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Please refer to the new problem sets available from here, since the data below is obsolete.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

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 |

System | N | r | Repulsion Energy |
---|---|---|---|

LiH | 4 | 12 | 0.9948810848 |

BeH | 5 | 12 | 1.5772794307 |

BH+ | 5 | 12 | 2.1782219849 |

BH | 6 | 12 | 2.1469378814 |

CH+ | 6 | 12 | 2.8075545972 |

CH | 7 | 12 | 2.8351312564 |

CH- | 8 | 12 | 2.9398736056 |

NH+ | 7 | 12 | 3.4619072364 |

NH | 8 | 12 | 3.5748318307 |

NH- | 9 | 12 | 3.5379567746 |

OH+ | 8 | 12 | 4.1145086908 |

OH | 9 | 12 | 4.3656986614 |

OH- | 10 | 12 | 4.3643484454 |

HF+ | 9 | 12 | 4.7578374036 |

HF | 10 | 12 | 5.1948028370 |

BH2 | 7 | 14 | 4.7269615539 |

CH2(1A1) | 8 | 14 | 6.0430274001 |

CH2(3B1) | 8 | 14 | 6.1757874267 |

NH2 | 9 | 14 | 7.5640948299 |

H2O+ | 9 | 14 | 8.7976559250 |

H2O | 10 | 14 | 9.1949655162 |

NH3 | 10 | 16 | 11.9103794143 |

H3O+ | 10 | 16 | 14.0016864732 |

Li2 | 6 | 20 | 1.7818082386 |

B2 | 10 | 20 | 8.3203969969 |

C2+ | 11 | 20 | 13.5783185773 |

C2 | 12 | 20 | 15.3322985626 |

C2- | 13 | 20 | 15.0239597508 |

LiF | 12 | 20 | 9.1359970094 |

BeO | 12 | 20 | 12.7234743166 |

NaH | 12 | 20 | 3.0841102782 |

BeF | 13 | 20 | 13.9973408993 |

BO | 13 | 20 | 17.5733416023 |

N2+ | 13 | 20 | 23.2261601585 |

N2 | 14 | 20 | 23.6218321955 |

CO+ | 13 | 20 | 22.7786816895 |

CO | 14 | 20 | 22.5121935230 |

BF | 14 | 20 | 18.8617633307 |

AlH | 14 | 20 | 4.1743350953 |

CF | 15 | 20 | 22.4686046910 |

O2+ | 15 | 20 | 30.3362091867 |

O2 | 16 | 20 | 28.0474898021 |

SiH | 15 | 20 | 4.8749631414 |

SiH- | 16 | 20 | 5.0261068426 |

NO- | 16 | 20 | 23.3154413407 |

NF | 16 | 20 | 25.3156402817 |

HS+ | 16 | 20 | 6.1603870664 |

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