132023.2261601585
N2142023.6218321955
CO+132022.7786816895
CO142022.5121935230
BF142018.8617633307
AlH14204.1743350953
CF152022.4686046910
O2+152030.3362091867
O2162028.0474898021
SiH15204.8749631414
SiH-16205.0261068426
NO-162023.3154413407
NF162025.3156402817
HS+16206.1603870664

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This page was last modified on Tuesday, May 2, 2017.