This GitHub repository is a "modern" presentation of the original RDM library by Nakata, Maho maho@riken.jp or chat95@mac.com hosted at http://nakatamaho.riken.jp/rdmsdp/sdp_rdm.html.
The
datadirectory contains only the eight largest problem Instances from the first table.
The RDM method is promising method, using 2-RDM as a basic variable and
minimize the total energy which is a linear to the Hamiltonian with respect to
so called N-representability conditions. Since N-representability condition is
known to be very hard to solve, we pose approximate N-representability
conditions like P, Q, G, T1, T2, or T2'. The total energies by
this method is comparable to CCSD(T), and these SDPs are really huge, and are
challenge in both mathematical programming and chemistry.
Try them with your SDP solver! Format is the SDPA's sparse format. You can solve problems with your SDP solver, which are available as SDPA, SDPA-GMP, SeDuMi, CSDP, and SDTP3 etc.
All files are gzip'ed to reduce the size. For molecules' case you should add the core energy to the optimal to reproduce the results. The rank is the twice of number of molecular orbitals and define the size of the problems. If the rank (twice # of MO) becomes bigger, problem size becomes bigger. Not all the results of 1D hubbard model are uploaded, also I recalculated. For the Hubbard models, you may need multiple precision version of SDP solver, like SDPA-GMP, SDPA-QD, or SDPA-DD.
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Problems: Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver
Maho Nakata, Bastiaan J. Braams, Katsuki Fujisawa, Mituhiro Fukuda, Jerome K. Percus, Makoto Yamashita, and Zhengji Zhao. Journal of chemical physics, 128, 16 164113 (2008) (5) DOI: 10.1063/1.2911696
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Basics: Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm.
Maho Nakata, Hiroshi Nakatsuji, Masahiro Ehara, Mituhiro Fukuda, Kazuhide Nakata, and Katsuki Fujisawa. Journal of Chemical Physics, 114, 8282-8292 (2001) (96) DOI: 10.1063/1.1360199
Randomly chosen from [1]. You should add the core energy to the optimal to reproduce the paper's results.
| Problems (dat-s, gzip'ed) | result (gzip'ed) | rank | core energy | comment |
|---|---|---|---|---|
| C.3P.DZ.pqg.dat-s.gz | C.3P.DZ.pqg.result.gz | 20 | 0.0 | PQG |
| C.3P.DZ.pqgt1.dat-s.gz | C.3P.DZ.pqgt1.result.gz | 20 | 0.0 | PQGT1 |
| C.3P.DZ.pqgt1t2.dat-s.gz | C.3P.DZ.pqgt1t2.result.gz | 20 | 0.0 | PQGT1T2 |
| C.3P.DZ.pqgt1t2p.dat-s.gz | C.3P.DZ.pqgt1t2p.result.gz | 20 | 0.0 | PQGT1T2' |
| Ne.1S.DZ.pqg.dat-s.gz | Ne.1S.DZ.pqg.result.gz | 20 | 0.0 | PQG |
| Ne.1S.DZ.pqgt1.dat-s.gz | Ne.1S.DZ.pqgt1.result.gz | 20 | 0.0 | PQGT1 |
