Rewriting
This commit is contained in:
parent
352276a99a
commit
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@ -140,6 +140,7 @@ $$
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[[file:h2o-dz-bfd.png]]
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*** QMC
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#+TBLFM: $11=(2.*$6+$9-$3) :: $12=sqrt(2.*$7*$7+$10*$10+$4*$4)
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#+NAME:h2o-dz-bfd-qmc
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| | H_{2}O | | | | H | | | O | | | |
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| $\mu$ | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | E_atomization | |
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@ -317,22 +318,22 @@ $$
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*** QMC
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#+NAME:h2o-tz-bfd-qmc
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| | H_{2}O | | | | H | | | O | | | |
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| $\mu$ | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | E_atomization | |
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|-------+--------+----------------+--------------+------+---------------+--------------+-------+----------------+--------------+--------------+--------------|
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| 1.e-6 | 11 | -17.2567442368 | 0.0000674814 | 1 | -0.4999898051 | 0.0000065175 | 32 | -15.8930902787 | 0.0000578329 | 0.36367435 | 8.9349534e-5 |
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| 0.20 | 23 | -17.2567293499 | 0.0000806448 | 1 | -0.5000210771 | 0.0000097491 | 18 | -15.8930200016 | 0.0000473829 | 0.36366719 | 9.4545295e-5 |
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| 0.30 | 53 | -17.2537172349 | 0.0005108024 | 1 | -0.4999868887 | 0.0000149003 | 22 | -15.8928444962 | 0.0000484284 | 0.36089896 | 5.1352550e-4 |
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| 0.50 | 1442 | -17.2577489156 | 0.0001590032 | 1 | -0.4999987389 | 0.0000138110 | 95 | -15.8933526777 | 0.0001305214 | 0.36439876 | 2.0663819e-4 |
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| 0.75 | 3213 | -17.2583975528 | 0.0002828675 | 1 | -0.5000191125 | 0.0000109315 | 431 | -15.8962312871 | 0.0000796553 | 0.36212804 | 2.9427536e-4 |
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| 1.00 | 6743 | -17.2609826285 | 0.0002158278 | 1 | -0.4999862089 | 0.0000119766 | 571 | -15.8985297947 | 0.0000845907 | 0.36248042 | 2.3243086e-4 |
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| 1.75 | 54540 | -17.2635480054 | 0.0001864936 | 1 | -0.4999666515 | 0.0000131903 | 1064 | -15.9030314207 | 0.0000811325 | 0.36058328 | 2.0423103e-4 |
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| 2.50 | 51691 | -17.2643468817 | 0.0003484087 | 1 | -0.4999801617 | 0.0000094324 | 1879 | -15.9044556541 | 0.0000797733 | 0.35993090 | 3.5767351e-4 |
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| 3.80 | 103059 | -17.2636697373 | 0.0002950991 | 1 | -0.5000085861 | 0.0000085475 | 1846 | -15.9046408769 | 0.0000732723 | 0.35901169 | 3.0429990e-4 |
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| 5.70 | 102599 | -17.2631675892 | 0.0003358884 | 1 | -0.5000055184 | 0.0000147803 | 1944 | -15.9042738928 | 0.0000731262 | 0.35888266 | 3.4439131e-4 |
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| 8.50 | 101803 | -17.2632963114 | 0.0003799317 | 1 | -0.5000010336 | 0.0000123807 | 1943 | -15.9044520693 | 0.0000761691 | 0.35884217 | 3.8788709e-4 |
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| inf | 200521 | -17.2638832283 | 0.0002702253 | 1 | -0.4999916320 | 0.0000135918 | 15699 | -15.9039263267 | 0.0000874602 | 0.35997364 | 2.8467609e-4 |
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#+TBLFM: $11=(2.*$6+$9-$3) :: $12=sqrt(2.*$7*$7+$10*$10+$4*$4)
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| | H_{2}O | | | | H | | | O | | | |
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| $\mu$ | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error | E_atomization | |
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|-------+---------+----------------+--------------+------+---------------+--------------+-------+----------------+--------------+--------------+--------------|
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| 1.e-6 | 23 | -17.2567442368 | 0.0000674814 | 1 | -0.4999898051 | 0.0000065175 | 32 | -15.8930902787 | 0.0000578329 | 0.36367435 | 8.9349534e-5 |
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| 0.20 | 23 | -17.2567293499 | 0.0000806448 | 1 | -0.5000210771 | 0.0000097491 | 18 | -15.8930200016 | 0.0000473829 | 0.36366719 | 9.4545295e-5 |
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| 0.30 | 219 | -17.2537172349 | 0.0005108024 | 1 | -0.4999868887 | 0.0000149003 | 22 | -15.8928444962 | 0.0000484284 | 0.36089896 | 5.1352550e-4 |
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| 0.50 | 1699 | -17.2577489156 | 0.0001590032 | 1 | -0.4999987389 | 0.0000138110 | 95 | -15.8933526777 | 0.0001305214 | 0.36439876 | 2.0663819e-4 |
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| 0.75 | 13362 | -17.2583975528 | 0.0002828675 | 1 | -0.5000191125 | 0.0000109315 | 431 | -15.8962312871 | 0.0000796553 | 0.36212804 | 2.9427536e-4 |
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| 1.00 | 25673 | -17.2609826285 | 0.0002158278 | 1 | -0.4999862089 | 0.0000119766 | 571 | -15.8985297947 | 0.0000845907 | 0.36248042 | 2.3243086e-4 |
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| 1.75 | 207475 | -17.2635480054 | 0.0001864936 | 1 | -0.4999666515 | 0.0000131903 | 1064 | -15.9030314207 | 0.0000811325 | 0.36058328 | 2.0423103e-4 |
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| 2.50 | 858123 | -17.2643468817 | 0.0003484087 | 1 | -0.4999801617 | 0.0000094324 | 1879 | -15.9044556541 | 0.0000797733 | 0.35993090 | 3.5767351e-4 |
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| 3.80 | 1621513 | -17.2636697373 | 0.0002950991 | 1 | -0.5000085861 | 0.0000085475 | 1846 | -15.9046408769 | 0.0000732723 | 0.35901169 | 3.0429990e-4 |
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| 5.70 | 1629655 | -17.2631675892 | 0.0003358884 | 1 | -0.5000055184 | 0.0000147803 | 1944 | -15.9042738928 | 0.0000731262 | 0.35888266 | 3.4439131e-4 |
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| 8.50 | 1643301 | -17.2632963114 | 0.0003799317 | 1 | -0.5000010336 | 0.0000123807 | 1943 | -15.9044520693 | 0.0000761691 | 0.35884217 | 3.8788709e-4 |
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| inf | 1631982 | -17.2638832283 | 0.0002702253 | 1 | -0.4999916320 | 0.0000135918 | 15699 | -15.9039263267 | 0.0000874602 | 0.35997364 | 2.8467609e-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-tz-bfd-qmc :output file :file h2o-tz-bfd-qmc.png
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reset
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@ -349,7 +350,7 @@ $$
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[[file:h2o-tz-bfd-qmc.png]]
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*** ECMD
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#+NAME:h2o-tz-bfd-ecmd
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| | H_{2}O | | H | | O | | |
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| $\mu$ | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | N_{det} | E(CIPSI) | E_atomization |
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@ -402,9 +403,6 @@ $$
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}
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#+END_SRC
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#+RESULTS:
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[[file:./coefs-h2o.png]]
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** TODO cc-pVQZ-BFD
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#+begin_example
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HYDROGEN
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@ -1986,7 +1984,7 @@ return result
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#+TBLFM: @>$7='(org-sbe "madformula" (data @5$7..@>>$7) ) :: @>$8='(org-sbe "maderrformula" (data @5$8..@>>$8) )
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***** MAD = 5.42 +/- 0.29
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*** TODO FCI
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*** DONE FCI
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**** CIPSI
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***** Table
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#+NAME: dz-cipsi-inf
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@ -2065,28 +2063,85 @@ return result
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| | | | MAD | 23.62 |
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#+TBLFM: @>$5='(org-sbe "madformula" (data @5$5..@>>$5) )
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***** MAD = 23.62
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**** TODO QMC with Jastrow
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**** QMC with Jastrow
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***** Table
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#+NAME: dz-dmc-inf
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| | Total E | | Delta E | | Reference | Error | |
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| | Hartree | | Hartree | | Hartree | kcal/mol | |
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|---------+------------+----------+----------+----------+-----------+------------+----------|
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| Be | -1.007625 | 0.000014 | 0.000000 | 0.000020 | | | |
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| C | -5.431715 | 0.000065 | 0.000000 | 0.000092 | | | |
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| Cl | -14.962307 | 0.000256 | 0.000000 | 0.000362 | | | |
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| F | -24.193487 | 0.000257 | 0.000000 | 0.000363 | | | |
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| H | -0.499996 | 0.000007 | 0.000000 | 0.000010 | | | |
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| Li | -0.196329 | 0.000004 | 0.000000 | 0.000006 | | | |
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| N | -9.798226 | 0.000105 | 0.000000 | 0.000149 | | | |
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| Na | -0.182136 | 0.000008 | 0.000000 | 0.000011 | | | |
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| O | -15.900621 | 0.000176 | 0.000000 | 0.000249 | | | |
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| P | -6.472697 | 0.000089 | 0.000000 | 0.000126 | | | |
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| S | -10.124922 | 0.000191 | 0.000000 | 0.000271 | | | |
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| Si | -3.765137 | 0.000063 | 0.000000 | 0.000089 | | | |
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|---------+------------+----------+----------+----------+-----------+------------+----------|
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| | | | | | | 5.38 | 0.19 |
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| BeH | -1.579924 | 0.000058 | 0.072304 | 0.000060 | 0.079400 | -4.452718 | 0.037652 |
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| C2H2 | -12.491177 | 0.001978 | 0.627755 | 0.001982 | 0.642400 | -9.189949 | 1.243661 |
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| C2H4 | -13.747858 | 0.002165 | 0.884445 | 0.002169 | 0.899000 | -9.133250 | 1.360919 |
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| C2H6 | -14.980890 | 0.002993 | 1.117486 | 0.002996 | 1.136900 | -12.182781 | 1.880250 |
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| CH2_1A1 | -6.715937 | 0.000274 | 0.284230 | 0.000282 | 0.288900 | -2.930337 | 0.176733 |
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| CH2_3B1 | -6.730926 | 0.000247 | 0.299220 | 0.000256 | 0.304100 | -3.062465 | 0.160633 |
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| CH3 | -7.415930 | 0.000433 | 0.484228 | 0.000439 | 0.490800 | -4.124162 | 0.275260 |
