Large amplitude vibrations of acetyl isocyanate, methyl cyanoformate, and acetyl cyanate

Samira Dalbouha and María L. Senent *
Departamento de Química y Física Teóricas, Instituto de Estructura de la Materia, CSIC, C/Serrano, 121, 28006 Madrid, Spain. E-mail:

Received 16th July 2018 , Accepted 19th September 2018

First published on 19th September 2018

The far infrared region of three detectable molecules sharing the empirical formula C3H3O2N, acetyl isocyanate CH3CONCO (AISO), methyl cyanoformate NC–COOCH3 (MCN) and acetyl cyanate CH3COOCN (ACN), is explored using explicitly correlated coupled cluster ab initio methods and a variational procedure designed for non-rigid species and large amplitude motions. The three isomeric forms display two conformers, cis and trans, of Cs symmetry that intertransform through the torsion of the central bond. This internal rotation interacts with the methyl group torsion generating a ground electronic state potential energy surface of six minima. Accurate rotational constants, centrifugal distortion constants, potential energy barriers, and surfaces, as well as, the low energy levels and their splittings, are provided. Far infrared energies are calculated up to 600 cm−1 which represent excitations of the torsional and the skeletal bending modes. Below 410 cm−1, 28, 14 and 20 vibrational energy levels and their splittings have been identified and classified for acetyl isocyanate, methyl cyanoformate, and acetyl cyanate, respectively. All the methyl torsion barriers are relatively low (∼300 cm−1) generating relevant tunneling effects. Computed spectroscopic parameters can help further interpretation and assignments of experimental rotational spectra using effective Hamiltonians.


So far, more than 160 different species have been detected in the interstellar medium (ISM), of which some thirty can be classified as prebiotic non-rigid organic molecules.1,2 Their spectra at low temperatures are dense and complex because they present various minima in the ground electronic state potential energy surfaces that intertransform through large amplitude vibrations (LAMs). Transitions among their low vibrational energy levels can contribute to the spectral confusion of the astrophysical surveys. However, they have attracted many astronomical efforts focused to their localization and to identify their formation channels because many of these species can be related to the problem of the origin of life. During the last years, special attention has been given to the search of organic cyanides and isocyanides reaching the identification of ∼50 different species, some of them present non-rigidity.3–9

The discovery of new chemical compounds and the interpretation of the recent radioastronomical observations require a previous laboratory characterization.10 Medium sized organic molecules imply the laboratory measurement of rotational spectra in the millimeter, submillimeter and microwave regions. Accurate assignments based on appropriate effective Hamiltonians are mandatory.11 In the case of non-rigid species, theoretical models must assume the intertransformation of the different minima through large amplitude vibrations, such as internal rotation or inversion modes, whose presence causes observable tunneling effects.12,13 The energy levels split into various components in the relatively low barriers which separate the equilibrium structures. Tunneling effects generate unexpected vibrationally averaged structures of the secondary conformers with relevant effects on the rotational constants.14 In addition, LAM energy levels are very low and can be populated at the low temperatures of the “hot cores” in regions of interstellar formation.1 For this reason, abundant organic species (i.e. methyl formate) were detected in vibrationally excited states.15–17

For the interpretation of the rotational spectra, a previous map of the low vibrational energy levels and their splitting components derived from far infrared spectroscopy or from highly correlated ab initio calculations, can be extremely helpful.13,18,19 This is the main objective of the present paper, where the far infrared region of three detectable molecules, acetyl isocyanate CH3CONCO, (AISO), methyl cyanoformate NC–COOCH3 (MCN), and acetyl cyanate CH3COOCN (ACN) is explored using state-of the art ab initio methods. The three species represent isomeric forms obeying the C3H3O2N empirical formula. We take into consideration that, in extraterrestrial sources, the existence of sets of isomeric forms is evident. In general, excluding diatomic species, ∼30% of all interstellar molecules have observed isomeric counterparts.20

