Supporting Information
ON THE ROLE OF THE TRIPLET STATE IN THE
CIS/TRANS ISOMERIZATION OF RHODOPSIN: A
CASPT2//CASSCF STUDY OF A MODEL
CHROMOPHORE
Remedios González-Luque,† Gloria Olaso-González,† Manuela Merchán,† Pedro B.
Coto,†,¶,* Luis Serrano-Andrés† and Marco Garavelli‡,*
Instituto de Ciencia Molecular, Universidad de Valencia, Apdo. 22085,
ES-46071, Valencia, Spain,
Interdisziplinäres Zentrum für Molekulare Materialien (ICMM),
Friedrich-Alexander-Universität Erlangen-Nürnberg Staudtstraβe 7/B2
D-91058 Erlangen, Germany,
and
Dipartimento di Chimica "G. Ciamician", Università di Bologna, via
Selmi 2, Bologna, I-40126 Italy
pedro.brana@uv.es, marco.garavelli@unibo.it
†
¶
‡
Universitat de València
Universität Erlangen-Nürnberg
Università di Bologna
1. Landau-Zener estimate of the SOC
The estimate for the spin-orbit coupling needed for a 30% population of the lowestlying T1 state can be calculated using a Landau-Zener model. The probability of
transition in this model can be expressed as:
2
P  1 e
'2
H SO
EST
t
(1)
where EST is the energy difference between S1 and T1. Assuming that roughly 30% of
the population will be transferred to the T1 state (which provides the value of P) and if
we also assume that the rate of change of EST is uniform along the trajectory (taking a
time of 200 fs for the appearance of the first ground state species1) we can get a rough
'
estimate for EST t of 4.6531E-06 a.u. Using (1) we obtain for H SO
a value of 113
cm-1, about two to three orders of magnitude of increase with respect to the electronic
only term which lies within the order of magnitude found in some organic molecules2
after inclusion of the vibronic contribution.
2. Evolution of the T1 population after a successful ISC
Figure S1 displays the MEP computed for the triplet state from the 3*/1*
singlet-triplet crossing. After a successful ISC, part of the T1 population ultimately will
revert to the singlet state in the cis form after surmounting a small energetic barrier as
shown by the MEP computation linking the
3
* minimum with the (T1/S0)X
intersystem crossing (see Figure S2),‡ thus not leading to any signal transduction
activation.
The slow picosecond decay component experimentally detected using time resolved
spectroscopic techniques would be the product of back transfer of population from T1 to
S1. It has to be stressed that even when the vertical energy does not match with the
wavelengths observed by Kandori et al.3 this cannot be directly compared, as for
‡
The profile depicted in Fig. S2 corresponds to CASPT2//CASSCF single point calculations. The fact
that the ISC optimized at the CASSCF level is not preserved at the CASPT2//CASSCF level indicates
that correlation effects may slightly alter the geometry of the ISC. However, the computation of the
CASPT2 optimized ISC is impossible at present due to computational limitations.
2
emission it is expected that the differences between computed vertical energy
differences and observed emission maximum will be more significant.
It is interesting to note also that the structures of both singlet triplet crossing points
show different bond length alternation (BLA) patterns, and in general a quite different
structure (see Figure S3). However, the degree of torsion of the isomerizing double
bond of both structures places them in the reactant side, with the BLA of (T1/S0)X being
quite similar to the one expected for the ground state minimum.
Table S1 compiles the Cartesian coordinates of the singlet-triplet crossing points
and each one of the points of the MEP, together with the computed electronic SOCs for
the interaction S0/T1 and S1/T1. Notice that the largest SOC values are reached in the
region of the singlet-triplet crossing (MEP coordinate 7-10 a.u.), where the ISC process
will be more efficient.
Figure S1. Minimum energy path leading to the triplet minimum from (S1/T1)X (CASPT2
energies and MEP coordinates in atomic units, line and color codes follow those of the main
text).
3
Figure S2. Minimum energy path leading to the T1 minimum from (T1/S0)X ISC (CASPT2
energies and MEP coordinates in atomic units, line and color codes follow those of the main
text).
