Supplementary data
The effects of two internal rotations in the microwave spectrum of
ethyl methyl ketone
Ha Vinh Lam Nguyena,b, Vinh Vana, Wolfgang Stahla, and Isabelle Kleinerb
a
Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, D-52074 Aachen,
Germany
b
Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), UMR 7583
(CNRS/Univ. Paris Est & Paris Diderot), Université de Paris Est, 61 avenue du Général de
Gaulle, F-94010 Créteil cedex, France
Corresponding author: Dr. Ha Vinh Lam Nguyen
Phone: +33 145 88 28 75
Email: lam.nguyen@lisa.u-pec.fr
1
Table S-1a: The rotational constants A, B, and C and the angles between the internal rotor
axis and the principal axes of inertia (i1,a), (i1,b), (i1,c) of the acetyl methyl group and (i2,a),
(i2,b), (i2,c) of the ethyl methyl group of conformer II calculated using various methods and
basis sets. All optimizations were performed at different levels of theory and the methods HF,
B3LYP, MP2, and CCSD using the Gaussian09 program package. Additionally, harmonic
frequency calculations were carried out to verify the nature of the stationary points.
Method/Basis set
HF/6-31G(d,p)
A
7.837
B
3.765
C
3.028
∠(i1,a)
54.95
∠(i1,b)
143.09
∠(i1,c)
100.12
∠(i2,a)
133.07
∠(i2,b)
90.69
∠(i2,c)
136.93
HF/6-31+G(d,p)
7.772
3.776
3.026
57.76
146.29
98.81
132.82
94.18
136.87
HF/6-31++G(d,p)
7.768
3.777
3.025
57.98
146.53
98.71
132.81
94.44
136.85
HF/6-311G(d,p)
7.813
3.778
3.034
56.65
145.03
99.33
132.89
92.71
136.98
HF/6-311+G(d,p)
7.774
3.785
3.031
58.59
147.23
98.41
132.79
95.08
136.76
HF/6-311++G(d,p)
7.773
3.786
3.031
58.65
147.29
98.39
132.78
95.14
136.76
HF/6-311++G(3df,2pd)
7.799
3.798
3.042
58.53
147.16
98.43
132.71
95.08
136.84
B3LYP/6-31G(d,p)
7.612
3.747
2.993
57.40
145.67
99.59
132.62
92.48
137.28
B3LYP/6-31+G(d,p)
7.589
3.743
2.984
59.21
147.76
98.63
132.71
94.86
136.88
B3LYP/6-31++G(d,p)
7.588
3.744
2.984
59.25
147.81
98.61
132.71
94.90
136.87
B3LYP/6-311G(d,p)
7.646
3.753
3.000
57.48
145.80
99.45
132.69
92.66
137.18
B3LYP/6-311+G(d,p)
7.614
3.759
2.996
59.67
148.28
98.41
132.68
95.27
136.84
B3LYP/6-311++G(d,p)
7.613
3.760
2.996
59.69
148.30
98.41
132.67
95.30
136.84
B3LYP/6-311++G(3df,2pd)
7.642
3.780
3.012
59.72
148.33
98.41
132.56
95.37
136.94
B3LYP/cc-pVDZ
7.608
3.745
2.992
57.43
145.71
99.56
132.71
92.33
137.20
B3LYP/cc-pVTZ
7.659
3.773
3.012
58.44
146.89
99.01
132.62
93.84
137.12
B3LYP/cc-pVQZ
7.654
3.778
3.013
59.25
147.81
98.61
132.60
94.83
136.99
MP2/6-31G(d,p)
7.649
3.798
3.030
54.87
142.64
101.08
132.28
88.82
137.70
MP2/6-31+G(d,p)
7.627
3.793
3.025
55.62
143.52
100.73
132.30
89.79
137.70
MP2/6-31++G(d,p)
7.619
3.796
3.026
55.89
143.81
100.65
132.24
