Threshold Photoelectron Spectrum of the Benzyl Radical
John D. Savee , Judit Zádora, Patrick Hembergerb, Balint Sztarayc, Andras Bodib, and David L.
Osborna,1
a
Combustion Research Facility, Mail Stop 9055, Sandia National Laboratories, Livermore, CA
94551-0969 USA
b
Paul Scherrer Institute, Villigen 5232, Switzerland
c
Department of Chemistry, University of the Pacific, Stockton, CA 95211 USA
a
Supplemental Online Material:
S1. Mass Spectra at 10.2 eV
S2. Threshold Photoelectron Spectrum of the Benzyl Radical
S3. Comparison of M06-2X and CASPT2 Franck-Condon Calculations
S4. CASPT2 Calculated Frequencies
S5. Effects of CH2 Orientation on Electronic Energies
1
Corresponding author; email: dlosbor@sandia.gov
1
S1. Mass Spectra at 10.2 eV
Figure S1. Mass spectra for bibenzyl at 300 K (pyrolysis off, black trace) and under pyrolysis
conditions (red trace) taken at a photon energy of 10.2 eV. Note that coincident photoelectrons of
all kinetic energies are used to produce these spectra.
2
S2. Threshold Photoelectron Spectrum of the Benzyl Radical
Table S1. Benzyl TPES obtained by pyrolysis of bibenzyl as discussed in the main text. Note that
raw data was shifted by +0.008 eV as discussed in the main text.
E (eV)
7.1078
7.1178
7.128
7.1381
7.1478
7.158
7.1677
7.1779
7.1878
7.1979
7.2075
7.218
7.2282
7.2383
7.248
7.2581
7.268
7.2782
7.2879
7.298
7.3082
7.318
7.3282
7.3377
7.3483
7.3582
7.3677
7.3774
7.3876
7.3982
7.4085
7.4183
7.4284
7.4375
7.4483
Intensity
(a.u.)
13.54
13.76
26.18
18.21
10.82
29.23
37.43
74.48
184.3
73.11
3.78
72.5
154.4
576.97
1778.21
893.21
-26.3
-83.79
46.1
88.63
600.18
1097.82
170.78
-32.22
-30.26
29.71
103.23
249.12
153.64
33.17
20.11
70.27
25.99
114.88
172.56
E (eV)
7.4581
7.4672
7.4775
7.488
7.4978
7.5071
7.5179
7.5278
7.538
7.5477
7.5578
7.5682
7.5783
7.5882
7.5977
7.6081
7.6183
7.6274
7.6382
7.6479
7.6582
7.6684
7.6786
7.6878
7.6981
7.7084
7.7178
7.728
7.7381
7.7486
7.7581
7.7679
7.7782
7.7875
7.7979
Intensity
(a.u.)
47.42
25.75
30.91
10.23
31.17
43.54
88.21
35.49
-18.68
-28.51
-44.08
24.06
38.99
19.41
18.75
11.75
-33.19
12.41
-8.1
36.27
-12.59
15.86
-15.75
-27.12
-0.59
1.91
6.89
-18.56
-30.62
-0.04
-23.25
9.86
5.65
-63.62
-12.59
E (eV)
7.8083
7.8176
7.8278
7.8378
7.8482
7.8587
7.8679
7.8775
7.8881
7.8985
7.908
7.9181
7.9279
7.9382
7.9484
7.9583
7.9679
7.9783
7.9878
7.9979
8.0081
8.0181
8.0282
8.0383
8.048
8.0581
8.0681
8.0778
8.0882
8.0982
8.1082
8.1173
8.1282
8.1375
8.1475
3
Intensity
(a.u.)
-11.22
7.99
-2.49
13.05
-47.02
14.73
-35.71
-39.23
1.66
13.24
18.38
-32.24
-7.49
-11.12
-8.33
31.43
30.71
42.14
13.19
23.38
42.8
6.45
-12.57
-7.55
-0.13
18.63
-21.56
22.54
38.11
14.55
13.78
23.03
-0.82
-3.34
24.66
E (eV)
8.1582
8.1678
8.1787
8.1878
8.1981
8.2075
8.218
8.2278
8.2383
8.2482
8.2585
8.2683
8.2781
8.2883
8.2986
8.3082
8.3178
8.3279
8.3383
8.3484
8.3582
8.3677
8.3786
8.3884
8.398
8.4081
8.418
8.4284
8.438
8.448
8.4576
8.4679
8.4776
8.4882
8.4981
Intensity
(a.u.)
