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#+TITLE : RSDFT-CIPSI
2020-04-28 11:35:58 +02:00
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Geometries are given in Angstrom.
Basis sets and pseudopotentials are given in GAMESS(US) format.
$$
\mu_i \approx \frac{1}{2} \frac{1.5^{i}}{1.5^3}
$$
* H_{2}O
Reference atomization energy : 0.371900 au
** XYZ file
Same Geometry as in doi:10.1063/1.4947093
#+begin_example
3
Water from doi:10.1063/1.4947093
O 0. 0. 0.
H -0.756950272703377558 0. -0.585882234512562827
H 0.756950272703377558 0. -0.585882234512562827
#+end_example
Nuclear repulsion energy : 6.983610526929691
** Pseudopotential
#+begin_example
H GEN 0 0
3
1.00000000 1 4.47692410
4.47692410 3 2.97636451
-4.32112340 2 3.01841596
O GEN 2 1
3
6.00000000 1 9.29793903
55.78763416 3 8.86492204
-38.81978498 2 8.62925665
1
38.41914135 2 8.71924452
#+end_example
*** cc-pVDZ-BFD
#+begin_example
HYDROGEN
S 9
1 0.013000 0.000706
2 0.029900 -0.002119
3 0.068770 0.057693
4 0.158170 0.230695
5 0.363792 0.277612
6 0.836721 0.169833
7 1.924458 0.097443
8 4.426254 0.029966
9 10.180385 -0.000452
S 1
1 0.170483 1.000000
P 9
1 0.003000 0.001242
2 0.007800 -0.000913
3 0.020281 -0.000054
4 0.052730 -0.000238
5 0.137097 -0.011530
6 0.356451 -0.018235
7 0.926774 -0.013929
8 2.409612 -0.009395
9 6.264991 -0.000347
OXYGEN
S 9
1 0.125346 0.055741
2 0.268022 0.304848
3 0.573098 0.453752
4 1.225429 0.295926
5 2.620277 0.019567
6 5.602818 -0.128627
7 11.980245 0.012024
8 25.616801 0.000407
9 54.775216 -0.000076
S 1
1 0.258551 1.000000
P 9
1 0.083598 0.044958
2 0.167017 0.150175
3 0.333673 0.255999
4 0.666627 0.281879
5 1.331816 0.242835
6 2.660761 0.161134
7 5.315785 0.082308
8 10.620108 0.039899
9 21.217318 0.004679
P 1
1 0.267865 1.000000
D 1
1 1.232753 1.000000
#+end_example
24 AOs, 23 MOs
**** HF energy:
| H2O | -16.94804007785208 |
| H | -0.4990452313322324 |
| O | -15.70594174131179 |
**** CCSD(T) dissociation energy: 0.333219 au
**** CIPSI with natural orbitals
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#+NAME:h2o-dz-bfd
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| | H_{2}O | | H | | O | | |
| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization |
|-------+--------+-------------------+------+--------------------+-------+-------------------+--------------|
| 1.e-6 | 11 | -17.2464827355670 | 1 | -0.497462910963732 | 32 | -15.8926592152696 | 0.35889770 |
| 0.20 | 23 | -17.2454472136151 | 1 | -0.497675271883671 | 18 | -15.8906553675359 | 0.35944130 |
| 0.30 | 53 | -17.2531752249923 | 1 | -0.500020054995876 | 22 | -15.8991860505193 | 0.35394906 |
| 0.50 | 1442 | -17.2627954176401 | 1 | -0.502301769176686 | 95 | -15.9113115088349 | 0.34688037 |
| 0.75 | 3213 | -17.2608600031439 | 1 | -0.501902392897537 | 431 | -15.9125649495245 | 0.34449027 |
| 1.00 | 6743 | -17.2526327790576 | 1 | -0.500915129067989 | 571 | -15.9054097072708 | 0.34539281 |
| 1.75 | 54540 | -17.2227612803246 | 1 | -0.499556360741909 | 1064 | -15.8778827081260 | 0.34576585 |
| 2.50 | 51691 | -17.2017620477491 | 1 | -0.499220775536428 | 1879 | -15.8599672611832 | 0.34335324 |
| 3.80 | 103059 | -17.1841520428494 | 1 | -0.499087178764149 | 1846 | -15.8450343476922 | 0.34094334 |
| 5.70 | 102599 | -17.1743644569390 | 1 | -0.499054690526038 | 1944 | -15.8372541996167 | 0.33900088 |
| 8.50 | 101803 | -17.1692969615481 | 1 | -0.499047296040090 | 1943 | -15.8333886253435 | 0.33781374 |
| $\infty$ | 200521 | -17.1644196532044 | 1 | -0.49904523 | 15699 | -15.8300247094224 | 0.33630448 |
| ExFCI | NA | -17.164669 | 1 | -0.49904523 | NA | -15.83002472 | 0.33655382 |
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#+TBLFM: $8=(2.*$5+ $7-$3)
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#+BEGIN_SRC gnuplot :var data=h2o-dz-bfd :output file :file h2o-dz-bfd.png
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reset
set grid
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set xrange [0.0:6]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(sr-PBE)-E(FCI)"
plot data u (1./$1):($3+17.164669) w p notitle , data u (1./ $1):($3+17.164669) sm cs title "H_{2}O", \
