Structure and Spectroscopy of C2HNO Isomers

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Structure and Spectroscopy of CHNO Isomers Marcin Gronowski, Piotr Eluszkiewicz, and Thomas Gage Custer J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b12609 • Publication Date (Web): 12 Apr 2017 Downloaded from http://pubs.acs.org on April 13, 2017

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The Journal of Physical Chemistry

Structure and Spectroscopy of C2HNO Isomers Marcin Gronowski*, Piotr Eluszkiewicz, Thomas Custer Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland *corresponding author, e-mail: [email protected], [email protected]

ACS Paragon Plus Environment


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Abstract Formyl cyanide has been detected toward Sgr B2 making this chemical and its potential isomers of astrophysical interest. We calculated the precise energies of the 5 most stable structural isomers of formyl cyanide and found that formyl isocyaniade and 2H-azirin-2-one are less stable than formyl cyanide by 55 and 125 kJ/mol respectively. We present our ab initio coupled cluster predictions of the spectroscopic parameters relevant to their gas phase rotational and vibrational spectroscopy. Parameters include ground vibrational state rotational constants, centrifugal distortion parameters, equilibrium electric dipole moments, and nuclear quadrupole coupling constants. Anharmonic vibrational frequencies together with infrared intensities of fundamental and non-fundamental modes were also calculated. The broader potential energy surface, including transition states and the minima they connect, were explored for these isomers at the B3LYP/aug-cc-pVTZ level of theory. Formyl cyanide can dissociate in an exothermic reaction to form HCN and CO or in an endothermic reaction to form HNC and CO. The activation energies for both processes are close to 260 kJ/mol. The activation barrier for conversion of of formyl cyaniade into formyl isocyanide is about 180 kJ/mol. The energetic barrier for the exothermic decomposition of formyl isocyaniade into HNC and CO is about 210 kJ/mol. The barrier for transformation of formyl isocyaniade into formyl cyanide is about 130 kJ/mol. Formyl isocyanide seems to be a stable chemical and could potentially survive in a dense molecular cloud if formed. These data are useful for future identification of members of this family of molecules in a laboratory or in space.


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Introduction The first spectroscopic studies of cyanoformaldehyde (formyl cyanide, 1), one of the simplest aldehydes, were reported in 1986 by Judge and coworkers and described the UV absorption and excitation spectra of the molecule. Their measurements provided vibrational frequencies in the first singlet excited state and, due to the presence of hot-bands, the ground state frequencies of the two lowest energy modes1. The microwave spectroscopy and rotational constants of cyanoformaldehyde, related to its molecular structure, were measured by Bogey at al. in 19952 and these measurements lead to its subsequent detection toward the star-forming region Sagittarius B2(N) 3. Although it was detected in space many years ago, the interstellar synthesis of cyanoformaldehyde has only recently been described4. Cyanoformaldehyde has also been the object of a number of theoretical studies. In the most recent of these5, the ground electronic state structural and rotational spectroscopy parameters were compared to those obtained experimentally2. This comparison provided information concerning the uncertainty of theoretical predictions for a structurally similar molecule, cyanovinylidene, whose spectroscopy has yet to be characterized. The cyanoformaldehyde “motif” appears in many related molecules where the carbonyl hydrogen is substituted for another atom or functional group. For example, cyanoformyl chlorides6, acetyl cyanide7, or carbonyl cyanide8 have all been studied as well as its sulfur-bearing analog and isomers9. To the best of our knowledge, the whole family of cyanoformaldehyde isomers has not been studied systematically in any theoretical or experimental work. Concerning individual isomers, very little is available in the literature. There is some theoretical work related to the stability and dissociation of cyanoformaldehyde10-11. Although isocyanides are widespread in interstellar clouds, as exemplified by magnesium hydride isocyanide12, isocyanoacetylene13, and hydrogen isocyanide14, the spectroscopy of isocyanoformaldehyde (2) has not been described. Another of the expected cyanoformaldehyde isomers, 2H-azirin-2-one (3), also does not seem to be described in any publication, although recent studies indicate that the sulphur analog of this chemical is a relatively



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stable isomer,9 with the implication being that 3 should also have a low energy. For detection of any of these in space, knowledge of spectroscopic parameters is crucial and this gap can be partially filled using quantum chemical methods.


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Methods Structures previously obtained9 for the family of C2HNS isomers and for nitrosoethyne15-16 were used as starting points for geometry optimizations. For planar, quasi-liner molecules containing 5 atoms, there are two dihedral angles. Each of these can have a value of either 0 or 180 degrees if planarity is maintained, depending on the chain conformation. We included all possible conformers by generating structures with each combination (0 and 180 degrees) for the two dihedral angles while leaving the rest of the geometric parameters unchanged. Separate calculations were performed for singlet and triplet potential energy surfaces at the B3LYP/aug-cc-pVTZ17-18 level. Atomic charges and bond orders were calculated at the same level of theory using the natural bond orbital (NBO) methodology19-21. The transition states were localized by the synchronous transit-guided quasiNewton method22-23 or by the Berny algorithm24. The nature of transition states were verified by frequency calculations. Intrinsic reaction coordinate (IRC)25 calculations were applied to identify minima connected by particular transition states. The DFT calculations were performed using Gaussian 09 26 software while the preparation of inputs and visualization of outputs employed Jmol27, Gabedit28, and ChemCraft 29. The five most stable isomers that were found using the procedure just described, were subjected to more precise ab initio calculations in order to obtain more accurate energies. The final energy value was calculated in a fashion inspired by the HEAT30 procedure in Cfour and described in our previous reports9, 31, using the equation:

