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32
Manuscript/sfBSE.tex
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@ -751,7 +751,31 @@ The excitation energies corresponding to the first singlet and triplet single ex
\subsection{Hydrogen molecule} \subsection{Hydrogen molecule}
\label{sec:H2} \label{sec:H2}
%=============================== %===============================
The second system of interest is the \ce{H2} molecule where we streched the bond. The ground state of the \ce{H2} molecule is a singlet with $(1\sigma_g)^2$ configuration. Three excited states were investigated during the streching: the singly excited state B${}^1 \Sigma_u^+$ with $(1\sigma_g )~ (1\sigma_u)$ configuration, the singly excited state E${}^1 \Sigma_g^+$ with $(1\sigma_g )~ (2\sigma_g)$ configuration and the doubly excited state F${}^1 \Sigma_g^+$ with $(1\sigma_u )~ (1\sigma_u)$ configuration.
\begin{figure}
\includegraphics[width=\linewidth]{H2_BSE_RHF.png}
\caption{
Excitation energies of the three states of interest [with respect to the singlet ground state] of \ce{H2} obtained with the cc-pVQZ basis. Three sets of curves are drawn, the solid curves are the reference (EOM-CCSD), the dashed curves are obtained with SF-BSE and the dotted curves are obtained with BSE with a RHF reference without using spin-flip.
All the spin-flip calculations have been performed with a UHF reference.
\label{fig:H2_BSE}}
\end{figure}
\begin{figure}
\includegraphics[width=\linewidth]{H2_CIS.png}
\caption{
Excitation energies of the three states of interest [with respect to the singlet ground state] of \ce{H2} obtained with the cc-pVQZ basis. Three sets of curves are drawn, the solid curves are the reference (EOM-CCSD), the dashed curves are obtained with SF-CIS and the dotted curves are obtained with CIS without using spin-flip.
All the spin-flip calculations have been performed with a UHF reference.
\label{fig:H2_CIS}}
\end{figure}
\begin{figure}
\includegraphics[width=\linewidth]{H2_TDDFT.png}
\caption{
Excitation energies of the three states of interest [with respect to the singlet ground state] of \ce{H2} obtained with the cc-pVQZ basis. Three sets of curves are drawn, the solid curves are the reference (EOM-CCSD), the dashed curves are obtained with SF-TDBHHLYP and the dotted curves are obtained with TDBHHLYP without using spin-flip.
All the spin-flip calculations have been performed with a UHF reference.
\label{fig:H2_TDDFT}}
\end{figure}
%=============================== %===============================
\subsection{Cyclobutadiene} \subsection{Cyclobutadiene}
\label{sec:CBD} \label{sec:CBD}
@ -786,8 +810,8 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations
SF-ADC(2)-s\fnm[2] & & & \\ SF-ADC(2)-s\fnm[2] & & & \\
SF-ADC(2)-x\fnm[2] & & & \\ SF-ADC(2)-x\fnm[2] & & & \\
SF-ADC(3)\fnm[2] & & & \\ SF-ADC(3)\fnm[2] & & & \\
SF-BSE@{\GOWO}@UHF\fnm[3] & & & \\ SF-BSE@{\GOWO}@UHF\fnm[3] & 1.438 & 2.704 &4.540 \\
SF-dBSE@{\GOWO}@UHF\fnm[3] & & & \\ SF-dBSE@{\GOWO}@UHF\fnm[3] & 1.403 &2.883 &4.621 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.} \fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.}
@ -814,8 +838,8 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations
SF-ADC(2)-s\fnm[2] & & & \\ SF-ADC(2)-s\fnm[2] & & & \\
SF-ADC(2)-x\fnm[2] & & & \\ SF-ADC(2)-x\fnm[2] & & & \\
SF-ADC(3)\fnm[2] & & & \\ SF-ADC(3)\fnm[2] & & & \\
SF-BSE@{\GOWO}@UHF\fnm[3] & & & \\ SF-BSE@{\GOWO}@UHF\fnm[3] & -0.049 & 1.189 & 1.480 \\
SF-dBSE@{\GOWO}@UHF\fnm[3] & & & \\ SF-dBSE@{\GOWO}@UHF\fnm[3] & 0.012 & 1.507 & 1.841 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.} \fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.}

