SUPPLEMENTARY MATERIAL
Equilibrium vs. Ground-State Planarity
of the CONH Linkage
Jean Demaison,a Attila G. Császár,b
Isabelle Kleiner,c and Harald Møllendald
a
Laboratoire de Physique des Lasers, Atomes et Molécules, UMR CNRS 8523, Université
de Lille I, 59655 Villeneuve d'Ascq Cedex, France, e-mail: jean.demaison@univ-lille1.fr
b
Laboratory of Molecular Spectroscopy, Institute of Chemistry, Eötvös University,
P.O. Box 32, H-1518 Budapest 112, Hungary, e-mail: csaszar@chem.elte.hu
c
Laboratoire Interuniversitaire des Systèmes Atmosphériques, Université de Paris XII, 61
avenue du Général De Gaulle, 94010 Créteil Cedex, France, e-mail: kleiner@lisa.univ-paris12.fr
d
Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway,
e-mail: harald.mollendal@kjemi.uio.no
Table of contents
Note that Table Sn in the Supplementary material corresponds to Table n (n = 1,…,9) of the
manuscript.
Table S1. Molecular structure of formamide, HCONH2, with distances (r) in Å and angles (∠)
in degrees.
Table S2. Structure of cyanamide, H2NCN, with distances (r) in Å and angles (∠) in degrees.
Table S3. Structure of acetamide, CH3C(O)NH2, with distances (r) in Å and angles (∠ and τ)
in degrees.
Table S4. Structure of urea, OC(NH2)2, with distances (r) in Å and angles (∠ and τ) in
degrees.
Table S5. Structure of carbamic acid, H2NCOOH, with distances (r) in Å and angles (∠ and
τ) in degrees.
Table S6. Computed Born–Oppenheimer equilibrium structures of methyl carbamate.
Table S8. Comparison between predicted and experimental rotational constants (in MHz) of
methyl carbamate.
Table S9. Computed equilibrium and experimental ground-state dipole moment components
(in debye) of methyl carbamate.
Table S17. Observed and calculated vibrational fundamentals (in cm−1) for methyl carbamate.
Table S18. Computed structures of dimethylether, (CH3)2O, distances (r) in Å and angles (∠)
in degrees.
2
rm(2)
SBR g
re
f
rs
e
reBO
MP2_AE
B3LYP
MP2_FC
CCSD(T)_AE
This work
CBSd
1.354
1.352
1.358(3)
1.361(4)
1.3547
1.3695
1.3608
1.3578
1.3547
1.3560
1.3565
1.3544
1.3547
1.3552
1.3543
1.3544
1.3517
1.3571
CCSD(T)_FC
VDZ
VTZ
VQZ
V(T/D)Z
VTZ
AVTZ
VQZ
VQZ
AVQZ
V(5,Q)Z c
wCVQZ
wCVQZ
VTZ
r(C–N)
Methoda
1.212
1.219
1.2139
1.210(4)
1.2097
1.2196
1.2140
1.2117
1.2106
1.2108
1.2120
1.2094
1.2132
1.2146
1.2134
1.2129
1.2107
1.2094
r(C=O)
1.003
1.002
1.0069 f
1.005(2)
1.0033
1.0153
1.0050
1.0043
1.0117
1.0029
1.0036
1.0024
1.0035
1.0043
1.0042
1.0035
1.0025
1.0064
r(NHs)b
1.000
1.002
1.0043 h
0.984(4)
1.0006
1.0124
1.0023
1.0017
1.0088
1.0002
1.0012
0.9997
1.0007
1.0016
1.0015
1.0008
0.9997
1.0038
r(NHa)b
1.097
1.098
1.106 h
1.112(3)
1.1001
1.1198
1.1025
1.1015
1.1087
1.0973
1.0973
1.0990
1.0992
1.0992
1.0994
1.0992
1.0977
1.105
r(CH)
125.0
124.7
124.61(10)
124.8(4)
124.63
125.03
124.89
124.71
125.01
124.95
124.79
124.73
124.74
124.62
124.65
124.74
124.74
125.02
∠OCN
119.3
118.5
119.4(16)
117.8(3)
119.18
119.02
119.22
119.20
119.22
119.25
119.28
119.21
119.19
119.25
119.20
119.18
119.16
119.41
∠CNHs
Table S1. Molecular structure of formamide, HCONH2, with distances (r) in Å and angles (∠) in degrees.