90.04
137.76
MP2/6-311G(d,p)
7.599
3.808
3.037
56.45
144.43
100.47
131.90
90.44
138.10
MP2/6-311+G(d,p)
7.549
3.816
3.034
59.12
147.44
99.31
131.73
93.56
138.05
MP2/6-311++G(d,p)
7.545
3.817
3.035
59.17
147.49
99.31
131.68
93.60
138.09
MP2/6-311++G(3df,2pd)
7.567
3.866
3.066
61.11
149.64
98.53
131.24
95.84
138.16
MP2/cc-pVDZ
7.519
3.788
3.015
57.93
146.10
99.85
131.85
92.02
138.08
MP2/cc-pVTZ
7.578
3.860
3.066
59.81
148.17
99.15
131.32
94.21
138.36
MP2/cc-pVQZ
7.596
3.873
3.074
60.59
149.07
98.74
131.30
95.27
138.21
CCSD/6-311++G(d,p)
7.569
3.783
3.013
59.17
147.63
98.93
132.08
94.25
137.60
CCSD/cc-pVDZ
7.538
3.754
2.993
58.07
146.38
99.42
132.23
92.84
137.63
CCSD/cc-pVTZ
7.615
3.825
3.043
59.86
148.37
98.70
131.86
94.97
137.71
2
Table S-1b: The rotational constants A, B, and C and the angles between the internal rotor
axis and the principal axes of inertia (i1,a), (i1,b), (i1,c) of the acetyl methyl group and (i2,a),
(i2,b), (i2,c) of the ethyl methyl group of conformer III calculated using various methods and
basis sets. All optimizations were performed at different levels of theory and the methods HF,
B3LYP, MP2, and CCSD using the Gaussian09 program package. Additionally, harmonic
frequency calculations were carried out to verify the nature of the stationary points.
Method/Basis set
HF/6-31G(d,p)
A
7.820
B
3.852
C
2.930
∠(i1,a)
103.81
∠(i1,b)
13.82
∠(i1,c)
90.55
∠(i2,a)
44.00
∠(i2,b)
64.99
∠(i2,c)
123.45
HF/6-31+G(d,p)
7.805
3.853
2.936
104.22
14.24
90.74
44.29
65.35
124.06
HF/6-31++G(d,p)
7.803
3.852
2.937
104.37
14.39
90.78
44.33
65.48
124.21
HF/6-311G(d,p)
7.817
3.857
2.942
104.38
14.40
90.73
44.34
65.51
124.24
HF/6-311+G(d,p)
7.812
3.858
2.944
104.43
14.45
90.79
44.43
65.59
124.40
HF/6-311++G(d,p)
7.808
3.857
2.945
104.61
14.64
90.85
44.49
65.76
124.60
HF/6-311++G(3df,2pd)
7.826
3.863
2.955
105.20
15.23
90.99
44.59
66.24
125.10
B3LYP/6-31G(d,p)
7.748
3.799
2.868
101.36
11.36
90.09
42.67
64.06
121.18
B3LYP/6-31+G(d,p)
7.732
3.799
2.873
101.89
11.89
90.30
42.99
64.34
121.78
B3LYP/6-31++G(d,p)
7.736
3.798
2.872
101.82
11.83
90.27
42.93
64.27
121.65
B3LYP/6-311G(d,p)
7.750
3.809
2.884
102.12
12.13
90.31
43.12
64.62
122.17
B3LYP/6-311+G(d,p)
7.748
3.813
2.889
102.12
12.12
90.37
43.23
64.65
122.31
B3LYP/6-311++G(d,p)
7.744
3.813
2.890
102.25
12.26
90.41
43.29
64.78
122.49
B3LYP/6-311++G(3df,2pd)
7.760
3.827
2.908
102.95
12.97
90.61
43.59
65.39
123.33
B3LYP/cc-pVDZ
7.760
3.794
2.861
101.00
11.00
89.95
42.30
63.74
120.48
B3LYP/cc-pVTZ
7.764
3.822
2.903
102.92
12.94
90.57
43.43
65.34
123.12
B3LYP/cc-pVQZ
7.761
3.826
2.909
103.14
13.15
90.66
43.62
65.54
123.49
MP2/6-31G(d,p)
7.736
3.863
2.916
100.59