13542
Notebooks/sf_methods_H2.nb
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142
output/H2/TDDFT/h2_tddft_eighth_excitation
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@ -1,71 +1,71 @@
30.0054 21.8448
29.3857 21.3572
28.7628 20.9026
28.1925 20.4789
27.6596 20.0844
27.1466 19.7172
26.6543 19.3754
26.1802 19.0572
25.7216 18.7604
25.2768 18.4834
24.8458 18.2246
24.4294 17.9830
24.0286 17.6351
23.6439 17.1967
23.2753 16.7883
22.9220 16.4081
22.5834 16.0546
22.2582 15.7266
21.9457 15.4226
21.6452 15.1413
21.3564 14.8813
21.0789 14.6410
20.8126 14.4191
20.5572 14.2143
20.3125 14.0253
20.0779 13.8507
19.8531 13.6895
19.6375 13.6409
19.4307 13.6324
19.2323 13.6303
19.0421 13.6341
18.8600 13.6433
18.6857 13.6575
18.5191 13.6761
18.3601 13.6988
18.2084 13.7250
18.0638 13.7542
17.9259 13.7858
17.7946 13.8194
17.6695 13.8543
17.5501 13.8902
17.4364 13.9265
17.3280 13.9628
17.2247 13.9988
17.1265 14.0342
17.0331 14.0685
16.9446 14.1016
16.8609 14.1333
16.7819 14.1633
16.7076 14.1914
16.6380 14.2177
16.5729 14.2419
16.5123 14.2641
16.4560 14.2842
16.4039 14.3022
16.3557 14.3181
16.3114 14.3320
16.2706 14.3438
16.2332 14.3537
16.1989 14.3618
16.1676 14.3682
16.1390 14.3730
16.1130 14.3763
16.0894 14.3783
16.0679 14.3791
16.0484 14.3789
16.0354 14.3778
16.0315 14.3759
16.0272 14.3733
16.0225 14.3702
16.0174 14.3666

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output/H2/TDDFT/h2_tddft_fifth_excitation
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@ -1,71 +1,71 @@
25.1131 19.0571
24.5075 18.5358
23.8244 18.0544
23.0856 17.6105
22.3462 17.2021
21.6386 16.8268
20.9664 16.4824
20.3273 16.1666
19.7207 15.8772
19.1476 15.6121
18.6092 15.3694
18.1053 15.1477
17.7578 14.9457
17.5484 14.6761
17.3545 14.3720
17.1754 14.0915
17.0105 13.8322
16.8589 13.5922
16.7196 13.3698
16.5920 13.1635
16.4753 13.0567
16.3690 12.9759
16.2727 12.8998
16.1858 12.8283
16.1081 12.7611
16.0389 12.6983
15.9779 12.6400
15.9244 12.5861
15.8782 12.5365
15.8388 12.4909
15.8058 12.4485
15.7791 12.4084
15.7583 12.3697
15.7432 12.3315
15.7333 12.2933
15.7284 12.2547
15.7280 12.2159
15.7316 12.1768
15.7388 12.1378
15.7492 12.0987
15.7621 12.0595
15.7772 12.0199
15.7941 11.9793
15.8121 11.9372
15.8311 11.8929
15.8505 11.8460
15.8700 11.7960
15.8894 11.7429
15.9084 11.6868
15.9266 11.6281
15.9439 11.5674
15.9602 11.5055
15.9752 11.4431
15.9888 11.3810
16.0009 11.3198
16.0115 11.2600
16.0206 11.2023
16.0280 11.1469
16.0339 11.0942
16.0383 11.0443
16.0413 10.9974
16.0429 10.9537
16.0433 10.9131
16.0427 10.8756
16.0411 10.8413
16.0386 10.8101
16.0308 10.7820
16.0148 10.7568
16.0004 10.7346
15.9873 10.7151
15.9754 10.6984