| Ne.1S.DZ.pqgt1t2.dat-s.gz | Ne.1S.DZ.pqgt1t2.result.gz | 20 | 0.0 | PQGT1T2 |
| Ne.1S.DZ.pqgt1t2p.dat-s.gz | Ne.1S.DZ.pqgt1t2p.result.gz | 20 | 0.0 | PQGT1T2' |
| O2+.2Pig.STO6G.pqg.dat-s.gz | O2+.2Pig.STO6G.pqg.result.gz | 20 | 3.033620918667e+01 | PQG |
| O2+.2Pig.STO6G.pqgt1.dat-s.gz | O2+.2Pig.STO6G.pqgt1.result.gz | 20 | 3.033620918667e+01 | PQGT1 |
| O2+.2Pig.STO6G.pqgt1t2.dat-s.gz | O2+.2Pig.STO6G.pqgt1t2.result.gz | 20 | 3.033620918667e+01 | PQGT1T2 |
| O2+.2Pig.STO6G.pqgt1t2p.dat-s.gz | O2+.2Pig.STO6G.pqgt1t2p.result.gz | 20 | 3.033620918667e+01 | PQGT1T2' |
| NH.1Delta.DZ.pqg.dat-s.gz | NH.1Delta.DZ.pqg.result.gz | 24 | 3.582091425394e+00 | PQG |
| NH.1Delta.DZ.pqgt1.dat-s.gz | NH.1Delta.DZ.pqgt1.result.gz | 24 | 3.582091425394e+00 | PQGT1 |
| NH.1Delta.DZ.pqgt1t2.dat-s.gz | NH.1Delta.DZ.pqgt1t2.result.gz | 24 | 3.582091425394e+00 | PQGT1T2 |
| NH.1Delta.DZ.pqgt1t2p.dat-s.gz | NH.1Delta.DZ.pqgt1t2p.result.gz | 24 | 3.582091425394e+00 | PQGT1T2' |
| CH.2Pir.DZ.pqg.dat-s.gz | CH.2Pir.DZ.pqg.result.gz | 24 | 2.835131256362e+00 | PQG |
| CH.2Pir.DZ.pqgt1.dat-s.gz | CH.2Pir.DZ.pqgt1.result.gz | 24 | 2.835131256362e+00 | PQGT1 |
| CH.2Pir.DZ.pqgt1t2.dat-s.gz | CH.2Pir.DZ.pqgt1t2.result.gz | 24 | 2.835131256362e+00 | PQGT1T2 |
| CH.2Pir.DZ.pqgt1t2p.dat-s.gz | CH.2Pir.DZ.pqgt1t2p.result.gz | 24 | 2.835131256362e+00 | PQGT1T2' |
| HF.1Sigma+.DZ.pqg.dat-s.gz | HF.1Sigma+.DZ.pqg.result.gz | 24 | 5.194757507570e+00 | PQG |
| HF.1Sigma+.DZ.pqgt1.dat-s.gz | HF.1Sigma+.DZ.pqgt1.result.gz | 24 | 5.194757507570e+00 | PQGT1 |
| HF.1Sigma+.DZ.pqgt1t2.dat-s.gz | HF.1Sigma+.DZ.pqgt1t2.result.gz | 24 | 5.194757507570e+00 | PQGT1T2 |
| HF.1Sigma+.DZ.pqgt1t2p.dat-s.gz | HF.1Sigma+.DZ.pqgt1t2p.result.gz | 24 | 5.194757507570e+00 | PQGT1T2' |
| F-.1S.DZ+d.pqg.dat-s.gz | F-.1S.DZ+d.pqg.result.gz | 26 | 0.0 | PQG |
| F-.1S.DZ+d.pqgt1.dat-s.gz | F-.1S.DZ+d.pqgt1.result.gz | 26 | 0.0 | PQGT1 |
| F-.1S.DZ+d.pqgt1t2.dat-s.gz | F-.1S.DZ+d.pqgt1t2.result.gz | 26 | 0.0 | PQGT1T2 |
| F-.1S.DZ+d.pqgt1t2p.dat-s.gz | F-.1S.DZ+d.pqgt1t2p.result.gz | 26 | 0.0 | PQGT1T2' |
| H2O.1A1.DZ.pqg.dat-s.gz | H2O.1A1.DZ.pqg.result.gz | 28 | 9.188690490978e+00 | PQG |
| H2O.1A1.DZ.pqgt1.dat-s.gz | H2O.1A1.DZ.pqgt1.result.gz | 28 | 9.188690490978e+00 | PQGT1 |
| H2O.1A1.DZ.pqgt1t2.dat-s.gz | H2O.1A1.DZ.pqgt1t2.result.gz | 28 | 9.188690490978e+00 | PQGT1T2 |
| H2O.1A1.DZ.pqgt1t2p.dat-s.gz | H2O.1A1.DZ.pqgt1t2p.result.gz | 28 | 9.188690490978e+00 | PQGT1T2' |
From [1]. Note not all results have been uploaded, and may not all problems are solved in the referenced paper. You may need multiple precision version of SDP solver like SDPA-GMP, SDPA-QD, or SDPA-DD.