data u (1./$1):($7+2.*$5+15.83002472+2.*0.49904523) w p notitle , data u (1./ $1):($7+2.*$5+15.83002472+2.*0.49904523) sm cs title "O"
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#+END_SRC
#+RESULTS:
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[[file:h2o-dz-bfd.png ]]
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**** QMC
#+NAME:h2o-dz-bfd-qmc
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| | H_{2}O | | | | H | | | O | | | |
| $\mu$ | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | E_atomization | |
|-------+--------+----------------+--------------+------+---------------+--------------+-------+----------------+--------------+--------------+--------------|
| 1.e-6 | 11 | -17.2535927658 | 0.0000616883 | 1 | -0.5000010174 | 0.0000172350 | 32 | -15.8925264785 | 0.0000403682 | 0.36106425 | 7.7647462e-5 |
| 0.20 | 23 | -17.2537299553 | 0.0000673868 | 1 | -0.5000031727 | 0.0000098305 | 18 | -15.8924339913 | 0.0000430385 | 0.36128962 | 8.1157691e-5 |
| 0.30 | 53 | -17.2534524288 | 0.0001389013 | 1 | -0.5000014039 | 0.0000201664 | 22 | -15.8923555444 | 0.0000469813 | 0.36109408 | 1.4937932e-4 |
| 0.50 | 1442 | -17.2539120512 | 0.0001475010 | 1 | -0.4999990746 | 0.0000135287 | 95 | -15.8932841728 | 0.0000500649 | 0.36062973 | 1.5693658e-4 |
| 0.75 | 3213 | -17.2551351593 | 0.0001757492 | 1 | -0.4999704651 | 0.0000123770 | 431 | -15.8944755650 | 0.0000643664 | 0.36071866 | 1.8798190e-4 |
| 1.00 | 6743 | -17.2566320269 | 0.0001881680 | 1 | -0.4999828909 | 0.0000123869 | 571 | -15.8966490353 | 0.0000779053 | 0.36001721 | 2.0440964e-4 |
| 1.75 | 54540 | -17.2595366309 | 0.0003193539 | 1 | -0.4999832501 | 0.0000118522 | 1064 | -15.9005460240 | 0.0000744481 | 0.35902411 | 3.2834491e-4 |
| 2.50 | 51691 | -17.2593693798 | 0.0002564347 | 1 | -0.5000182128 | 0.0000122194 | 1879 | -15.9014139890 | 0.0000803966 | 0.35791897 | 2.6929723e-4 |
| 3.80 | 103059 | -17.2586706893 | 0.0002222800 | 1 | -0.4999868144 | 0.0000178879 | 1846 | -15.9012320417 | 0.0000671972 | 0.35746502 | 2.3358899e-4 |
| 5.70 | 102599 | -17.2577349871 | 0.0002927319 | 1 | -0.5000137286 | 0.0000197492 | 1944 | -15.9008305913 | 0.0000792190 | 0.35687694 | 3.0454503e-4 |
| 8.50 | 101803 | -17.2572986405 | 0.0002283964 | 1 | -0.4999852648 | 0.0000097121 | 1943 | -15.9006922550 | 0.0000730561 | 0.35663586 | 2.4018901e-4 |
| inf | 200521 | -17.2567650693 | 0.0005779960 | 1 | -0.5000103856 | 0.0000211133 | 15699 | -15.9005181702 | 0.0000914524 | 0.35622613 | 5.8594749e-4 |
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#+TBLFM: $11=(2.*$6+ $9-$3) :: $12=sqrt(2.*$7*$7+$10* $10+$4*$4)
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#+BEGIN_SRC gnuplot :var data=h2o-dz-bfd-qmc :output file :file h2o-dz-bfd-qmc.png
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reset
set grid
set xrange [0.0:6]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(srCIPSI/DMC)-E(FCI/DMC)"
plot data u (1./$1):($3+17.2567650693):4 w error notitle , data u (1./ $1):($3+17.2567650693) sm cs title "H_{2}O", \
data u (1./$1):($9+2.*$6+2.*.5000103856+15.9005181702):(sqrt($10**2+4.*$7**2)) w error notitle , data u (1./ $1):($9+2.*$6+2.* .5000103856+15.9005181702) sm cs title "O"
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#+END_SRC
#+RESULTS:
[[file:h2o-dz-bfd-qmc.png ]]
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**** ECMD
#+NAME:h2o-dz-bfd-ecmd
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| | H_{2}O | | H | | O | | |
| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization |
|-------+--------+----------------+------+-------------+-------+----------------+--------------|
| 1.e-6 | 11 | -16.9448707424 | 1 | -0.49904523 | 32 | -15.7028012993 | 0.24397898 |
| 0.20 | 23 | -17.2242666759 | 1 | -0.49904523 | 18 | -15.8913535806 | 0.33482264 |
| 0.30 | 53 | -17.2213647451 | 1 | -0.49904523 | 22 | -15.8860197374 | 0.33725455 |
| 0.50 | 1442 | -17.2460034776 | 1 | -0.49904523 | 95 | -15.8897226418 | 0.35819038 |
| 0.75 | 3213 | -17.2538396234 | 1 | -0.49904523 | 431 | -15.8911624468 | 0.36458672 |