121.1
119.9
121.35(58)
121.8(5)
121.09
121.41
121.08
121.08
121.06
121.12
121.11
121.12
121.09
121.09
121.06
121.09
121.10
121.32
∠CNHa
112.3(20)
i
112.0
112.7
112.53
111.58
112.21
112.49
112.20
112.21
112.41
112.51
112.43
112.60
112.56
112.44
112.49
112.17
∠HCN
Assuming the validity of the following additive corrections: VQZ CCSD(T)_FC + [V(5,Q)Z – VQZ] MP2_FC + [wCVQZ MP2_AE – wCVQZ
VQZ on H atoms and V5Z on all other atoms.
s = syn (resp. a = anti) with respect to C=O bond.
FC = frozen-core approximation, AE = all electrons correlated.
i
h
g
f
e
Not determined.
Fixed at the MP2/6-311G(d,p) value.
SRB = semirigid bender model, Ref. 43.
Ref.. 6.
Ref. 3.
4
these improvements is also reported in Table 1.
MP2 level, and for the effects caused by the use of a more complete basis, estimated at the V(5,Q)Z MP2 level. The structure corresponding to
within the frozen-core approximation may be improved by correcting them for the effects of inner-shell correlation estimated here at the wCVQZ
order to estimate the effects of core correlation, the cc-pwCVQZ basis set was used at the MP2 level. The structural data for FA computed
decrease being as small as 0.0004 Å for the C–N bond length, whereas for the C=O bond length there is a negligible increase of 0.0002 Å. In
Improving the basis set from VQZ to V(5,Q)Z, again at the MP2 level, shows that convergence is practically achieved at the VQZ level, the
MP2 level, leads to an almost negligible change in the structural parameters, except for the C=O bond length, which is increased by 0.0014 Å.
the largest variation is observed for the C–N bond length, which is shortened by 0.0031 Å. Taking diffuse functions into account, at the AVQZ
MP2_FC]. Improving the basis set from VTZ to VQZ in the CCSD(T) optimizations shows that convergence in the structure is almost achieved,
d
c
b
a
Table S1 cont.
Table S2. Structure of cyanamide, H2NCN, with distances (r) in Å and angles (∠) in
degrees.
τf
Methoda
r(C≡N)
r(N–C)
r(N–H)
∠HNC
CCSD(T)_FC VDZ
1.1801
1.3736
1.0225
110.52 119.56
176.47
VTZ
1.1655
1.3577
1.0101
112.49 116.70
176.80
VQZ
1.1621
1.3531
1.0086
113.08 115.81
176.86
VQZ
1.1689
1.3471
1.0074
113.44 115.31
176.73
A'VQZ b
1.1694
1.3474
1.0081
113.57 115.20
176.75
V(5,Q)Z c
1.1685
1.3456
1.0077
113.76 114.82
176.84
wCVQZ
1.1685
1.3468
1.0075
113.44 115.33
176.74
MP2_AE
wCVQZ
1.1655
1.3433
1.0061
113.74 114.91
176.84
B3LYP
VTZ
1.1548
1.3407
1.0091
115.15 112.80
177.24
reBO
Best estimate d
1.1587
1.3482
1.0072
113.39 115.39
177.06
MP2_FC
SRBe
1.1645
rs h
1.160(5) 1.346(5)
1.3301(5) 0.9994
5
g
1.001(15) 115.6
∠NCN
g
174.8
112.0
180g
Table S2 cont.
a
FC = frozen-core approximation, AE =all electrons correlated.
b
cc-pVQZ on H and aug-cc-pVQZ on other atoms.
c
cc-pVQZ on H and cc-pV5Z on other atoms.
d
Assuming the validity of the following additive corrections: VQZ CCSD(T) +
[cc-pwCVQZ(AE) – cc-pwCVQZ (FC) + cc-pV(5,Q)Z – cc-pVQZ] MP2.