6.88
-3
36.84
5.92
-29.72
36.46
-11.1
17.35
-9.19
14.98
40.88
38.84
-1.03
-19.46
38.18
-15.24
48.36
12.05
18.56
-1.38
19.46
36.94
46.94
73.31
8.56
-11.1
19.83
15.53
18.67
2.71
36.33
28.14
3
-32.06
36.65
E (eV)
8.5082
8.5177
8.5275
8.5373
8.5476
8.5584
8.5678
8.5777
8.5881
8.5976
8.6074
8.6175
8.6277
8.6384
8.6482
8.6578
8.6686
8.6789
8.6884
8.698
8.7081
8.7177
8.7285
8.7383
8.7479
8.7578
8.7681
8.7779
8.7878
8.798
8.8082
8.8182
8.8281
8.8381
8.8485
Intensity
(a.u.)
33.09
31.69
4.7
-11.48
57.53
70.98
14.58
79.84
42.48
52.98
83.73
37.83
24.91
55.93
32.73
100.41
10.91
2.49
82.51
60.81
41.18
84.28
21.48
7.77
110.16
68.25
42.11
-5.23
-7.78
94.27
67.56
62.01
51.79
45.5
10.5
E (eV)
8.8581
8.8683
8.8786
8.888
8.8979
8.9082
8.9169
8.9276
8.9373
8.9483
8.9579
8.9683
8.978
8.988
8.998
9.008
9.0183
9.0285
9.0385
9.0489
9.0582
9.0682
9.0776
9.0881
9.0979
9.1086
9.1168
9.1282
9.1384
9.1478
9.1583
9.1685
9.1782
9.188
9.1974
Intensity
(a.u.)
17.57
36.11
143.11
14.67
83.52
58.44
71.77
15.94
90.96
73.43
35.32
118.63
106.76
174.34
97.28
115.34
141.39
132.71
103.95
95.1
190.36
125.8
208.1
214.13
172.5
85.23
258.38
200.94
178.56
235.78
492.11
1216.1
1999.45
599.12
144.19
E (eV)
9.2084
9.2187
9.2274
9.2386
9.2489
9.2578
9.268
9.2785
9.2876
9.2974
9.3075
9.3175
9.3281
9.338
9.3482
9.3584
9.3677
9.3783
9.3881
9.3981
9.4087
9.4182
9.4282
9.4379
9.4487
9.4585
9.4681
9.4776
9.488
9.498
9.5081
9.518
9.5278
9.5376
9.5481
4
Intensity
(a.u.)
172.77
345.3
714.79
1520.3
647.06
-53.99
100.64
269.93
424.68
854.15
770.21
237.2
269.88
326.11
208.27
508.7
769.58
225.9
268.61
209.3
315
322.86
351.69
178.94
141.43
177.05
376.26
310.93
354.82
231.07
226.73
239.2
228.23
376.33
337.17
E (eV)
9.5579
9.5673
9.5774
9.588
9.5974
9.6077
9.6184
9.6285
9.6378
9.6477
9.6583
9.6686
9.677
9.6883
9.6977
9.7073
9.7182
9.728
9.7387
9.748
9.7581
9.768
9.7782
9.7885
9.7974
9.8082
9.8179
9.8279
9.837
9.8476
9.8579
9.8679
9.8784
9.8879
9.8977
Intensity
(a.u.)
284.33
331.04
274.3
317.41
299.89
423.5
655.47
266.94
315.18
354.92
378.94
410.98
655.65
391.06
331.36
479.94
434.12
453.73
527.88
467.99
512.52
553.35
541.83
518.44
635.43
637.55
514.59
345.15
345.86
295.76
328.64
485.7
263.69
261.7
217.93
E (eV)
9.9074
9.9187
9.928
9.9376
9.9489
9.9577
9.968
9.9773
9.9877
9.9973
10.0073
10.0185
10.0284
10.0387
10.0479
10.0583
10.0675
10.0785
10.0875
10.0985
10.1079
10.1172
10.1284
10.1381
10.1471
10.1575
10.1679
10.1784
10.1889
10.1993
10.2081
10.217
10.2283
10.2377
10.2481
Intensity
(a.u.)