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output/H2/TDDFT/h2_tddft_first_excitation
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@ -1,71 +1,71 @@
15.2020 13.6986
14.6802 12.9486
14.1787 12.1973
13.6965 11.4452
13.2342 10.6936
12.7917 9.9446
12.3671 9.2006
11.9587 8.4645
11.5650 7.7387
11.1849 7.0252
10.8175 6.3249
10.4622 5.6374
10.1184 4.9602
9.7857 4.2885
9.4637 3.6130
9.1521 2.9155
8.8509 2.1553
8.5597 1.1857
8.2786 -1.1372
8.0073 -1.8767
7.7456 -2.3115
7.4935 -2.6100
7.2506 -2.8247
7.0167 -2.9812
6.7915 -3.0945
6.5747 -3.1745
6.3661 -3.2282
6.1652 -3.2608
5.9719 -3.2762
5.7857 -3.2775
5.6063 -3.2672
5.4335 -3.2473
5.2670 -3.2195
5.1064 -3.1851
4.9515 -3.1453
4.8021 -3.1010
4.6578 -3.0531
4.5184 -3.0022
4.3837 -2.9490
4.2535 -2.8940
4.1275 -2.8375
4.0056 -2.7799
3.8876 -2.7217
3.7732 -2.6629
3.6624 -2.6039
3.5550 -2.5449
3.4508 -2.4860
3.3498 -2.4274
3.2517 -2.3692
3.1565 -2.3115
3.0641 -2.2544
2.9744 -2.1980
2.8872 -2.1423
2.8024 -2.0874
2.7201 -2.0334
2.6401 -1.9802
2.5623 -1.9279
2.4866 -1.8765
2.4131 -1.8261
2.3415 -1.7766
2.2720 -1.7280
2.2043 -1.6805
2.1384 -1.6338
2.0744 -1.5882
2.0121 -1.5435
1.9514 -1.4997
1.8924 -1.4570
1.8350 -1.4151
1.7792 -1.3742
1.7248 -1.3342
1.6719 -1.2950

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output/H2/TDDFT/h2_tddft_fourth_excitation
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@ -1,71 +1,71 @@
21.8448 16.8001
21.3572 16.4370
20.9026 16.1032
20.4789 15.7980
20.0844 15.5193
19.7172 15.2638
19.3754 15.0281
19.0572 14.8096
18.7604 14.6069
18.4834 14.4189
18.2246 14.2447
17.9830 14.0836
17.7578 13.9343
17.5484 13.7959
17.3545 13.6674
17.1754 13.5477
17.0105 13.4361
16.8589 13.3318
16.7196 13.2341
16.5920 13.1426
16.4753 12.9721
16.3690 12.7942
16.2727 12.6289
16.1858 12.4751
16.1081 12.3320
16.0389 12.1986
15.9779 12.0744
15.9244 11.9584
15.8782 11.8502
15.8388 11.7490
15.8058 11.6545
15.7791 11.5661
15.7583 11.4834
15.7432 11.4059
15.7333 11.3334
15.7284 11.2656
15.6207 11.2022
15.4416 11.1429
15.2722 11.0876
15.1139 11.0360
14.9682 10.9879
14.8369 10.9431
14.7220 10.9014
14.6251 10.8624
14.5475 10.8259
14.4905 10.7915
14.4546 10.7591
14.4397 10.7284
14.4455 10.6993
14.4709 10.6715
14.5140 10.6450
14.5730 10.6198
14.6453 10.5958
14.7283 10.5732
14.8191 10.5518
14.9149 10.5318
15.0131 10.5132
15.1112 10.4959
15.2072 10.4801
15.2993 10.4657
15.3862 10.4528
15.4672 10.4411
15.5415 10.4307
15.6090 10.4214
15.6695 10.4130
15.7231 10.4053
15.7700 10.3981
15.8106 10.3911
15.8453 10.3840
15.8746 10.3766
15.8988 10.3687

