Developers:LCAOStart Benchmark

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This is a benchmark of the different LCAOStart options.

Technical details

SVN revision

This benchmark was done using SVN revision 14733. The source was modified to allow freezing the density/KS potential during the first 3 SCF iterations for some of the runs.

Environment/Hardware

GCC 4.8.3 20140911

Intel(R) Core(TM) i7 CPU X 980 @ 3.33GHz

Test set

Systems

The test set consists of 11 systems:

  1. Alanine
  2. Alanine dimer
  3. Alanine trimer
  4. Alanine tetramer
  5. Ascidiacyclamide
  6. Benzene
  7. Betaine (zwitterion - separated formal charges)
  8. Methane
  9. Nitrogen-substituted graphene nanoflake model
  10. Oxyluciferin anion
  11. Tetraazacubane

Input files

All the input files shared the same skeleton:

CalculationMode = gs
Units = eV_Angstrom
ExperimentalFeatures = yes
FromScratch = yes

XYZCoordinates = "adjusted.xyz"
MaximumIter = -1

For most systems the Spacing and Radius were set to:

Spacing = 0.2
Radius = 4.0

with the exceptions of methane:

Spacing = 0.25
Radius = 3.5

and benzene:

Spacing = 0.15
Radius = 5.0

All systems are neutral, with the exception of oxyluciferin:

ExcessCharge = -1

and the graphene nanoflake:

ExcessCharge = 1

The graphene nanoflake was considered to be spin-polarized.

All the geometries can be found here.

All the different options for LCAOStart were benchmarked for three different cases: CG eigensolver, RMMDIIS eigensolver with no extra states, and RMMDISS eigensolver with 20% extra states.

Results

Summary

Average relative differences of the number of SCF iterations, in percentage, with respect to the lcao_none option with the potential updated every SCF iteration.
Potential updated every SCF iteration Potential fixed during the first 3 SCF iterations
System lcao_none lcao_simple lcao_states lcao_full lcao_none lcao_simple lcao_states lcao_full
CG 0.0 28.1 0.8 48.1 24.3 38.9 32.3 67.7
RMMDIIS 0.0 82.3 -34.7 -28.7 -4.2 94.1 -36.9 -33.2
RMMDIIS + 20% extra states 0.0 32.4 -37.8 -32.0 -0.4 34.2 -23.1 -30.2


Average relative differences of the total number of matrix-vector products, in percentage, with respect to the lcao_none option with the potential updated every SCF iteration.
Potential updated every SCF iteration Potential fixed during the first 3 SCF iterations
System lcao_none lcao_simple lcao_states lcao_full lcao_none lcao_simple lcao_states lcao_full
CG 0.0 29.2 0.2 44.6 22.9 43.1 28.7 63.2
RMMDIIS 0.0 85.7 -35.6 -29.5 -4.2 98.0 -38.0 -34.2
RMMDIIS + 20% extra states 0.0 34.2 -39.6 -33.5 -0.1 36.4 -24.1 -31.4

Number of SCF iterations

Number of SCF iterations using the CG eigensolver.
Potential updated every SCF iteration Potential fixed during the first 3 SCF iterations
System lcao_none lcao_simple lcao_states lcao_full lcao_none lcao_simple lcao_states lcao_full
1ALA 12 12 11 14 14 14 14 16
2ALA 16 19 14 19 18 16 16 24
3ALA 27 44 41 43 39 70 54 126
4ALA 12 12 11 12 15 14 14 14
ASC 13 13 13 12 16 16 16 17
benzene 12 20 11 9 14 19 14 12
betaine 13 17 12 12 15 18 15 15
methane 8 8 8 8 11 11 11 11
N-GNF 38 82 45 222 49 58 75 94
oxyluciferin 14 16 13 14 18 15 16 18
tetraazacubane 11 11 10 10 13 13 13 13


Number of SCF iterations using the RMMDIIS eigensolver with no extra states.
Potential updated every SCF iteration Potential fixed during the first 3 SCF iterations
System lcao_none lcao_simple lcao_states lcao_full lcao_none lcao_simple lcao_states lcao_full
1ALA 62 97 40 51 77 72 42 43
2ALA 108 197 92 83 112 140 74 77
3ALA 178 111 83 106 172 143 98 91
4ALA 59 59 45 34 76 118 38 40
ASC 107 80 55 50 98 47 45 47
benzene 50 185 33 35 51 213 33 33
betaine 60 372 30 42 54 441 40 40
methane 43 43 43 43 29 29 29 29
N-GNF 389 203 323 371 151 231 320 411
oxyluciferin 112 95 48 46 126 95 53 55
tetraazacubane 51 103 27 43 50 98 34 39