| Problems (dat-s, gzip'ed) | result (gzip'ed) | rank | U/t | comment |
|---|---|---|---|---|
| hubbard_X4N4p.1000.0.pqg.dat-s.gz | hubbard_X4N4p.1000.0.pqg.result.gz | 8 | 1000.0 | PQG |
| hubbard_X4N4p.1000.0.pqgt1.dat-s.gz | hubbard_X4N4p.1000.0.pqgt1.result.gz | 8 | 1000.0 | PQGT1 |
| hubbard_X4N4p.1000.0.pqgt1t2.dat-s.gz | hubbard_X4N4p.1000.0.pqgt1t2.result.gz | 8 | 1000.0 | PQGT1T2 |
| hubbard_X4N4p.1000.0.pqgt1t2p.dat-s.gz | hubbard_X4N4p.1000.0.pqgt1t2p.result.gz | 8 | 1000.0 | PQGT1T2' |
| hubbard_X4N4p.10000.0.pqg.dat-s.gz | hubbard_X4N4p.10000.0.pqg.result.gz | 8 | 10000.0 | PQG |
| hubbard_X4N4p.10000.0.pqgt1.dat-s.gz | hubbard_X4N4p.10000.0.pqgt1.result.gz | 8 | 10000.0 | PQGT1 |
| hubbard_X4N4p.10000.0.pqgt1t2.dat-s.gz | hubbard_X4N4p.10000.0.pqgt1t2.result.gz | 8 | 10000.0 | PQGT1T2 |
| hubbard_X4N4p.10000.0.pqgt1t2p.dat-s.gz | hubbard_X4N4p.10000.0.pqgt1t2p.result.gz | 8 | 10000.0 | PQGT1T2' |
| hubbard_X4N4p.100000.0.pqg.dat-s.gz | hubbard_X4N4p.100000.0.pqg.result.gz | 8 | 100000.0 | PQG |
| hubbard_X4N4p.100000.0.pqgt1.dat-s.gz | hubbard_X4N4p.100000.0.pqgt1.result.gz | 8 | 100000.0 | PQGT1 |
| hubbard_X4N4p.100000.0.pqgt1t2.dat-s.gz | hubbard_X4N4p.100000.0.pqgt1t2.result.gz | 8 | 100000.0 | PQGT1T2 |
| hubbard_X4N4p.100000.0.pqgt1t2p.dat-s.gz | hubbard_X4N4p.100000.0.pqgt1t2p.result.gz | 8 | 100000.0 | PQGT1T2' |
| hubbard_X6N6p.1000.0.pqg.dat-s.gz | hubbard_X6N6p.1000.0.pqg.result.gz | 12 | 1000.0 | PQG |
| hubbard_X6N6p.1000.0.pqgt1.dat-s.gz | hubbard_X6N6p.1000.0.pqgt1.result.gz | 12 | 1000.0 | PQGT1 |
| hubbard_X6N6p.1000.0.pqgt1t2.dat-s.gz | hubbard_X6N6p.1000.0.pqgt1t2.result.gz | 12 | 1000.0 | PQGT1T2 |
| hubbard_X6N6p.1000.0.pqgt1t2p.dat-s.gz | hubbard_X6N6p.1000.0.pqgt1t2p.result.gz | 12 | 1000.0 | PQGT1T2' |
| hubbard_X6N6p.10000.0.pqg.dat-s.gz | hubbard_X6N6p.10000.0.pqg.result.gz | 12 | 10000.0 | PQG |
| hubbard_X6N6p.10000.0.pqgt1.dat-s.gz | hubbard_X6N6p.10000.0.pqgt1.result.gz | 12 | 10000.0 | PQGT1 |