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| CH3Cl | -22.511728 | 0.003261 | 0.617719 | 0.003272 | 0.631000 | -8.333880 | 2.053169 |
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| CH4 | -8.092352 | 0.001733 | 0.660654 | 0.001735 | 0.670300 | -6.052881 | 1.088669 |
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| CH | -6.063309 | 0.000142 | 0.131598 | 0.000156 | 0.133900 | -1.444348 | 0.098110 |
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| Cl2 | -30.006770 | 0.001417 | 0.082156 | 0.001507 | 0.094000 | -7.432073 | 0.945753 |
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| ClF | -39.247103 | 0.001471 | 0.091309 | 0.001515 | 0.100100 | -5.516449 | 0.950520 |
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| ClO | -30.948491 | 0.002849 | 0.085563 | 0.002866 | 0.104700 | -12.008590 | 1.798595 |
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| CN | -15.511536 | 0.001716 | 0.281595 | 0.001721 | 0.288800 | -4.521091 | 1.079775 |
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| CO | -21.740502 | 0.002046 | 0.408166 | 0.002055 | 0.413700 | -3.472682 | 1.289362 |
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| CO2 | -37.838828 | 0.001777 | 0.605871 | 0.001812 | 0.621400 | -9.744893 | 1.137305 |
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| CS | -15.809393 | 0.002280 | 0.252755 | 0.002289 | 0.274000 | -13.331407 | 1.436248 |
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| F2 | -48.437580 | 0.002788 | 0.050606 | 0.002835 | 0.062200 | -7.275352 | 1.779096 |
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| H2CO | -22.914591 | 0.002667 | 0.582263 | 0.002674 | 0.596700 | -9.059348 | 1.677865 |
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| H2O | -17.257153 | 0.000554 | 0.356541 | 0.000582 | 0.371900 | -9.637832 | 0.365219 |
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| H2O2 | -33.210861 | 0.001813 | 0.409628 | 0.001847 | 0.429400 | -12.406998 | 1.158935 |
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| H2S | -11.410576 | 0.000694 | 0.285663 | 0.000720 | 0.292000 | -3.976713 | 0.451833 |
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| H3COH | -24.133288 | 0.001467 | 0.800970 | 0.001480 | 0.818700 | -11.126046 | 0.928505 |
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| H3CSH | -18.293307 | 0.003131 | 0.736687 | 0.003138 | 0.757000 | -12.746473 | 1.969176 |
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| HCl | -15.630053 | 0.000503 | 0.167751 | 0.000564 | 0.171000 | -2.039062 | 0.354034 |
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| HCN | -16.216313 | 0.002143 | 0.486376 | 0.002146 | 0.496900 | -6.603748 | 1.346757 |
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| HCO | -22.262328 | 0.002545 | 0.429996 | 0.002552 | 0.444700 | -9.226696 | 1.601523 |
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| HF | -24.908111 | 0.000426 | 0.214628 | 0.000498 | 0.226100 | -7.198764 | 0.312367 |
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| HOCl | -31.608392 | 0.001374 | 0.245468 | 0.001409 | 0.264700 | -12.068155 | 0.883968 |
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| Li2 | -0.431300 | 0.000009 | 0.038642 | 0.000012 | 0.038900 | -0.162060 | 0.007643 |
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| LiF | -24.606552 | 0.000507 | 0.216736 | 0.000568 | 0.222000 | -3.303261 | 0.356414 |
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| LiH | -0.788098 | 0.000017 | 0.091774 | 0.000019 | 0.092430 | -0.411737 | 0.011790 |
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| N2 | -19.949099 | 0.001829 | 0.352648 | 0.001841 | 0.364600 | -7.499767 | 1.155305 |
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| N2H4 | -22.254991 | 0.001486 | 0.658557 | 0.001501 | 0.699600 | -25.754667 | 0.941605 |
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| Na2 | -0.390694 | 0.000021 | 0.026422 | 0.000027 | 0.026800 | -0.237078 | 0.016780 |
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| NaCl | -15.300352 | 0.001292 | 0.155910 | 0.001317 | 0.157400 | -0.935284 | 0.826560 |
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| NH | -10.425927 | 0.000232 | 0.127706 | 0.000255 | 0.133500 | -3.635724 | 0.159726 |
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| NH2 | -11.079579 | 0.000445 | 0.281362 | 0.000457 | 0.290400 | -5.671417 | 0.286744 |
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| NH3 | -11.758534 | 0.000858 | 0.460322 | 0.000865 | 0.475500 | -9.524365 | 0.542585 |
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| NO | -25.925608 | 0.002478 | 0.226761 | 0.002487 | 0.244500 | -11.131121 | 1.560528 |
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| O2 | -31.978613 | 0.002212 | 0.177370 | 0.002240 | 0.192400 | -9.431204 | 1.405783 |
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| OH | -16.563942 | 0.000322 | 0.163325 | 0.000367 | 0.170200 | -4.313827 | 0.230286 |
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| P2 | -13.109626 | 0.002003 | 0.164231 | 0.002011 | 0.186000 | -13.660387 | 1.262016 |
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| PH2 | -7.712455 | 0.000403 | 0.239766 | 0.000413 | 0.244000 | -2.656750 | 0.259404 |
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| PH3 | -8.350324 | 0.000878 | 0.377640 | 0.000883 | 0.389000 | -7.128757 | 0.553934 |
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| S2 | -20.401043 | 0.002564 | 0.151199 | 0.002593 | 0.164000 | -8.032937 | 1.626850 |
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| Si2 | -7.640979 | 0.000961 | 0.110705 | 0.000969 | 0.121000 | -6.460521 | 0.608056 |
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| Si2H6 | -11.365871 | 0.002677 | 0.835623 | 0.002680 | 0.849000 | -8.394027 | 1.681992 |
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| SiH2_1A1 | -5.006581 | 0.000257 | 0.241453 | 0.000265 | 0.243000 | -0.970756 | 0.166341 |
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| SiH2_3B1 | -4.974331 | 0.000249 | 0.209203 | 0.000258 | 0.210000 | -0.499925 | 0.161639 |
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| SiH3 | -5.624316 | 0.000625 | 0.359192 | 0.000629 | 0.363000 | -2.389674 | 0.394463 |
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| SiH4 | -6.276132 | 0.001187 | 0.511013 | 0.001189 | 0.515000 | -2.502072 | 0.746197 |
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| SiO | -19.954964 | 0.002217 | 0.289206 | 0.002225 | 0.306700 | -10.977712 | 1.396411 |
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| SO2 | -42.290926 | 0.002157 | 0.364762 | 0.002194 | 0.414400 | -31.148522 | 1.377029 |
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| SO | -26.212229 | 0.002411 | 0.186686 | 0.002425 | 0.200700 | -8.794218 | 1.521950 |
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|---------+------------+----------+----------+----------+-----------+------------+----------|
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| | | | | | | 7.38 | 1.08 |
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#+TBLFM: @>$7='(org-sbe "madformula" (data @5$7..@>>$7) ) :: @>$8='(org-sbe "maderrformula" (data @5$8..@>>$8) )
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***** MAD = 8.05 +/- 0.42
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***** Figure
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#+BEGIN_SRC gnuplot :var data=data-g2-qmc-fci-jast :output file :file data-g2-qmc-dz-fci-jast.png
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reset
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set xtics rotate
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plot data u 7:xtic(1) w l notitle, data u :7:8 w err notitle, 1 notitle, -1 notitle, \
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data2 u 7:xtic(1) w l notitle, data2 u :7:8 w err notitle, 1 notitle, -1 notitle
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#+END_SRC
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#+RESULTS:
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[[file:data-g2-qmc-dz-1.0-jast.png]]
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***** MAD = 7.38 +/- 1.08
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** pVTZ, BFD
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*** DONE CCSD(T)
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**** Table
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@ -4210,8 +4265,6 @@ for name, basis, method, mu in data:
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#+RESULTS:
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[[file:rsdft.csv]]
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** RUNNING
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- DZ FCI DMC
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** TODO Temps CPU pour DMC
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@ -4305,3 +4358,53 @@ for name, basis, method, mu in data:
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- [ ] DMC TZ FCI (tres cher...)
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- [ ] DMC TZ Hartree-Fock
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* Work
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** Figure 1
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#+NAME:tab1
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| $\mu$ | | N_{det} | E(DMC) | Error | N_{det} | E(DMC) | Error |
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|------+------------+--------+----------------+--------------+---------+----------------+--------------|
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| 0.00 | 0. | 11 | -17.2535927658 | 0.0000616883 | 23 | -17.2567442368 | 0.0000674814 |
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| 0.20 | 0.16666667 | 23 | -17.2537299553 | 0.0000673868 | 23 | -17.2567293499 | 0.0000806448 |
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| 0.50 | 0.33333333 | 1442 | -17.2539120512 | 0.0001475010 | 1699 | -17.2577489156 | 0.0001590032 |
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| 0.75 | 0.42857143 | 3213 | -17.2551351593 | 0.0001757492 | 13362 | -17.2583975528 | 0.0002828675 |
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| 1.00 | 0.5 | 6743 | -17.2566320269 | 0.0001881680 | 25673 | -17.2609826285 | 0.0002158278 |
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| 1.75 | 0.63636364 | 54540 | -17.2595366309 | 0.0003193539 | 207475 | -17.2635480054 | 0.0001864936 |
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| 2.50 | 0.71428571 | 51691 | -17.2593693798 | 0.0002564347 | 858123 | -17.2643468817 | 0.0003484087 |
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| 3.80 | 0.79166667 | 103059 | -17.2586706893 | 0.0002222800 | 1621513 | -17.2636697373 | 0.0002950991 |
|
||||
| 5.70 | 0.85074627 | 102599 | -17.2577349871 | 0.0002927319 | 1629655 | -17.2631675892 | 0.0003358884 |
|
||||
| 8.50 | 0.89473684 | 101803 | -17.2572986405 | 0.0002283964 | 1643301 | -17.2632963114 | 0.0003799317 |
|
||||
| inf | 1 | 200521 | -17.2567650693 | 0.0005779960 | 1631982 | -17.2638832283 | 0.0002702253 |
|
||||
#+TBLFM: $2=$1/($1+1)
|
||||
|
||||
#+BEGIN_SRC gnuplot :var data=tab1 :output file :file ../Manuscript/h2o-dmc.pdf
|
||||
set termoption font "Times"
|
||||
set termoption fontscale 0.6
|
||||
reset
|
||||
set grid
|
||||
set xrange [.0:1.00]
|
||||
set key top right
|
||||
|
||||
set xlabel "{/Symbol m}"
|
||||
set ylabel "E_{DMC}"
|
||||
set format y "%.3f"
|
||||
|
||||
set ytics 0.001
|
||||
set xtics ("DFT" 0, "0.2" 0.2/1.2, "0.5" 0.5/1.5, "0.75" 0.75/1.75, "1.0" 0.5, \
|
||||
"1.75" 1.75/2.75, "2.5" 2.5/3.5, "3.8" 3.8/4.8, "5.7" 5.7/6.7, "8.5" 8.5/9.5, "FCI" 1)
|
||||
|
||||
set style fill transparent solid 0.25 # partial transparency
|
||||
set style fill noborder # no separate top/bottom lines
|
||||
|
||||
plot data u 2:($4+$5):($4-$5) w filledcurves notitle lc "blue", \
|
||||
data u 2:4 w l lc "blue" title "VDZ-BFD",\
|
||||
data u 2:($7+$8):($7-$8) w filledcurves notitle lc "red", \
|
||||
data u 2:7 w l lc "red" title "VTZ-BFD"
|
||||
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS:
|
||||
[[file:../Manuscript/h2o-dmc.pdf]]
|
||||
|
||||
|
||||
|
|
|
|||
Binary file not shown.