10.60
90.46
43.57
64.54
122.60
MP2/6-31+G(d,p)
7.696
3.867
2.928
101.45
11.48
90.86
44.24
65.24
123.92
MP2/6-31++G(d,p)
7.689
3.866
2.930
101.67
11.71
90.94
44.36
65.46
124.23
MP2/6-311G(d,p)
7.714
3.871
2.922
100.19
10.20
90.35
43.87
64.38
122.79
MP2/6-311+G(d,p)
7.673
3.877
2.938
101.15
11.18
90.80
44.61
65.28
124.35
MP2/6-311++G(d,p)
7.667
3.877
2.939
101.30
11.33
90.84
44.69
65.41
124.54
MP2/6-311++G(3df,2pd)
7.727
3.904
2.961
101.52
11.55
90.81
44.70
65.49
124.61
MP2/cc-pVDZ
7.681
3.834
2.892
100.13
10.13
90.23
43.36
64.34
122.19
MP2/cc-pVTZ
7.760
3.897
2.946
100.63
10.64
90.49
44.02
64.75
123.28
MP2/cc-pVQZ
7.780
3.910
2.957
100.87
10.89
90.54
44.14
64.84
123.48
CCSD/6-311++G(d,p)
7.676
3.852
2.919
101.64
11.66
90.60
44.38
64.94
123.83
CCSD/cc-pVDZ
7.673
3.812
2.878
100.81
10.81
90.14
43.33
64.15
122.00
CCSD/cc-pVTZ
7.778
3.876
2.929
101.02
11.03
90.26
43.70
64.30
122.54
3
Table S-2: Geometry parameters in the principal inertial axes of conformer I, II, and III of
ethyl methyl ketone calculated at the MP2/6-311++G(d,p) level of theory. The atoms are
numbered according to Figure 1.
Conformer I
C1
O2
C3
H4
H5
H6
C7
C8
H9
H10
H11
H12
H13
Conformer II
Conformer III
a /Å
b /Å
c /Å
a /Å
b /Å
c /Å
a /Å
b /Å
c /Å
0.507201
0.428960
1.840622
1.967441
2.653093
1.869795
–0.726304
–2.033237
–2.888184
–2.070816
–2.123991
–0.688922
–0.624073
0.094081
1.311521
–0.623929
–1.034179
0.073402
–1.462752
–0.792847
–0.023044
–0.701123
0.493731
0.732836
–1.328025
–1.565189
–0.022231
–0.022968
0.049329
1.057414
–0.157934
–0.652258
–0.080582
0.066178
0.001203
1.028141
–0.716456
–1.039361
0.692625
0.520319
0.974263
1.296857
1.587860
2.189847
0.668774
–0.877069
–1.899256
–2.913152
–1.855584
–1.701089
–0.930453
–1.088027
0.118807
1.217952
–1.158754
–1.588315
–0.951749
–1.897493
–0.034388
–0.130789
–0.228335
0.768856
–0.998255
–0.929687
0.844402
0.115998
–0.159873
–0.129208
0.835918
–0.719828
–0.637025
0.690082
–0.453846
–0.057308
–1.073267
–1.090873
1.318721
1.305415
–0.553596
–1.392073
–0.850854
–0.402575
–1.930058
–0.419350
0.842316
1.933513
2.919033
1.780039
1.941979
0.981204
0.894154
–0.105770
–0.927393
1.382292
1.890700
1.539148
1.820081
–0.518393
0.120267
–0.250389
–0.127039
1.208904
–0.212876
–1.609037
0.083251
–0.252252
0.060896
0.919474
0.046003
–0.845673
0.513852
–0.356509
–0.063181
–1.411329
–0.257000
1.558837
0.466487
Table S-3a: Fourier coefficients of the potential function for a rotation of the entire ethyl
group around the dihedral angle φ1 = ∠(O2,C1,C7,C8) calculated in 1° steps using different
methods and the 6-311++G(d,p) basis set (see Figure 2). The potential is expanded as
15
V( )  a 0   a n cos(n  ) .