The C3H3O2N isomers, contemplated in this paper, could represent a new step of the search of complex astrophysical cyanides and isocyanide. In recent works, we provided spectroscopic parameters for various C2H3ON isomers and their isotopologues.9,12,21 We considered five different compounds methyl isocyanate, methyl cyanate, methyl fulminate, acetonitrile N-oxide, and glycolonitrile. In the last case, whose search resulted in a non-detection, the recorded rotational spectrum was interpreted with the help of theoretical calculations.12 So far, a unique C2H3ON isomer, methyl isocyanate, has been detected.22,23 This species displays a very complex spectrum because the rotational constants are strongly dependent on the skeletal bending vibrations.12 For this case and for other species which assignments are extremely risky for unexpected causes, very accurate ab initio calculations and appropriate models can be crucial tools for their interpretation. In general, the explicitly correlated coupled cluster theory (CCSD(T)-F12) employed in the present paper24,25 provide very accurate and helpful structures and parameters.13,26 The employed variational model provides accurate values of the transitions, splittings and potential energy barriers of non-rigid molecules.12

To our knowledge, previous works on C3H3O2N isomers are unusual perhaps because they are really toxic species and, with the exception of isocyanates, they offer few technical applications. For acetyl cyanate, structural and spectroscopic studies are not available. In 1993, Krutules et al.27 measured the Raman and infrared spectra of acetyl isocyanate and performed ab initio calculations. Their main interest was to determine the relative stability the two conformers suggesting an energy difference of 433 cm−1. The microwave spectrum of the most stable cis-conformer was first analyzed by Landsberg and Iqbal in 1980,28 determining the rotational parameters for the A and E methyl torsional components of the ground vibrational state. The V3 barrier and the dipole moment components μa, and μb were established to be 356 cm−1 (1018 ± 15 cal mol−1), 0.95 D, and 1.48 D.28 The geometric structure of acetyl isocyanate29 was determined from electron diffraction intensities and previous microwave rotational constants.28 Very recently, in 2009, Uchida et al.30 observed the microwave spectra of two isotopic species (13CH3C(O)NCO and CD3C(O)NCO) in the frequency range from 26.5 to 40 GHz. They determined the energy difference between conformers in 1049 cm−1.

Methyl cyanoformate (MCN) is notoriously known for being an ingredient in dangerous cyanide-based pesticides. For the first time, the barrier of the methyl internal rotation (1172 ± 30 cal mol−1 ∼ 410 cm−1) was measured by Williams et al. in 197131 from the splittings of the microwave lines. They established the torsional fundamental at 181 cm−1. They observed the dipole moment to be 4.23 ± 0.04 D. Finally, in 1992, Durig et al.32 measured and assigned the microwave spectra of seven isotopic species in the frequency region between 26.5–40.0 GHz. The V3 barrier and the dipole moment components μa and μb were established to be 406.6 cm−1, 4.17 D, and 0.71 D. They obtain the rotational constants to be A0 = 9553.449(42) MHz, B0 = 2465.7289(67) and C0 = 1983.268 2(60) MHz.

Theoretical background, results and discussion

Theoretical background

The equilibrium structures and the potential energy surfaces were calculated with explicitly correlated coupled cluster theory, CCSD(T)-F12b,24,25 implemented in MOLPRO33 using the corresponding default options. Furthermore, full-dimensional anharmonic force fields were computed with second order Möller–Plesset theory (MP2) implemented in GAUSSIAN.34 These force fields were applied to determine the vibrational corrections of the surfaces and the anharmonic contributions,35 which are less dependent on the level of theory that the first order spectroscopic properties. For the CCSD(T)-F12 calculations, the cc-pVTZ basis set atomic orbitals36 were employed in connection with the corresponding basis sets for the density fitting and the resolution of the identity. The aug-cc-pVTZ basis set (denoted by AVTZ)37 was used in the MP2 calculations. Before the selection of the basis sets, we achieved several tests we different methodologies. We realize that the employed basis sets for the most expensive calculations reduce the computation time without losing accuracy.

The three isomeric structures, AISO (acetyl isocyanate), MCN (methyl cyanoformate) and ACN (acetyl cyanate) present two dissimilar equilibrium geometries, cis and trans, that intertransform through the torsion of the N–COCH3 (AISO), the C–OCH3 (MCN) and the O–COCH3 (ACN) bonds, respectively. Two torsional motions, the CH3 group torsion (θ) and the central bond torsion (α) are responsible for the non-rigidity generating ground electronic state potential energy surfaces of six minima. The torsional coordinates θ and α can be computed from the dihedral angles with the equations:

θ = (H1C2XY + H2C2XY + H3C2XY)/3 − 180°(1)
α = C3YXC2 − 180°(2)
where X and Y represent the atoms C1 and N of AISO, O1 and C1 of MCN, and C1 and O1 of ACN, respectively. Fig. 1 can help to understand the labelling of the atoms.

image file: c8cp04490b-f1.tif
Fig. 1 The structure of the three C3O2H3N isomers.