167.65
94.33
255.08
130.9
174.11
15.47
17.19
41.69
142.3
82.5
110.5
77.6
54.84
-52.28
22.27
-13.5
20.99
72.86
-85.59
-75.51
-32.43
-24.87
-83.15
13.34
5.21
71.98
-11.27
100.04
113.73
101.41
19.43
97.35
-16.72
10.83
44.2
E (eV)
10.2577
10.2681
10.277
10.2877
10.2974
10.3088
10.3179
10.327
10.3378
10.347
10.3581
10.368
10.3796
10.3877
10.3984
10.4086
10.4194
10.4276
10.4379
10.4488
10.4592
10.4673
10.4786
10.4868
10.4971
Intensity
(a.u.)
-59.97
173.74
-36.02
27.06
-50.72
101.93
17.38
30.6
16.33
28.62
98.64
6.9
59.47
71.45
58.01
91.53
42.97
35.23
63.44
-7.49
25.16
143.37
136.63
-87.99
99.34
5
S3. Comparison of M06-2X and CASPT2 Franck-Condon Calculations
0.4
+
X <-- X
CASPT2
M06-2X
Intensity
0.3
0.2
0.1
0.0
-0.1
0.0
0.1
Photon Energy (eV)
0.2
0.3
Figure S2. Comparison of FCF derived intensities for the X +  X transition of benzyl using
CASPT2(6,6)/cc-pVDZ (blue) and M06-2X/6-311++G(d,p) (red) methods. The origin peaks
have been aligned at an energy of 0.0 eV.
0.25
+
a <-- X
CASPT2
M06-2X
Intensity
0.20
0.15
0.10
0.05
0.00
-0.1
0.0
0.1
Photon Energy (eV)
0.2
0.3
Figure S3. Comparison of FCF derived intensities for the a   X transition of benzyl using
CASPT2(6,6)/cc-pVDZ (blue) and M06-2X/6-311++G(d,p) (red) methods. The origin peaks
have been aligned at an energy of 0.0 eV.
6
S4. CASPT2 Calculated Frequencies
Table S2. CASPT2(6,6)/cc-pVDZ harmonic normal modes of the X state of the benzyl radical.
‘Mode Number’ follows the Mulliken convention.
Mode Number
MOLPRO Label
Symmetry
Freq. (cm-1)
1
35
a1
3255
2
33
a1
3237
3
31
a1
3222
4
30
a1
3201
5
29
a1
1616
6
27
a1
1525
7
26
a1
1493
8
22
a1
1307
9
21
a1
1182
10
18
a1
1036
11
17
a1
986
12
12
a1
830
13
6
a1
522
14
14
a2
922
15
11
a2
806
16
5
a2
495
17
3
a2
370
18
15
b1
923
19
13
b1
851
20
10
b1
709
21
9
b1
674
22
7
b1
592
23
4
b1
452
24
1
b1
193
25
36
b2
3317
26
34
b2
3244
27
32
b2
3225
28
28
b2
1597
29
25
b2
1480
30
24
b2
1418
31
23
b2
1335
32
20
b2
1170
33
19
b2
1112
34
16
b2
979
35
8
b2
613
36
2
b2
354
7
Table S3. CASPT2(6,6)/cc-pVDZ harmonic normal modes of the X + state of benzylium ion.
‘Mode Number’ follows the Mulliken convention.
Mode Number
MOLPRO Label
Symmetry
Freq. (cm-1)
1
35
a1
3278
2
33
a1
3252
3
31
a1
3246
4
30
a1
3192
5
29
a1
1710
6
27
a1
1584
7
25
a1
1498
8
23
a1
1386
9
21
a1
1209
10
17
a1
1023
11
14
a1
990
12
10
a1
825
13
5
a1
525
14
13
a2
985
15
11
a2
842
16
8
a2
637
17
2
a2
324
18
18
b1
1049
19
16
b1
1004
20
12
b1
974
21
9
b1
767
22
7
b1
597
23
4
b1
403
24
1
b1
167
25
36
b2
3313
26
34
b2
3276
27
32
b2
3249
28
28
b2
1593
29
26
b2
1544
30
24
b2
1467
31
22
b2
1345
32
20
b2
1198
33
19
b2
1133
34
15
b2
996
35
6
b2
594
36
3
b2
356
8
Table S4. CASPT2(6,6)/cc-pVDZ harmonic normal modes of the a  state of the benzylium ion.
‘Mode Number’ follows the Mulliken convention.
