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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}
\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}
\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)-x\fnm[2] & & & \\
SF-ADC(3)\fnm[2] & & & \\
SF-BSE@{\GOWO}@UHF\fnm[3] & & & \\
SF-dBSE@{\GOWO}@UHF\fnm[3] & & & \\
SF-BSE@{\GOWO}@UHF\fnm[3] & 1.438 & 2.704 &4.540 \\
SF-dBSE@{\GOWO}@UHF\fnm[3] & 1.403 &2.883 &4.621 \\
\end{tabular}
\end{ruledtabular}
\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)-x\fnm[2] & & & \\
SF-ADC(3)\fnm[2] & & & \\
SF-BSE@{\GOWO}@UHF\fnm[3] & & & \\
SF-dBSE@{\GOWO}@UHF\fnm[3] & & & \\
SF-BSE@{\GOWO}@UHF\fnm[3] & -0.049 & 1.189 & 1.480 \\
SF-dBSE@{\GOWO}@UHF\fnm[3] & 0.012 & 1.507 & 1.841 \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.}

13544
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
29.3857
28.7628
28.1925
27.6596
27.1466
26.6543
26.1802
25.7216
25.2768
24.8458
24.4294
24.0286
23.6439
23.2753
22.9220
22.5834
22.2582
21.9457
21.6452
21.3564
21.0789
20.8126
20.5572
20.3125
20.0779
19.8531
19.6375
19.4307
19.2323
19.0421
18.8600
18.6857
18.5191
18.3601
18.2084
18.0638
17.9259
17.7946
17.6695
17.5501
17.4364
17.3280
17.2247
17.1265
17.0331
16.9446
16.8609
16.7819
16.7076
16.6380
16.5729
16.5123
16.4560
16.4039
16.3557
16.3114
16.2706
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16.1989
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16.1390
16.1130
16.0894
16.0679
16.0484
16.0354
16.0315
16.0272
16.0225
16.0174
21.8448
21.3572
20.9026
20.4789
20.0844
19.7172
19.3754
19.0572
18.7604
18.4834
18.2246
17.9830
17.6351
17.1967
16.7883
16.4081
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15.7266
15.4226
15.1413
14.8813
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14.0253
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13.6761
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13.7250
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13.7858
13.8194
13.8543
13.8902
13.9265
13.9628
13.9988
14.0342
14.0685
14.1016
14.1333
14.1633
14.1914
14.2177
14.2419
14.2641
14.2842
14.3022
14.3181
14.3320
14.3438
14.3537
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14.3682
14.3730
14.3763
14.3783
14.3791
14.3789
14.3778
14.3759
14.3733
14.3702
14.3666

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output/H2/TDDFT/h2_tddft_fifth_excitation
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@ -1,71 +1,71 @@
25.1131
24.5075
23.8244
23.0856
22.3462
21.6386
20.9664
20.3273
19.7207
19.1476
18.6092
18.1053
17.7578
17.5484
17.3545
17.1754
17.0105
16.8589
16.7196
16.5920
16.4753
16.3690
16.2727
16.1858
16.1081
16.0389
15.9779
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15.8782
15.8388
15.8058
15.7791
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15.7432
15.7333
15.7284
15.7280
15.7316
15.7388
15.7492
15.7621
15.7772
15.7941
15.8121
15.8311
15.8505
15.8700
15.8894
15.9084
15.9266
15.9439
15.9602
15.9752
15.9888
16.0009
16.0115
16.0206
16.0280
16.0339
16.0383
16.0413
16.0429
16.0433
16.0427
16.0411
16.0386
16.0308
16.0148
16.0004
15.9873
15.9754
19.0571
18.5358
18.0544
17.6105
17.2021
16.8268
16.4824
16.1666
15.8772
15.6121
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15.1477
14.9457
14.6761
14.3720
14.0915
13.8322
13.5922
13.3698
13.1635
13.0567
12.9759
12.8998
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12.7611
12.6983
12.6400
12.5861
12.5365
12.4909
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12.4084
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12.2547
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12.0595
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11.9793
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11.8929
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11.7429
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10.9131
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10.8413
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10.7820
10.7568
10.7346
10.7151
10.6984

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output/H2/TDDFT/h2_tddft_first_excitation
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@ -1,71 +1,71 @@
15.2020
14.6802
14.1787
13.6965
13.2342
12.7917
12.3671
11.9587
11.5650
11.1849
10.8175
10.4622
10.1184
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9.1521
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8.5597
8.2786
8.0073
7.7456
7.4935
7.2506
7.0167
6.7915
6.5747
6.3661
6.1652
5.9719
5.7857
5.6063
5.4335
5.2670
5.1064
4.9515
4.8021
4.6578
4.5184
4.3837
4.2535
4.1275
4.0056
3.8876
3.7732
3.6624
3.5550
3.4508
3.3498
3.2517
3.1565
3.0641
2.9744
2.8872
2.8024
2.7201
2.6401
2.5623
2.4866
2.4131
2.3415
2.2720
2.2043
2.1384
2.0744
2.0121
1.9514
1.8924
1.8350
1.7792
1.7248
1.6719
13.6986
12.9486
12.1973
11.4452
10.6936
9.9446
9.2006
8.4645
7.7387
7.0252
6.3249
5.6374
4.9602
4.2885
3.6130
2.9155
2.1553
1.1857
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-1.3342
-1.2950