All the six mentioned minimum energy structures can be classified in the Cs symmetry group and the three isomers in the G6 Molecular Symmetry Group (MSG). On the base of the vibrational energies, the two torsional motions can be separated from the high frequency modes. On the base of the symmetry of the vibrational normal modes, the two torsions can be separated from the remaining large amplitude vibrations because internal rotations are “out-of-plane” motions whereas other existing low frequency modes are “in-plane” skeletal bending modes. Then, to determine variationally the torsional energies, the following Hamiltonian can be applied:38,39

image file: c8cp04490b-t1.tif(3)

In this equation, Veff(θ,α) represents the effective potential given by:

Veff(θ,α) = V(θ,α) + V′(θ,α) + VZPVE(θ,α)(4)
where V(θ,α) is the ab initio two-dimensional potential energy surface determined from the CCSD(T)-F12b energies of a set of selected geometries. The Podolsky pseudopotential V′(θ,α) and the Bij(θ,α) kinetic energy parameters were determined from the chosen geometries using the ENEDIM code.40VZPVE(θ,α) represents the zero point vibrational energy correction, which was determined at the MP2 level of theory within the harmonic approximation.41

The torsional energies were calculated variationally using ENEDIM.40 To achieve a full description of the far infrared region, the low vibrational energies related to the in-plane large amplitude vibrations, are also provided. The levels corresponding to the skeletal bending modes were determined using second order perturbation theory and the MP2 anharmonic force fields. This approximation allows predict possible displacements of the levels due to Fermi interactions and to deliberate the validity of the variational two-dimensional model.

Equilibrium geometries and equilibrium rotational constants

In Table 1, the CCSD(T)-F12b energies and equilibrium rotational constants, as well as, the MP2 dipole moments corresponding to the two planar conformers cis and trans of the three isomeric forms AISO, MCN and ACN, are shown. The most stable structure, cis-AISO (cis-acetyl isocyanate) is the reference for relative energies. For cis-MCN and cis-ACN, the vibrationally corrected relative energies E+ZPEr were computed to be 7312 cm−1 and 7716 cm−1, respectively, after determining the zero point vibrational energies (ZPE) using the anharmonic fundamentals. Although cis-ACN has not attracted previous scientific interest, both cis-structures present similar stabilities and comparable probabilities for detection in gas phase sources. Furthermore, electric properties support the significance of cis-ACN (μ = 6.0267 D) with respect to cis-AISO and cis-MCN which permanent dipole moments were determined to be 2.9360 D and to be 4.0713 D, respectively. trans-AISO dipole moment is also relevant.
Table 1 CCSD(T)-F12 total electronic energies (E, in Hartrees), relative energies between isomers ER and conformers cis and trans, (Er, in cm−1), equilibrium rotational constants (in MHz), dipole moments (in D), and torsional energy barriers (in cm−1)
Acetyl isocyanate Methyl cyanoformate Acetyl cyanate
cis image file: c8cp04490b-u1.tif image file: c8cp04490b-u2.tif image file: c8cp04490b-u3.tif
E −320.943359 −320.910369 −320.907464
E R 0 7241 7878
E +ZPEr 0 7312 7716
A e 10792.4808 9638.5775 10528.2506
B e 2230.3598 2469.1112 2487.2961
C e 1869.6444 1990.2155 2037.3159
μ 2.9360 4.0713 6.0267
trans image file: c8cp04490b-u4.tif image file: c8cp04490b-u5.tif image file: c8cp04490b-u6.tif
E −320.940648 −320.902577 −320.904396
E r 595 1710 673
A e 9631.1852 4760.9319 9144.2075
B e 2312.6668 3976.7398 2653.2468
C e 1886.6997 2197.0872 2082.9325
μ 3.0379 3.8999 6.0267

Acetyl isocyanate Methyl cyanoformate Acetyl cyanate
Calc. Exp. Calc. Exp.
V cis 3 352 35628 393 406.632 256
V trans 3 391 316 525
V cis→trans 1005 4081 2351
V trans→cis 410 2371 1678

Table 1 displays the internal rotation barriers corresponding to the two torsional modes. The cis → trans processes represented in Fig. 2, are restricted by energy barriers of 1005 cm−1 (AISO), 4081 cm−1 (MCN), and 2351 cm−1 (ACN). All of them are too high to endure the intertransformation at the interstellar temperatures. Thus, the cis and trans conformers can coexist in the same gas source as different species as occur with other organic targets such as methyl formate for which various rotamers were detected independently.41 The cis → trans barriers of methyl formate (4826 cm−1)14 and methyl cyanoformate are of the same order of magnitude.

image file: c8cp04490b-f2.tif
Fig. 2 One dimensional cuts of the potential energy surfaces corresponding to the cis → trans intertransformation processes.