n 1
a0
a1
a2
a3
a4
a5
a6
a7
a8
a9
a10
a11
a12
a13
a14
a15
MP2/6-311++G(d,p)
Hartree
cm−1
–231.850313975
–0.001115520 –244.8
0.000105036
23.1
–0.000613297 –134.6
0.000093505
20.5
–0.000171030
–37.5
0.000115516
25.4
0.000044774
9.8
0.000012300
2.7
–0.000017366
–3.8
0.000042894
9.4
–0.000003669
–0.8
–0.000003019
–0.7
0.000008842
1.9
0.000014369
3.2
–0.000009811
–2.2
B3LYP/6-311++G(d,p)
Hartree
cm−1
–232.541194036
–0.001214411
–266.5
–0.000178029
–39.1
–0.000521105
–114.4
–0.000004982
–1.1
–0.000098689
–21.7
0.000105058
23.1
0.000024452
5.4
–0.000013445
–3.0
0.000007877
1.7
0.000022591
5.0
–0.000007900
–1.7
0.000002065
0.5
0.000012319
2.7
0.000001745
0.4
0.000001396
0.3
HF/6-311++G(d,p)
Hartree
cm−1
–231.059834886
–0.001403667
–308.1
–0.000025244
–5.5
–0.000652321
–143.2
0.000018988
4.2
–0.000126662
–27.8
0.000116813
25.6
0.000037989
8.3
–0.000012946
–2.8
–0.000001200
–0.3
0.000028056
6.2
–0.000005553
–1.2
–0.000002964
–0.7
0.000010691
2.3
0.000003071
0.7
–0.000005083
–1.1
4
Table S-3b: Fourier coefficients of the potential function for a rotation of the acetyl methyl
group around the dihedral angle φ2 = ∠(O2,C1,C3,H4) calculated in 1° steps using different
methods and the 6-311++G(d,p) basis set (see Figure 5). The potential is expanded as
15
V( )  a 0   a n cos(n  ) .
n 1
a0
a3
a6
a9
a12
a15
MP2/6-311++G(d,p)
Hartree
cm−1
–231.851605777
–0.000303480
–66.6
0.000103680
22.8
0.000015073
3.3
0.000006936
1.5
0.000002798
0.6
B3LYP/6-311++G(d,p)
Hartree
cm−1
–232.542863062
–0.000258887
–56.8
0.000071577
15.7
0.000007194
1.6
0.000002433
0.5
–
HF/6-311++G(d,p)
Hartree
cm−1
–231.061553203
–0.000382224
–83.9
0.000080420
17.7
0.000007773
1.7
0.000002698
0.6
–
Table S-3c: Fourier coefficients of the potential function for a rotation of the ethyl methyl
group around the dihedral angle φ3 = ∠(C1,C7,C8,H9) calculated in 1° steps using different
methods and the 6-311++G(d,p) basis set (see Figure 6). The potential is expanded as
15
V( )  a 0   a n cos(n  ) .
n 1
a0
a3
a6
MP2/6-311++G(d,p)
Hartree
cm−1
–231.849871444
0.002030712
445.7
0.000098425
21.6
B3LYP/6-311++G(d,p)
Hartree
cm−1
–232.541549247
0.001603272
351.9
0.000093824
20.6
HF/6-311++G(d,p)
Hartree
cm−1
–231.059744819
0.002175349
477.4
0.000074312
16.3
5
Table S–4: Coefficients of the two–dimensional Fourier expansion for the energy potential
surface calculated at the MP2/6–311++G(d,p) and B3LYP/6–311++G(d,p) level of theory in a
grid of 10° (Figure 3 and 4). Due to symmetry, only data points in the range from φ1 = 0° to
25
180° and φ2 = 0° to 120° are needed. The potential is expanded as V(1 ,  2 )   Vi f i .