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output/H2/TDDFT/h2_tddft_ninth_excitation
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@ -1,71 +1,71 @@
36.2882 22.1432
36.0689 21.3735
35.8827 20.9026
35.7336 20.4789
35.6158 20.0844
35.5195 19.7172
35.4362 19.3754
34.9474 19.0572
34.4453 18.7604
33.9463 18.4834
33.4611 18.2246
32.9950 17.9830
32.5465 17.7578
32.1093 17.5484
31.6764 17.3545
31.2439 17.1754
30.8124 17.0105
30.3853 16.8589
29.9652 16.7196
29.5521 16.5920
29.1443 16.4753
28.7397 16.3690
28.3373 16.2727
27.9381 16.1858
27.5445 16.1081
27.1601 16.0389
26.7879 15.7719
26.4295 15.4342
26.0846 15.1125
25.7506 14.8084
25.4239 14.5230
25.1012 14.2570
24.7800 14.0105
24.4594 13.7828
24.1395 13.6988
23.8215 13.7250
23.5072 13.7542
23.1984 13.7858
22.8968 13.8194
22.6039 13.8543
22.3201 13.8902
22.0454 13.9265
21.7792 13.9628
21.5202 13.9988
21.2670 14.0342
21.0185 14.0685
20.7736 14.1016
20.5316 14.1333
20.2921 14.1633
20.0552 14.1914
19.8211 14.2177
19.5903 14.2419
19.3635 14.2641
19.1414 14.2842
18.9245 14.3022
18.7133 14.3181
18.5082 14.3320
18.3097 14.3438
18.1183 14.3537
17.9347 14.3618
17.7592 14.3682
17.5923 14.3730
17.4338 14.3763
17.2839 14.3783
17.1426 14.3791
17.0101 14.3789
16.8864 14.3778
16.7716 14.3759
16.6658 14.3733
16.5686 14.3702
16.4798 14.3666

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output/H2/TDDFT/h2_tddft_second_excitation
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@ -1,71 +1,71 @@
16.8001 14.8214
16.4370 14.4546
16.1032 14.1180
15.7980 13.6965
15.5193 13.2342
15.2638 12.7917
15.0281 12.3671
14.8096 11.9587
14.6069 11.5650
14.4189 11.1849
14.2447 10.8175
14.0836 10.4622
13.9343 10.1184
13.7959 9.7857
13.6674 9.4637
13.5477 9.1521
13.4361 8.8509
13.3318 8.5597
13.2341 8.2786
13.1426 8.0073
13.0567 7.7456
12.9759 7.4935
12.8998 7.2506
12.8283 7.0167
12.7611 6.7915
12.6983 6.5747
12.6400 6.3661
12.5861 6.1652
12.5365 5.9719
12.4909 5.7857
12.4485 5.6063
12.4084 5.4335
12.3697 5.2670
12.3315 5.1064
12.2933 4.9515
12.2547 4.8021
12.2159 4.6578
12.1768 4.5184
12.1378 4.3837
12.0987 4.2535
12.0595 4.1275
12.0199 4.0056
11.9793 3.8876
11.9372 3.7732
11.8929 3.6624
11.8460 3.5550
11.7960 3.4508
11.7429 3.3498
11.6868 3.2517
11.6281 3.1565
11.5674 3.0641
11.5055 2.9744
11.4431 2.8872
11.3810 2.8024
11.3198 2.7201
11.2600 2.6401
11.2023 2.5623
11.1469 2.4866
11.0942 2.4131
11.0443 2.3415
10.9974 2.2720
10.9537 2.2043
10.9131 2.1384
10.8756 2.0744
10.8413 2.0121
10.8101 1.9514
10.7820 1.8924
10.7568 1.8350
10.7346 1.7792
10.7151 1.7248
10.6984 1.6719

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output/H2/TDDFT/h2_tddft_seventh_excitation
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@ -1,71 +1,71 @@
29.8258 21.8448
29.2879 21.3572
28.7391 20.5869
28.1925 19.8054
27.6596 19.0647
27.1466 18.3827
26.6543 17.7593
26.1802 17.1898
25.7216 16.6696
25.2768 16.1950
24.8458 15.7622
24.4294 15.3675
24.0286 15.0067
23.6439 14.7624
23.2753 14.5969
22.9220 14.4483
22.5834 14.3156
22.2582 14.1977
21.9457 14.0936
21.6452 14.0023
21.3564 13.9228
21.0789 13.8545
20.8126 13.7965
20.5572 13.7483
20.3125 13.7093
20.0779 13.6787
19.8531 13.6561
19.6375 13.6409
19.4307 13.6324
19.2323 13.6303
19.0421 13.6341
18.8600 13.6433
18.6857 13.6575
18.5191 13.6761
18.3601 13.5731
18.2084 13.3806
18.0638 13.2050
17.9259 13.0463
17.7946 12.9049
17.6695 12.7818
17.5501 12.6776
17.4364 12.5932
17.3280 12.5289
17.2247 12.4848
17.1265 12.4606
17.0331 12.4556
16.9446 12.4688
16.8609 12.4990
16.7819 12.5447
16.7076 12.6044
16.6380 12.6764
16.5729 12.7588
16.5123 12.8495
16.4560 12.9466
16.4039 13.0479
16.3557 13.1513
16.3114 13.2548
16.2706 13.3565
16.2332 13.4549
16.1989 13.5487
16.1676 13.6370
16.1390 13.7190
16.1130 13.7944
16.0894 13.8630
16.0679 13.9248
16.0484 13.9800
16.0354 14.0288
16.0315 14.0715
16.0272 14.1086
16.0225 14.1404
16.0174 14.1675