| 1.00 | 6743 | -17.2445547711 | 1 | -0.49904523 | 571 | -15.8836840393 | 0.36278027 |
| 1.75 | 54540 | -17.2028094097 | 1 | -0.49904523 | 1064 | -15.8550921703 | 0.34962678 |
| 2.50 | 51691 | -17.1821264648 | 1 | -0.49904523 | 1879 | -15.8417340743 | 0.34230193 |
| 3.80 | 103059 | -17.1707019945 | 1 | -0.49904523 | 1846 | -15.8339576594 | 0.33865388 |
| 5.70 | 102599 | -17.1663719591 | 1 | -0.49904523 | 1944 | -15.8311365603 | 0.33714494 |
| 8.50 | 101803 | -17.1648836325 | 1 | -0.49904523 | 1943 | -15.8300240953 | 0.33676908 |
| $\infty$ | 200521 | -17.1644196534 | 1 | -0.49904523 | 15699 | -15.8301288718 | 0.33620032 |
| ExFCI | NA | -17.164669 | 1 | -0.49904523 | NA | -15.83002472 | 0.33655382 |
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#+TBLFM: $8=(2.*$5+ $7-$3)
#+BEGIN_SRC gnuplot :var data=h2o-dz-bfd-ecmd :output file :file h2o-dz-bfd-ecmd.png
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reset
set grid
set xrange [0.0:6]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(ECMD)"
plot data u (1./$1):($3+17.164669) w p notitle , data u (1./ $1):($3+17.164669) sm cs title "H_{2}O", \
data u (1./$1):($7+2.*$5+2.*0.49904523+15.83002472) w p notitle , data u (1./ $1):($7+2.*$5+2.*0.49904523+15.83002472) sm cs title "O"
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#+END_SRC
#+RESULTS:
[[file:h2o-dz-bfd-ecmd.png ]]
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*** cc-pVTZ-BFD
#+begin_example
HYDROGEN
S 9
1 0.013000 0.000706
2 0.029900 -0.002119
3 0.068770 0.057693
4 0.158170 0.230695
5 0.363792 0.277612
6 0.836721 0.169833
7 1.924458 0.097443
8 4.426254 0.029966
9 10.180385 -0.000452
S 1
1 0.170654 1.000000
P 9
1 0.003000 0.001242
2 0.007800 -0.000913
3 0.020281 -0.000054
4 0.052730 -0.000238
5 0.137097 -0.011530
6 0.356451 -0.018235
7 0.926774 -0.013929
8 2.409612 -0.009395
9 6.264991 -0.000347
P 1
1 0.495357 1.000000
D 1
1 0.955745 1.000000
OXYGEN
S 9
1 0.125346 0.055741
2 0.268022 0.304848
3 0.573098 0.453752
4 1.225429 0.295926
5 2.620277 0.019567
6 5.602818 -0.128627
7 11.980245 0.012024
8 25.616801 0.000407
9 54.775216 -0.000076
S 1
1 1.686633 1.000000
S 1
1 0.237997 1.000000
P 9
1 0.083598 0.044958
2 0.167017 0.150175
3 0.333673 0.255999
4 0.666627 0.281879
5 1.331816 0.242835
6 2.660761 0.161134
7 5.315785 0.082308
8 10.620108 0.039899
9 21.217318 0.004679
P 1
1 0.184696 1.000000
P 1
1 0.600621 1.000000
D 1
1 0.669340 1.000000
D 1
1 2.404278 1.000000
F 1
1 1.423104 1.000000
#+end_example
62 AOs, 55 MOs
**** HF energy:
| H2O | -16.95323238971265 |
| H | -0.4990429174703885 |
| O | -15.70800126366209 |
**** CCSD(T) dissociation energy: 0.359559 au
**** CIPSI with natural orbitals
2020-04-27 02:11:06 +02:00
#+NAME: h2o-tz-bfd
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| | H_{2}O | | H | | O | | |
| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization |
|-------+---------+-------------------+------+--------------------+--------+-------------------+--------------|
| 1.e-6 | 23 | -17.2523870798208 | 1 | -0.497455949623173 | 56 | -15.8943418199011 | 0.36313336 |
| 0.20 | 23 | -17.2517850749956 | 1 | -0.497667829593971 | 44 | -15.8925846521328 | 0.36386476 |
| 0.30 | 219 | -17.2602989385967 | 1 | -0.500012863167701 | 44 | -15.9011337704962 | 0.35913944 |
| 0.50 | 1699 | -17.2712812851578 | 1 | -0.502296128041502 | 387 | -15.9149780380730 | 0.35171099 |
| 0.75 | 13362 | -17.2742507881653 | 1 | -0.501898409513286 | 1133 | -15.9199259292212 | 0.35052804 |
| 1.00 | 25673 | -17.2705814448750 | 1 | -0.500911996264451 | 2291 | -15.9169272791252 | 0.35183017 |
| 1.75 | 207475 | -17.2550176120029 | 1 | -0.499553910797633 | 9594 | -15.9020240076499 | 0.35388578 |
| 2.50 | 858123 | -17.2461435031256 | 1 | -0.499218425280479 | 21911 | -15.8938546433323 | 0.35385201 |
| 3.80 | 1621513 | -17.2393621693893 | 1 | -0.499084857864629 | 18329 | -15.8877260665965 | 0.35346639 |
| 5.70 | 1629655 | -17.2358436456985 | 1 | -0.499052375301986 | 21941 | -15.8850092841849 | 0.35272961 |
| 8.50 | 1643301 | -17.2339427191574 | 1 | -0.499044981913016 | 42217 | -15.8838759830564 | 0.35197677 |