n 1
i
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
MP2/6–311++G(d,p)
fi
Vi/Hartree
1
–231.8493904
cos(1φ1)
–0.0012296
cos(2φ1)
–
cos(3φ2)
–0.0008500
cos(3φ1)
–0.0009740
cos(4φ1)
–0.0001477
sin(1φ1)sin(3φ2)
–0.0000485
cos(1φ1)sin(3φ2)
–0.0000041
cos(1φ1)cos(6φ2)
–0.0000080
sin(1φ1)sin(6φ2)
–0.0000259
cos(2φ1)cos(3φ2)
–0.0001072
cos(2φ1)sin(6φ2)
–0.0000022
sin(3φ1)sin(3φ2)
–0.0002509
sin(4φ1)sin(3φ2)
–
cos(3φ1)sin(3φ2)
–0.0000041
sin(3φ1)sin(6φ2)
–0.0000512
sin(4φ1)sin(3φ2)
–0.0002086
sin(4φ1)sin(6φ2)
–0.0000084
cos(4φ1)sin(6φ2)
–0.0000022
cos(5φ1)cos(3φ2)
–0.0001249
cos(5φ1)sin(3φ2)
–0.0000041
cos(5φ1)cos(6φ2)
–0.0000245
sin(6φ1)sin(3φ2)
–0.0000937
sin(6φ1)sin(6φ2)
–0.0000189
cos(6φ1)sin(6φ2)
–0.0000022
B3LYP/6–31G(d,p)
Vi/Hartree
–232.5404295
–0.0012619
–0.0001332
–0.0007179
–0.0008660
–0.0001399
–
–
–
–0.0000261
–0.0000586
–
–0.0002642
–0.0001300
–
–
–
–
–
–0.0000699
–
–
–0.0000591
–
–
6
Table S-5: Observed AA (A), AE (E2), EA (E1), EE (E3), and EE*(E4) species frequencies
(Obs.) of ethyl methyl ketone. Obs.  Calc. values as obtained after a fit with XIAM (a) and
BELGI-Cs-2tops (b).
J Ka Kc
upper level
1 1
0
J Ka Kc
lower level
1 0 1
1
1
1
0
0
0
2
0
2
1
0
1
2
1
1
1
1
0
2
1
1
2
0
2
2
1
2
1
0
1
2
1
2
1
1
1
2
2
0
1
1
0
2
2
0
1
1
1
2
2
0
2
1
1
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
EA
EE
EE*
AA
AE
AA
AE
EA
Obs.
Obs.  Calc. Obs.  Calc.
GHz
kHz a
kHz b
7.0360231
30.2
7
7.0355596
27.8
5
7.0363796
25.6
4
12.3257383
–6.7
–3
12.3256903
–5.6
–2
12.0226182
–18.1
–2
12.0229768
–16.6
–2
12.0221691
–16.9
–1
12.6049800
–3.4
–2
12.6049744
–3.9
–3
12.5991344
1.5
–1
12.5991344
1.5
–2
12.5991344
12.6
9
13.5411337
–3.2
–3
13.5411337
5.0
4
13.3901063
–15.5
–2
13.3903042
–13.0
–2
13.3899015
–11.3
1
7.7686606
–1.6
–1
7.7686104
–1.5
–1
7.8269941
12.2
6
7.8267262
9.3
2
7.8271524
7.7
2
17.8189373
–7.4
–3
17.8188888
–6.5
–2
17.6643924
–9.7
–3
17.6645441
–5.8
0
17.6641501
–8.9
–3
11.8380003
–5.4
–3
11.8380003
–2.9
–1
11.9834907
8.4
–4
11.9832883
14.0
2
11.9836950
11.4
–1
32.1664213
25.1
1
32.1656484
24.9
2
32.1668986
26.4
1
32.4195907
–10.6
–4
32.4194523
–14.5
–8
18.0268849
–9.7
–2
18.0267603
–9.7
–1
18.7763146
40.6
3
7
2
2
0
2
1
1
2
2
1
1
1
0
2
2
1
1
1
1
2
2
1
2
1
2
3
0
3
2
0
2
3
0
3
2
1
2
3
1
2
2
1
1
3
1
2
3
0
3
3
1
3
2
0
2
3
1
3
2
1
2
3
2
1
2
1
1
3
2
1
3
1
2