Mode Number
MOLPRO Label
Symmetry
Freq. (cm-1)
1
35
a1
3280
2
33
a1
3248
3
31
a1
3235
4
30
a1
3218
5
28
a1
1583
6
27
a1
1538
7
26
a1
1501
8
22
a1
1301
9
21
a1
1200
10
19
a1
1055
11
16
a1
974
12
11
a1
824
13
7
a1
509
14
17
a2
989
15
13
a2
874
16
6
a2
465
17
2
a2
295
18
15
b1
971
19
12
b1
840
20
10
b1
753
21
9
b1
722
22
5
b1
397
23
4
b1
361
24
1
b1
162
25
36
b2
3344
26
34
b2
3249
27
32
b2
3238
28
29
b2
1624
29
25
b2
1447
30
24
b2
1408
31
23
b2
1328
32
20
b2
1175
33
18
b2
1014
34
14
b2
943
35
8
b2
510
36
3
b2
345
9
Table S5. CASPT2(6,6)/cc-pVDZ harmonic normal modes of the A + state of the benzylium ion.
‘Mode Number’ follows the Mulliken convention.
Mode Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
MOLPRO Label
35
33
31
30
28
27
26
22
21
18
17
11
7
16
13
3
2
14
12
10
9
6
5
1
36
34
32
29
25
24
23
20
19
15
8
4
Symmetry
a1
a1
a1
a1
a1
a1
a1
a1
a1
a1
a1
a1
a1
a2
a2
a2
a2
b1
b1
b1
b1
b1
b1
b1
b2
b2
b2
b2
b2
b2
b2
b2
b2
b2
b2
b2
10
Freq (cm-1)
3284
3258
3235
3213
1590
1539
1486
1278
1201
1046
980
816
507
979
877
319
278
924
838
720
614
406
376
176
3345
3262
3236
1685
1430
1396
1347
1197
1047
958
604
346.68
Table S6. CASPT2(6,6)/cc-pVDZ harmonic normal modes of the b  state of the benzylium ion.
‘Mode Number’ follows the Mulliken convention.
Mode Number
MOLPRO Label
Symmetry
Freq. (cm-1)
1
35
a1
3274
2
33
a1
3260
3
31
a1
3250
4
30
a1
3208
5
28
a1
1682
6
26
a1
1481
7
25
a1
1461
8
22
a1
1232
9
20
a1
1137
10
18
a1
968
11
15
a1
941
12
11
a1
789
13
7
a1
504
14
17
a2
961
15
13
a2
828
16
5
a2
437
17
2
a2
170
18
14
b1
920
19
12
b1
809
20
10
b1
768
21
9
b1
717
22
6
b1
458
23
4
b1
373
24
1
b1
118
25
36
b2
3350
26
34
b2
3271
27
32
b2
3252
28
29
b2
2598
29
27
b2
1530
30
24
b2
1392
31
23
b2
1332
32
21
b2
1203
33
19
b2
1114
34
16
b2
954
35
8
b2
658
36
3
b2
337
11
S5. Effects of CH2 Orientation on Electronic Energies
In the present study electronic states of the benzyl radical and the benzylium ion were
investigated in C2v configurations in which the CH2 group attached to the phenyl ring was
oriented in planar and out-of-plane geometries. Using the atom labels in Fig. 4(a) of the main
text, these two configurations are related by simple rotation around the C1-C2 bond. Figure S4
presents a Walsh diagram correlating CASPT2(6,6)/AVTZ//CASPT2(6,6)/VDZ electronic
energies for the electronic states of benzylium in these two configurations, where 0 indicates the
planar configuration and 90 represents the out-of-plane configuration. Calculations include
orbital symmetries and the corresponding geometries were optimized to a stationary point in C2v
symmetry. States are labeled X + , a  , A + , b  , B , in order of increasing energy at their global
minimum. These labels do not change at different geometries, even though their relative energies
and irreducible representation may change. The correlation of planar and out-of-plane states
were tested by scans of the CH2 rotor, although lines in Fig. S4 do not represent these
intermediate electronic energies. Each state in Fig. S4 is represented by a particular symbol,
which is solid at the minimum energy configuration. Open symbols represent saddle points on
the PES (see comments on individual states below). Frequency calculations were done at the
same level of theory, but without orbital symmetries, a necessity for the numerical determination
of the Hessian.