When
enlarging the basis from VTZ to VQZ, the largest variation at the CCSD(T) level is found
for the N–C bond length, which is shortened by 0.0046 Å. Improving the basis set from
VQZ to V(5,Q)Z, at the MP2 level, shows that convergence is practically achieved at the
VQZ level, the bond length decreases are as small as 0.0013 Å for the N–C bond and
0.0005 Å for the C≡N bond. Addition of diffuse functions at the VQZ MP2 level
increases the N–C and C≡N bond lengths by 0.0003 and 0.0005 Å, respectively. These
increases are quite small and, as they are expected to rapidly decrease with the size of the
basis set, they should be completely negligible at the V5Z level. The currently most
reliable equilibrium structural data for cyanamide, computed at the frozen-core VQZ
CCSD(T) level, may be improved by correcting them for the effects of inner-shell
correlation, estimated at the wCVQZ MP2 level, and for the effects caused by a more
complete basis, estimated at the V(5,Q)Z MP2 level, resulting in reBO of Table 2.
e
SRB = semirigid bender model, Ref. 49.
f
Dihedral angle (NCN, CNH).
g
Not given in the original work.
h
Ref.. 50.
6
Table S3. Structure of acetamide, CH3C(O)NH2, with distances (r) in Å and angles (∠ and τ) in
degrees.a
Parameter
f
r(NHs)
r(NHt) f
r(CN)
r(C=O)
r(CC)
r(CH1)
r(CH2)
r(CH3)
∠(HNH)
∠(CNHs)
∠(CNHt)
∠(NCO)
∠(NCC)
∠(OCC)
∠(CCH1)
∠(CCH2)
∠(CCH3)
∠(H1CH2)
∠(H1CH3)
∠(H2CH3)
τ(OCNHs)
τ(CCNHs)
τ(OCNHt)
τ(CCNHt)
τ(NCCH1)
τ(NCCH2)
τ(NCCH3)
τ(OCCH1)
τ(OCCH2)
τ(OCCH3)
MP2b
VTZ
VQZ
1.0045 1.0033
1.0017 1.0003
1.3668 1.3621
1.2193 1.2178
1.5109 1.5083
1.0845 1.0837
1.0892 1.0878
1.0875 1.0864
118.63 119.28
117.46 118.05
121.11 121.84
122.34 122.20
114.75 115.11
122.91 122.69
108.74 108.68
108.91 108.63
112.34 112.73
108.32 108.19
109.89 109.86
108.55 108.65
−9.13
−5.39
170.79 173.92
−169.92 −174.88
10.00
4.44
152.30 147.98
−89.86 −94.52
30.43
25.94
−27.78 −32.71
90.07
84.79
−149.64 −154.75
CCSD(T)c
V(T/D)Z
1.0115
1.0091
1.3641
1.2150
1.5081
1.0915
1.0974
1.0957
118.58
117.47
121.08
122.26
114.82
122.92
108.90
109.18
111.88
108.58
109.91
108.32
−9.08
170.99
−169.63
10.44
159.55
−82.04
37.86
−20.37
98.04
−142.07
7
re d
rg e
VTZ
1.003
1.000
1.362
1.216
1.509
1.082
1.086
1.085
119.28
118.05
121.84
122.20
115.11
122.69
108.68
108.63
112.73
108.19
109.86
108.65
−5.39
173.92
−174.88
4.44
147.98
−94.52
25.94
−32.71
84.79
−154.75
1.380(4)
1.220(3)
1.519(6)
122.0(6)
115.1(16)
123.0
Table S3 cont.
a
FC = frozen-core approximation, AE = all electrons correlated. The hydrogen H2 is
approximately perpendicular to the heavy-atom plane.
b
Frozen-core optimizations.
c
All-electron optimizations.