|
|
@ -0,0 +1,311 @@
|
|||
@article{Lev-PNAS-79,
|
||||
author = {M. Levy},
|
||||
journal = {Proc. Natl. Acad. Sci. U.S.A.},
|
||||
pages = {6062},
|
||||
year = {1979},
|
||||
volume = {76}
|
||||
}
|
||||
|
||||
@article{Lie-IJQC-83,
|
||||
author = {E. H. Lieb},
|
||||
title = {},
|
||||
journal = {Int. J. Quantum Chem.},
|
||||
pages = {24},
|
||||
year = {1983},
|
||||
volume = {{24}}
|
||||
}
|
||||
|
||||
@incollection{Sav-INC-96,
|
||||
author = {A. Savin},
|
||||
title = {On Degeneracy, Near Degeneracy and Density Functional Theory},
|
||||
booktitle = {Recent Developments of Modern Density Functional Theory},
|
||||
publisher = {Elsevier},
|
||||
address = {Amsterdam},
|
||||
editor = {J. M. Seminario},
|
||||
pages = {327-357},
|
||||
year = {1996}
|
||||
}
|
||||
|
||||
@article{TouColSav-PRA-04,
|
||||
author = {J. Toulouse and F. Colonna and A. Savin},
|
||||
title = {Long-range--short-range separation of the electron-electron interaction in density-functional theory},
|
||||
publisher = {APS},
|
||||
year = {2004},
|
||||
journal = {Phys. Rev. A},
|
||||
volume = {70},
|
||||
number = {6},
|
||||
pages = {062505},
|
||||
keywords = {density functional theory; wave functions; exchange interactions (electron); electron correlations}
|
||||
}
|
||||
|
||||
@article{FraMusLupTou-JCP-15,
|
||||
author = {O. Franck and B. Mussard and E. Luppi and J. Toulouse},
|
||||
title = {Basis convergence of range-separated density-functional theory},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {142},
|
||||
pages = {074107},
|
||||
year = {2015}
|
||||
}
|
||||
|
||||
@article{GinPraFerAssSavTou-JCP-18,
|
||||
author = {Emmanuel Giner and Barth\'elemy Pradines and Anthony Fert\'e and Roland Assaraf and Andreas Savin and Julien Toulouse},
|
||||
title = {Curing basis-set convergence of wave-function theory using
|
||||
density-functional theory: A systematically improvable approach},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {149},
|
||||
pages = {194301},
|
||||
year = {2018}
|
||||
}
|
||||
|
||||
%PBE functional
|
||||
@article{PerBurErn-PRL-96,
|
||||
author = {J. P. Perdew and K. Burke and M. Ernzerhof},
|
||||
title = {Generalized Gradient Approximation Made Simple},
|
||||
journal = {Phys. Rev. Lett.},
|
||||
pages = {3865},
|
||||
year = {1996},
|
||||
volume = {77}
|
||||
}
|
||||
|
||||
@article{GolWerStoLeiGorSav-CP-06,
|
||||
author = {E. Goll and H.-J. Werner and H. Stoll and T. Leininger and P. Gori-Giorgi and A. Savin},
|
||||
journal = {Chem. Phys.},
|
||||
volume = {329},
|
||||
pages = {276},
|
||||
year = {2006}
|
||||
}
|
||||
|
||||
%Beyond LDA for short-range functionals
|
||||
@article{TouColSav-JCP-05,
|
||||
author = {J. Toulouse and F. Colonna and A. Savin},
|
||||
title = {Short-range exchange and correlation energy density functionals: Beyond the local-density approximation},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {122},
|
||||
pages = {014110},
|
||||
year = {2005},
|
||||
note = {}
|
||||
}
|
||||
|
||||
% CCSD(T)+PBE
|
||||
@article{GolWerSto-PCCP-05,
|
||||
author = {Erich Goll and Hans-Joachim Werner and Hermann Stoll},
|
||||
journal = {Phys. Chem. Chem. Phys.},
|
||||
volume = {7},
|
||||
pages = {3917},
|
||||
year = {2005}
|
||||
}
|
||||
|
||||
|
||||
|
||||
@misc{g09,
|
||||
author={M. J. Frisch and G. W. Trucks and H. B. Schlegel and G. E. Scuseria and M. A. Robb and J. R. Cheeseman and G. Scalmani and V. Barone and B. Mennucci and G. A. Petersson and H. Nakatsuji and M. Caricato and X. Li and H. P. Hratchian and A. F. Izmaylov and J. Bloino and G. Zheng and J. L. Sonnenberg and M. Hada and M. Ehara and K. Toyota and R. Fukuda and J. Hasegawa and M. Ishida and T. Nakajima and Y. Honda and O. Kitao and H. Nakai and T. Vreven and Montgomery, {Jr.}, J. A. and J. E. Peralta and F. Ogliaro and M. Bearpark and J. J. Heyd and E. Brothers and K. N. Kudin and V. N. Staroverov and R. Kobayashi and J. Normand and K. Raghavachari and A. Rendell and J. C. Burant and S. S. Iyengar and J. Tomasi and M. Cossi and N. Rega and J. M. Millam and M. Klene and J. E. Knox and J. B. Cross and V. Bakken and C. Adamo and J. Jaramillo and R. Gomperts and R. E. Stratmann and O. Yazyev and A. J. Austin and R. Cammi and C. Pomelli and J. W. Ochterski and R. L. Martin and K. Morokuma and V. G. Zakrzewski and G. A. Voth and P. Salvador and J. J. Dannenberg and S. Dapprich and A. D. Daniels and Ö. Farkas and J. B. Foresman and J. V. Ortiz and J. Cioslowski and D. J. Fox},
|
||||
title={Gaussian 09 {R}evision {D}.01},
|
||||
note={Gaussian Inc. Wallingford CT 2009}
|
||||
}
|
||||
|
||||
@article{Burkatzki_2008,
|
||||
Author = {Burkatzki, M. and Filippi, Claudia and Dolg, M.},
|
||||
Doi = {10.1063/1.2987872},
|
||||
Issn = {1089-7690},
|
||||
Journal = {The Journal of Chemical Physics},
|
||||
Month = {Oct},
|
||||
Number = {16},
|
||||
Pages = {164115},
|
||||
Publisher = {AIP Publishing},
|
||||
Title = {Energy-consistent small-core pseudopotentials for 3d-transition metals adapted to quantum Monte Carlo calculations},
|
||||
Url = {http://dx.doi.org/10.1063/1.2987872},
|
||||
Volume = {129},
|
||||
Year = {2008},
|
||||
Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2987872}
|
||||
}
|
||||
|
||||
@article{Garniron_2019,
|
||||
author = {Garniron, Yann and Applencourt, Thomas and
|
||||
Gasperich, Kevin and Benali, Anouar and Ferté, Anthony and
|
||||
Paquier, Julien and Pradines, Barthélémy and Assaraf, Roland and Reinhardt, Peter and
|
||||
Toulouse, Julien and Barbaresco, Pierrette and Renon, Nicolas and
|
||||
David, Grégoire and Malrieu, Jean-Paul and Véril, Mickaël and
|
||||
Caffarel, Michel and Loos, Pierre-François and Giner, Emmanuel and
|
||||
Scemama, Anthony},
|
||||
title = {{Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs}},
|
||||
journal = {J. Chem. Theory Comput.},
|
||||
volume = {15},
|
||||
number = {6},
|
||||
pages = {3591--3609},
|
||||
year = {2019},
|
||||
month = {Jun},
|
||||
issn = {1549-9618},
|
||||
publisher = {American Chemical Society},
|
||||
doi = {10.1021/acs.jctc.9b00176}
|
||||
}
|
||||
|
||||
@article{Scemama_2013,
|
||||
author = {Scemama, Anthony and Caffarel, Michel and
|
||||
Oseret, Emmanuel and Jalby, William},
|
||||
title = {{Quantum Monte Carlo for large chemical systems: Implementing efficient strategies
|
||||
for petascale platforms and beyond}},
|
||||
journal = {J. Comput. Chem.},
|
||||
volume = {34},
|
||||
number = {11},
|
||||
pages = {938--951},
|
||||
year = {2013},
|
||||
month = {Apr},
|
||||
issn = {0192-8651},
|
||||
publisher = {John Wiley {\&} Sons, Ltd},
|
||||
doi = {10.1002/jcc.23216}
|
||||
}
|
||||
|
||||
@article{Zen_2019,
|
||||
author = {Zen, Andrea and Brandenburg, Jan Gerit and
|
||||
Michaelides, Angelos and Alfé, Dario},
|
||||
title = {{A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials:
|
||||
Improving reproducibility and reducing the trial-wave-function bias}},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {151},
|
||||
number = {13},
|
||||
pages = {134105},
|
||||
year = {2019},
|
||||
month = {Oct},
|
||||
issn = {0021-9606},
|
||||
publisher = {American Institute of Physics},
|
||||
doi = {10.1063/1.5119729}
|
||||
}
|
||||
|
||||
|
||||
@article{Caffarel_2016,
|
||||
author = {Caffarel, Michel and Applencourt, Thomas and
|
||||
Giner, Emmanuel and Scemama, Anthony},
|
||||
title = {{Communication: Toward an improved control of the fixed-node error in quantum
|
||||
Monte Carlo: The case of the water molecule}},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {144},
|
||||
number = {15},
|
||||
pages = {151103},
|
||||
year = {2016},
|
||||
month = {Apr},
|
||||
issn = {0021-9606},
|
||||
publisher = {American Institute of Physics},
|
||||
doi = {10.1063/1.4947093}
|
||||
}
|
||||
|
||||
@article{Pople_1989,
|
||||
author = {Pople, John A. and Head-Gordon, Martin and
|
||||
Fox, Douglas J. and Raghavachari, Krishnan and Curtiss, Larry A.},
|
||||
title = {{Gaussian{-}1 theory: A general procedure for prediction of molecular energies}},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {90},
|
||||
number = {10},
|
||||
pages = {5622--5629},
|
||||
year = {1989},
|
||||
month = {May},
|
||||
issn = {0021-9606},
|
||||
publisher = {American Institute of Physics},
|
||||
doi = {10.1063/1.456415}
|
||||
}
|
||||
|
||||
@article{Curtiss_1990,
|
||||
author = {Curtiss, Larry A. and Jones, Christopher and
|
||||
Trucks, Gary W. and Raghavachari, Krishnan and Pople, John A.},
|
||||
title = {{Gaussian{-}1 theory of molecular energies for second{-}row compounds}},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {93},
|
||||
number = {4},
|
||||
pages = {2537--2545},
|
||||
year = {1990},
|
||||
month = {Aug},
|
||||
issn = {0021-9606},
|
||||
publisher = {American Institute of Physics},
|
||||
doi = {10.1063/1.458892}
|
||||
}
|
||||
|
||||
@article{Holmes_2017,
|
||||
author = {Holmes, Adam A. and Umrigar, C. J. and
|
||||
Sharma, Sandeep},
|
||||
title = {{Excited states using semistochastic heat-bath configuration interaction}},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {147},
|
||||
number = {16},
|
||||
pages = {164111},
|
||||
year = {2017},
|
||||
month = {Oct},
|
||||
issn = {0021-9606},
|
||||
publisher = {American Institute of Physics},
|
||||
doi = {10.1063/1.4998614}
|
||||
}
|
||||
|
||||
@article{Scemama_2018,
|
||||
author = {Scemama, Anthony and Garniron, Yann and
|
||||
Caffarel, Michel and Loos, Pierre-François},
|
||||
title = {{Deterministic Construction of Nodal Surfaces within Quantum Monte Carlo:
|
||||
The Case of FeS}},
|
||||
journal = {J. Chem. Theory Comput.},
|
||||
volume = {14},
|
||||
number = {3},
|
||||
pages = {1395--1402},
|
||||
year = {2018},
|
||||
month = {Mar},
|
||||
issn = {1549-9618},
|
||||
publisher = {American Chemical Society},
|
||||
doi = {10.1021/acs.jctc.7b01250}
|
||||
}
|
||||
|
||||
@article{Scemama_2018b,
|
||||
author = {Scemama, Anthony and Benali, Anouar and
|
||||
Jacquemin, Denis and Caffarel, Michel and Loos, Pierre-François},
|
||||
title = {{Excitation energies from diffusion Monte Carlo using selected configuration
|
||||
interaction nodes}},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {149},
|
||||
number = {3},
|
||||
pages = {034108},
|
||||
year = {2018},
|
||||
month = {Jul},
|
||||
issn = {0021-9606},
|
||||
publisher = {American Institute of Physics},
|
||||
doi = {10.1063/1.5041327}