| hubbard_X6N6p.10000.0.pqgt1t2.dat-s.gz | hubbard_X6N6p.10000.0.pqgt1t2.result.gz | 12 | 10000.0 | PQGT1T2 |
| hubbard_X6N6p.10000.0.pqgt1t2p.dat-s.gz | hubbard_X6N6p.10000.0.pqgt1t2p.result.gz | 12 | 10000.0 | PQGT1T2' |
| hubbard_X6N6p.100000.0.pqg.dat-s.gz | hubbard_X6N6p.100000.0.pqg.result.gz | 12 | 100000.0 | PQG |
| hubbard_X6N6p.100000.0.pqgt1.dat-s.gz | hubbard_X6N6p.100000.0.pqgt1.result.gz | 12 | 100000.0 | PQGT1 |
| hubbard_X6N6p.100000.0.pqgt1t2.dat-s.gz | hubbard_X6N6p.100000.0.pqgt1t2.result.gz | 12 | 100000.0 | PQGT1T2 |
| hubbard_X6N6p.100000.0.pqgt1t2p.dat-s.gz | hubbard_X6N6p.100000.0.pqgt1t2p.result.gz | 12 | 100000.0 | PQGT1T2' |
| hubbard_X8N8p.1000.0.pqg.dat-s.gz | hubbard_X8N8p.1000.0.pqg.result.gz | 16 | 1000.0 | PQG |
| hubbard_X8N8p.1000.0.pqgt1.dat-s.gz | hubbard_X8N8p.1000.0.pqgt1.result.gz | 16 | 1000.0 | PQGT1 |
| hubbard_X8N8p.1000.0.pqgt1t2.dat-s.gz | hubbard_X8N8p.1000.0.pqgt1t2.result.gz | 16 | 1000.0 | PQGT1T2 |
| hubbard_X8N8p.1000.0.pqgt1t2p.dat-s.gz | hubbard_X8N8p.1000.0.pqgt1t2p.result.gz | 16 | 1000.0 | PQGT1T2' |
| hubbard_X8N8p.10000.0.pqg.dat-s.gz | hubbard_X8N8p.10000.0.pqg.result.gz | 16 | 10000.0 | PQG |
| hubbard_X8N8p.10000.0.pqgt1.dat-s.gz | hubbard_X8N8p.10000.0.pqgt1.result.gz | 16 | 10000.0 | PQGT1 |
| hubbard_X8N8p.10000.0.pqgt1t2.dat-s.gz | hubbard_X8N8p.10000.0.pqgt1t2.result.gz | 16 | 10000.0 | PQGT1T2 |
| hubbard_X8N8p.10000.0.pqgt1t2p.dat-s.gz | hubbard_X8N8p.10000.0.pqgt1t2p.result.gz | 16 | 10000.0 | PQGT1T2' |
| hubbard_X8N8p.100000.0.pqg.dat-s.gz | hubbard_X8N8p.100000.0.pqg.result.gz | 16 | 100000.0 | PQG |
| hubbard_X8N8p.100000.0.pqgt1.dat-s.gz | hubbard_X8N8p.100000.0.pqgt1.result.gz | 16 | 100000.0 | PQGT1 |
| hubbard_X8N8p.100000.0.pqgt1t2.dat-s.gz | hubbard_X8N8p.100000.0.pqgt1t2.result.gz | 16 | 100000.0 | PQGT1T2 |
| hubbard_X8N8p.100000.0.pqgt1t2p.dat-s.gz | hubbard_X8N8p.100000.0.pqgt1t2p.result.gz | 16 | 100000.0 | PQGT1T2' |