d
VQZ MP2 + offset corrections. The frozen-core VQZ MP2 level allows us to obtain
accurate X−H (X = C, N) bond lengths. The equilibrium structure was estimated using
the frozen-core VQZ MP2 structure and correcting, when necessary, the bond lengths by
a small offset. The offsets for the NH, CN and CO bond lengths have already been
discussed in Section 3.3. For the CH bonds, an offset of re – r[VQZ MP2] = 0.0013 Å
was used. For the CC bond, the offset was estimated to be 0.0008 Å from ethane, C2H6.39
The good agreement between the frozen-core VQZ MP2 (after offset corrections) and the
all-electron V(T,D)Z CCSD(T) distances between the heavy atoms indicates that the
derived bond lengths are likely to be reliable. On the other hand, the large variation of the
dihedral angles when improving the basis set from VTZ to VQZ in the MP2 optimization,
up to 5.6° for τ(CCNHt), shows that their accuracy is not better than a few degrees.
e
Ref. 56.
f
s = syn (resp. a = anti) with respect to C=O bond.
8
Table S4. Structure of urea, OC(NH2)2, with distances (r) in Å and angles (∠ and τ) in
degrees.a
Parameter
b
CCSD(T) c
MP2
rs
reBO
d
r(C=O)
1.2211
VTZ
1.2162
r(C−N)
1.3779
1.3856
1.3811
1.3834
1.3835
1.3814
1.3817
r(N−Hs)
0.9978
1.0060
1.0048
1.0138
1.0050
1.0038
1.0047
r(N−Ha)
1.0212
1.0059
1.0045
1.0137
1.0048
1.0037
1.0047
∠(OCN)
122.64
123.40
123.22
123.32
123.35
123.17
123.17
∠(CNHs)
119.21
116.28
117.06
116.03
116.16
116.73
116.73
∠(CNHa)
112.78
112.27
112.76
112.20
112.32
112.63
112.63
∠(NCNHs)
23.2
31.57
30.07
32.38
31.51
30.62
30.62
∠(NCNHa)
169.2
165.35
166.09
165.43
165.27
165.79
165.79
a
VQZ
1.2148
V(T,D)Z
1.2121
VTZ
1.2119
VQZ
1.2113
1.2116
The true equilibrium structure is expected to be close to the all-electron VQZ CCSD(T)
results, the computed bond lengths being slightly too short.35 From our work on
formamide (Tables 1 and S1), it may be concluded that the C=O and C−N bond lengths are
too short by 0.0003 Å and the NH bond lengths by 0.0009 Å. It is possible to check these
predictions using the frozen-core VQZ MP2 structure and correcting, when necessary, the
bond lengths by a small offset. For the N–H bond, the offset is approximately zero.[39]
For the C=O and C−N bonds, the offsets were determined in this work (see Sections 3.7
and 3.8): for the C–N bond, it is approximately zero, for the C=O bond, it is about –0.0023
Å. The MP2 and CCSD(T) calculations, after offset corrections, are in good agreement
and allow us to determine a reliable reBO that is given in Table 3.
b
c
d
Ref. 61.
All electrons correlated.
All-electron VQZ CCSD(T) + offset corrections, see text.