|
||||
}
|
||||
|
||||
@article{Giner_2015,
|
||||
author = {Giner, Emmanuel and Scemama, Anthony and
|
||||
Caffarel, Michel},
|
||||
title = {{Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule
|
||||
F2 using selected configuration interaction trial wavefunctions}},
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {142},
|
||||
number = {4},
|
||||
pages = {044115},
|
||||
year = {2015},
|
||||
month = {Jan},
|
||||
issn = {0021-9606},
|
||||
publisher = {American Institute of Physics},
|
||||
doi = {10.1063/1.4905528}
|
||||
}
|
||||
|
||||
@article{Coldwell_1977,
|
||||
author = {Coldwell, Robert Lynn},
|
||||
title = {{Zero Monte Carlo error or quantum mechanics is easier}},
|
||||
journal = {Int. J. Quantum Chem.},
|
||||
volume = {12},
|
||||
number = {S11},
|
||||
pages = {215--222},
|
||||
year = {1977},
|
||||
month = {Jan},
|
||||
issn = {0020-7608},
|
||||
publisher = {John Wiley {\&} Sons, Ltd},
|
||||
doi = {10.1002/qua.560120826}
|
||||
}
|
||||
|
||||
@article{Umrigar_2005,
|
||||
author = {Umrigar, C. J. and Filippi, Claudia},
|
||||
title = {{Energy and Variance Optimization of Many-Body Wave Functions}},
|
||||
journal = {Phys. Rev. Lett.},
|
||||
volume = {94},
|
||||
number = {15},
|
||||
pages = {150201},
|
||||
year = {2005},
|
||||
month = {Apr},
|
||||
issn = {1079-7114},
|
||||
publisher = {American Physical Society},
|
||||
doi = {10.1103/PhysRevLett.94.150201}
|
||||
}
|
||||
|
||||
|
|
@ -0,0 +1,376 @@
|
|||
\documentclass[aip,jcp,reprint,noshowkeys,superscriptaddress]{revtex4-1}
|
||||
\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amsmath,amssymb,amsfonts,physics,mhchem,xspace,subfigure}
|
||||
|
||||
\usepackage[T1]{fontenc}
|
||||
\usepackage[utf8]{inputenc}
|
||||
|
||||
\usepackage{txfonts}
|
||||
|
||||
\usepackage[
|
||||
colorlinks=true,
|
||||
citecolor=blue,
|
||||
breaklinks=true
|
||||
]{hyperref}
|
||||
\urlstyle{same}
|
||||
|
||||
\newcommand{\alert}[1]{\textcolor{red}{#1}}
|
||||
\definecolor{darkgreen}{HTML}{009900}
|
||||
\usepackage[normalem]{ulem}
|
||||
|
||||
\newcommand{\LCT}{Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France}
|
||||
\newcommand{\ANL}{Argonne Leadership Computing Facility, Argonne National Laboratory, Argonne, IL 60439, United States}
|
||||
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\title{Enabling high accuracy diffusion Monte Carlo calculations with
|
||||
range-separated density functional theory and selected configuration interaction}
|
||||
|
||||
\author{Anthony Scemama}
|
||||
\affiliation{\LCPQ}
|
||||
\author{Emmanuel Giner}
|
||||
\email{emmanuel.giner@lct.jussieu.fr}
|
||||
\affiliation{\LCT}
|
||||
\author{Anouar Benali}
|
||||
\email{benali@anl.gov}
|
||||
\affiliation{\ANL}
|
||||
\author{Pierre-Fran\c{c}ois Loos}
|
||||
\email{loos@irsamc.ups-tlse.fr}
|
||||
\affiliation{\LCPQ}
|
||||
|
||||
|
||||
\begin{abstract}
|
||||
\end{abstract}
|
||||
|
||||
\maketitle
|
||||
|
||||
|
||||
\section{Introduction}
|
||||
\label{sec:intro}
|
||||
|
||||
|
||||
\section{Range-separated DFT in a nutshell}
|
||||
\label{sec:rsdft}
|
||||
|
||||
\subsection{Exact equations}
|
||||
\label{sec:exact}
|
||||
|
||||
The exact ground-state energy of a $N$-electron system with
|
||||
nuclei-electron potential $v_\mathrm{ne}(\textbf{r})$ can be expressed
|
||||
by the following minimization over $N$-representable densities
|
||||
$n$~\cite{Lev-PNAS-79,Lie-IJQC-83}
|
||||
\begin{equation}
|
||||
E_0 = \min_n \left\{ \mathcal{F}[n] + \int v_\mathrm{ne}(\textbf{r}) n(\textbf{r}) \mathrm{d} \textbf{r} \right\},
|
||||
\label{E0}
|
||||
\end{equation}
|
||||
with the standard constrained-search universal density functional
|
||||
\begin{equation}
|
||||
\mathcal{F}[n] = \min_{\Psi\rightarrow n} \left \langle\Psi|\hat{T}+\hat{W}_\mathrm{ee}|\Psi \right \rangle,
|
||||
\label{Fn}
|
||||
\end{equation}
|
||||
where $\hat{T}$ and $\hat{W}_\mathrm{ee}$ are the kinetic-energy and
|
||||
Coulomb electron-electron interaction operators, respectively. The
|
||||
minimizing multideterminant wave function in Eq.~\eqref{Fn} will be
|
||||
denoted by $\Psi[n]$. In RS-DFT, the universal density functional is
|
||||
decomposed as~\cite{Sav-INC-96,TouColSav-PRA-04}
|
||||
\begin{equation}
|
||||
\mathcal{F}[n] = \mathcal{F}^{\mathrm{lr},\mu}[n] + \bar{E}_{\mathrm{Hxc}}^{\mathrm{sr,}\mu}[n],
|
||||
\label{Fdecomp}
|
||||
\end{equation}
|
||||
where $\mathcal{F}^{\mathrm{lr},\mu}[n]$ is a long-range (lr)
|
||||
universal density functional
|
||||
\begin{equation}
|
||||
\label{lr_univ_fonc}
|
||||
\mathcal{F}^{\mathrm{lr},\mu}[n]= \min_{\Psi\rightarrow n} \left
|
||||
\langle\Psi|\hat{T}+\hat{W}_\mathrm{ee}^{\mathrm{lr},\mu}|\Psi
|
||||
\right \rangle,
|
||||
\end{equation}
|
||||
and $\bar{E}_{\mathrm{Hxc}}^{\,\mathrm{sr,}\mu}[n]$ is the
|
||||
complementary short-range (sr) Hartree-exchange-correlation (Hxc)
|
||||
density functional. In Eq.~(\ref{lr_univ_fonc}),
|
||||
$\hat{W}_\mathrm{ee}^{\mathrm{lr}}$ is the long-range
|
||||
electron-electron interaction defined as
|
||||
\begin{equation}
|
||||
\hat{W}_\mathrm{ee}^{\mathrm{lr},\mu} = \frac{1}{2} \iint w_{\mathrm{ee}}^{\mathrm{lr},\mu}(r_{12}) \hat{n}_2(\textbf{r}_1,\textbf{r}_2)
|
||||
\mathrm{d} \textbf{r}_1 \mathrm{d} \textbf{r}_2,
|
||||
\end{equation}
|
||||
with the error-function potential
|
||||
$w_{\mathrm{ee}}^{\mathrm{lr},\mu}(r_{12})=\mathrm{erf}(\mu\, r_{12}
|
||||
)/r_{12}$ (expressed with the interelectronic distance $r_{12} =
|
||||
||\textbf{r}_1-\textbf{r}_2||$) and the pair-density operator
|
||||
$\hat{n}_2(\textbf{r}_1, \textbf{r}_2)=\hat{n}(\textbf{r}_1)
|
||||
\hat{n}(\textbf{r}_2) - \delta(\textbf{r}_1-\textbf{r}_2)
|
||||
\hat{n}(\textbf{r}_1)$ where $\hat{n}(\textbf{r})$ is the density
|
||||
operator. The range-separation parameter $\mu$ corresponds to an
|
||||
inverse distance controlling the range of the separation and the
|
||||
strength of the interaction at $r_{12} = 0$. For a given density, we
|
||||
will denote by $\Psi^\mu[n]$ the minimizing multideterminant wave
|
||||
function in Eq.~\eqref{lr_univ_fonc}. Inserting the decomposition of
|
||||
Eq.~\eqref{Fdecomp} into Eq.~\eqref{E0}, and recomposing the two-step
|
||||
minimization into a single one, leads to the following expression for
|
||||
the exact ground-state electronic energy
|
||||
\begin{equation}
|
||||
\label{min_rsdft} E_0= \min_{\Psi} \left\{
|
||||
\left
|
||||
\langle\Psi|\hat{T}+\hat{W}_\mathrm{{ee}}^{\mathrm{lr},\mu}+\hat{V}_{\mathrm{ne}}|\Psi\right
|
||||
\rangle
|
||||
+ \bar{E}^{\mathrm{sr},\mu}_{\mathrm{Hxc}}[n_\Psi]\right\},
|
||||
\end{equation}
|
||||
where the minimization is done over normalized $N$-electron
|
||||
multideterminant wave functions, $\hat{V}_{\mathrm{ne}} = \int
|
||||
v_{\mathrm{ne}} (\textbf{r}) \hat{n}(\textbf{r}) \mathrm{d}
|
||||
\textbf{r}$, and $n_\Psi$ refers to the density of $\Psi$, i.e.
|
||||
$n_\Psi(\textbf{r})=\left \langle\Psi|\hat{n}(\textbf{r})|\Psi\right
|
||||
\rangle$.
|
||||
The minimizing multideterminant wave function $\Psi^\mu$ in
|
||||
Eq.~\eqref{min_rsdft} can be determined by the self-consistent
|
||||
eigenvalue equation
|
||||
\begin{equation}
|
||||
\label{rs-dft-eigen-equation}
|
||||
\hat{H}^\mu[n_{\Psi^{\mu}}] \ket{\Psi^{\mu}}= \mathcal{E}^{\mu} \ket{\Psi^{\mu}},
|
||||
\end{equation}
|
||||
with the long-range interacting Hamiltonian
|
||||
\begin{equation}
|
||||
\label{H_mu}
|
||||
\hat{H}^\mu[n_{\Psi^{\mu}}] = \hat{T}+\hat{W}_{\mathrm{ee}}^{\mathrm{lr},\mu}+\hat{V}_{\mathrm{ne}}+ \hat{\bar{V}}_{\mathrm{Hxc}}^{\mathrm{sr},\mu}[n_{\Psi^{\mu}}],
|
||||
\end{equation}
|
||||
where
|
||||
$\hat{\bar{V}}_{\mathrm{Hxc}}^{\mathrm{sr},\mu}[n]=\int \delta \bar{E}^{\mathrm{sr},\mu}_{\mathrm{Hxc}}[n]/\delta n(\textbf{r}) \, \hat{n}(\textbf{r}) \mathrm{d} \textbf{r}$
|
||||
is the complementary short-range Hartree-exchange-correlation
|
||||
potential operator. Note that $\Psi^{\mu}$ is not the exact physical
|
||||
ground-state wave function but only an effective wave
|
||||
function. However, its density $n_{\Psi^{\mu}}$ is the exact physical
|
||||
ground-state density. Once $\Psi^{\mu}$ has been calculated, the exact
|
||||
electronic ground-state energy is obtained by
|
||||
\begin{equation}
|
||||
\label{E-rsdft}
|
||||
E_0= \braket{\Psi^{\mu}|\hat{T}+\hat{W}_\mathrm{{ee}}^{\mathrm{lr},\mu}+\hat{V}_{\mathrm{ne}}|\Psi^{\mu}}+\bar{E}^{\mathrm{sr},\mu}_{\mathrm{Hxc}}[n_{\Psi^\mu}].
|
||||
\end{equation}
|
||||
Note that, for $\mu=0$, the long-range interaction vanishes,
|
||||
$w_{\mathrm{ee}}^{\mathrm{lr},\mu=0}(r_{12}) = 0$, and thus RS-DFT
|
||||
reduces to standard KS-DFT. For $\mu\to\infty$, the long-range
|
||||
interaction becomes the standard Coulomb interaction,
|
||||
$w_{\mathrm{ee}}^{\mathrm{lr},\mu\to\infty}(r_{12}) = 1/r_{12}$, and
|
||||
thus RS-DFT reduces to standard wave-function theory (WFT).
|
||||
|
||||
\subsection{Approximations}
|
||||
\label{sec:approx}
|
||||
|
||||
Provided that the exact short-range complementary functional is known
|
||||
and that the wave function $\Psi^{\mu}$ is developed in a complete
|
||||
basis set, the theory is exact and therefore provides the exact
|
||||
density and ground state energy whatever value of $\mu$ is chosen to
|
||||
split the universal Levy-Lieb functional (see Eqs. \eqref{Fdecomp} and
|
||||
\eqref{lr_univ_fonc}). Of course in practice, two kind of
|
||||
approximations must be made: i) the approximation of the wave function
|
||||
by using a finite basis set, ii) the approximation on the exact
|
||||
complementary functionals. As long as approximations are made, the
|
||||
theory is not exact anymore and might depend on $\mu$.
|
||||
|
||||
Despite its $\mu$ dependence, approximated RS-DFT schemes provide
|
||||
potentially appealing features as: i) the approximated wave function
|
||||
$\Psi^{\mu}$ is an eigenvector of a non-divergent operator
|
||||
$\hat{H}^\mu[n_{\Psi^{\mu}}]$ (see Eqs. \eqref{H_mu} and
|
||||
\eqref{rs-dft-eigen-equation}) and therefore converges more rapidly
|
||||
with respect to the basis set~\cite{FraMusLupTou-JCP-15}, and also
|
||||
produces more compact wave function~\cite{GinPraFerAssSavTou-JCP-18}
|
||||
as it will be illustrated here, ii) the semi-local approximations for
|
||||
RS-DFT complementary functionals are usually better suited to describe
|
||||
the remaining short-range part of the electron-electron correlation.