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
EA
EE
EE*
AA
AE
EA
18.7753464
18.7769991
31.4834070
31.4832491
31.4289323
31.4294194
31.4281646
20.4969770
20.4968160
19.4454439
19.4461319
19.4444682
18.7013165
18.7013061
18.6929380
18.6929209
13.4873587
13.4873938
13.6276724
13.6275256
13.6278976
20.2558691
20.2558691
20.1981200
20.1982040
20.1980172
9.3232265
9.3231741
9.3321760
9.3319945
9.3322520
22.9204430
22.9203978
22.8191584
22.8192101
22.8190015
17.7064850
17.7064850
17.7538993
17.7538044
17.7539867
37.9862285
37.9852756
37.9868815
17.1382505
17.1381127
17.7881081
39.9
38.7
–13.1
–12.3
–0.7
2.1
1.0
–7.5
–10.3
–6.1
–10.9
–12.4
0.0
–2.6
2.0
–1.2
3.0
3.0
5.2
10.4
13.2
–12.6
–0.6
–8.1
–3.9
–7.9
–0.2
1.5
2.1
3.3
5.0
–7.3
–4.7
–4.8
–5.3
–16.6
–4.2
–0.1
5.4
6.0
6.9
35.7
34.1
36.8
–8.3
–14.7
43.8
6
2
–5
–4
0
1
0
–2
–5
6
–1
0
2
–1
–1
–5
2
1
–7
–3
–2
–11
–1
–1
1
–3
–2
0
5
3
8
0
2
–1
–2
–12
–1
3
0
0
0
0
–1
0
0
–5
1
8
3
2
1
3
1
2
3
2
2
2
1
1
3
2
2
2
1
2
3
2
2
2
2
1
3
2
2
3
1
2
3
2
2
3
1
3
3
3
0
3
2
1
3
3
1
3
2
2
4
0
4
3
1
3
4
1
3
3
2
2
4
1
3
4
0
4
4
1
4
3
0
3
4
2
2
4
1
3
EE
EE*
AA
AE
EA
EE
EE*
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
AA
AE
EA
EE
EE*
AA
AE
EA
EE*
AA
17.7870749
17.7888625
36.9764814
36.9763314
35.8682476
35.8693338
35.8669021
38.6299724
38.6306401
38.6290326
19.0342198
19.0342198
15.6701266
15.6711171
15.6688854
21.8246985
21.8245480
20.8760831
20.8768332
20.8750442
31.6690901
31.6692719
32.1177042
32.1169436
32.1179990
32.0814527
32.0808068
31.1322954
31.1325975
31.1315277
20.3597672
20.3597963
20.4417166
20.4416546
20.4418348
10.1755240
10.1756164
11.6404423
11.6403873
11.6271443
11.6269953
11.6271666
27.7405462
27.7405104
27.6643827
27.6642976
16.3549333
41.0
41.8
–11.5
–13.2
–30.7
–14.1
–33.6
–19.3
–7.5
–9.4
10.4
8.1
–23.6
–23.2
–25.6
–6.8
–5.0
–14.7
–16.5
–18.3
–29.9
–28.5
–26.8
–24.8
–25.0
–28.5
–25.0
57.8
55.1
52.8
–0.7
0.5
5.5
6.2
7.5
20.5
–7.4
1.4
6.0
–2.0
–3.7
–7.6
–9.0
–0.3
–10.7
2.8
–6.9
2
1
–1
–3
–3
11
–5
–7
1
2
12
9
–2
–2
–2
–3
–1
4
–1
0
–20
–19
4
7
6
–19
–13
10
8
6
1
0
–3
–3
–3
15
–16
–1
1
5
0
–2
1
9
–7
7
2
9
4
2
2
4
1
3
4
2
3
4
1
3
4
2
3
4
1
4
4
3
1
4
2
2
4
3
2
4
2
3
5
0
5
4
1
4
5
1
4
4
2
3
5
1
4
5
0
5
5
1
5
4
0
4
5
2
3
5
1
4
5
3
2
5
2
3
AE
EA
EE
EE*
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
AA
AE
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