| $\infty$ | 1631982 | -17.2316182510754 | 1 | -0.499042917477163 | 282793 | -15.8825637842011 | 0.35096863 |
| ExFCI | | -17.23217115 | | -0.499042917477163 | | -15.88257866 | 0.35150666 |
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#+TBLFM: $8=(2.*$5+ $7-$3)
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#+BEGIN_SRC gnuplot :var data=h2o-tz-bfd :output file :file h2o-tz-bfd.png
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reset
set grid
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set xrange [0.0:6]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(sr-PBE)-E(FCI)"
plot data u (1./$1):($3+17.23217115) w p notitle , data u (1./ $1):($3+17.23217115) sm cs title "H_{2}O", \
data u (1./$1):($7+2.*$5+15.88257866+2.*0.499042917477163) w p notitle , data u (1./ $1):($7+2.*$5+15.88257866+2.*0.499042917477163) sm cs title "O"
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#+END_SRC
#+RESULTS:
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[[file:h2o-tz-bfd.png ]]
2020-04-28 11:35:58 +02:00
**** QMC
#+NAME:h2o-tz-bfd-qmc
| | H_{2}O | | | | H | | | O | | | |
| $\mu$ | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | E_atomization | |
|-------+--------+----------------+--------------+------+---------------+--------------+-------+----------------+--------------+--------------+--------------|
| 1.e-6 | 11 | -17.2567326254 | 0.0000724793 | 1 | -0.4999898051 | 0.0000065175 | 32 | -15.8930902787 | 0.0000578329 | 0.36366274 | 9.3181805e-5 |
| 0.20 | 23 | -17.2567536447 | 0.0000743643 | 1 | -0.5000210771 | 0.0000097491 | 18 | -15.8930200016 | 0.0000473829 | 0.36369149 | 8.9248407e-5 |
| 0.30 | 53 | -17.2547622642 | 0.0003546142 | 1 | -0.4999868887 | 0.0000149003 | 22 | -15.8928444962 | 0.0000484284 | 0.36194399 | 3.5852556e-4 |
| 0.50 | 1442 | -17.2576923660 | 0.0001643026 | 1 | -0.4999987389 | 0.0000138110 | 95 | -15.8933526777 | 0.0001305214 | 0.36434221 | 2.1074313e-4 |
| 0.75 | 3213 | -17.2583975528 | 0.0002339741 | 1 | -0.5000191125 | 0.0000109315 | 431 | -15.8962312871 | 0.0000796553 | 0.36212804 | 2.4764459e-4 |
| 1.00 | 6743 | -17.2607638883 | 0.0002138894 | 1 | -0.4999862089 | 0.0000119766 | 571 | -15.8985297947 | 0.0000845907 | 0.36226168 | 2.3063204e-4 |
| 1.75 | 54540 | -17.2635747066 | 0.0002019783 | 1 | -0.4999666515 | 0.0000131903 | 1064 | -15.9030314207 | 0.0000811325 | 0.36060998 | 2.1846209e-4 |
| 2.50 | 51691 | -17.2642334959 | 0.0002520822 | 1 | -0.4999801617 | 0.0000094324 | 1879 | -15.9044556541 | 0.0000797733 | 0.35981752 | 2.6473979e-4 |
| 3.80 | 103059 | -17.2637768189 | 0.0002593775 | 1 | -0.5000085861 | 0.0000085475 | 1846 | -15.9046408769 | 0.0000732723 | 0.35911877 | 2.6979925e-4 |
| 5.70 | 102599 | -17.2632074160 | 0.0002601711 | 1 | -0.5000055184 | 0.0000147803 | 1944 | -15.9042738928 | 0.0000731262 | 0.35892249 | 2.7105969e-4 |
| 8.50 | 101803 | -17.2634081426 | 0.0002622590 | 1 | -0.5000010336 | 0.0000123807 | 1943 | -15.9044520693 | 0.0000761691 | 0.35895401 | 2.7365686e-4 |
| inf | 200521 | -17.2639511202 | 0.0002622429 | 1 | -0.4999916320 | 0.0000135918 | 15699 | -15.9039263267 | 0.0000874602 | 0.36004153 | 2.7711027e-4 |
#+TBLFM: $11=(2.*$6+ $9-$3) :: $12=sqrt(2.*$7*$7+$10* $10+$4*$4)
#+BEGIN_SRC gnuplot :var data=h2o-tz-bfd-qmc :output file :file h2o-tz-bfd-qmc.png
reset
set grid
set xrange [0.0:6]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(srCIPSI/DMC)-E(FCI/DMC)"
plot data u (1./$1):($3+17.2639511202):4 w error notitle , data u (1./ $1):($3+17.2639511202) sm cs title "H_{2}O", \
data u (1./$1):($9+2.*$6+2.*.4999916320+15.9039263267):(sqrt($10**2+4.*$7**2)) w error notitle , data u (1./ $1):($9+2.*$6+2.* .4999916320+15.9039263267) sm cs title "O"
#+END_SRC
#+RESULTS:
[[file:h2o-tz-bfd-qmc.png ]]
2020-04-26 01:41:24 +02:00
2020-04-27 19:27:09 +02:00
**** ECMD
#+NAME:h2o-tz-bfd-ecmd
2020-04-27 19:38:57 +02:00
| | H_{2}O | | H | | O | | |
| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization |
|-------+---------+----------------+------+---------------+--------+----------------+--------------|
| 1.e-6 | 23 | -16.9474227226 | 1 | -0.4990429175 | 56 | -15.7018131902 | 0.24752370 |