|
||||
|
||||
In this work, we use the short-range version of the
|
||||
Perdew-Burke-Ernzerhof (PBE)~\cite{PerBurErn-PRL-96} exchange and
|
||||
correlation functionals of Ref.~\onlinecite{GolWerStoLeiGorSav-CP-06}
|
||||
(see also Refs.~\onlinecite{TouColSav-JCP-05,GolWerSto-PCCP-05}) which
|
||||
takes the form
|
||||
\begin{eqnarray}
|
||||
\bar{E}^{\mathrm{sr},\mu,\textsc{pbe}}_{\mathrm{x/c}}[n] = \int \bar{e}_\mathrm{{x/c}}^\mathrm{sr,\mu,\textsc{pbe}}(n(\textbf{r}),\nabla n(\textbf{r})) \, \mathrm{d}\textbf{r}.
|
||||
\end{eqnarray}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\section{Computational details}
|
||||
\label{sec:comp-details}
|
||||
|
||||
All the calculations were made using BFD
|
||||
pseudopotentials\cite{Burkatzki_2008} with the associated double, triple
|
||||
and quadruple zeta basis sets.
|
||||
CCSD(T) and DFT calculations were made with
|
||||
\emph{Gaussian09},\cite{g09} using an unrestricted Hartree-Fock
|
||||
determinant as a reference for open-shell systems. All the CIPSI
|
||||
calculations and range-separated CIPSI calculations were made with
|
||||
\emph{Quantum Package}.\cite{Garniron_2019,qp2_2020}
|
||||
Quantum Monte Carlo calculations were made with QMC=Chem,\cite{scemama_2013}
|
||||
in the determinant localization approximation.\cite{Zen_2019}
|
||||
|
||||
In the determinant localization approximation, only the determinantal
|
||||
component of the trial wave function is present in the expression of
|
||||
the wave function on which the pseudopotential is localized. Hence,
|
||||
the pseudopotential operator does not depend on the Jastrow factor, as
|
||||
it is the case in all-electron calculations. This improves the
|
||||
reproducibility of the results, as they depend only on parameters
|
||||
optimized in a deterministic framework.
|
||||
|
||||
|
||||
\section{Influence of the range-separation parameter on the fixed-node
|
||||
error}
|
||||
\label{sec:mu-dmc}
|
||||
\begin{table}[h]
|
||||
\caption{Fixed-node energies of the water molecule.}
|
||||
\label{tab:h2o-dmc}
|
||||
\centering
|
||||
\begin{tabular}{crlrl}
|
||||
\hline
|
||||
& \multicolumn{2}{c}{BFD-VDZ} & \multicolumn{2}{c}{BFD-VTZ}\\
|
||||
$\mu$ & $N_{\text{det}}$ & E(DMC) & $N_{\text{det}}$ & E(DMC)\\
|
||||
\hline
|
||||
$0.00$ & $11$ & $-17.253\,59(6)$ & $23$ & $-17.256\,74(7)$\\
|
||||
$0.20$ & $23$ & $-17.253\,73(7)$ & $23$ & $-17.256\,73(8)$\\
|
||||
$0.30$ & $53$ & $-17.253\,4(2)$ & $219$ & $-17.253\,7(5)$\\
|
||||
$0.50$ & $1\,442$ & $-17.253\,9(2)$ & $16\,99$ & $-17.257\,7(2)$\\
|
||||
$0.75$ & $3\,213$ & $-17.255\,1(2)$ & $13\,362$ & $-17.258\,4(3)$\\
|
||||
$1.00$ & $6\,743$ & $-17.256\,6(2)$ & $256\,73$ & $-17.261\,0(2)$\\
|
||||
$1.75$ & $54\,540$ & $-17.259\,5(3)$ & $207\,475$ & $-17.263\,5(2)$\\
|
||||
$2.50$ & $51\,691$ & $-17.259\,4(3)$ & $858\,123$ & $-17.264\,3(3)$\\
|
||||
$3.80$ & $103\,059$ & $-17.258\,7(3)$ & $1\,621\,513$ & $-17.263\,7(3)$\\
|
||||
$5.70$ & $102\,599$ & $-17.257\,7(3)$ & $1\,629\,655$ & $-17.263\,2(3)$\\
|
||||
$8.50$ & $101\,803$ & $-17.257\,3(3)$ & $1\,643\,301$ & $-17.263\,3(4)$\\
|
||||
$\infty$ & $200\,521$ & $-17.256\,8(6)$ & $1\,631\,982$ & $-17.263\,9(3)$\\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=\columnwidth]{h2o-dmc.pdf}
|
||||
\caption{Fixed-node energies of the water molecule with variable
|
||||
values of $\mu$.}
|
||||
\label{fig:h2o-dmc}
|
||||
\end{figure}
|
||||
The water molecule was taken at the equilibrium
|
||||
geometry,\cite{Caffarel_2016} and RSDFT-CIPSI wave functions were
|
||||
generated with BFD pseudopotentials and the corresponding double-zeta
|
||||
basis set using multiple values of the range-separation parameter
|
||||
$\mu$. The convergence criterion for stopping the CIPSI calculation
|
||||
was set to 1~m$E_h$ on the PT2 correction. Then, these wave functions
|
||||
were used as trial wave functions for FN-DMC calculations, and the
|
||||
corresponding energies are shown in table~\ref{tab:h2o-dmc} and
|
||||
figure~\ref{fig:h2o-dmc}.
|
||||
|
||||
|
||||
\section{Atomization energy benchmarks}
|
||||
\label{sec:atomization}
|
||||
|
||||
Atomization energies are challenging for post-Hartree-Fock methods
|
||||
because their calculation requires a perfect balance in the
|
||||
description of atoms and molecules. Basis sets used in molecular
|
||||
calculations are atom-centered, so they are always better adapted to
|
||||
atoms than molecules and atomization energies usually tend to be
|
||||
underestimated.
|
||||
In the context of FN-DMC calculations, the nodal surface is imposed by
|
||||
the trial wavefunction which is expanded on an atom-centered basis
|
||||
set. So we expect the fixed-node error to be also related to the basis
|
||||
set incompleteness error.
|
||||
Increasing the size of the basis set improves the description of
|
||||
the density and of electron correlation, but also reduces the
|
||||
imbalance in the quality of the description of the atoms and the
|
||||
molecule, leading to more accurate atomization energies.
|
||||
|
||||
Another important feature required to get accurate atomization
|
||||
energies is size-extensivity, since the numbers of correlated electrons
|
||||
in the isolated atoms are different from the number of correlated
|
||||
electrons in the molecule.
|
||||
In the context of selected CI calculations, when the variational energy is
|
||||
extrapolated to the FCI energy\cite{Holmes_2017} there is obviously no
|
||||
size-consistence error. But when the selected wave function is used
|
||||
for as a reference for post-Hartree-Fock methods or QMC calculations,
|
||||
there is a residual size-consistence error originating from the
|
||||
truncation of the determinant space.
|
||||
|
||||
QMC calculations can be made size-consistent by extrapolating the
|
||||
FN-DMC energy to estimate the energy obtained with the FCI as a trial
|
||||
wave function.\cite{Scemama_2018,Scemama_2018b} Alternatively, the
|
||||
size-consistence error can be reduced by choosing the number of
|
||||
selected determinants such that the sum of the PT2 corrections on the
|
||||
atoms is equal to the PT2 correction of the molecule, enforcing that
|
||||
the variational dissociation potential energy surface (PES) is
|
||||
parallel to the perturbatively corrected PES, which is an accurate
|
||||
estimate of the FCI PES.\cite{Giner_2015}
|
||||
|
||||
Another source of size-consistence error in QMC calculation may originate
|
||||
from the Jastrow factor. Usually, the Jastrow factor contains
|
||||
one-electron, two-electron and one-nucleus-two-electron terms.
|
||||
The problematic part is the two-electron term, whose simplest form can
|
||||
be expressed as
|
||||
\begin{equation}
|
||||
J_\text{ee} = \sum_i \sum_{j<i} \frac{a r_{ij}}{1 + b r_{ij}}.
|
||||
\end{equation}
|
||||
$a$ is determined by cusp conditions, and $b$ is obtained by energy
|
||||
or variance minimization.\cite{Coldwell_1977,Umrigar_2005}
|
||||
One can easily see that this parameterization of the two-body
|
||||
interation is not size-consistent. The dissociation of a
|
||||
heteroatomic diatomic molecule $AB$ with a parameter $b_{AB}$
|
||||
will lead to two different two-body Jastrow factors on each atom, each
|
||||
with its own optimal value $b_A$ and $b_B$. To remove the
|
||||
size-consistence error on a PES using this ansätz for $J_\text{ee}$,
|
||||
one needs to impose that the parameters of $J_\text{ee}$ are fixed:
|
||||
$b_A = b_B = b_{AB}$.
|
||||
|
||||
When pseudopotentials are used in a QMC calculation, it is common
|
||||
practice to localize the pseudopotential on the complete wave
|
||||
function. If the wave function is not size-consistent, so will be the
|
||||
locality approximation. Recently, the determinant localization
|
||||
approximation was introduced.\cite{Zen_2019} This approximation
|
||||
consists in removing the Jastrow factor from the wave function on
|
||||
which the pseudopotential is localized.
|
||||
The great advantage of this approximation is that the FN-DMC energy
|
||||
within this approximation only depends on the parameters of the
|
||||
determinantal component. Using a size-inconsistent Jastrow factor, or
|
||||
a non-optimal Jastrow factor will not introduce an additional
|
||||
size-consistence error in FN-DMC calculations, although it will
|
||||
reduce the statistical errors by reducing the variance of the local energy.
|
||||
|
||||
|
||||
The energy computed within density functional theory is extensive, and
|
||||
as it is a mean-field method the convergence to the complete basis set
|
||||
(CBS) limit is relatively fast. Hence, DFT methods are very well adapted to
|
||||
the calculation of atomization energies, especially with small basis
|
||||
sets, but going to the CBS limit will converge to biased atomization
|
||||
energies because of the use of approximate density functionals.
|
||||
|
||||
On the other hand, the convergence of the FCI energies to the CBS
|
||||
limit will be slower because of the description of short-range electron
|
||||
correlation with atom-centered functions, but ultimately the exact
|
||||
energy will be reached.
|
||||
|
||||
|
||||
The 55 molecules of the benchmark for the Gaussian-1
|
||||
theory\cite{Pople_1989,Curtiss_1990} were chosen to test the quality
|
||||
of the RSDFT-CIPSI trial wave functions for energy differences.
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%%---------------------------------------
|
||||
\begin{acknowledgments}
|
||||
An award of computer time was provided by the Innovative and Novel
|
||||
Computational Impact on Theory and Experiment (INCITE) program. This
|
||||
research has used resources of the Argonne Leadership Computing
|
||||
Facility, which is a DOE Office of Science User Facility supported
|
||||
under Contract DE-AC02-06CH11357. AB, was supported by the
|
||||
U.S. Department of Energy, Office of Science, Basic Energy Sciences,
|
||||
Materials Sciences and Engineering Division, as part of the
|
||||
Computational Materials Sciences Program and Center for Predictive
|
||||
Simulation of Functional Materials.