16.3548034
16.7664708
16.7655369
16.7671440
14.3833228
14.3841315
14.3822692
23.6161846
23.6160337
22.9140159
22.9146617
22.9130744
31.1209421
31.1207730
31.8152465
31.8143520
31.8156678
32.3016808
32.3013828
31.1050946
31.1037594
27.0746462
27.0746706
27.1265031
27.1264864
27.1265740
18.2872423
18.2873532
19.0131986
19.0123997
19.0142073
14.8287808
14.8287174
14.8007224
14.8005902
32.4373657
32.4373275
15.9511395
15.9510193
16.1358960
16.1352194
16.1363274
30.1714544
30.1712376
31.0529527
31.0517857
31.0536384
–10.8
36.5
35.1
37.3
–18.1
–20.3
–21.0
–6.3
–2.2
–15.7
–14.4
–18.2
–17.1
–14.9
–18.1
–20.8
–19.3
–18.1
–19.1
48.5
46.8
–4.5
0.9
9.1
21.1
13.7
3.4
6.2
14.1
17.7
20.0
1.7
4.1
–0.6
–3.8
–7.7
–6.4
–3.6
–5.7
21.5
19.7
18.9
–13.1
–11.1
–8.1
–15.3
–10.4
–1
–1
1
1
–1
–3
–2
–4
–1
3
0
0
–6
–2
5
5
5
–8
–8
3
4
0
3
5
16
7
1
–1
–2
0
0
–3
–4
7
–1
4
6
4
4
0
0
0
0
3
2
–1
1
10
5
3
3
5
2
4
6
0
6
5
1
5
6
1
5
5
2
4
6
1
5
6
0
6
6
1
6
5
0
5
6
2
4
5
3
3
6
2
4
6
1
5
6
2
5
6
1
6
6
3
3
6
2
4
6
3
4
6
2
4
6
3
4
6
2
5
7
0
7
6
1
6
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
EA
EE
AA
AE
EA
EE
EE*
AA
AE
AA
AE
EA
EE
EE*
AA
AE
AA
AE
EA
EE
EE*
EA
EE
EE*
AA
AE
EA
EE
EE*
AE
32.7286641
32.7284106
31.3427329
31.3434458
31.3415672
33.5320163
33.5320361
33.5641127
33.5640929
33.5641490
26.5473372
26.5474383
27.0000092
26.9995069
27.0007066
18.8914159
18.8913393
18.8492001
18.8490918
37.1703242
37.1702931
37.1226238
37.1226033
37.1225704
9.9894292
9.9896714
16.1707540
16.1706419
16.2307680
16.2303167
16.2309958
28.5967356
28.5965727
28.8382637
28.8380387
29.7242236
29.7228513
29.7251191
26.6473823
26.6490122
26.6453140
33.4383498
33.4381113
32.0500697
32.0509964
32.0486902
39.7162112
–8.3
–12.7
38.6
37.6
35.5
–10.5
–1.9
2.0
–1.7
0.3
–5.2
0.1
3.8
9.3
15.2
4.6
4.3
–5.4
6.3
–9.2
–5.3
–5.2
–11.5
–5.4
3.1
11.6
–1.9
–3.2
3.1
3.2
2.2
4.1
9.8
–4.7
–4.4
–1.1
–6.5
–3.7
14.2
17.0
8.9
–7.3
–9.0
29.9
27.1
21.9
–9.8
3
–1
4
0
2
–2
5
1
–5
–3
–3
–3
–4
–1
0
–1
–6
1
7
6
9
4
–3
4
2
5
6
5
0
–1
1
4
7
8
12
–4
–2
–5
0
1
–2
5
4
4
–2
–3
2
11
7
7
0
1
7
6
6
6
1
2
6
5
7
1
6
7
0
7
7
2
5
6
3
4
7
2
5
7
1
6
7
2
6
6
3
3
7
2
6
7
1
7
7
3
5
7
2
5
7
3
5
7
2
6
8
1
7
8
0
8
8
2
6
8
1
7
8
2
7
7
3
4
8
2
7
8
1
8
8
3
5
7
4
4
8
3
6
8
2
6
8
3
6
8
2
7
EA
AA
AE
EE*
AA
AE
EA
EE
EE*
AA
AE
AA
AE
EA
EE
EE*
AA
AE
AA
AE
EA