4
Figure S3. Molecular structure at the S1/S0 (A), T1/S1 (B) and T1/S0 (C) crossing points. Some
geometrical parameters and the dihedral angle of the isomerizing double bond (C11-C12) are
shown.
5
Table S1. Cartesian coordinates x, y, z (in Å) of the structures located on the PBS11
[S1, 1(ππ*)] state MEP and of the S0/T1 STC Spin-orbit coupling (SOC) values are also
included. The MEP coordinate is given in atomic units and SOC in cm-1.
______________________________________________________________________
MEP coordinate: 0.00 au
SOC (S0/T1) = 0.01 cm-1
SOC (S1/T1) = 0.02 cm-1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
x
y
z
0.845949
0.904834
0.763572
-0.591181
-0.946321
-0.297537
-0.648921
-0.424801
-0.737934
-0.430475
-0.660467
-0.401317
0.201503
0.300120
0.851230
-2.124001
-1.372734
0.680784
0.625173
2.185545
0.922017
1.315326
0.586351
1.241666
-0.064643
1.114354
1.432428
-0.145485
-0.693788
-1.119658
0.017915
-0.725438
-1.574980
-2.312159
0.026845
-1.083368
-2.524171
-1.848341
-2.923394
-0.621681
-1.372538
1.559161
0.860348
1.834112
0.099881
2.166643
2.997692
2.418337
1.370009
0.716317
-0.353783
3.155187
4.693009
5.353879
5.000552
3.532887
2.697809
1.248567
0.357581
-1.078483
-1.819508
-3.241128
-4.098187
-3.894111
-5.010897
-5.040139
3.132278
-1.623679
-2.532184
2.632867
2.594651
-6.121221
-6.118136
-7.001488
-4.159650
-5.948891
-2.521603
-2.169109
-1.832662
-5.117248
-3.726557
-1.286666
-1.448878
-2.683194
-1.118076
0.714347
0.912423
2.158894
3.129371
3.860281
5.277765
5.587248
5.027281
6.431371
4.990481
5.049138
1.510540
2.884016
2.958096
3.057122
1.553481
2.913979
-2.665817
-2.733570
-1.368726
-0.767637
-0.897018
-1.739993
-1.823467
-0.835492
-0.875463
0.228971
0.383759
1.414827
2.723750
3.518123
4.824194
-0.036109
-2.132360
3.157228
-4.098270
-2.149747
5.536717
6.456705
5.194921
5.293959
3.138030
4.146246
2.467978
3.155772
1.233413
-0.455541
1.041744
-2.984972
-2.088514
-2.327688
0.075291
-2.748542
-0.280857
1.016418
-0.146406
0.283831
-1.249622
-0.705370
-1.460323
-3.211406
-3.373311
-2.107819
-2.810401
-1.154755
-4.764442
-4.161321
-4.475450
6
______________________________________________________________________
MEP coordinate: 2.50 au
SOC (S0/T1) = 0.09 cm-1
SOC (S1/T1) = 0.08 cm-1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
x
y
z
0.983198
0.884865
0.441135
-0.949949
-1.114331
-0.240780
-0.394166
-0.419888
-0.532785
-0.439827
-0.348320
-0.248549
0.114243
0.139103
0.459061
-2.379103
-0.735683
0.449651
1.072187
2.264863
0.499044
0.725740
0.299570
0.693457
-0.099451
0.946692
1.107625
-0.451909
-0.480017
-0.362265
-0.425491
0.136020
-1.037697
-1.491242
-0.312129
-0.416137
-2.642615
-2.291409
-3.209375
-1.198792
-1.695343
1.141093
0.432187
1.845163
0.169105
2.358649
3.143402
2.277781
1.854201
1.318729
0.141594
4.060743
5.372230
5.158910
4.539059
3.387229
3.161084
2.015962
0.698221
-0.420628
-1.713776
-2.907103
-4.253093
-4.785407
-6.194158
-6.926921
2.593835
-0.191100
-3.907175
4.434626
3.295985
-8.242745
-8.736497
-8.795015
-6.447336