|
||||
\end{acknowledgments}
|
||||
|
||||
|
||||
\bibliography{rsdft-cipsi-qmc}
|
||||
|
||||
\end{document}
|
||||
|
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|
@ -0,0 +1,519 @@
|
|||
%merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked
|
||||
%Control: key (0)
|
||||
%Control: author (8) initials jnrlst
|
||||
%Control: editor formatted (1) identically to author
|
||||
%Control: production of article title (-1) disabled
|
||||
%Control: page (0) single
|
||||
%Control: year (1) truncated
|
||||
%Control: production of eprint (0) enabled
|
||||
\begin{thebibliography}{37}%
|
||||
\makeatletter
|
||||
\providecommand \@ifxundefined [1]{%
|
||||
\@ifx{#1\undefined}
|
||||
}%
|
||||
\providecommand \@ifnum [1]{%
|
||||
\ifnum #1\expandafter \@firstoftwo
|
||||
\else \expandafter \@secondoftwo
|
||||
\fi
|
||||
}%
|
||||
\providecommand \@ifx [1]{%
|
||||
\ifx #1\expandafter \@firstoftwo
|
||||
\else \expandafter \@secondoftwo
|
||||
\fi
|
||||
}%
|
||||
\providecommand \natexlab [1]{#1}%
|
||||
\providecommand \enquote [1]{``#1''}%
|
||||
\providecommand \bibnamefont [1]{#1}%
|
||||
\providecommand \bibfnamefont [1]{#1}%
|
||||
\providecommand \citenamefont [1]{#1}%
|
||||
\providecommand \href@noop [0]{\@secondoftwo}%
|
||||
\providecommand \href [0]{\begingroup \@sanitize@url \@href}%
|
||||
\providecommand \@href[1]{\@@startlink{#1}\@@href}%
|
||||
\providecommand \@@href[1]{\endgroup#1\@@endlink}%
|
||||
\providecommand \@sanitize@url [0]{\catcode `\\12\catcode `\$12\catcode
|
||||
`\&12\catcode `\#12\catcode `\^12\catcode `\_12\catcode `\%12\relax}%
|
||||
\providecommand \@@startlink[1]{}%
|
||||
\providecommand \@@endlink[0]{}%
|
||||
\providecommand \url [0]{\begingroup\@sanitize@url \@url }%
|
||||
\providecommand \@url [1]{\endgroup\@href {#1}{\urlprefix }}%
|
||||
\providecommand \urlprefix [0]{URL }%
|
||||
\providecommand \Eprint [0]{\href }%
|
||||
\providecommand \doibase [0]{http://dx.doi.org/}%
|
||||
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|
||||
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|
||||
\providecommand \bibfield [0]{\@secondoftwo}%
|
||||
\providecommand \translation [1]{[#1]}%
|
||||
\providecommand \BibitemOpen [0]{}%
|
||||
\providecommand \bibitemStop [0]{}%
|
||||
\providecommand \bibitemNoStop [0]{.\EOS\space}%
|
||||
\providecommand \EOS [0]{\spacefactor3000\relax}%
|
||||
\providecommand \BibitemShut [1]{\csname bibitem#1\endcsname}%
|
||||
\let\auto@bib@innerbib\@empty
|
||||
%</preamble>
|
||||
\bibitem [{\citenamefont {Levy}(1979)}]{Lev-PNAS-79}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
|
||||
{Levy}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Proc.
|
||||
Natl. Acad. Sci. U.S.A.}\ }\textbf {\bibinfo {volume} {76}},\ \bibinfo
|
||||
{pages} {6062} (\bibinfo {year} {1979})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Lieb}(1983)}]{Lie-IJQC-83}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.~H.}\ \bibnamefont
|
||||
{Lieb}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Int. J.
|
||||
Quantum Chem.}\ }\textbf {\bibinfo {volume} {{24}}},\ \bibinfo {pages} {24}
|
||||
(\bibinfo {year} {1983})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Savin}(1996)}]{Sav-INC-96}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
|
||||
{Savin}},\ }in\ \href@noop {} {\emph {\bibinfo {booktitle} {Recent
|
||||
Developments of Modern Density Functional Theory}}},\ \bibinfo {editor}
|
||||
{edited by\ \bibinfo {editor} {\bibfnamefont {J.~M.}\ \bibnamefont
|
||||
{Seminario}}}\ (\bibinfo {publisher} {Elsevier},\ \bibinfo {address}
|
||||
{Amsterdam},\ \bibinfo {year} {1996})\ pp.\ \bibinfo {pages}
|
||||
{327--357}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Toulouse}\ \emph {et~al.}(2004)\citenamefont
|
||||
{Toulouse}, \citenamefont {Colonna},\ and\ \citenamefont
|
||||
{Savin}}]{TouColSav-PRA-04}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{Toulouse}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Colonna}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Savin}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Phys. Rev. A}\
|
||||
}\textbf {\bibinfo {volume} {70}},\ \bibinfo {pages} {062505} (\bibinfo
|
||||
{year} {2004})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Franck}\ \emph {et~al.}(2015)\citenamefont {Franck},
|
||||
\citenamefont {Mussard}, \citenamefont {Luppi},\ and\ \citenamefont
|
||||
{Toulouse}}]{FraMusLupTou-JCP-15}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {O.}~\bibnamefont
|
||||
{Franck}}, \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Mussard}},
|
||||
\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Luppi}}, \ and\ \bibinfo
|
||||
{author} {\bibfnamefont {J.}~\bibnamefont {Toulouse}},\ }\href@noop {}
|
||||
{\bibfield {journal} {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf
|
||||
{\bibinfo {volume} {142}},\ \bibinfo {pages} {074107} (\bibinfo {year}
|
||||
{2015})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Perdew}\ \emph
|
||||
{et~al.}(1996{\natexlab{a}})\citenamefont {Perdew}, \citenamefont {Burke},\
|
||||
and\ \citenamefont {Ernzerhof}}]{PerBurErn-PRL-96}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~P.}\ \bibnamefont
|
||||
{Perdew}}, \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {Burke}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Ernzerhof}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Phys. Rev. Lett.}\
|
||||
}\textbf {\bibinfo {volume} {77}},\ \bibinfo {pages} {3865} (\bibinfo {year}
|
||||
{1996}{\natexlab{a}})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Goll}\ \emph {et~al.}(2006)\citenamefont {Goll},
|
||||
\citenamefont {Werner}, \citenamefont {Stoll}, \citenamefont {Leininger},
|
||||
\citenamefont {Gori-Giorgi},\ and\ \citenamefont
|
||||
{Savin}}]{GolWerStoLeiGorSav-CP-06}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
|
||||
{Goll}}, \bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont {Werner}},
|
||||
\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont {Stoll}}, \bibinfo
|
||||
{author} {\bibfnamefont {T.}~\bibnamefont {Leininger}}, \bibinfo {author}
|
||||
{\bibfnamefont {P.}~\bibnamefont {Gori-Giorgi}}, \ and\ \bibinfo {author}
|
||||
{\bibfnamefont {A.}~\bibnamefont {Savin}},\ }\href@noop {} {\bibfield
|
||||
{journal} {\bibinfo {journal} {Chem. Phys.}\ }\textbf {\bibinfo {volume}
|
||||
{329}},\ \bibinfo {pages} {276} (\bibinfo {year} {2006})}\BibitemShut
|
||||
{NoStop}%
|
||||
\bibitem [{\citenamefont {Toulouse}\ \emph {et~al.}(2005)\citenamefont
|
||||
{Toulouse}, \citenamefont {Colonna},\ and\ \citenamefont
|
||||
{Savin}}]{TouColSav-JCP-05}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{Toulouse}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Colonna}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Savin}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {J. Chem. Phys.}\
|
||||
}\textbf {\bibinfo {volume} {122}},\ \bibinfo {pages} {014110} (\bibinfo
|
||||
{year} {2005})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Goll}\ \emph {et~al.}(2005)\citenamefont {Goll},
|
||||
\citenamefont {Werner},\ and\ \citenamefont {Stoll}}]{GolWerSto-PCCP-05}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
|
||||
{Goll}}, \bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont {Werner}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {H.}~\bibnamefont {Stoll}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Phys. Chem. Chem.
|
||||
Phys.}\ }\textbf {\bibinfo {volume} {7}},\ \bibinfo {pages} {3917} (\bibinfo
|
||||
{year} {2005})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Hohenberg}\ and\ \citenamefont
|
||||
{Kohn}(1964)}]{Hohenberg1964}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
|
||||
{Hohenberg}}\ and\ \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
|
||||
{Kohn}},\ }\href {\doibase 10.1103/PhysRevB.7.1912} {\bibfield {journal}
|
||||
{\bibinfo {journal} {Phys. Rev.}\ }\textbf {\bibinfo {volume} {136}},\
|
||||
\bibinfo {pages} {B864} (\bibinfo {year} {1964})},\ \Eprint
|
||||
{http://arxiv.org/abs/1108.5632} {arXiv:1108.5632} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Kohn}\ and\ \citenamefont
|
||||
{Sham}(1965{\natexlab{a}})}]{kohn1965physrev}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
|
||||
{Kohn}}\ and\ \bibinfo {author} {\bibfnamefont {L.~J.}\ \bibnamefont
|
||||
{Sham}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Physical
|
||||
Review}\ }\textbf {\bibinfo {volume} {140}},\ \bibinfo {pages} {A1133}
|
||||
(\bibinfo {year} {1965}{\natexlab{a}})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Sun}\ \emph {et~al.}(2017)\citenamefont {Sun},
|
||||
\citenamefont {Berkelbach}, \citenamefont {Blunt}, \citenamefont {Booth},
|
||||
\citenamefont {Guo}, \citenamefont {Li}, \citenamefont {Liu}, \citenamefont
|
||||
{McClain}, \citenamefont {Sayfutyarova}, \citenamefont {Sharma},
|
||||
\citenamefont {Wouters},\ and\ \citenamefont {Chan}}]{PYSCF}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {Q.}~\bibnamefont
|
||||
{Sun}}, \bibinfo {author} {\bibfnamefont {T.~C.}\ \bibnamefont {Berkelbach}},
|
||||
\bibinfo {author} {\bibfnamefont {N.~S.}\ \bibnamefont {Blunt}}, \bibinfo
|
||||
{author} {\bibfnamefont {G.~H.}\ \bibnamefont {Booth}}, \bibinfo {author}
|
||||
{\bibfnamefont {S.}~\bibnamefont {Guo}}, \bibinfo {author} {\bibfnamefont
|
||||
{Z.}~\bibnamefont {Li}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{Liu}}, \bibinfo {author} {\bibfnamefont {J.~D.}\ \bibnamefont {McClain}},
|
||||
\bibinfo {author} {\bibfnamefont {E.~R.}\ \bibnamefont {Sayfutyarova}},
|
||||
\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Sharma}}, \bibinfo
|
||||
{author} {\bibfnamefont {S.}~\bibnamefont {Wouters}}, \ and\ \bibinfo
|
||||
{author} {\bibfnamefont {G.~K.}\ \bibnamefont {Chan}},\ }\href {\doibase
|
||||
10.1002/wcms.1340} {\enquote {\bibinfo {title} {Pyscf: the python‐based
|
||||
simulations of chemistry framework},}\ } (\bibinfo {year} {2017}),\ \Eprint
|
||||
{http://arxiv.org/abs/https://onlinelibrary.wiley.com/doi/pdf/10.1002/wcms.1340}
|
||||
{https://onlinelibrary.wiley.com/doi/pdf/10.1002/wcms.1340} \BibitemShut
|
||||
{NoStop}%
|
||||
\bibitem [{\citenamefont {Kohn}\ and\ \citenamefont
|
||||
{Sham}(1965{\natexlab{b}})}]{Kohn1965}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
|
||||
{Kohn}}\ and\ \bibinfo {author} {\bibfnamefont {L.~J.}\ \bibnamefont
|
||||
{Sham}},\ }\href {\doibase 10.1103/PhysRev.140.A1133} {\bibfield {journal}
|
||||
{\bibinfo {journal} {Physical Review}\ }\textbf {\bibinfo {volume} {140}},\
|
||||
\bibinfo {pages} {A1133} (\bibinfo {year} {1965}{\natexlab{b}})}\BibitemShut
|
||||
{NoStop}%
|
||||
\bibitem [{\citenamefont {Perdew}\ \emph
|
||||
{et~al.}(1996{\natexlab{b}})\citenamefont {Perdew}, \citenamefont {Burke},\
|
||||
and\ \citenamefont {Ernzerhof}}]{PBE}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~P.}\ \bibnamefont
|
||||
{Perdew}}, \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {Burke}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Ernzerhof}},\ }\href
|
||||
{\doibase 10.1103/PhysRevLett.77.3865} {\bibfield {journal} {\bibinfo
|
||||
{journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {77}},\ \bibinfo
|
||||
{pages} {3865} (\bibinfo {year} {1996}{\natexlab{b}})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Becke}(1993)}]{B3LYP1}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~D.}\ \bibnamefont
|
||||
{Becke}},\ }\href {\doibase 10.1063/1.464913} {\bibfield {journal} {\bibinfo
|
||||
{journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo {volume}
|
||||
{98}},\ \bibinfo {pages} {5648} (\bibinfo {year} {1993})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1063/1.464913}
|
||||
{https://doi.org/10.1063/1.464913} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Lee}\ \emph {et~al.}(1988)\citenamefont {Lee},
|
||||
\citenamefont {Yang},\ and\ \citenamefont {Parr}}]{B3LYP2}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
|
||||
{Lee}}, \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont {Yang}}, \ and\
|
||||
\bibinfo {author} {\bibfnamefont {R.~G.}\ \bibnamefont {Parr}},\ }\href
|