Figure S4. Walsh diagram showing electronic energies for correlated electronic states of
benzylium with planar (0) and out-of-plane (90) CH2 configurations in C2v symmetry. Black
lines represent singlet states and blue represents triplet states. See text for further details.
12
Details of the calculations on planar and out-of-plane states are presented below but can be
summarized as follows: the X + , a  , and A + states have well-defined minima at planar
configurations, and the corresponding out-of-plane structures are saddle points; the B state has
a global minimum at the out-of-plane configuration with the planar configuration being a saddle
point; the PES for the b  state appears very flat along the CH2 rotor coordinate, and we
tentatively assign this state as having free-rotor-like behavior for the CH2 group.
X + 1A1 (): planar, minimum
The minimum energy structure of the ground state, confirmed by both DFT and CASPT2
calculations. The –CH2 rotor corresponds to a 625 cm-1 CH2 torsion normal mode.
X + 1A1 (): out-of-plane, saddle point
This configuration is a saddle point characterized at the M06-2X level by a 1509i cm-1 frequency
belonging to a normal mode in which the –CH2 group rotates around the C1-C2 bond. CASPT2
frequency calculations were not reliably obtained, likely because of the proximity of the B 1A2
state. However, they support that this out-of-plane geometry is a saddle point with an electronic
energy ~0.02 eV larger than that for the B state in this configuration.
a  3B2 (): planar, minimum
All calculations support this configuration as a minimum. The –CH2 rotor corresponds to a 465
cm-1 CH2 torsion normal mode.
a  3B1 (): out-of-plane, saddle point
CASPT2 calculations yield an imaginary frequency of 1259i cm-1 that is associated with the
–CH2 rotor.
A + 1B2 (): planar, minimum
This is a well-defined minimum with two normal modes containing –CH2 torsion character (277
and 319 cm-1).
A + 1B1 (): out-of-plane, likely saddle point
We could not obtain a consistent set of frequencies for this configuration, but both the overall
change in the potential energy and partial scans along the CH2 rotation coordinate suggest that
this is a saddle point.
b  3A1 (): planar, very flat potential
It was difficult to obtain convergence for frequency calculations on this state. Depending on the
details of the calculation, we get a minimum with a 437 cm-1 -CH2 torsion or a saddle point with
169i cm-1 corresponding to the same mode (and also a large imaginary frequency for a ring
distortion mode). The dependence of the electronic energy on the –CH2 rotor suggests that,
within numerical accuracy, this is a saddle point.
13
b  3A2 (): out-of-plane, saddle point
CASPT2 frequency calculations converge with an imaginary frequency (187i cm-1) that
corresponds to a –CH2 torsion mode. The dependence of the electronic energy on the –CH2 rotor
suggests that this configuration may be a minimum, so the presence of an imaginary frequency
likely reflects the relative flatness of the b  PES along this coordinate.
Scans of the b  electronic energy along the CH2 torsional mode were performed, and no C2
extrema were found between the C2v planar and out-of-plane geometries. The electronic energies
for the planar and out-of-plane structures differ by ~0.05 eV, which is close to the accuracy of
these calculations, even for internal rotational barriers. These observations indicate that the –CH2
group behaves as a (almost) free rotor. In Franck-Condon simulations for the b   X transition,
we employed the harmonic frequencies and geometry determined for the planar b  3A1 structure
and found that only one mode dominated the simulated spectrum, the ν12 stretching mode (789
cm-1). The frequency of this mode does not change significantly at planar or out-of-plane
configurations (789 cm-1 vs. 792 cm-1) nor do any other C-C and C-H bond lengths or bond
angles. Thus, the active modes predicted by the Franck-Condon simulations using the planar
configuration of the b  state should be relatively unaltered by the presence of the –CH2 freerotor.
B 1A1 (): planar, likely saddle point
This state is the second 1A1 state in the planar configuration. Although we were unable to obtain
a consistent set of frequencies, scans of the -CH2 rotation support that this is a saddle point.
B 1A2 (): out-of-plane, minimum
Calculated frequencies and scans along the –CH2 rotation coordinate suggest that this is a
minimum. The –CH2 rotor is coupled to several other normal modes and is best correlated with a
mode with a frequency of 3056 cm-1. We note that this frequency is surprisingly large and may
indicate that further calculations are necessary to fully characterize this state. However, because
its equilibrium geometry is far from that of neutral benzyl radical it is unlikely that transitions to
this state are observed in the TPES spectrum in the present work.
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