| 0.20 | 23 | -17.2261065833 | 1 | -0.4990429175 | 44 | -15.8890274854 | 0.33899326 |
| 0.30 | 219 | -17.2347208976 | 1 | -0.4990429175 | 44 | -15.8852236174 | 0.35141145 |
| 0.50 | 1699 | -17.2565233809 | 1 | -0.4990429175 | 387 | -15.8977227918 | 0.36071475 |
| 0.75 | 13362 | -17.2763408603 | 1 | -0.4990429175 | 1133 | -15.9062325977 | 0.37202243 |
| 1.00 | 25673 | -17.2765522162 | 1 | -0.4990429175 | 2291 | -15.9076662553 | 0.37080013 |
| 1.75 | 207475 | -17.2553166617 | 1 | -0.4990429175 | 9594 | -15.8963737107 | 0.36085712 |
| 2.50 | 858123 | -17.2436535008 | 1 | -0.4990429175 | 21911 | -15.8895990392 | 0.35596863 |
| 3.80 | 1621513 | -17.2363656023 | 1 | -0.4990429175 | 18329 | -15.8850079618 | 0.35327181 |
| 5.70 | 1629655 | -17.2333460576 | 1 | -0.4990429175 | 21941 | -15.8832438185 | 0.35201640 |
| 8.50 | 1643301 | -17.2322131312 | 1 | -0.4990429175 | 42217 | -15.8827440572 | 0.35138324 |
| $\infty$ | 1631982 | -17.2316182511 | 1 | -0.4990429175 | 282793 | -15.8825637842 | 0.35096863 |
| ExFCI | | -17.23217115 | | -0.4990429175 | | -15.88257866 | 0.35150666 |
2020-04-27 19:27:09 +02:00
#+TBLFM: $8=(2.*$5+ $7-$3)
#+BEGIN_SRC gnuplot :var data=h2o-tz-bfd-ecmd :output file :file h2o-tz-bfd-ecmd.png
reset
set grid
2020-04-28 11:35:58 +02:00
set xrange [0.0:6]
2020-04-27 19:27:09 +02:00
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(ECMD)"
2020-04-28 11:35:58 +02:00
plot data u (1./$1):($3+17.23217115) w p notitle , data u (1./ $1):($3+17.23217115) sm cs title "H_{2}O", \
data u (1./$1):($7+2.*$5+2.*0.4990429175+15.88257866) w p notitle , data u (1./ $1):($7+2.*$5+2.*0.4990429175+15.88257866) sm cs title "O"
2020-04-27 19:27:09 +02:00
#+END_SRC
#+RESULTS:
[[file:h2o-tz-bfd-ecmd.png ]]
2020-04-28 11:35:58 +02:00
**** Analyzis of coefficients
#+BEGIN_SRC R :results output file graphics :file "./coefs-h2o.png" :exports results :width 1000 :height 600
coefs <- list()
mus = c("1.e-6", "0.20", "0.30", "0.50", "0.75", "1.00", "1.75", "2.50", "3.80", "5.70", "8.50")
for (mu in mus) {
filename = paste0("/dev/shm/tmp/Anouar/H2O/dz_bfd/h2o_dz_bfd_ ", mu,"/determinants/psi_coef.gz")
coefs[[mu ]] <- sort(abs(read.table(filename,skip=2)$V1), decreasing=TRUE)[1:100000]
}
coefs_df <- as.data.frame(do.call(cbind, coefs))
plot(coefs_df[,"0.50"],log="xy",type= "n",xlab="Determinant",ylab= "|C_i|")
i <- 1
colors = topo.colors(length(mus))
for (mu in mus) {
lines(coefs_df[,mu],type="l",col=colors[i],title=mu)
i <- i+1
}
#+END_SRC
#+RESULTS:
[[file:./coefs-h2o.png ]]
2020-04-26 01:41:24 +02:00
*** cc-pVQZ-BFD
#+begin_example
HYDROGEN
S 9
1 0.013000 0.000706
2 0.029900 -0.002119
3 0.068770 0.057693
4 0.158170 0.230695
5 0.363792 0.277612
6 0.836721 0.169833
7 1.924458 0.097443
8 4.426254 0.029966
9 10.180385 -0.000452
S 1
1 0.120599 1.000000
S 1
1 0.404783 1.000000
S 1
1 0.715129 1.000000
P 9
1 0.003000 0.001242
2 0.007800 -0.000913
3 0.020281 -0.000054
4 0.052730 -0.000238
5 0.137097 -0.011530
6 0.356451 -0.018235
7 0.926774 -0.013929
8 2.409612 -0.009395
9 6.264991 -0.000347
P 1
1 0.774536 1.000000
P 1
1 0.263038 1.000000
D 1
1 2.315883 1.000000
D 1
1 0.636656 1.000000
F 1
1 1.130819 1.000000
OXYGEN
S 9
1 0.125346 0.055741
2 0.268022 0.304848
3 0.573098 0.453752
4 1.225429 0.295926
5 2.620277 0.019567
6 5.602818 -0.128627
7 11.980245 0.012024
8 25.616801 0.000407
9 54.775216 -0.000076
S 1
1 0.224380 1.000000
S 1
1 0.843157 1.000000
S 1
1 1.351771 1.000000
P 9
1 0.083598 0.044958
2 0.167017 0.150175
3 0.333673 0.255999
4 0.666627 0.281879
5 1.331816 0.242835
6 2.660761 0.161134
7 5.315785 0.082308
8 10.620108 0.039899
9 21.217318 0.004679
P 1
1 0.148562 1.000000
P 1
1 0.452364 1.000000
P 1
1 1.106737 1.000000
D 1
1 0.455711 1.000000
D 1
1 1.344331 1.000000
D 1
1 4.008867 1.000000
F 1
1 0.876289 1.000000
F 1
1 2.763115 1.000000
G 1
1 1.759081 1.000000
#+end_example
139 AOs, 114 MOs
**** HF energy:
| H2O | -16.95323238971265 |
| H | -0.4999159485752356 |
| O | -15.70838239857190 |
**** CCSD(T) dissociation energy: ??? au
**** CIPSI with natural orbitals
2020-04-27 02:11:06 +02:00
#+NAME:h2o-qz-bfd
2020-04-27 19:38:57 +02:00
| | H_{2}O | | H | | O | | | | | |
| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization | | | |
|-------+---------+-------------------+------+--------------------+---------+-------------------+--------------+---+---+---|
2020-04-28 11:35:58 +02:00
| 1.e-6 | 23 | -17.2550713148646 | 1 | -0.498770397586525 | 41 | -15.8945440099478 | 0.36298651 | | | |
| 0.20 | 23 | -17.2544983309796 | 1 | -0.498943556678728 | 39 | -15.8927491298105 | 0.36386209 | | | |
| 0.30 | 214 | -17.2631125033426 | 1 | -0.501238867081562 | 88 | -15.9015447645282 | 0.35909000 | | | |
| 0.50 | 3355 | -17.2753425267816 | 1 | -0.503289490954576 | 369 | -15.9156299499914 | 0.35313359 | | | |
| 0.75 | 24685 | -17.2791002023973 | 1 | -0.502729685060127 | 2152 | -15.9216014051348 | 0.35203943 | | | |
| 1.00 | 51016 | -17.2763349199718 | 1 | -0.501722057158799 | 4324 | -15.9193017992612 | 0.35358901 | | | |
| 1.75 | 832153 | -17.2646439398390 | 1 | -0.500400995599045 | 14431 | -15.9068519442068 | 0.35699000 | | | |
| 2.50 | 1657867 | -17.2591970797300 | 1 | -0.500081369220756 | 30186 | -15.9011704544825 | 0.35786389 | | | |
| 3.80 | 3393009 | -17.2568806209183 | 1 | -0.499955311987831 | 94180 | -15.8985952759131 | 0.35837472 | | | |
| 5.70 | 6849236 | -17.2565805594566 | 1 | -0.499924811823201 | 101131 | -15.8978811997698 | 0.35884974 | | | |
2020-04-27 19:38:57 +02:00
| 8.50 | 6501453 | -17.2563271562921 | 1 | -0.499917882290281 | 94108 | -15.8976152329438 | 0.35887616 | | | |
| $\infty$ | 6555322 | -17.2555127230293 | 1 | -0.499915948575730 | 1614219 | -15.8976190012628 | 0.35806182 | | | |
| ExFCI | | -17.25606450 | | -0.499915948575730 | | -15.89763971 | 0.35859289 | | | |
2020-04-26 01:41:24 +02:00
#+TBLFM: $8=(2.*$5+ $7-$3)
2020-04-27 02:11:06 +02:00
#+BEGIN_SRC gnuplot :var data=h2o-qz-bfd :output file :file h2o-qz-bfd.png
reset
set grid
2020-04-28 11:35:58 +02:00
set xrange [0.0:6]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(sr-PBE)-E(FCI)"
plot data u (1./$1):($3+17.25606450) w p notitle , data u (1./ $1):($3+17.25606450) sm cs title "H_{2}O", \
data u (1./$1):($7+2.*$5+2.*0.499915948575730+15.89763971) w p notitle , data u (1./ $1):($7+2.*$5+2.*0.499915948575730+15.89763971) sm cs title "O"
2020-04-27 02:11:06 +02:00
#+END_SRC
2020-04-28 11:35:58 +02:00
#+RESULTS:
[[file:h2o-qz-bfd.png ]]
2020-04-27 02:11:06 +02:00
** All-electron
* C_{2}
Data taken from doi:10.1021/ct300504f
Reference atomization energy : 146.9(5) kcal/mol = 0.2341(8) au
** XYZ file
Same Geometry as in doi:10.1021/ct300504f
#+begin_example
2
C2
C 0. 0. -0.62125
C 0. 0. 0.62125
#+end_example
Nuclear repulsion energy : 6.814354426334003
** Pseudopotential
#+begin_example
C GEN 2 1
3
4.00000000 1 8.35973821
33.43895285 3 4.48361888
-19.17537323 2 3.93831258
1
22.55164191 2 5.02991637
#+end_example
*** cc-pVDZ-BFD
#+begin_example
CARBON
S 9
1 0.051344 0.013991
2 0.102619 0.169852
3 0.205100 0.397529
4 0.409924 0.380369
5 0.819297 0.180113
6 1.637494 -0.033512
7 3.272791 -0.121499
8 6.541187 0.015176
9 13.073594 -0.000705
S 1
1 0.127852 1.000000
P 9
1 0.029281 0.001787
2 0.058547 0.050426
3 0.117063 0.191634
4 0.234064 0.302667
5 0.468003 0.289868
6 0.935757 0.210979
7 1.871016 0.112024
8 3.741035 0.054425
9 7.480076 0.021931
P 1
1 0.149161 1.000000
D 1
1 0.561160 1.000000
#+end_example
28 AOs, 26 MOs
**** HF energy:
| C2 | -10.67893455005543 |
| C | -5.328989707682060 |
**** i-FCIQMC dissociation energy: 129.95(8) kcal/mol = 0.2071(1) au
**** CIPSI with natural orbitals
#+NAME:c2-dz-bfd
2020-04-27 19:38:57 +02:00
| | C_{2} | | C | | |
| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization |
|-------+---------+-------------------+------+-------------------+--------------|
2020-04-28 11:35:58 +02:00
| 1.e-6 | NA | NA | 22 | -5.41505706988073 | -10.830114 |
| 0.20 | NA | NA | 9 | -5.41545184840256 | -10.830904 |
| 0.30 | NA | NA | 21 | -5.42042892115798 | -10.840858 |
| 0.50 | NA | NA | 135 | -5.42445651484712 | -10.848913 |
2020-04-27 19:38:57 +02:00
| 0.75 | 52960 | -11.0308445085580 | 163 | -5.42281416310061 | 0.18521618 |
| 1.00 | 104403 | -11.0323357336759 | 330 | -5.42008673295876 | 0.19216227 |