||||
{\doibase 10.1103/PhysRevB.37.785} {\bibfield {journal} {\bibinfo {journal}
|
||||
{Phys. Rev. B}\ }\textbf {\bibinfo {volume} {37}},\ \bibinfo {pages} {785}
|
||||
(\bibinfo {year} {1988})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Vosko}\ \emph {et~al.}(1980)\citenamefont {Vosko},
|
||||
\citenamefont {Wilk},\ and\ \citenamefont {Nusair}}]{B3LYP3}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.~H.}\ \bibnamefont
|
||||
{Vosko}}, \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont {Wilk}}, \ and\
|
||||
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Nusair}},\ }\href
|
||||
{\doibase 10.1139/p80-159} {\bibfield {journal} {\bibinfo {journal}
|
||||
{Canadian Journal of Physics}\ }\textbf {\bibinfo {volume} {58}},\ \bibinfo
|
||||
{pages} {1200} (\bibinfo {year} {1980})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1139/p80-159}
|
||||
{https://doi.org/10.1139/p80-159} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Stephens}\ \emph {et~al.}(1994)\citenamefont
|
||||
{Stephens}, \citenamefont {Devlin}, \citenamefont {Chabalowski},\ and\
|
||||
\citenamefont {Frisch}}]{B3LYP4}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.~J.}\ \bibnamefont
|
||||
{Stephens}}, \bibinfo {author} {\bibfnamefont {F.~J.}\ \bibnamefont
|
||||
{Devlin}}, \bibinfo {author} {\bibfnamefont {C.~F.}\ \bibnamefont
|
||||
{Chabalowski}}, \ and\ \bibinfo {author} {\bibfnamefont {M.~J.}\ \bibnamefont
|
||||
{Frisch}},\ }\href {\doibase 10.1021/j100096a001} {\bibfield {journal}
|
||||
{\bibinfo {journal} {The Journal of Physical Chemistry}\ }\textbf {\bibinfo
|
||||
{volume} {98}},\ \bibinfo {pages} {11623} (\bibinfo {year} {1994})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1021/j100096a001}
|
||||
{https://doi.org/10.1021/j100096a001} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Adamo}\ and\ \citenamefont
|
||||
{Barone}(1999)}]{adamo1999jchemphys}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
|
||||
{Adamo}}\ and\ \bibinfo {author} {\bibfnamefont {V.}~\bibnamefont {Barone}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {The Journal of
|
||||
Chemical Physics}\ }\textbf {\bibinfo {volume} {110}},\ \bibinfo {pages}
|
||||
{6158} (\bibinfo {year} {1999})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Zhang}\ and\ \citenamefont
|
||||
{Yang}(1998)}]{PhysRevLett.80.890}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {Y.}~\bibnamefont
|
||||
{Zhang}}\ and\ \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont {Yang}},\
|
||||
}\href {\doibase 10.1103/PhysRevLett.80.890} {\bibfield {journal} {\bibinfo
|
||||
{journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {80}},\ \bibinfo
|
||||
{pages} {890} (\bibinfo {year} {1998})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Zhao}\ and\ \citenamefont {Truhlar}(2006)}]{M06-L}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {Y.}~\bibnamefont
|
||||
{Zhao}}\ and\ \bibinfo {author} {\bibfnamefont {D.~G.}\ \bibnamefont
|
||||
{Truhlar}},\ }\href {\doibase 10.1063/1.2370993} {\bibfield {journal}
|
||||
{\bibinfo {journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo
|
||||
{volume} {125}},\ \bibinfo {pages} {194101} (\bibinfo {year} {2006})},\
|
||||
\Eprint {http://arxiv.org/abs/https://doi.org/10.1063/1.2370993}
|
||||
{https://doi.org/10.1063/1.2370993} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Bender}\ and\ \citenamefont
|
||||
{Davidson}(1969)}]{Bender69}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {C.~F.}\ \bibnamefont
|
||||
{Bender}}\ and\ \bibinfo {author} {\bibfnamefont {E.~R.}\ \bibnamefont
|
||||
{Davidson}},\ }\href {\doibase 10.1103/PhysRev.183.23} {\bibfield {journal}
|
||||
{\bibinfo {journal} {Phys. Rev.}\ }\textbf {\bibinfo {volume} {183}},\
|
||||
\bibinfo {pages} {23} (\bibinfo {year} {1969})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Whitten}\ and\ \citenamefont
|
||||
{Hackmeyer}(1969)}]{Whitten69}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~L.}\ \bibnamefont
|
||||
{Whitten}}\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
|
||||
{Hackmeyer}},\ }\href {\doibase 10.1063/1.1671985} {\bibfield {journal}
|
||||
{\bibinfo {journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo
|
||||
{volume} {51}},\ \bibinfo {pages} {5584} (\bibinfo {year} {1969})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1063/1.1671985}
|
||||
{https://doi.org/10.1063/1.1671985} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Huron}\ \emph {et~al.}(1973)\citenamefont {Huron},
|
||||
\citenamefont {Malrieu},\ and\ \citenamefont {Rancurel}}]{Huron73}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
|
||||
{Huron}}, \bibinfo {author} {\bibfnamefont {J.~P.}\ \bibnamefont {Malrieu}},
|
||||
\ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Rancurel}},\
|
||||
}\href {\doibase 10.1063/1.1679199} {\bibfield {journal} {\bibinfo
|
||||
{journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo {volume}
|
||||
{58}},\ \bibinfo {pages} {5745} (\bibinfo {year} {1973})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1063/1.1679199}
|
||||
{https://doi.org/10.1063/1.1679199} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Buenker}\ \emph {et~al.}(1978)\citenamefont
|
||||
{Buenker}, \citenamefont {Peyerimhoff},\ and\ \citenamefont
|
||||
{Butscher}}]{Buenker78}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {R.~J.}\ \bibnamefont
|
||||
{Buenker}}, \bibinfo {author} {\bibfnamefont {S.~D.}\ \bibnamefont
|
||||
{Peyerimhoff}}, \ and\ \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
|
||||
{Butscher}},\ }\href {\doibase 10.1080/00268977800100581} {\bibfield
|
||||
{journal} {\bibinfo {journal} {Molecular Physics}\ }\textbf {\bibinfo
|
||||
{volume} {35}},\ \bibinfo {pages} {771} (\bibinfo {year} {1978})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1080/00268977800100581}
|
||||
{https://doi.org/10.1080/00268977800100581} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Evangelisti}\ \emph {et~al.}(1983)\citenamefont
|
||||
{Evangelisti}, \citenamefont {Daudey},\ and\ \citenamefont
|
||||
{Malrieu}}]{EVANGELISTI1983}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
|
||||
{Evangelisti}}, \bibinfo {author} {\bibfnamefont {J.-P.}\ \bibnamefont
|
||||
{Daudey}}, \ and\ \bibinfo {author} {\bibfnamefont {J.-P.}\ \bibnamefont
|
||||
{Malrieu}},\ }\href {\doibase https://doi.org/10.1016/0301-0104(83)85011-3}
|
||||
{\bibfield {journal} {\bibinfo {journal} {Chemical Physics}\ }\textbf
|
||||
{\bibinfo {volume} {75}},\ \bibinfo {pages} {91 } (\bibinfo {year}
|
||||
{1983})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Cimiraglia}(1985)}]{Cimiraglia1985}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
|
||||
{Cimiraglia}},\ }\href {\doibase 10.1063/1.449362} {\bibfield {journal}
|
||||
{\bibinfo {journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo
|
||||
{volume} {83}},\ \bibinfo {pages} {1746} (\bibinfo {year} {1985})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1063/1.449362}
|
||||
{https://doi.org/10.1063/1.449362} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Chirlian}\ and\ \citenamefont
|
||||
{Francl}(1987)}]{Chirlian1987}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {L.~E.}\ \bibnamefont
|
||||
{Chirlian}}\ and\ \bibinfo {author} {\bibfnamefont {M.~M.}\ \bibnamefont
|
||||
{Francl}},\ }\href {\doibase 10.1002/jcc.540080616} {\bibfield {journal}
|
||||
{\bibinfo {journal} {Journal of Computational Chemistry}\ }\textbf {\bibinfo
|
||||
{volume} {8}},\ \bibinfo {pages} {894} (\bibinfo {year} {1987})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.540080616}
|
||||
{https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.540080616} \BibitemShut
|
||||
{NoStop}%
|
||||
\bibitem [{\citenamefont {Giner}\ \emph {et~al.}(2013)\citenamefont {Giner},
|
||||
\citenamefont {Scemama},\ and\ \citenamefont {Caffarel}}]{Giner2013}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
|
||||
{Giner}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Caffarel}},\ }\href
|
||||
{\doibase 10.1139/cjc-2013-0017} {\bibfield {journal} {\bibinfo {journal}
|
||||
{Canadian Journal of Chemistry}\ }\textbf {\bibinfo {volume} {91}},\ \bibinfo
|
||||
{pages} {879} (\bibinfo {year} {2013})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1139/cjc-2013-0017}
|
||||
{https://doi.org/10.1139/cjc-2013-0017} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Caffarel}\ \emph {et~al.}(2014)\citenamefont
|
||||
{Caffarel}, \citenamefont {Giner}, \citenamefont {Scemama},\ and\
|
||||
\citenamefont {Ramírez-Solís}}]{Caffarel2014}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
|
||||
{Caffarel}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Giner}},
|
||||
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}}, \ and\
|
||||
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Ramírez-Solís}},\
|
||||
}\href {\doibase 10.1021/ct5004252} {\bibfield {journal} {\bibinfo
|
||||
{journal} {Journal of Chemical Theory and Computation}\ }\textbf {\bibinfo
|
||||
{volume} {10}},\ \bibinfo {pages} {5286} (\bibinfo {year} {2014})},\ \bibinfo
|
||||
{note} {pMID: 26583212},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1021/ct5004252}
|
||||
{https://doi.org/10.1021/ct5004252} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Caffarel}\ \emph
|
||||
{et~al.}(2016{\natexlab{a}})\citenamefont {Caffarel}, \citenamefont
|
||||
{Applencourt}, \citenamefont {Giner},\ and\ \citenamefont
|
||||
{Scemama}}]{Caffarel16}%
|
||||
\BibitemOpen
|
||||
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|
||||
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|
||||
{Applencourt}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Giner}},
|
||||
\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}},\ }\href
|
||||
{http://scitation.aip.org/content/aip/journal/jcp/144/15/10.1063/1.4947093}
|
||||
{\bibfield {journal} {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf
|
||||
{\bibinfo {volume} {144}},\ \bibinfo {eid} {151103} (\bibinfo {year}
|
||||
{2016}{\natexlab{a}})}\BibitemShut {NoStop}%
|
||||
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|
||||
{Garniron}, \citenamefont {Gasperich}, \citenamefont {Applencourt},
|
||||
\citenamefont {Benali}, \citenamefont {Fert{\'e}}, \citenamefont {Paquier},
|
||||
\citenamefont {Pradines}, \citenamefont {Assaraf}, \citenamefont {Reinhardt},
|
||||
\citenamefont {Toulouse}, \citenamefont {Barbaresco}, \citenamefont {Renon},
|
||||
\citenamefont {David}, \citenamefont {Malrieu}, \citenamefont {V{\'e}ril},
|
||||
\citenamefont {Caffarel}, \citenamefont {Loos}, \citenamefont {Giner},\ and\
|
||||
\citenamefont {Scemama}}]{QP2}%
|
||||
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|
||||
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|
||||
{Garniron}}, \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {Gasperich}},
|
||||
\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Applencourt}}, \bibinfo
|
||||
{author} {\bibfnamefont {A.}~\bibnamefont {Benali}}, \bibinfo {author}
|
||||
{\bibfnamefont {A.}~\bibnamefont {Fert{\'e}}}, \bibinfo {author}
|
||||
{\bibfnamefont {J.}~\bibnamefont {Paquier}}, \bibinfo {author} {\bibfnamefont
|
||||
{B.}~\bibnamefont {Pradines}}, \bibinfo {author} {\bibfnamefont
|
||||
{R.}~\bibnamefont {Assaraf}}, \bibinfo {author} {\bibfnamefont
|
||||
{P.}~\bibnamefont {Reinhardt}}, \bibinfo {author} {\bibfnamefont
|
||||
{J.}~\bibnamefont {Toulouse}}, \bibinfo {author} {\bibfnamefont
|
||||
{P.}~\bibnamefont {Barbaresco}}, \bibinfo {author} {\bibfnamefont
|
||||
{N.}~\bibnamefont {Renon}}, \bibinfo {author} {\bibfnamefont
|
||||
{G.}~\bibnamefont {David}}, \bibinfo {author} {\bibfnamefont {J.~P.}\
|
||||
\bibnamefont {Malrieu}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
|
||||
{V{\'e}ril}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Caffarel}},
|
||||
\bibinfo {author} {\bibfnamefont {P.~F.}\ \bibnamefont {Loos}}, \bibinfo
|
||||
{author} {\bibfnamefont {E.}~\bibnamefont {Giner}}, \ and\ \bibinfo {author}
|
||||
{\bibfnamefont {A.}~\bibnamefont {Scemama}},\ }\href {\doibase
|
||||
10.1021/acs.jctc.9b00176} {\bibfield {journal} {\bibinfo {journal} {J.