9
Table S5. Structure of carbamic acid, H2NCOOH, with distances (r) in Å and angles (∠ and
τ) in degrees.a
Parameter
r(C–N)
r(N–Hcis/=O)
r(N–Htrans)
r(C=O)
r(C–O)
r(O–H)
∠CNHcis
∠CNHtrans
∠HNH
∠N–C=O
∠N–C–O
∠O=C–O
∠C–O–H
∠O–C–N–Hcis
HF
VTZ AVQZ
1.3446
0.9887
0.9886
1.1878
1.3301
0.9437
117.85
120.39
119.87
125.47
111.33
123.19
107.70
7.64
1.3426
0.9879
0.9878
1.1871
1.3286
0.9427
118.37
120.91
120.35
125.38
111.44
123.18
107.92
3.40
VTZ
MP2
AVTZ
CCSD(T)a
B3LYP
VQZ V(T,D)Z VTZ AVTZ VTZ
1.3604
1.0021
1.0023
1.2105
1.3599
0.9655
116.06
118.59
118.40
126.02
110.20
123.75
104.56
14.79
1.3587
1.0029
1.0032
1.2128
1.3605
0.9670
116.69
119.21
118.98
125.95
110.27
123.75
105.02
12.92
1.3557
1.0008
1.0010
1.2088
1.3571
0.9639
116.72
119.27
119.11
125.97
110.31
123.70
104.94
12.54
1.3568
1.0091
1.0096
1.2070
1.3544
0.9722
116.37
118.84
118.67
125.88
110.50
123.60
104.90
13.72
1.3581
1.0009
1.0012
1.2066
1.3552
0.9630
116.16
118.63
118.38
125.90
110.48
123.60
104.88
14.57
1.3577
1.0014
1.0020
1.2076
1.3547
0.9634
116.38
118.85
118.66
125.86
110.42
123.70
105.43
14.00
1.3569
1.0025
1.0031
1.2083
1.3622
0.9654
117.58
120.40
119.48
125.88
110.62
123.49
105.77
9.10
∠O=C–N–Hcis −173.08 −176.92 −166.97 −168.63 −168.94 −167.84 −167.06 −167.65 −171.90
∠O–C–N–Htrans 172.02 176.49 165.19 167.39 167.59
∠O=C–N–Htrans
τ(NCOH)
τ(OCOH)
−8.70
−3.84 −16.57 −14.16 −13.90
165.88 165.22 166.18 170.93
−15.68 −16.41 −15.46 −10.07
−178.97 −179.52 −178.05 −178.12 −178.28 −178.10 −178.16 −177.74 −178.75
0.33
0.17
0.25
0.37
0.28
0.38
0.25
0.66
0.28
10
Table S5 cont.
a
In correlated level geometry optimizations all electrons were correlated. The
reBO equilibrium structure is practically identical to the all-electron VTZ CCSD(T) results of
column 8. The true equilibrium structure of CA is expected to be close to the all-electron
VTZ CCSD(T) results.35 As for urea, it is possible to check this point using the frozen-core
VQZ MP2 structure and correcting, when necessary, the ab initio bond lengths by a small
offset. For the N–H bond, the offset is approximately zero.38 For the CO and CN bonds,
the offsets were determined in this work (see Sections 3.7 and 3.8). For the C–N, C=O, and
C–O bonds they are approximately zero, –0.0023 Å, and –0.0017 Å, respectively. Finally,
for the O–H bond the offset is estimated to be approximately zero, based on work on formic
acid.85 These corrections confirm that the all-electron VTZ CCSD(T) structure is indeed
close to the true equilibrium structure, with an accuracy better than 0.003 Å.
11
Table S6. Computed Born–Oppenheimer equilibrium structures of methyl carbamate.
Parameter B3LYP B3LYP
VTZ AVTZ
N1−C2
1.363 1.361
N1−H9
1.003 1.003
N1−H10
1.004 1.003
C2=O3
1.209 1.210
C2−O4
1.356 1.356
O4−C5
1.433 1.435
C5−H6
1.089 1.088
C5−H7
1.089 1.088
C5−H8
1.086 1.086
C2N1H9
116.73 117.47
C2N1H10
119.42 120.16
H9N1H10
118.67 119.35
N1C2O3
125.33 125.23
N1C2O4
110.10 110.24
O3C2O4
124.56 124.52
C2O4C5
115.00 115.21
O4C5H6
110.75 110.65
O4C5H7
110.70 110.60
O4C5H8
105.55 105.48
H6C5H7
108.97 109.14
H6C5H8
110.44 110.48
H7C5H8
110.40 110.46
H9N1C2O3 13.12 10.18
H9N1C2O4 −168.25 −170.90
H10N1C2O3 167.39 170.41
H10N1C2O4 −13.98 −10.67
N1C2O4C5 −177.85 −178.22
O3C2O4C5
0.79
0.71
C2O4C5H6 −60.22 −60.34
C2O4C5H7 60.76 60.72