| 1.75 | 408078 | -11.0314245120875 | 509 | -5.41456475332999 | 0.20229501 |
| 2.50 | 822205 | -11.0291998069478 | 513 | -5.41233203015442 | 0.20453575 |
| 3.80 | 703001 | -11.0267092471890 | 511 | -5.41095120348554 | 0.20480684 |
| 5.70 | 715415 | -11.0251197032813 | 498 | -5.41028104327860 | 0.20455762 |
| 8.50 | 1421782 | -11.0243736638120 | 498 | -5.40994218754541 | 0.20448929 |
| $\infty$ | 722672 | -11.0229208360228 | 498 | -5.40958049910186 | 0.20375984 |
| ExFCI | NA | -11.02347855 | | -5.40960365 | 0.20427125 |
2020-04-27 02:11:06 +02:00
#+TBLFM: $6=(2.*$5-$3)
#+BEGIN_SRC gnuplot :var data=c2-dz-bfd :output file :file c2-dz-bfd.png
reset
set grid
2020-04-28 11:35:58 +02:00
set xrange [0.0:6]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(sr-PBE)-E(FCI)"
plot data u (1./$1):($3+11.02347855) w p notitle , data u (1./ $1):($3+11.02347855) sm cs title "C_{2}", \
data u (1./$1):(2.*$5+2.*5.40960365) w p notitle , data u (1./ $1):(2.*$5+2.*5.40960365) sm cs title "C"
2020-04-27 02:11:06 +02:00
#+END_SRC
#+RESULTS:
[[file:c2-dz-bfd.png ]]
2020-04-28 11:35:58 +02:00
**** QMC
#+NAME:c2-dz-bfd-qmc
| | C_2 | | | C | | | | |
| $\mu$ | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | E_atomization | |
|-------+---------+----------------+--------------+------+---------------+--------------+-----------------+---------------------------|
| 1.e-6 | NA | NA | NA | 22 | -5.4167052434 | 0.0000222156 | -10.833410 - NA | sqrt(9.8706577e-10 + NA^2) |
| 0.20 | NA | NA | NA | 9 | -5.4165906853 | 0.0000221124 | -10.833181 - NA | sqrt(9.7791647e-10 + NA^2) |
| 0.30 | NA | NA | NA | 21 | -5.4188382207 | 0.0000229444 | -10.837676 - NA | sqrt(1.0528910e-9 + NA^2) |
| 0.50 | NA | NA | NA | 135 | -5.4223620093 | 0.0000352887 | -10.844724 - NA | sqrt(2.4905847e-9 + NA^2) |
| 0.75 | 52960 | -11.0820433720 | 0.0002115860 | 163 | -5.4269017472 | 0.0000303835 | 0.22823988 | 2.1590495e-4 |
| 1.00 | 104403 | -11.0881137121 | 0.0002180137 | 330 | -5.4297546085 | 0.0000282413 | 0.22860450 | 2.2164186e-4 |
| 1.75 | 408078 | -11.0919649694 | 0.0002479501 | 509 | -5.4319232617 | 0.0000273252 | 0.22811845 | 2.5094339e-4 |
| 2.50 | 822205 | -11.0912801356 | 0.0003000786 | 513 | -5.4320468517 | 0.0000326056 | 0.22718643 | 3.0360075e-4 |
| 3.80 | 703001 | -11.0910410057 | 0.0002770448 | 511 | -5.4319428879 | 0.0000258094 | 0.22715523 | 2.7943885e-4 |
| 5.70 | 715415 | -11.0914323663 | 0.0002898056 | 498 | -5.4318199101 | 0.0000282036 | 0.22779255 | 2.9253747e-4 |
| 8.50 | 1421782 | -11.0903763997 | 0.0003034897 | 498 | -5.4318044503 | 0.0000339472 | 0.22676750 | 3.0726344e-4 |
| inf | 722672 | -11.0906066753 | 0.0002685622 | 498 | -5.4317735738 | 0.0000258448 | 0.22705953 | 2.7103794e-4 |
#+TBLFM: $8=(2.*$6-$3) :: $9=sqrt(2.*$7*$7+ $4*$4)
#+BEGIN_SRC gnuplot :var data=c2-dz-bfd-qmc :output file :file c2-dz-bfd-qmc.png
reset
set grid
set xrange [0.0:2]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(srCIPSI/DMC)-E(FCI/DMC)"
plot data u (1./$1):($3+11.09066753):4 w error notitle , data u (1./ $1):($3+11.09066753) sm cs title "C_{2}", \
data u (1./$1):($9+2.*$6+2.*5.4317735738):(sqrt($10**2+4.*$7**2)) w error notitle , data u (1./ $1):($9+2.*$6+2.*5.4317735738) sm cs title "C"
#+END_SRC
#+RESULTS:
[[file:c2-dz-bfd-qmc.png ]]
**** Analyzis of coefficients
#+BEGIN_SRC R :results output file graphics :file "./coefs-c2.png" :exports results :width 1000 :height 600
coefs <- list()
mus = c("0.75", "1.00", "1.75", "2.50", "3.80", "5.70", "8.50")
for (mu in mus) {
filename = paste0("/dev/shm/tmp/Anouar/C2/dz_bfd/c2_dz_bfd_ ", mu,"/determinants/psi_coef.gz")
coefs[[mu ]] <- sort(abs(read.table(filename,skip=2)$V1), decreasing=TRUE)[1:100000]
}
coefs_df <- as.data.frame(do.call(cbind, coefs))
plot(coefs_df[,"1.00"],log="xy",type= "n",xlab="Determinant",ylab= "|C_i|")
i <- 1
colors = topo.colors(length(mus))
for (mu in mus) {
lines(coefs_df[,mu],type="l",col=colors[i],title=mu)
i <- i+1
}
#+END_SRC
#+RESULTS:
[[file:./coefs-c2.png ]]
2020-04-27 02:11:06 +02:00
*** cc-pVTZ-BFD
#+begin_example
CARBON
S 9
1 0.051344 0.013991
2 0.102619 0.169852
3 0.205100 0.397529