-6.761613
-4.447054
-3.102842
-3.470517
-4.983232
-2.823631
-1.758893
0.165871
-1.057203
0.532439
0.474711
2.243608
1.938261
1.994725
3.276067
4.189761
5.296143
4.513998
6.103400
5.878047
6.031182
2.375608
3.899689
3.034353
5.172802
3.585617
4.865637
-0.287712
0.513773
1.954598
1.972045
1.002997
-0.014177
-0.931389
-0.550698
-1.439820
-0.878845
-1.611120
-1.158002
0.098843
0.196852
1.344222
1.242336
-2.917553
1.279962
-1.779777
0.098694
1.376148
2.213083
0.567280
2.273497
-0.685904
2.073682
0.979540
1.695147
-1.913834
-2.681664
0.192113
-3.388520
-3.443016
-3.091843
0.496594
-1.980614
0.425164
2.145957
1.401751
2.971539
1.731086
2.477377
2.489083
0.477539
0.026591
-0.469297
-0.107588
1.150938
-1.924589
-2.408421
-2.137088
7
______________________________________________________________________
MEP coordinate: 5.06 au
SOC (S0/T1) = 0.16 cm-1
SOC (S1/T1) = 0.13 cm-1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
x
y
z
0.830237
0.872274
0.754146
-0.584561
-0.918817
-0.277166
-0.573165
-0.654575
-0.886101
-0.737080
-0.579854
-0.423869
0.214742
0.245375
0.814830
-2.089634
-1.265418
0.853532
0.590116
2.182605
0.873273
1.283760
0.500435
1.253190
-0.204259
1.693247
1.228317
0.139016
-0.873039
-0.579568
-0.724758
-0.384785
-1.833551
-1.880086
-0.457225
-0.620414
-2.525186
-1.797747
-2.868719
-0.612447
-1.385394
1.566031
0.833149
1.789859
0.053315
2.176803
2.983300
2.422802
1.290021
0.744848
-0.412814
3.173528
4.712183
5.353625
4.978596
3.507431
2.680551
1.256764
0.368433
-1.003612
-1.827409
-3.176013
-4.086092
-3.892704
-5.020825
-5.036712
3.105768
-1.640989
-2.582524
2.678136
2.617248
-6.123596
-6.090069
-6.999757
-4.158704
-5.935719
-2.730894
-2.051848
-1.941654
-5.051199
-3.687839
-1.295927
-1.896190
-2.546667
-0.978625
0.753036
0.839203
2.152928
3.074814
3.857805
5.257192
5.544012
5.030726
6.432578
5.021028
5.070896
1.531326
2.929083
2.959351
3.165307
1.610405
2.917016
-2.698057
-2.741807
-1.366359
-0.745893
-0.858218
-1.737724
-1.823572
-0.751585
-0.873557
0.322848
0.315326
1.474331
2.669928
3.581512
4.837447
0.009007
-2.186936
3.070662
-4.137286
-2.207887
5.613758
6.519627
5.318625
5.268202
3.235408
3.736725
2.206759
3.579015
1.313702
-0.629961
1.255688
-2.770757
-2.029196
-2.780206
0.232856
-2.809610
-0.253383
1.056070
-0.072833
0.304862
-1.220898
-0.721992
-1.447040
-3.232673
-3.361756
-2.189615
-2.870875
-1.207563
-4.807421
-4.247889
-4.478340
8
______________________________________________________________________
MEP coordinate: 7.65 au
SOC (S0/T1) = 0.28 cm-1
SOC (S1/T1) = 0.19 cm-1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
x
y
z
0.970923
0.864092
0.449946
-0.931657
-1.094453
-0.226549
-0.350890
-0.618249
-0.651643
-0.740496
-0.262098
-0.323099
0.169798
0.080680
0.477010
-2.353746
-0.583190
0.730435
1.024214
2.273160
0.460720
0.744833
0.152824
0.836082
-0.301892
1.549485
1.103347
-0.039971
-0.825343
0.227968
-1.148711
0.445766
-1.055599
-1.094530
-0.729371
-0.106442
-2.667985
-2.232150
-3.164768
-1.169262
-1.690279
1.166710
0.434516