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output/H2/TDDFT/h2_tddft_sixth_excitation
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@ -1,71 +1,71 @@
29.8258 19.0571
29.2879 18.5358
28.7391 18.0544
28.1563 17.6105
27.5781 17.2021
27.0263 16.8268
26.4886 16.4824
25.9539 16.1666
25.4198 15.8772
24.8934 15.6121
24.3854 15.3694
23.9019 15.1477
23.4408 14.9457
22.9947 14.7624
22.5563 14.5969
22.1217 14.4483
21.6908 14.3156
21.2664 14.1977
20.8526 14.0936
20.4534 14.0023
20.0713 13.9228
19.7061 13.8545
19.3553 13.7965
19.0156 13.7483
18.6845 13.7093
18.3612 13.6787
18.0465 13.6561
17.7421 13.5406
17.4501 13.4029
17.1723 13.2756
16.9099 13.1578
16.6632 13.0487
16.4314 12.9477
16.2129 12.8542
16.0059 12.7676
15.8088 12.6875
15.7280 12.6134
15.7316 12.5450
15.7388 12.4818
15.7492 12.4237
15.7621 12.3702
15.7772 12.3211
15.7941 12.2759
15.8121 12.2343
15.8311 12.1959
15.8505 12.1604
15.8700 12.1274
15.8894 12.0966
15.9084 12.0679
15.9266 12.0410
15.9439 12.0159
15.9602 11.9926
15.9752 11.9709
15.9888 11.9510
16.0009 11.9329
16.0115 11.9167
16.0206 11.9023
16.0280 11.8899
16.0339 11.8794
16.0383 11.8710
16.0413 11.8647
16.0429 11.8603
16.0433 11.8579
16.0427 11.8571
16.0411 11.8579
16.0386 11.8600
16.0308 11.8630
16.0148 11.8668
16.0004 11.8709
15.9873 11.8750
15.9754 11.8788

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output/H2/TDDFT/h2_tddft_tenth_excitation
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@ -1,71 +1,71 @@
38.2593 25.1131
37.5341 24.5075
36.9788 23.8244
36.6170 23.0856
36.2889 22.3462
35.8932 21.6386
35.4371 20.9664
35.3624 20.3273
35.2998 19.7207
35.2515 19.1476
35.2194 18.6092
35.2020 18.1053
35.1950 17.7578
35.1925 17.5484
35.1897 17.3545
35.1831 17.1754
35.1704 17.0105
35.1500 16.8589
35.1197 16.7196
35.0768 16.5920
35.0186 16.4753
34.9435 16.3690
34.8523 16.2727
34.7477 16.1858
34.6332 16.1081
34.5113 16.0389
34.3828 15.9779
34.2462 15.9244
34.0984 15.8782
33.9364 15.8388
33.7594 15.8058
33.5697 15.7791
33.3734 15.7583
33.1777 15.7432
32.9898 15.7333
32.8154 15.7284
32.6582 15.6207
32.5206 15.4416
32.4036 15.2722
32.3080 15.1139
32.2337 14.9682
32.1806 14.8369
32.1481 14.7220
32.1355 14.6251
32.1420 14.5475
32.1662 14.4905
32.2068 14.4546
32.2622 14.4397
32.3305 14.4455
32.4096 14.4709
32.4970 14.5140
32.5899 14.5730
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33.0721 15.8746
33.0876 14.9794

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output/H2/TDDFT/h2_tddft_third_excitation
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@ -1,71 +1,71 @@
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