C2O4C5Hs −179.76 −179.84
BO b
MP2_FC
CCSD(T)_AE re
6-311a VTZ AVTZ
VQZ
V(D,T)Z
1.359 1.367
1.365
1.362
1.363
1.362
1.002 1.003
1.004
1.002
1.010
1.002
1.002 1.003
1.004
1.002
1.011
1.002
1.209 1.211
1.214
1.209
1.207
1.207
1.348 1.354
1.354
1.351
1.349
1.351
1.426 1.431
1.434
1.429
1.428
1.429
1.085 1.086
1.087
1.085
1.095
1.087
1.085 1.086
1.087
1.085
1.095
1.087
1.083 1.084
1.084
1.083
1.092
1.084
116.92 115.25 115.90 115.88
115.57
115.88
119.35 117.57 118.23 118.23
117.87
118.23
119.03 117.58 118.20 118.25
117.90
118.25
125.47 125.61 125.49 125.51
125.40
125.51
110.00 109.76 109.92 109.92
110.06
109.92
124.51 124.60 124.57 124.54
124.51
124.54
113.91 113.22 113.42 113.49
113.63
113.49
110.60 110.66 110.45 110.57
110.76
110.57
110.55 110.60 110.37 110.50
110.69
110.50
105.54 105.50 105.32 105.44
105.59
105.44
109.11 109.00 109.26 109.11
108.87
109.11
110.51 110.55 110.71 110.61
110.47
110.61
110.49 110.51 110.69 110.58
110.45
110.58
12.59 17.59
16.02
15.88
16.52
15.88
−168.83 −164.39 −165.79 −165.90
−165.25
−165.90
168.09 163.05 165.00 164.91
163.64
164.91
−13.33 −18.93 −16.81 −16.86
−18.12
−16.86
−177.93 −177.31 −177.30 −177.46
−177.39
−177.46
0.67
0.74
0.90
0.79
0.87
0.79
−60.44 −60.12 −60.36 −60.24
−60.40
−60.24
60.52 60.77
60.57
60.66
60.45
60.66
−180.01 −179.72 −179.93 −179.82
−179.99
−179.82
12
Table S6 cont.
a
b
6-311+G(3df,2p), all electrons correlated.
reBO of MC is obtained through the assumption that the re – r[VQZ MP2] offsets are
0.0013 and –0.0027 Å for the C–H and C=O bond lengths, respectively. For the bond
angles and for the other bond lengths the offsets were assumed to be negligible. The allelectron VTZ CCSD(T) level of theory is known to give results close to the equilibrium
structure for first row atoms.35 Comparison of the estimated equilibrium and the allelectron V(T,D)Z CCSD(T) structures is in agreement with this conclusion. Of course,
comparison of the X–H bond lengths is not truly meaningful, partly because the VDZ
basis set used for H is too small. The VQZ MP2 structure of MC presented in Table S6 is
likely to be accurate with the exception of the structure around N (particularly the
dihedral angles).
13
Table S8. Comparison between predicted and experimental rotational constants (in MHz) of
methyl carbamate.
Methoda
Exp.
A
v=0
∆A
b
10719.4
B
∆B
b
C
∆C
4399.1
3182.9
3.247
3.387
Semiexp. equil.d
ab initio equil.e
10801.5
10707.4
−0.77
0.11
4438.7 −0.90
4449.1 –1.14
3213.7 −0.97
3209.8 –0.85
RHF
3-21G*
10778.3
−0.55
4340.7
3154.6
VDZ
11066.7
−3.24
VTZ
11160.2
VDZ
MP2
MP2
∆c
b
0.89
3.342
3.112
4442.8 −0.99
3238.8 −1.76
3.381
−4.11
4453.6 −1.24
3249.2 −2.08
3.221
10509.3
1.96
4408.7 −0.22
3176.0
0.22
3.598
VTZ
10680.2
0.37
4442.0 −0.97
3204.5 −0.68
3.384
AVTZ
10730.3
−0.10
4367.7
3167.3
0.49
3.245
VQZ
10733.7
−0.13
4449.4 −1.14
3212.2 −0.92
3.335
6-311+G(3df,2p) 10762.4
−0.40
4452.4 −1.21
3214.9 −1.01
3.265
1.33
0.71
CCSD(T) V(T,D)Z
10755.2
−0.33
4444.1 −1.02
3212.2 −0.94
3.407
B3LYP VTZ
10722.8
−0.03
4375.8
0.53
3171.8
0.35
3.292
B3LYP AVTZ
10730.3
−0.10
4367.7
0.71
3167.3
0.49
3.245
10725.4
−0.06
4380.4
0.43
3172.0
0.34
3.165
10733.0
−0.13
4369.7
0.67
3167.1
0.63
3.171
B3LYP VTZ f
B3LYP AVTZ
a
f
The frozen-core approximation has been employed in the VDZ, VTZ, AVTZ, and VQZ
MP2 computations.