The six equilibrium structures show low methyl torsional barriers V3 (see Fig. 3). In the cases of cis-AISO and cis-MCN, for which previous works are available, the theoretical parameters compare well with the experimental data.28,32 The Vcis3 and Vtrans3 were computed to be 352 and 351 cm−1 (AISO), 393 and 316 cm−1 (MCN), and 256 and 525 cm−1 (ACN) which are of the order of magnitude of the methanol (378 cm−1),42 acetone (247 cm−1),43 or cis-methyl formate (368 cm−1).14 Important torsional splittings can be expected.

image file: c8cp04490b-f3.tif
Fig. 3 The methyl torsional barriers (in cm−1).

Table 2 collects the ground vibrational state rotational parameters which are compared with previous experimental data.28,32 The centrifugal distortion constants are parameters of the A-reduction Hamiltonian (Ir representation). The ground vibrational state rotational constants A0, B0 and C0 were computed form the corresponding equilibrium parameters (Ae, Be and Ce) using the following equation:9,12,13

B0 = Be (CCSD(T)-F12) + ΔBcoree (CCSD(T)) + ΔBvib (MP2)(5)
where ΔBvib represents the vibrational contribution to the rotational constants derived from the VPT2 αri vibration–rotation interaction parameters determined using the MP2 cubic force fields, and ΔBcoree contains the effect of the core-electron correlation. For cis-AISO and cis-MCN, the computed values are in a very good agreement with the available laboratory data. As was previously observed in studies of similar molecular species,9,13 the agreement is extremely good for B0 and C0 and good for A0. In our previous study of methyl isocyanate,9 we found an important vibrational dependence on the rotational constants with the skeletal bending modes. This effect makes arduous the assignments but it is not so relevant in acetyl isocyanate, which presents a “more standard” behavior. However, the effect of the ν14 mode on the rotational constants of cis-AISO and trans-AISO and of ν13 on the parameters is not negligible.

Table 2 Ground vibrational state parameters of the A-reduction Hamiltonian (Ir). Rotational constants computed from the CCSD(T)-F12 equilibrium parameters. Centrifugal distortion constants computed with MP2 and VPT2
Acetyl isocyanate
cis trans
This work Exp.28 This work
A 0 (MHz) 10745.992 10773.160 (0.025) 9494.9218
B 0 (MHz) 2229.071 2222.693 (0.005) 2314.1985
C 0 (MHz) 1865.250 1862.934 (0.005) 1881.5012
Δ J (kHz) 0.2166 0.4882 (0.0414) 0.2601
Δ K (kHz) 145.9015 10.5489 (5.5544) 44.0303
Δ JK (kHz) 21.0598 8.6492 (0.2429) 20.3698
δ J (kHz) −0.0394 0.0728 (0.0028) −0.0188
δ K (kHz) 5.7139 5.0906 (0.2451) 6.866058

Methyl cyanoformate
cis trans
This work Exp.32 This work
A 0 (MHz) 9529.469 9553.449(42) 4768.4847
B 0 (MHz) 2469.533 2465.7289(67) 3941.0526
C 0 (MHz) 1984.344 1983.2682(60) 2186.1218
Δ J (kHz) 0.1771 0.40(10) 2.7267
Δ K (kHz) 13.8906 5(13) 11.2063
Δ JK (kHz) 6.1230 2.40(11) −9.5818
δ J (kHz) 0.0346 0.115(23) 1.2728
δ K (kHz) 3.1429 −0.0(12) −0.3811

Acetyl cyanate
cis trans
This work This work
A 0 (MHz) 10471.1929 9038.0379
B 0 (MHz) 2483.8046 2645.7936
C 0 (MHz) 2031.5229 2072.3682
Δ J (kHz) 0.2559 0.3444
Δ K (kHz) 30.6729 6.5900
Δ JK (kHz) 0.0004 8.0233
δ J (kHz) 0.0061 0.0498
δ K (kHz) 3.5587 3.5108

