THE RDM METHOD PROBLEMS IN SDPA SPARSE FORMAT

INTRODUCTION

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 comprable 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.

NOTES

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.

All data in one file

t2p.molecules.20170504.tar.xz

CITATIONS (CITATION COUNT BY THE WEB OF SCIENCE)

SDP PROBLEM FILES IN SDPA SPARCE FORMAT

ATOMS and MOLECULES

Randomly chosen from Journal of chemical physics 128, 16 164113 (2008). 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

3.033620918667+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'

1D HUBBARD MODEL WITH HIGH CORRELATION LIMITS

From Journal of chemical physics 128, 16 164113 (2008). 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

U/t=1000.0

PQG

hubbard_X4N4p.1000.0.pqgt1.dat-s.gz

hubbard_X4N4p.1000.0.pqgt1.result.gz

8

U/t=1000.0

PQGT1

hubbard_X4N4p.1000.0.pqgt1t2.dat-s.gz

hubbard_X4N4p.1000.0.pqgt1t2.result.gz

8

U/t=1000.0

PQGT1T2

hubbard_X4N4p.1000.0.pqgt1t2p.dat-s.gz

hubbard_X4N4p.1000.0.pqgt1t2p.result.gz

8

U/t=1000.0

PQGT1T2'

hubbard_X4N4p.10000.0.pqg.dat-s.gz

hubbard_X4N4p.10000.0.pqg.result.gz

8

U/t=10000.0

PQG

hubbard_X4N4p.10000.0.pqgt1.dat-s.gz

hubbard_X4N4p.10000.0.pqgt1.result.gz

8

U/t=10000.0

PQGT1

hubbard_X4N4p.10000.0.pqgt1t2.dat-s.gz

hubbard_X4N4p.10000.0.pqgt1t2.result.gz

8

U/t=10000.0

PQGT1T2

hubbard_X4N4p.10000.0.pqgt1t2p.dat-s.gz

hubbard_X4N4p.10000.0.pqgt1t2p.result.gz

8

U/t=10000.0

PQGT1T2'

hubbard_X4N4p.100000.0.pqg.dat-s.gz

hubbard_X4N4p.100000.0.pqg.result.gz

8

U/t=100000.0

PQG

hubbard_X4N4p.100000.0.pqgt1.dat-s.gz

hubbard_X4N4p.100000.0.pqgt1.result.gz

8

U/t=100000.0

PQGT1

hubbard_X4N4p.100000.0.pqgt1t2.dat-s.gz

hubbard_X4N4p.100000.0.pqgt1t2.result.gz

8

U/t=100000.0

PQGT1T2

hubbard_X4N4p.100000.0.pqgt1t2p.dat-s.gz

hubbard_X4N4p.100000.0.pqgt1t2p.result.gz

8

U/t=100000.0

PQGT1T2'

hubbard_X6N6p.1000.0.pqg.dat-s.gz

hubbard_X6N6p.1000.0.pqg.result.gz

12

U/t=1000.0

PQGT1

hubbard_X6N6p.1000.0.pqgt1.dat-s.gz

hubbard_X6N6p.1000.0.pqgt1.result.gz

12

U/t=1000.0

PQGT1

hubbard_X6N6p.1000.0.pqgt1t2.dat-s.gz

hubbard_X6N6p.1000.0.pqgt1t2.result.gz

12

U/t=1000.0

PQGT1T2

hubbard_X6N6p.1000.0.pqgt1t2p.dat-s.gz

hubbard_X6N6p.1000.0.pqgt1t2p.result.gz

12

U/t=1000.0

PQGT1T2'

hubbard_X6N6p.10000.0.pqg.dat-s.gz

hubbard_X6N6p.10000.0.pqg.result.gz

12

U/t=10000.0

PQG

hubbard_X6N6p.10000.0.pqgt1.dat-s.gz

hubbard_X6N6p.10000.0.pqgt1.result.gz

12

U/t=10000.0

PQGT1

hubbard_X6N6p.10000.0.pqgt1t2.dat-s.gz

hubbard_X6N6p.10000.0.pqgt1t2.result.gz

12

U/t=10000.0

PQGT1T2

hubbard_X6N6p.10000.0.pqgt1t2p.dat-s.gz

hubbard_X6N6p.10000.0.pqgt1t2p.result.gz

12

U/t=10000.0

PQGT1T2'

hubbard_X6N6p.100000.0.pqg.dat-s.gz

hubbard_X6N6p.100000.0.pqg.result.gz

12

U/t=100000.0

PQG

hubbard_X6N6p.100000.0.pqgt1.dat-s.gz

hubbard_X6N6p.100000.0.pqgt1.result.gz

12

U/t=100000.0

PQGT1

hubbard_X6N6p.100000.0.pqgt1t2.dat-s.gz

hubbard_X6N6p.100000.0.pqgt1t2.result.gz

12

U/t=100000.0

PQGT1T2

hubbard_X6N6p.100000.0.pqgt1t2p.dat-s.gz

hubbard_X6N6p.100000.0.pqgt1t2p.result.gz

12

U/t=100000.0

PQGT1T2'

hubbard_X8N8p.1000.0.pqg.dat-s.gz

hubbard_X8N8p.1000.0.pqg.result.gz

16

U/t=1000.0

PQG

hubbard_X8N8p.1000.0.pqgt1.dat-s.gz

hubbard_X8N8p.1000.0.pqgt1.result.gz

16

U/t=1000.0

PQGT1

hubbard_X8N8p.1000.0.pqgt1t2.dat-s.gz

hubbard_X8N8p.1000.0.pqgt1t2.result.gz

16

U/t=1000.0

PQGT1T2

hubbard_X8N8p.1000.0.pqgt1t2p.dat-s.gz

hubbard_X8N8p.1000.0.pqgt1t2p.result.gz

16

U/t=1000.0

PQGT1T2'

hubbard_X8N8p.10000.0.pqg.dat-s.gz

hubbard_X8N8p.10000.0.pqg.result.gz

16

U/t=10000.0

PQG

hubbard_X8N8p.10000.0.pqgt1.dat-s.gz

hubbard_X8N8p.10000.0.pqgt1.result.gz

16

U/t=10000.0

PQGT1

hubbard_X8N8p.10000.0.pqgt1t2.dat-s.gz

hubbard_X8N8p.10000.0.pqgt1t2.result.gz

16

U/t=10000.0

PQGT1T2

hubbard_X8N8p.10000.0.pqgt1t2p.dat-s.gz

hubbard_X8N8p.10000.0.pqgt1t2p.result.gz

16

U/t=10000.0

PQGT1T2'

hubbard_X8N8p.100000.0.pqg.dat-s.gz

hubbard_X8N8p.100000.0.pqg.result.gz

16

U/t=100000.0

PQG

hubbard_X8N8p.100000.0.pqgt1.dat-s.gz

hubbard_X8N8p.100000.0.pqgt1.result.gz

16

U/t=100000.0

PQGT1

hubbard_X8N8p.100000.0.pqgt1t2.dat-s.gz

hubbard_X8N8p.100000.0.pqgt1t2.result.gz

16

U/t=100000.0

PQGT1T2

hubbard_X8N8p.100000.0.pqgt1t2p.dat-s.gz

hubbard_X8N8p.100000.0.pqgt1t2p.result.gz

16

U/t=100000.0

PQGT1T2'

CITATIONS (CITATION COUNT BY THE WEB OF SCIENCE)

CORRESPONDANCE

Nakata, Maho: e-mail: maho@riken.jp or chat95@mac.com 
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