b
∆A
c
∆
d
Semi-experimental value of the equilibrium rotational constants, calculated employing
= A0 – Acalc.; ∆A = B0 – Bcalc.; ∆C = C0 – Ccalc, all in %.
= Ia + Ib – Ic (in uÅ2).
the measured ground-state rotational constants and vibrational averaging corrections
computed at the all-electron 6-31G* MP2 level.
e
Corresponding to reBO of Table 6.
f
Planar heavy-atom skeleton (Cs point-group symmetry).
14
Table S9. Computed equilibrium and experimental ground-state dipole moment
components (in debye) of methyl carbamate.a
µa
Method
µb
µc
µtot
0.163(2)
2.294(9)
0c
2.300(9)
VTZ
0.222
2.412
0.757
2.538
AVTZ
0.204
2.462
0.671
2.560
VQZ
0.238
2.459
0.673
2.560
MP2
6-31G*
0.115
2.089
0.862d
2.263
CCSD(T)
V(T,D)Z
0.234
2.215
0.710
2.338
CCSD(T)b
V(T,D)Z
0.435
2.354
0.0
2.394
B3LYP
VTZ
0.347
2.353
0.512
2.433
AVTZ
0.200
2.410
0.374
2.447
Exp.
MP2
a
All electrons have been correlated in the computations except VTZ, AVTZ, and VQZ
MP2.
b
Obtained at the optimized structure under the constraint of a planar heavy-atom
skeleton.
c
The fit performed as part of this study results in (µc)2 = –0.001.
d
The corresponding vibrationally averaged ground-state value, based on a normal-
coordinate expansion, is 0.573 D, significantly lower than the equilibrium value but still
far from zero.
15
Table S17. Observed and calculated vibrational fundamentals (in cm−1) for methyl carbamate.
Assignmenta
exp.b
NH2 antisym stretch
NH2 sym stretch
CH3 antisym stretch
CH3 sym stretch
C=O stretch
NH2 bending
3591
3474
exp.c
HF
6-31G*d
B3LYP
VTZe
3551
3435
2957
2874
1781 1747vs
1593 1583s
3554
3439
2990
2906
1785
1598
3642
3518
3008
2942
1764
1575
3740.1
3610.8
3118.7
3050.2
1790.9
1614.2
3770
3639
3229
3132
1874vs
1664s
3612
3496
3083
3011
1844
1619
7 CH3 antisym deform
1460vs
1475
1468
1502.9
1564
1527
8 CH3 sym deform
[1369]
1462
1443
1477.9
1527
1491
1345vs
1195
1108
1075s
1360
1203
1123
1076
1322
1185
1093
1059
1351.1
1214.7
1115.5
1083.8
1410vs
1244
1163
1119
1371
1218
1120
1093
13 H3C−O stretch
14 C=O rock
15 OCN deform
880
702
520
873
652
460
848
651
461
866.1
665.2
474.6
897
674
475
868
660
446
16
a"
17
18
19
20
21
22
23
24
COC deform
320s
282
294
291.0
423vs
−h
CH3 antisym stretch
CH3 antisym deform
CH3 rock
NH2 wag
C=O wag
2998
1447
1071
793
673
–
–
–
2980
1466
1161
784
511
276
165
126
3036
1448
1151
766
507
284
160
108
3147.4
1485.6
1178.1
785.1
523.1
225.3
163.1
112.8
3255
1550
1211
774
524
302
172
129
3110
1511
1187
729
515
300
163
111
a'
1
2
3
4
5
6
9
10
11
12
C−N stretch
OC-O stretch
NH2 rock
CH3 rock
203
16
B3LYP 6-31G* MP2
AVTZf Harm.g Anharm.