Potential energy surfaces of reduce dimensionality

The two-dimensional potential energy surfaces (2D-PES) were computed using 26 geometries selected for different values of the H1C2XY and C3YXC2 dihedral angles (H1C2XY = 0, 90, 180, −90°; C3YXC2 = 0, 30, 60, 90, 120, 150 and 180°) (see eqn (1) and (2)). In all the geometries, the remaining internal coordinates were allowed to be relaxed. For efficiency, the selected structures were optimized at the CCSD(T)-F12 level of theory and, later on, the energies were vibrationally corrected using MP2. The energies were fitted to double Fourier series:
image file: c8cp04490b-t2.tif(6)

The expansion coefficients resulting potential energy surfaces (Fig. 4), are shown in Table 3:

image file: c8cp04490b-f4.tif
Fig. 4 The 2D-PES of acetyl isocyanate.
Table 3 Expansion coefficients of the one-dimensional potentials (in cm−1)
A cc mn
0 0 875.087 2756.493 1705.913
0 1 −268.508 −581.618 −230.857
0 2 −369.671 −1675.182 −1036.482
0 3 −34.832 −235.416 −179.727
0 4 −2.668 104.187 20.921
0 5 1.345 16.616 5.941
0 6 1.871 −7.561 2.659
3 0 −200.574 −181.223 −212.232
3 1 12.870 7.697 26.706
3 2 14.470 54.248 39.296
3 3 −2.332 −26.573 39.145
3 4 1.218 −53.133 −21.390
3 5 −0.211 −0.097 6.039
3 6 0.074 3.847 −0.452
6 0 6.220 −3.210 −2.913
6 1 2.299 0.261 3.320
6 2 −0.791 −4.839 −8.216
6 3 0.160 0.437 2.333
6 4 −0.017 −3.687 6.025
6 5 −0.177 0.059 1.293
6 6 −0.094 −1.854 −4.699
A ss mn
3 1 −32.757 20.905 −42.727
3 2 −22.162 −38.899 −57.270
3 3 0.643 18.453 −62.114
3 4 −2.130 51.550 21.513
3 5 −0.980 4.106 8.519

Totally symmetric double Fourier series (see eqn (7)) were also employed for the linear fitting kinetic energy parameters Bθα(θ,α). The Acc00 independent coefficients are shown in Table 4.

Table 4 A cc00 coefficients of the AISO, MCN, and ACN independent terms of the torsional kinetic energy parameters (in cm−1)
A cc00(Bθθ) 5.5552 5.9415 5.5443
A cc00(Bαα) 1.6581 1.3812 1.0070
A cc00(Bθα) −0.1788 −0.8244 −0.1489

Although multidimensional models have been developed,11 commonly, rotational spectroscopists employ effective Hamiltonians depending on a single large amplitude motion (1D) for assignments treating independently the different conformers. To help future assignments performed with these popular tools, we provide the one-dimensional potential energy surfaces (1D-PES) depending on the methyl torsional mode. The analytical expression is:

image file: c8cp04490b-t3.tif(7)
In this paper, the 1D-PES were determined optimizing 20 curvilinear internal coordinates at the CCSD(T)-F12 level of theory. The vibrational corrections were computed at the MP2 level of theory (Table 5).

Table 5 Expansion coefficients of the one-dimensional potentials
1Dcis 1Dtrans 1Dcis 1Dtrans 1Dcis 1Dtrans
A0 179.772 205.592 208.677 174.638 129.435 274.362
A3 −175.884 −195.663 −196.383 −158.044 −128.171 −162.442
A6 −3.888 −9.930 −12.294 −16.594 −1.264 −11.92