4 0.409924 0.380369
5 0.819297 0.180113
6 1.637494 -0.033512
7 3.272791 -0.121499
8 6.541187 0.015176
9 13.073594 -0.000705
S 1
1 0.921552 1.000000
S 1
1 0.132800 1.000000
P 9
1 0.029281 0.001787
2 0.058547 0.050426
3 0.117063 0.191634
4 0.234064 0.302667
5 0.468003 0.289868
6 0.935757 0.210979
7 1.871016 0.112024
8 3.741035 0.054425
9 7.480076 0.021931
P 1
1 0.126772 1.000000
P 1
1 0.376742 1.000000
D 1
1 0.329486 1.000000
D 1
1 1.141611 1.000000
F 1
1 0.773485 1.000000
#+end_example
2020-04-28 11:35:58 +02:00
68 AOs, 58 MOs
2020-04-27 02:11:06 +02:00
**** HF energy:
| C2 | |
| C | |
**** i-FCIQMC dissociation energy: 139.69(8) kcal/mol = 0.2226(1) au
**** CIPSI with natural orbitals
#+NAME: c2-tz-bfd
2020-04-28 11:35:58 +02:00
| | C_{2} | | C | | |
| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization |
|-------+--------+ --------------+------+ -------------------+-----------------+
| 1.e-6 | NA | NA | 17 | -5.41553696548016 | -10.831074 - NA |
| 0.20 | NA | NA | 17 | -5.41613005236001 | -10.832260 - NA |
| 0.30 | NA | NA | 38 | -5.42137104699040 | -10.842742 - NA |
| 0.50 | NA | NA | 138 | -5.42636764143841 | -10.852735 - NA |
| 0.75 | NA | NA | 270 | -5.42679122653394 | -10.853582 - NA |
| 1.00 | NA | NA | 528 | -5.42639163352912 | -10.852783 - NA |
| 1.75 | NA | NA | 1077 | -5.42634487557905 | -10.852690 - NA |
| 2.50 | NA | NA | 1034 | -5.42684001117528 | -10.853680 - NA |
| 3.80 | NA | NA | 2172 | -5.42757813990369 | -10.855156 - NA |
| 5.70 | NA | NA | 2160 | -5.42782845289081 | -10.855657 - NA |
| 8.50 | NA | NA | 2166 | -5.42790762317720 | -10.855815 - NA |
| $\infty$ | 722672 | NA | 2156 | -5.42791084828515 | -10.855822 - NA |
| ExFCI | NA | -11.02343265 | | -5.42800915 | 0.16741435 |
#+TBLFM: $6=(2.*$5-$3)
2020-04-27 02:11:06 +02:00
2020-04-28 11:35:58 +02:00
#+BEGIN_SRC gnuplot :var data=c2-tz-bfd :output file :file c2-tz-bfd.png
reset
set grid
set xrange [0.0:6]
set xtics 0.5
set xlabel "1/$\mu$"
set ylabel "E(sr-PBE)-E(FCI)"
plot data u (1./$1):($3+11.02347855) w p notitle , data u (1./ $1):($3+11.02347855) sm cs title "C_{2}", \
data u (1./$1):(2.*$5+2.*5.42800915) w p notitle , data u (1./ $1):(2.*$5+2.*5.42800915) sm cs title "C"
#+END_SRC
#+RESULTS:
[[file:c2-tz-bfd.png ]]
2020-04-27 19:38:57 +02:00
# #+RESULTS:
# [[file:c2-tz-bfd.png]]
2020-04-27 02:11:06 +02:00
*** cc-pVQZ-BFD
#+begin_example
CARBON
S 9
1 0.051344 0.013991
2 0.102619 0.169852
3 0.205100 0.397529
4 0.409924 0.380369
5 0.819297 0.180113
6 1.637494 -0.033512
7 3.272791 -0.121499
8 6.541187 0.015176
9 13.073594 -0.000705
S 1
1 0.109576 1.000000
S 1
1 0.846879 1.000000
S 1
1 0.269659 1.000000
P 9
1 0.029281 0.001787
2 0.058547 0.050426
3 0.117063 0.191634
4 0.234064 0.302667
5 0.468003 0.289868
6 0.935757 0.210979
7 1.871016 0.112024
8 3.741035 0.054425
9 7.480076 0.021931
P 1
1 0.105389 1.000000
P 1
1 0.313254 1.000000
P 1
1 0.804681 1.000000
D 1
1 0.240171 1.000000
D 1
1 0.684884 1.000000
D 1
1 2.013760 1.000000
F 1
1 0.457302 1.000000
F 1
1 1.324930 1.000000
G 1
1 1.034180 1.000000
#+end_example
2020-04-27 19:27:09 +02:00
138 AOs, _ MOs
2020-04-27 02:11:06 +02:00
HF energy:
**** HF energy:
| C2 | |
| C | |
**** CCSD(T) dissociation energy: ??? au
**** CIPSI with natural orbitals
#+NAME:c2-qz-bfd
2020-04-27 19:38:57 +02:00
| | C_{2} | | C | | |
| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization |
|-------+--------+--------------+------+-------------+--------------|
| 1.e-6 | | | | | 0. |
| 0.20 | | | | | 0. |
| 0.30 | | | | | 0. |
| 0.50 | | | | | 0. |
| 0.75 | | | | | 0. |
| 1.00 | | | | | 0. |
| 1.75 | | | | | 0. |
| 2.50 | | | | | 0. |
| 3.80 | | | | | 0. |
| 5.70 | | | | | 0. |
| 8.50 | | | | | 0. |
| $\infty$ | 722672 | | | | 0. |
| ExFCI | NA | -11.02343265 | | -5.40960365 | 0.20422535 |
2020-04-27 02:11:06 +02:00
#+TBLFM: $8=(2.*$5+ $7-$3)
2020-04-27 19:38:57 +02:00
# #+BEGIN_SRC gnuplot :var data=c2-qz-bfd :output file :file c2-qz-bfd.png
# reset
# set log x
# set grid
# set xrange [0.01:100]
# set xtics 0.1
# plot data u 1:6 w lp notitle
# #+END_SRC
2020-04-26 01:41:24 +02:00
** All-electron
2020-04-27 19:27:09 +02:00