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output/H2/TDDFT/h2_tddft_fourth_excitation
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@ -1,71 +1,71 @@
21.8448
21.3572
20.9026
20.4789
20.0844
19.7172
19.3754
19.0572
18.7604
18.4834
18.2246
17.9830
17.7578
17.5484
17.3545
17.1754
17.0105
16.8589
16.7196
16.5920
16.4753
16.3690
16.2727
16.1858
16.1081
16.0389
15.9779
15.9244
15.8782
15.8388
15.8058
15.7791
15.7583
15.7432
15.7333
15.7284
15.6207
15.4416
15.2722
15.1139
14.9682
14.8369
14.7220
14.6251
14.5475
14.4905
14.4546
14.4397
14.4455
14.4709
14.5140
14.5730
14.6453
14.7283
14.8191
14.9149
15.0131
15.1112
15.2072
15.2993
15.3862
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15.5415
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15.6695
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15.8106
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15.8746
15.8988
16.8001
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16.1032
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15.5193
15.2638
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13.2341
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12.9721
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12.6289
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11.9584
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10.4528
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10.4307
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10.4130
10.4053
10.3981
10.3911
10.3840
10.3766
10.3687

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output/H2/TDDFT/h2_tddft_ninth_excitation
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@ -1,71 +1,71 @@
36.2882
36.0689
35.8827
35.7336
35.6158
35.5195
35.4362
34.9474
34.4453
33.9463
33.4611
32.9950
32.5465
32.1093
31.6764
31.2439
30.8124
30.3853
29.9652
29.5521
29.1443
28.7397
28.3373
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27.5445
27.1601
26.7879
26.4295
26.0846
25.7506
25.4239
25.1012
24.7800
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23.8215
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22.8968
22.6039
22.3201
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21.2670
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19.1414
18.9245
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16.7716
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16.5686
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22.1432
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20.9026
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18.4834
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17.9830
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17.5484
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17.1754
17.0105
16.8589
16.7196
16.5920
16.4753
16.3690
16.2727
16.1858
16.1081
16.0389
15.7719
15.4342
15.1125
14.8084
14.5230
14.2570
14.0105
13.7828
13.6988
13.7250
13.7542
13.7858
13.8194
13.8543
13.8902
13.9265
13.9628
13.9988
14.0342
14.0685
14.1016
14.1333
14.1633
14.1914
14.2177
14.2419
14.2641
14.2842
14.3022
14.3181
14.3320
14.3438
14.3537
14.3618
14.3682
14.3730
14.3763
14.3783
14.3791
14.3789
14.3778
14.3759
14.3733
14.3702
14.3666

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

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

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

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38.2593
37.5341
36.9788
36.6170
36.2889
35.8932
35.4371
35.3624
35.2998
35.2515
35.2194
35.2020
35.1950
35.1925
35.1897
35.1831
35.1704
35.1500
35.1197
35.0768
35.0186
34.9435
34.8523
34.7477
34.6332
34.5113
34.3828
34.2462
34.0984
33.9364
33.7594
33.5697
33.3734
33.1777
32.9898
32.8154
32.6582
32.5206
32.4036
32.3080
32.2337
32.1806
32.1481
32.1355
32.1420
32.1662
32.2068
32.2622
32.3305
32.4096
32.4970
32.5899
32.6853
32.7801
32.8710
32.9552
33.0298
33.0929
33.1429
33.1792
33.2017
33.2107
33.0821
33.0633
33.0512
33.0454
33.0453
33.0501
33.0594
33.0721
33.0876
25.1131
24.5075
23.8244
23.0856
22.3462
21.6386
20.9664
20.3273
19.7207
19.1476
18.6092
18.1053
17.7578
17.5484
17.3545
17.1754
17.0105
16.8589
16.7196
16.5920
16.4753
16.3690
16.2727
16.1858
16.1081
16.0389
15.9779
15.9244
15.8782
15.8388
15.8058
15.7791
15.7583
15.7432
15.7333
15.7284
15.6207
15.4416
15.2722
15.1139
14.9682
14.8369
14.7220
14.6251
14.5475
14.4905
14.4546
14.4397
14.4455
14.4709
14.5140
14.5730
14.6453
14.7283
14.8191
14.9149
15.0131
15.1112
15.2072
15.2993
15.3862
15.4672
15.5415
15.6090
15.6695
15.7231
15.7700
15.8106
15.8453
15.8746
14.9794

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21.8448
21.3572
20.9026
20.4789
20.0844
19.7172
19.3754
19.0572
18.7604
18.4834
18.2246
17.9830
17.6351
17.1967
16.7883
16.4081
16.0546
15.7266
15.4226
15.1413
14.8813
14.6410
14.4191
14.2143
14.0253
13.8507
13.6895
13.5406
13.4029
13.2756
13.1578
13.0487
12.9477
12.8542
12.7676
12.6875
12.6134
12.5450
12.4818
12.4237
12.3702
12.3211
12.2759
12.2343
12.1959
12.1604
12.1274
12.0966
12.0679
12.0410
12.0159
11.9926
11.9709
11.9510
11.9329
11.9167
11.9023
11.8899
11.8794
11.8710
11.8647
11.8603
11.8579
11.8571
11.8579
11.8600
11.8630
11.8668
11.8709
11.8750
11.8788
15.2020
14.6802
14.1787
13.8102
13.5293
13.2726
13.0377
12.8223
12.6249
12.4441
12.2787
12.1277
11.9897
11.8638
11.7488
11.6435
11.5472
11.4589
11.3780
11.3038
11.2356
11.1730
11.1152
11.0619
11.0125
10.9670
10.9250
10.8865
10.8510
10.8181
10.7869
10.7565
10.7256
10.6931
10.6581
10.6197
10.5776
10.5314
10.4811
10.4265
10.3675
10.3044
10.2373
10.1666
10.0932
10.0177
9.9410
9.8641
9.7879
9.7131
9.6404
9.5703
9.5034
9.4397
9.3797
9.3235
9.2710
9.2224
9.1776
9.1365
9.0990
9.0651
9.0346
9.0075
8.9835
8.9625
8.9444
8.9291
8.9164
8.9062
8.8983