1.815771
0.130317
2.375192
3.136400
2.308851
1.767547
1.309765
0.070758
4.072761
5.373630
5.139689
4.501908
3.348294
3.137181
2.001574
0.681713
-0.382054
-1.734688
-2.833481
-4.236019
-4.774850
-6.208229
-6.914771
2.551391
-0.173902
-3.921731
4.472916
3.327206
-8.248705
-8.714695
-8.820266
-6.417290
-6.771164
-4.409806
-2.979407
-3.707065
-4.899610
-2.700749
-1.838500
-0.105061
-0.993421
0.732228
0.444306
2.187673
1.947495
1.904216
3.233384
4.146943
5.247542
4.499996
6.078348
5.893271
6.026561
2.415940
3.949472
3.050452
5.250711
3.653054
4.865153
-0.293166
0.524619
1.970216
2.001366
1.036525
-0.000139
-0.901379
-0.549841
-1.458425
-0.932892
-1.575137
-1.106599
0.050541
0.214106
1.326345
1.289835
-2.951221
1.166355
-1.780915
0.061733
1.414997
2.246589
0.658881
2.205545
-0.620283
1.678979
0.790583
1.901637
-1.790670
-2.524047
0.055870
-3.294959
-3.473686
-3.244470
0.492227
-1.927900
0.451262
2.155327
1.525646
3.001370
1.766474
2.475880
2.513787
0.475743
0.056683
-0.520608
-0.151274
1.109331
-1.917624
-2.430983
-2.121866
9
______________________________________________________________________
MEP coordinate: 10.12 au
SOC (S0/T1) = 0.24 cm-1
SOC (S1/T1) = 0.34 cm-1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
x
y
z
0.809162
0.850030
0.748453
-0.587187
-0.927695
-0.282484
-0.560793
-0.819544
-0.984451
-1.050819
-0.507128
-0.555123
0.241691
0.148079
0.819362
-2.097128
-1.077559
1.120416
0.540279
2.172564
0.807563
1.300156
0.294686
1.418110
-0.468375
2.081197
1.304972
0.630685
-1.325031
0.044028
-1.453403
-0.092372
-1.616072
-1.605158
-0.807874
-0.455580
-2.597870
-1.783373
-2.829927
-0.609826
-1.389127
1.563688
0.831219
1.761093
0.023426
2.169678
2.957859
2.434021
1.217798
0.706040
-0.473362
3.169938
4.709565
5.346961
4.974673
3.505217
2.670883
1.246023
0.380124
-1.003714
-1.833515
-3.079535
-3.975153
-3.929810
-4.998653
-5.047197
3.114136
-1.669453
-2.732441
2.688957
2.614888
-6.090179
-6.065522
-6.919357
-4.222211
-5.841698
-3.018012
-2.152542
-2.081798
-4.728396
-3.450986
-1.386803
-1.880668
-2.603114
-1.046868
0.765056
0.799383
2.210184
2.994085
3.914522
5.250124
5.542868
5.017349
6.425803
5.018867
5.070114
1.528603
2.929566
2.953897
3.194329
1.625294
2.919616
-2.696831
-2.736625
-1.358909
-0.732183
-0.844112
-1.717936
-1.786679
-0.731921
-0.884428
0.299730
0.375020
1.549920
2.660252
3.620871
4.817453
0.030701
-2.235682
2.948737
-4.137172
-2.238955
5.653893
6.517216
5.448919
5.150762
3.357871
3.358905
2.055592
3.668196
1.505548
-0.472992
1.191734
-2.643816
-2.159222
-2.944594
0.270529
-2.754577
-0.283822
1.065119
0.021613
0.319502
-1.201934
-0.722197
-1.435752
-3.238810
-3.345241
-2.223699
-2.918584
-1.242979
-4.816625
-4.269467
-4.450869
10
S0/T1 ISC
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
0.883913
0.918243
0.565673
-0.854185
-1.151664
-0.367851
-0.657535
-0.608292
-0.848370
-0.715119
-0.830360
-0.794159
0.304241
0.074454
1.047992
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11
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