The far infrared spectrum

Tables 6–8 summarize the low energy levels corresponding to the three isomeric forms. Levels are assigned to the cis and trans minima and classified using the representations of the G6 and Cs groups. The G6 MSG contains two non-degenerate representations A1 and A2 and one two-degenerate representation E. The torsional levels were determined variationally using two different models of reduced dimensionality (1D and 2D) and using vibrational second order perturbation theory (VPT2). This last theory was employed to determine the energies corresponding to excitations of the skeletal bending modes (in plane), the combinations of bending and torsional excitations, and for predicting Fermi displacements. The VPT2 energies were computed with the formula.
image file: c8cp04490b-t4.tif(8)
where ωi represent the harmonic fundamentals, νi and vj are vibrational quanta, and xij are the anharmonic constants.
Table 6 Low energy levels of acetyl isocyanate (in cm−1)a
Variational VPT2
v θ v α 1D 2D VPT2
a Predicted displacements due to Fermi resonances.
0 0 A1 0.000 0.000 a′ 0
E 0.023
0 1 A2 78.423 ν 21 a′′ 75
E 78.441
ν 14 a′ 115
1 0 A2 122.172 122.863 ν 20 a′′ 120
E 121.409 122.093
0 2 A1 154.864 2ν21 a′ 150
E 154.878
ν 14 ν 21 a′′ 190
1 1 A1 201.429 ν 20 ν 21 a′ 196
E 200.952
2 0 A1 217.194 218.135 2ν20 a′ 226
E 225.202 226.003
0 3 A2 229.259 3ν21 a′′ 225
E 229.271
2ν14 a′ 231
ν 14 ν 20 a′′ 236
ν 142ν21 a′ 264
1 2 A2 278.123 ν 202ν21 a′′ 272
E 277.817
0 4 A1 301.544 4ν21 a′ 300
E 301.553
2 1 A2 298.462 2ν20ν21 a′′ 303
E 306.718
2ν14ν21 a′′ 305
3 0 A2 329.329 329.663 a′′ 319
E 289.816 288.981
ν 14 3ν21 a′′ 338
ν 14 2ν20 a′ 344
3ν14 a′ 346
1 3 A1 352.636 a′ 348
E 352.637
2ν14ν20 a′′ 353
0 5 A2 371.648 5ν21 a′′ 374
E 371.655
2ν14 2ν21 a′ 378
2 2 A1 376.569 a′ 381
E 385.544
ν 13 a′ 382
3 1 A1 410.039 a′ 398
E 368.793
4 0 A1 344.740 344.076 a′ 399
E 403.744 403.521
ZPVE 65.336 105.189
0 0 A1 0.000 0.000 a′ 0
E 0.011
0 1 A2 56.556 ν 21 a′′ 54
E 56.554
0 2 A1 111.088 2ν21 a′ 108
E 111.082
ν 14 a′ 113
1 0 A2 131.747 136.335 ν 20 a′′ 135
E 131.333 135.878
ν 14 ν 21 a′′ 157
0 3 A2 163.305 3ν21 a′′ 161
E 163.351
1 1 A1 191.764 ν 20 ν 21 a′ 188
E 191.977
ν 142ν21 a′ 201
0 4 A1 213.160 4ν21 a′ 213
E 213.157
2ν14 a′ 226
1 2 A2 245.491 ν 202ν21 a′′ 241
E 245.653
ν 143ν21 a′′ 244
ν 14 ν 20 a′′ 249
2 0 A1 236.444 245.188 2ν20 a′′ 255
E 242.021 250.699
ZPVE 665.874 680.519

Table 7 Low energy levels of methyl cyanoformate (in cm−1)a
Variational VPT2
v θ v α 1D 2D VPT2
a Predicted displacements due to Fermi resonances.
0 0 A1 0.000 0.000 a′ 0
E 0.011 0.013
1 0 A2 135.905 129.580 ν 21 a′′ 125
E 135.416 129.181
0 1 A2 155.782 ν 20 a′′ 142
E 155.664
ν 14 a′ 167
2 0 A1 241.506 236.268 2ν21 a′ 249
E 247.961 242.262
1 1 A1 277.046 ν 20 ν 21 a′ 263
E 277.394
2 0 A1 308.549 2ν20 a′ 277
E 308.334
ν 14 ν 21 a′′ 293
ν 14 ν 20 a′′ 309
ν 19 a′′ 312
ν 13 a′ 312
3 0 A2 353.689 348.442 3ν21 a′′ 370
E 317.376 313.429
2 1 A2 382.792 ν 202ν21 a′′ 381
E 386.010
1 2 A2 425.136 2ν20ν21 a′′ 393
E 424.495
0 3 A2 459.904 3ν20 a′′ 407
E 457.994
ν 142ν21 a′ 416
ν 19 ν 21 a′ 436
ν 13 ν 21 a′′ 440
ν 142ν20 a′ 444
ν 19 ν 20 a′ 453
ν 13 ν 20 a′′ 457
2ν14ν21 a′′ 460
2ν14ν20 a′′ 476
ν 13 ν 14 a′ 479
ν 14 ν 19 a′′ 480
4 0 A1 370.991 367.693 4ν21 a′ 489
E 427.777 424.495
3 1 A1 492.831 ν 203ν21 a′ 498
E 386.010
2 2 A1 529.831 2ν202ν21 a′ 508
E 426.619
1 3 A1 575.262 3ν20ν21 518
E 457.994
0 4 A1 595.885 4ν20 a′ 529
E 504.341
ZPVE 73.451 149.033
0 0 A1 0.000 0.000 a′ 0
E 0.024 0.033
0 1 A2 95.071 ν 21 a′ 96
E 94.629
1 0 A2 123.507 142.070 ν 20 a′ 142
E 122.486 141.223
ν 14 a′′ 161
0 2 A1 180.701 2ν21 a′ 186
E 184.357
1 1 A1 217.052 ν 20 ν 21 a′′ 227
E 223.061
ν 19 a′′ 241
ν 14 ν 21 a′′ 255
0 3 A2 270.586 3ν21 a′′ 270
E 270.134
2 0 A1 208.133 267.414 2ν20 a′ 276
E 218.561 254.393
ZPVE 1778.326 1762.953