Table S17. cont.
a
Although the equilibrium structure of MC is not planar, its effective heavy-atom
skeleton in the ground-state is planar (see text); therefore, the original a’ and a” labeling
of Ref. 78, based on the assumption of Cs point-group symmetry, is maintained here.
b
Ref. 79. The infrared spectrum has been observed in the gas phase. Only five
fundamentals have been reported.
c
Ref. 78. Infrared spectra observed in solution and in different solvents.
d
All directly computed harmonic frequencies have been scaled, to account for model
deficiencies in the calculation and the neglect of anharmonicity, by a single scaling factor
of 0.8929.80
e
All directly computed harmonic frequencies have been scaled, to account for model
deficiencies in the calculation and the neglect of anharmonicity, by a scaling factors of
0.965 for CH stretching modes and 0.975 for all other modes.81
f
Directly computed, unscaled frequencies.
g
The strongest vibrations are denoted by vs = very strong.
h
Problem with the VPT2 treatment.
17
Table S18. Computed structures of dimethylether, (CH3)2O, distances (r) in Å and angles (∠)
in degrees.a
r(CO)
r(CHs)
r(CHa)
∠OCHs
∠OCHa
HaCOC
VTZ
1.4084
1.0858
1.0947 110.584 107.589
111.371
60.534
VQZ
1.4066
1.0846
1.0934 110.818 107.548
111.249
60.508
AVQZ
1.4085
1.0849
1.0937 110.826 107.488
111.128
60.497
V(Q,5)Z
1.4069
1.0848
1.0936 110.881 107.501
111.171
60.497
MT
1.4053
1.0843
1.0931 110.661 107.615
111.379
60.528
MT(ae) a
1.4025
1.0827
1.0915 110.753 107.665
111.397
60.527
CCSD(T) VDZ
1.4135
1.1035
1.1132 110.736 107.494
111.751
60.578
VTZ
1.4109
1.0889
1.0979 110.766 107.601
111.371
60.540
VQZ
1.4087
1.0878
1.0967 111.058 107.565
111.253
60.521
V(Q,5)Z b
1.4090
1.0878
1.0967 111.121 107.565
111.253
60.521
AVDZ
1.4271
1.1019
1.1107 110.775 107.204
111.112
60.586
AVTZ
1.4144
1.0896
1.0984 110.921 107.459
111.111
60.510
AVQZ c
1.4106
1.0881
1.0970 111.066 107.505
111.132
60.509
AV∞Z d
1.4089
1.0879
1.0968 111.066 107.515
111.132
60.509
1.4101
1.0884
1.0976 112.608 107.415
111.614
60.680
This work 1.4062
1.0862
1.0951 111.212 107.614
111.272
60.520
1.410(3) 1.091(7) 1.100(5) 111.7(4) 107.2(6)
110.8(4)
60.42
This work 1.408(3) 1.090(3) 1.097(1) 111.7(2) 107.2(2)
111.7(4)
59.7(4)
Method
MP2
B3LYP VTZ
re
e
rs
f
rm(2)
∠COC
a
Frozen core optimizations at the correlated levels. MT = Martin-Taylor basis.
b
V(Q,5)Z CCSD(T) = VQZ CCSD(T) + V(Q,5)Z MP2 – VQZ MP2.
c
AVQZ CCSD(T) = VQZ CCSD(T) + AVQZ MP2 –VQZ MP2.
d
Exponential extrapolation: r(n) = r(∞) + be–cn, n = D, T, Q.
e
V(Q,5)Z CCSD(T) + core correction computed at the MP2 level.
f
Ref. 86.
18