EE
EE*
AA
AE
EA
EE
EE*
AA
AE
AA
AE
EA
EE
EE*
AA
AE
AA
AE
EA
EE*
AA
AE
EA
EE
EE*
AA
39.7341959
34.8172324
34.8173194
35.1002299
23.6977609
23.6976713
23.6385719
23.6384631
23.6385195
18.5824360
18.5826577
17.2035540
17.2034602
17.2097830
17.2094559
17.2098930
9.8989056
9.8991142
31.7542735
31.7540947
24.8151234
24.8165222
24.8132898
34.5006922
34.5004628
33.2975923
33.2985709
33.2961757
29.0155853
29.0154834
19.1901314
19.1900370
19.1747467
19.1745009
19.1748029
14.2182521
14.2184549
35.3082733
35.3080914
35.0790168
35.0787472
8.8009026
8.8013135
22.5529148
22.5539978
22.5514040
35.9727850
0.4
–13.6
–7.6
6.2
0.1
1.9
–11.2
–0.2
–0.5
–8.9
–2.4
–2.6
6.2
–4.6
–9.1
–12.0
0.5
3.2
6.3
6.4
20.0
18.7
15.2
–5.8
–1.4
15.2
19.1
13.8
–6.0
4.5
–7.6
–5.8
–15.3
–13.0
–16.9
–3.3
–2.4
4.2
11.7
–16.5
–9.5
–12.8
–2.3
18.7
15.8
9.8
–17.8
2
–5
–5
–2
–4
–9
–4
2
0
–3
–4
7
15
7
–1
1
2
3
7
3
0
–3
0
9
13
–4
–6
–5
–7
–4
8
6
3
0
1
0
–1
5
8
–3
0
2
5
–1
–3
–3
0
12
8
9
3
2
6
7
8
9
2
1
7
8
9
2
8
8
3
5
9
3
6
8
4
4
9
3
6
8
4
5
9
3
6
9
2
7
9
3
7
8
4
4
EE*
AA
AE
EA
EE
AA
AE
EA
EE*
EA
EE*
AA
AE
AA
EA
EE
EE*
AA
AE
35.0644665
22.2143499
22.2142606
22.1895109
22.1893257
17.5154810
17.5156767
16.9337546
16.9327040
15.6675876
15.6667497
16.9276382
16.9279857
24.6445340
24.8405001
24.8395706
24.8410276
12.7640798
12.7643487
5.2
–15.2
–12.9
–18.5
–3.9
–5.0
–4.6
–18.2
–19.2
71.4
80.8
–36.2
–27.4
–15.1
–15.4
–18.8
–18.0
–16.1
–8.3
–8
9
6
–2
6
–4
–3
14
15
–7
–4
–6
–7
1
–15
–14
–16
–4
–1
Figure S-F1: A spectrum showing the AA and AE species of the 221 ← 212 transition of ethyl
methyl ketone with their hyperfine structures (see text). The line width is approximately
20 kHz (FWHH). For this spectrum 165 FIDs were co–added.
13
Figure S-F2: An enlarged scale in the range from φ1, φ2 = 60° to +60° of the potential
surface of ethyl methyl ketone obtained by rotating the ethyl group and the acetyl methyl
group calculated at the MP2/6–311++G(d,p) level of theory. A clearly double minimum was
observed.
Figure S-F3: An enlarged scale in the range from φ1, φ2 = 60° to +60° of the potential
surface of ethyl methyl ketone obtained by rotating the ethyl group and the acetyl methyl
group calculated at the B3LYP /6–311++G(d,p) level of theory. Here, the double minimum is
smoother than by using the MP2/6–311++G(d,p) level of theory.
14