Table 8 Low energy levels of acetyl cyanate (in cm−1)a
Variational VPT2
v θ v α 1D 2D VPT2
a Predicted displacements due to Fermi resonances.
0 0 A1 0 0.000 a′ 0
E 0.087 0.0913
1 0 A2 101.407 96.459 ν 21 a′′ 97
E 99.165 95.0044
0 1 A2 109.435 ν 20 a′′ 114
E 108.550
ν 14 a′ 160
2 0 A1 169.794 167.040 2ν21 a′ 197
E 183.872 180.810
1 1 A1 199.557 ν 20 ν 21 a′ 203
E 199.143
0 2 A1 216.835 2ν20 a′ 223
E 215.750
ν 14 ν 21 a′′ 257
ν 14 ν 20 a′′ 274
2 1 A2 273.173 ν 202ν21 a′′ 295
E 288.275
3 0 A2 285.505 287.021 3ν21 a′′ 301
E 234.199 232.118
1 2 A2 301.909 2ν20ν21 a′′ 304
E 302.019
2ν14 a′ 320
0 3 A2 323.050 3ν20 a′′ 327
E 322.118
ν 14 ν 21 a′′ 356
ν 13 a′ 374
2 2 A1 396.227 2ν202ν21 a′ 389
E 394.068
3 1 A1 379.705 ν 203ν21 a′ 391
E 342.458
1 3 A1 404.354 ν 212ν20 a′ 400
E 404.273
4 0 A1 291.057 288.978 4ν21 a′ 407
E 357.852 356.688
2ν14ν21 a′′ 416
0 4 A1 428.980 4ν20 a′ 425
E 428.139
ZPVE 54.209 106.740
0 0 A1 0.000 0.000 a′ 0
E 0.002
0 1 A2 80.994 ν 21 a′′ 82
E 80.485
1 0 A2 154.905 159.361 ν 20 a′′ 155
E 154.801 159.252
0 2 A1 159.293 2ν21 a′ 164
E 159.295
ν 14 a′ 173
1 1 A1 235.845 ν 20 ν 21 a′ 236
E 235.789
0 3 A2 236.507 3ν21 a′′ 243
E 236.509
ν 142ν21 a′′ 254
2 0 A1 287.270 312.193 2ν20 a′ 291
E 289.219 295.649
ZPVE 755.700 778.578

AISO energy levels are shown in Table 6. We found that cis-methyl isocyanate displays 28 energy levels below 410 cm−1 which correspond to the low frequency mode fundamentals and overtones, to combination levels involving the two torsional modes and the ν13 and ν14 skeletal bending modes. The tunneling components of the torsional fundamentals were computed at 78.423 cm−1 and 78.441 cm−1 (ν21, CN torsion) and 122.863 cm−1 and 122.093 cm−1 (ν20, methyl torsion). The skeletal bending fundamentals were found to be ν14 = 115 cm−1 and ν13 = 382 cm−1. Small displacements of the ν14 fundamental and the 2ν21 overtone due to Fermi interactions are predicted.

cis-Methyl cyanoformate (see Table 7) displays 14 vibrational levels below 410 cm−1. The tunneling components of the two torsional fundamentals were found to lie at 129.580 cm−1 and 129.581 cm−1 (ν21, methyl torsion) and 155.782 cm−1 and 155.664 cm−1 (ν20, CO torsion). The skeletal bending fundamentals were found to be ν14 = 167 cm−1, ν13 = 312 cm−1, and ν19 = 312 cm−1. Small displacements of the ν13 fundamental and the 2ν20 overtone and the ν20ν21, are predicted.