|
||||
Chem. Theory Comput.}\ }\textbf {\bibinfo {volume} {15}},\ \bibinfo {pages}
|
||||
{3591} (\bibinfo {year} {2019})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {{Fert{\'e}}}\ \emph {et~al.}(2019)\citenamefont
|
||||
{{Fert{\'e}}}, \citenamefont {{Giner}},\ and\ \citenamefont
|
||||
{{Toulouse}}}]{2019JChPh.150h4103F}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
|
||||
{{Fert{\'e}}}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
|
||||
{{Giner}}}, \ and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{{Toulouse}}},\ }\href {\doibase 10.1063/1.5082638} {\bibfield {journal}
|
||||
{\bibinfo {journal} {\jcp}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo
|
||||
{eid} {084103} (\bibinfo {year} {2019})},\ \Eprint
|
||||
{http://arxiv.org/abs/1901.08321} {arXiv:1901.08321 [physics.chem-ph]}
|
||||
\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Kim}\ \emph {et~al.}(2018)\citenamefont {Kim},
|
||||
\citenamefont {Baczewski}, \citenamefont {Beaudet}, \citenamefont {Benali},
|
||||
\citenamefont {Bennett}, \citenamefont {Berrill}, \citenamefont {Blunt},
|
||||
\citenamefont {Borda}, \citenamefont {Casula}, \citenamefont {Ceperley},
|
||||
\citenamefont {Chiesa}, \citenamefont {Clark}, \citenamefont {Clay},
|
||||
\citenamefont {Delaney}, \citenamefont {Dewing}, \citenamefont {Esler},
|
||||
\citenamefont {Hao}, \citenamefont {Heinonen}, \citenamefont {Kent},
|
||||
\citenamefont {Krogel}, \citenamefont {Kylänpää}, \citenamefont {Li},
|
||||
\citenamefont {Lopez}, \citenamefont {Luo}, \citenamefont {Malone},
|
||||
\citenamefont {Martin}, \citenamefont {Mathuriya}, \citenamefont {McMinis},
|
||||
\citenamefont {Melton}, \citenamefont {Mitas}, \citenamefont {Morales},
|
||||
\citenamefont {Neuscamman}, \citenamefont {Parker}, \citenamefont {Flores},
|
||||
\citenamefont {Romero}, \citenamefont {Rubenstein}, \citenamefont {Shea},
|
||||
\citenamefont {Shin}, \citenamefont {Shulenburger}, \citenamefont {Tillack},
|
||||
\citenamefont {Townsend}, \citenamefont {Tubman}, \citenamefont {Goetz},
|
||||
\citenamefont {Vincent}, \citenamefont {Yang}, \citenamefont {Yang},
|
||||
\citenamefont {Zhang},\ and\ \citenamefont {Zhao}}]{Kim_2018}%
|
||||
\BibitemOpen
|
||||
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|
||||
{Kim}}, \bibinfo {author} {\bibfnamefont {A.~D.}\ \bibnamefont {Baczewski}},
|
||||
\bibinfo {author} {\bibfnamefont {T.~D.}\ \bibnamefont {Beaudet}}, \bibinfo
|
||||
{author} {\bibfnamefont {A.}~\bibnamefont {Benali}}, \bibinfo {author}
|
||||
{\bibfnamefont {M.~C.}\ \bibnamefont {Bennett}}, \bibinfo {author}
|
||||
{\bibfnamefont {M.~A.}\ \bibnamefont {Berrill}}, \bibinfo {author}
|
||||
{\bibfnamefont {N.~S.}\ \bibnamefont {Blunt}}, \bibinfo {author}
|
||||
{\bibfnamefont {E.~J.~L.}\ \bibnamefont {Borda}}, \bibinfo {author}
|
||||
{\bibfnamefont {M.}~\bibnamefont {Casula}}, \bibinfo {author} {\bibfnamefont
|
||||
{D.~M.}\ \bibnamefont {Ceperley}}, \bibinfo {author} {\bibfnamefont
|
||||
{S.}~\bibnamefont {Chiesa}}, \bibinfo {author} {\bibfnamefont {B.~K.}\
|
||||
\bibnamefont {Clark}}, \bibinfo {author} {\bibfnamefont {R.~C.}\ \bibnamefont
|
||||
{Clay}}, \bibinfo {author} {\bibfnamefont {K.~T.}\ \bibnamefont {Delaney}},
|
||||
\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Dewing}}, \bibinfo
|
||||
{author} {\bibfnamefont {K.~P.}\ \bibnamefont {Esler}}, \bibinfo {author}
|
||||
{\bibfnamefont {H.}~\bibnamefont {Hao}}, \bibinfo {author} {\bibfnamefont
|
||||
{O.}~\bibnamefont {Heinonen}}, \bibinfo {author} {\bibfnamefont {P.~R.~C.}\
|
||||
\bibnamefont {Kent}}, \bibinfo {author} {\bibfnamefont {J.~T.}\ \bibnamefont
|
||||
{Krogel}}, \bibinfo {author} {\bibfnamefont {I.}~\bibnamefont {Kylänpää}},
|
||||
\bibinfo {author} {\bibfnamefont {Y.~W.}\ \bibnamefont {Li}}, \bibinfo
|
||||
{author} {\bibfnamefont {M.~G.}\ \bibnamefont {Lopez}}, \bibinfo {author}
|
||||
{\bibfnamefont {Y.}~\bibnamefont {Luo}}, \bibinfo {author} {\bibfnamefont
|
||||
{F.~D.}\ \bibnamefont {Malone}}, \bibinfo {author} {\bibfnamefont {R.~M.}\
|
||||
\bibnamefont {Martin}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
|
||||
{Mathuriya}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {McMinis}},
|
||||
\bibinfo {author} {\bibfnamefont {C.~A.}\ \bibnamefont {Melton}}, \bibinfo
|
||||
{author} {\bibfnamefont {L.}~\bibnamefont {Mitas}}, \bibinfo {author}
|
||||
{\bibfnamefont {M.~A.}\ \bibnamefont {Morales}}, \bibinfo {author}
|
||||
{\bibfnamefont {E.}~\bibnamefont {Neuscamman}}, \bibinfo {author}
|
||||
{\bibfnamefont {W.~D.}\ \bibnamefont {Parker}}, \bibinfo {author}
|
||||
{\bibfnamefont {S.~D.~P.}\ \bibnamefont {Flores}}, \bibinfo {author}
|
||||
{\bibfnamefont {N.~A.}\ \bibnamefont {Romero}}, \bibinfo {author}
|
||||
{\bibfnamefont {B.~M.}\ \bibnamefont {Rubenstein}}, \bibinfo {author}
|
||||
{\bibfnamefont {J.~A.~R.}\ \bibnamefont {Shea}}, \bibinfo {author}
|
||||
{\bibfnamefont {H.}~\bibnamefont {Shin}}, \bibinfo {author} {\bibfnamefont
|
||||
{L.}~\bibnamefont {Shulenburger}}, \bibinfo {author} {\bibfnamefont {A.~F.}\
|
||||
\bibnamefont {Tillack}}, \bibinfo {author} {\bibfnamefont {J.~P.}\
|
||||
\bibnamefont {Townsend}}, \bibinfo {author} {\bibfnamefont {N.~M.}\
|
||||
\bibnamefont {Tubman}}, \bibinfo {author} {\bibfnamefont {B.~V.~D.}\
|
||||
\bibnamefont {Goetz}}, \bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
|
||||
{Vincent}}, \bibinfo {author} {\bibfnamefont {D.~C.}\ \bibnamefont {Yang}},
|
||||
\bibinfo {author} {\bibfnamefont {Y.}~\bibnamefont {Yang}}, \bibinfo {author}
|
||||
{\bibfnamefont {S.}~\bibnamefont {Zhang}}, \ and\ \bibinfo {author}
|
||||
{\bibfnamefont {L.}~\bibnamefont {Zhao}},\ }\href {\doibase
|
||||
10.1088/1361-648x/aab9c3} {\bibfield {journal} {\bibinfo {journal} {Journal
|
||||
of Physics: Condensed Matter}\ }\textbf {\bibinfo {volume} {30}},\ \bibinfo
|
||||
{pages} {195901} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Caffarel}\ \emph
|
||||
{et~al.}(2016{\natexlab{b}})\citenamefont {Caffarel}, \citenamefont
|
||||
{Applencourt}, \citenamefont {Giner},\ and\ \citenamefont
|
||||
{Scemama}}]{Caffarel2016}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
|
||||
{Caffarel}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
|
||||
{Applencourt}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Giner}},
|
||||
\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}},\ }\href
|
||||
{\doibase 10.1063/1.4947093} {\bibfield {journal} {\bibinfo {journal} {The
|
||||
Journal of Chemical Physics}\ }\textbf {\bibinfo {volume} {144}},\ \bibinfo
|
||||
{pages} {151103} (\bibinfo {year} {2016}{\natexlab{b}})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1063/1.4947093}
|
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{https://doi.org/10.1063/1.4947093} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Scemama}\ \emph {et~al.}(2018)\citenamefont
|
||||
{Scemama}, \citenamefont {Benali}, \citenamefont {Jacquemin}, \citenamefont
|
||||
{Caffarel},\ and\ \citenamefont {Loos}}]{H2O-exci}%
|
||||
\BibitemOpen
|
||||
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|
||||
{Scemama}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Benali}},
|
||||
\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Jacquemin}}, \bibinfo
|
||||
{author} {\bibfnamefont {M.}~\bibnamefont {Caffarel}}, \ and\ \bibinfo
|
||||
{author} {\bibfnamefont {P.-F.}\ \bibnamefont {Loos}},\ }\href {\doibase
|
||||
10.1063/1.5041327} {\bibfield {journal} {\bibinfo {journal} {The Journal of
|
||||
Chemical Physics}\ }\textbf {\bibinfo {volume} {149}},\ \bibinfo {pages}
|
||||
{034108} (\bibinfo {year} {2018})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1063/1.5041327}
|
||||
{https://doi.org/10.1063/1.5041327} \BibitemShut {NoStop}%
|
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\bibitem [{\citenamefont {{Scemama}}\ \emph {et~al.}(2019)\citenamefont
|
||||
{{Scemama}}, \citenamefont {{Caffarel}}, \citenamefont {{Benali}},
|
||||
\citenamefont {{Jacquemin}},\ and\ \citenamefont {{Loos}}}]{H2O-exci-PP}%
|
||||
\BibitemOpen
|
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|
||||
{{Scemama}}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
|
||||
{{Caffarel}}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
|
||||
{{Benali}}}, \bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
|
||||
{{Jacquemin}}}, \ and\ \bibinfo {author} {\bibfnamefont {P.-F.}\ \bibnamefont
|
||||
{{Loos}}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {arXiv
|
||||
e-prints}\ ,\ \bibinfo {eid} {arXiv:1904.00678}} (\bibinfo {year} {2019})},\
|
||||
\Eprint {http://arxiv.org/abs/1904.00678} {arXiv:1904.00678
|
||||
[physics.chem-ph]} \BibitemShut {NoStop}%
|
||||
\end{thebibliography}%
|
||||
|
|
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|
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@CONTROL{REVTEX41Control}
|
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@CONTROL{apsrev41Control,author="08",editor="1",pages="0",title="",year="1"}
|
||||
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Reference in New Issue