Number of SCF iterations using the RMMDIIS eigensolver with 20% extra states.
Potential updated every SCF iteration Potential fixed during the first 3 SCF iterations
System lcao_none lcao_simple lcao_states lcao_full lcao_none lcao_simple lcao_states lcao_full
1ALA 43 42 26 28 47 40 27 25
2ALA 56 49 29 41 54 44 31 37
3ALA 62 69 35 60 55 53 102 59
4ALA 40 40 28 28 39 38 27 22
ASC 41 39 22 22 43 34 22 23
benzene 40 183 33 36 42 182 33 39
betaine 44 45 24 22 42 57 29 23
methane 22 2 22 22 30 30 30 30
N-GNF 82 77 26 24 53 78 28 25
oxyluciferin 53 51 26 23 50 54 23 25
tetraazacubane 34 39 25 26 35 41 27 25

Number of matrix-vector products

Total number of matrix-vector products using the CG eigensolver.
Potential updated every SCF iteration Potential fixed during the first 3 SCF iterations
System lcao_none lcao_simple lcao_states lcao_full lcao_none lcao_simple lcao_states lcao_full
1ALA 4719 4685 4518 5480 5666 5658 5512 6383
2ALA 11227 12889 9712 13473 12797 11697 11536 17374
3ALA 27141 43993 36040 37398 38999 73498 52410 121933
4ALA 16495 16236 15231 15818 20331 19623 19218 19469
ASC 42632 42120 41272 40410 51658 51848 51374 56978
benzene 4393 7721 3755 3248 4919 7220 4550 3960
betaine 6624 9640 6318 6334 8022 9911 7527 7759
methane 687 687 687 687 777 777 777 777
N-GNF 107563 223023 142762 603383 154009 196033 232098 265523
oxyluciferin 12743 14625 11902 13554 16082 14187 14191 16267
tetraazacubane 4894 5096 4481 4372 5567 5749 5315 5348


Total number of matrix-vector products using the RMMDIIS eigensolver with no extra states.
Potential updated every SCF iteration Potential fixed during the first 3 SCF iterations
System lcao_none lcao_simple lcao_states lcao_full lcao_none lcao_simple lcao_states lcao_full
1ALA 7542 11952 4770 6156 9432 8802 5022 5148
2ALA 23712 43648 20128 18112 24608 30880 16096 16768
3ALA 56626 35052 26036 33442 54694 45356 30866 28612
4ALA 23880 23880 18000 13380 31020 48660 15060 15900
ASC 104228 77390 52540 47570 95282 44588 42600 44588
benzene 5025 19200 3240 3450 5130 22140 3240 3240
betaine 9720 62136 4680 6696 8712 73728 6360 6360
methane 1144 1144 1144 1144 752 752 752 752
N-GNF 400784 208088 332408 382136 154216 237096 329300 423576
oxyluciferin 30760 26000 12840 12280 34680 26000 14240 14800
tetraazacubane 6840 14120 3480 5720 6700 13420 4460 5160


Total number of matrix-vector products using the RMMDIIS eigensolver with 20% extra states.
Potential updated every SCF iteration Potential fixed during the first 3 SCF iterations
System lcao_none lcao_simple lcao_states lcao_full lcao_none lcao_simple lcao_states lcao_full
1ALA 6292 6138 3674 3982 6908 5830 3828 3520
2ALA 14326 12464 7144 10336 13794 11134 7676 9272
3ALA 23045 25740 12650 22275 20350 19580 38445 21890
4ALA 19080 19080 13032 13032 18576 18072 12528 10008
ASC 46240 43860 23630 23630 48620 37910 23630 24820
benzene 4770 22788 3888 4266 5022 22788 3888 4644
betaine 8497 8700 4437 4031 8091 11136 5452 4234
methane 695 695 695 695 975 975 975 975
N-GNF 99502 93272 29726 27234 63368 94518 32218 28480
oxyluciferin 17088 16416 8016 7008 16080 17424 7008 7680
tetraazacubane 5352 6192 3840 4008 5520 6528 4176 3840