Finally, cis-acetyl cyanate (see Table 8) displays 20 vibrational energy levels below 410 cm−1. The components of the two torsional fundamentals were found to lie at 96.459 cm−1 and 96.004 cm−1 (ν21, methyl torsion) and 109.435 cm−1 and 108.550 cm−1 (ν20, CO torsion). The skeletal bending fundamentals were found to be ν14 = 160 cm−1 and ν13 = 374 cm−1. Displacements due to Fermi interactions are not predicted for the cis levels. Very small displacements are obtained for the trans-levels ν14 and 2ν21.

Some of the low energy levels are shifted due to Fermi interactions. Predicted displacements have been taken into consideration to obtain the energis of Tables 6–8. In the case of AISO (see Table 6) the ν14 and 21cis-levels and the ν14 and the 2ν21trans-levels are shifted −1.8 cm−1, +1.8 cm−1, +13.2 cm−1 and −13.2 cm−1, respectively. For MCN, the cis-levels ν13, 2ν20, and ν20ν21 are displaced +37.5 cm−1, −41.2 cm−1, and 3.9 cm−1. The trans-levels ν14 and 2ν21 are also shifted.

At very low energy, in the region of the methyl torsional fundamentals and overtones, both models 1D and 2D provide alike results. It can be inferred that this 1D model considered frequently in the spectrum assignments using effective Hamiltonians can be sufficient to analyze the spectra at very low temperatures. In addition, the VPT2 theory which is not the proper model to treat non-rigid species neglecting the splittings provides reasonable low energies.


CCSD(T)-F12 calculations confirm that the three C3H3O2N isomers present two different equilibrium structures cis and trans of Cs symmetry that can intertransform by internal rotation of the central bond. The cis → trans processes are restricted by energy barriers of 1005 cm−1 (AISO), 4081 cm−1 (MCN), and 2351 cm−1 (ACN). A second torsional mode, the methyl group internal rotation, contributes to generate a potential energy surface of six minima. The Vcis3 and Vtrans3 were computed to be 352 and 351 cm−1 (AISO), 393 and 316 cm−1 (MCN), and 256 and 525 cm1 (ACN). All these barriers which are relatively low produce relevant tunneling effects.

The cis-conformers of MCN and ACN appear 7312 cm−1 and 7716 cm−1 over the most stable structure cis-AISO. Both cis-MCN and cis-ACN show similar stabilities and comparable lye probabilities for detection in gas phase sources. Furthermore, electric properties support the significance of cis-ACN (μ = 6.0267 D) with respect to cis-AISO and cis-MCN. Although, previous attention was not given to ACN, this species can be a good candidate for detection using radioastronomy.

Two dimensional potential energy surfaces were compute at the CCSD(T)-F12 level of theory to determine variationally the low vibrational energy levels and their splittings. Then, the far infrared spectrum has been explored. The most stable molecules, cis-methyl isocyanate displays 28 energy levels below 410 cm−1 which correspond to the low frequency mode fundamentals and overtones, as well as, to combination levels involving the two torsional modes and the ν13 and ν14 skeletal bending modes. The tunneling components of the torsional fundamentals were computed at 78.423 cm−1 and 78.441 cm−1 (ν21, CN torsion) and 122.863 cm−1 and 122.093 cm−1 (ν20, methyl torsion). Small displacements of the ν14 bending fundamental and the 2ν21 overtone due to Fermi interactions are predicted.

The other stable conformers, cis-methyl cyanoformate and cis-acetyl cyanate, display 14 and 20 vibrational levels below 410 cm−1. In the last case, Fermi displacements are not expected. Whereas in a previous study of methyl isocyanate, we found an important vibrational dependence on the rotational constants with the skeletal bending modes, acetyl isocyanate presents a “more standard” behavior. However, the effect of the ν14 mode on the rotational constants of cis-AISO and trans-AISO and of ν13 is not negligible.

Conflicts of interest

There are no conflicts to declare.


This research was supported by the FIS2016-76418-P project of the MINECO, Spain. The authors also acknowledge the COST Actions CM1401 ‘‘Our Astrochemical History” and CM1405 ‘‘Molim”. The authors acknowledge the CESGA and CTI-CSIC computers centers for high computing facilities.


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