,

=

,

,

, , ,

, + − + − + − &,

,"# % , , + ! + $ + $ + $

(1) where the letters X, Y, Z in each energy term ',( refer to energy type, method by which energy is derived, and basis set used, respectively. For energy type, X, we calculated the total energy (total),



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correlation energy (corr), mass-velocity and Darwin term (MVD2)32-33, diagonal Born-Oppenheimer correction (DBOC)34, and zero-point (ZPE). Methods used, Y, included the following ab initio methods: coupled-cluster singles, doubles, and triples (CCSDT)35-37, coupled-cluster singles and doubles with perturbative treatment of triples (CCSD(T))38-41, coupled-cluster singles and doubles (CCSD)42-44; and Møller-Plesset perturbation theory truncated at second-order (MP2)45-46. Basis sets used, Z, included triple- (cc-pVTZ), quadruple- (cc-pVQZ), quintuple- (cc-pV5Z), and sextuple- (cc-pV6Z) Dunning's correlation-consistent basis sets18, 47 as well as two basis sets with tight core48 and diffuse49 functions (aug-cc-pCVQZ, aug-cc-pCVTZ). Complete basis set (CBS) limits of correlation energies were estimated from the 1⁄* + law50-51, by the same formula as was given in previous reports9, 31. All contributions to the energy were calculated assuming the CCSD(T)/cc-pVQZ geometry with the % , exception of the diagonal Born-Oppenheimer corrections, which used the CCSD/cc-pVQZ &,

geometry and zero point energies,

which used the CCSD(T)/cc-pVTZ geometry. The all-

electron correlation approach and CFOUR v.152 software were applied for these more accurate energy computations. All calculations concerning vibrations and anharmonicity were performed at the CCSD(T)/cc-pVTZ level. Vibrational perturbation theory truncated at second-order (VPT2)53 with cubic and quartic force fields54-56 were applied in calculation of anharmonic vibrational frequencies of fundamental, overtone, and combinational modes. The ground vibrational state electric dipole moment (-. ) and the distortion constants were calculated at the same level of theory. The zero-point vibrational &,

energy (

) is also anharmonic. Those calculations were performed in CFOUR v.152

software. A second approach includes vibrational self-consistent field (VSCF) vibrational Møller-Plesset perturbation theory (VMP2)

57

57

calculations and

. Such calculations use multimode

expansion58-60 of potential energy surfaces around the equilibrium structure. The normal modes were obtained during numerical calculations of harmonic frequencies61-62 preceded by geometry optimizations.63 One and two body terms were included. In order to reduce computational time, the


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frozen core approximation was used during CCSD(T)64-65 calculation of the potential energy surface. We denote this as fc-CCSD(T). Dipole surfaces were computed at the Hartree-Fock level. All calculations of this sort were performed in Molpro 2012.166-67 Both approaches were also applied when calculating differences between equilibrium and ground state rotational constants. Nuclear quadrupole coupling tensors / were derived from the relation: / = 0.23496474 9 : [MHz] where the molecular electric field gradient tensor : was calculated at the CCSD/aug-cc-pCVTZ level (using the CCSD(T)/cc-pVQZ geometry and CFOUR v.152) where the nitrogen electric quadrupole moment 9 was 20.44 mbarn.68 Vibrational corrections for electric-field gradients weren’t computed, because they are not significant in most cases.69



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Results and discussion Concerning energy comparisons, the B3LYP/aug-cc-pVTZ calculated energies listed on Fig. 1 provide only rough information about ordering and spacing. The likely accuracy of the values listed should be kept in mind. Energy separations between polyynes and their respective cumulenes at this level of theory are predicted to have a mean unsigned error of the order of 26 kJ/mol70. For cyanodiacetylene isomers71, the mean unsigned differences between energies calculated by B3LYP/aug-cc-pVTZ and CCSD(T)/cc-pVTZ are on the order of 31 kJ/mol. Our more accurate energy calculations were undertaken to improve the accuracy of the energy determination for isomers 1-5, the results of which are collected in Tab. 1. The CCSD(T)/cc-pVQZ calculations are a core part of our more accurate calculations. The CCSD(T) calculations with quadruple-zeta basis sets produces atomization energies with errors on the order 14 kJ/mol43. In addition, we include extrapolation to the complete basis set limit and several minor corrections. While each of the energy terms affect the total energy of individual species, the relative energies between isomers are much more important for this work. To determine the significance of each of the energy terms contributing to individual species, we calculated the standard deviation of the mean value of each energy term for all five isomers (Tab. S1

, ,"# in Supporting Info). The terms ! and have the biggest influence on the relative

energy with calculated standard deviations of 97 and 33 kJ/mol, respectively. The ZPE correction also significantly shapes the relative energy, with a standard deviation on the order 2.3 kJ/mol. The

,

, distribution of the − term has a standard deviation two times smaller than ZPE

correction. The rest of energy terms are characterized by even smaller standard deviation and they importance for relative energies is small. Overall, we expect that the accuracy of the predicted relative energies will be on the order of 10 kJ/mol.


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Fig. 1. Structures corresponding to the deepest minima on singlet and triplet potential energy surfaces (energies less than 260 kJ/mol relative to 1) calculated using B3LYP/aug-cc-pVTZ. The grey boxes around labels indicate ground electronic states. Singlet-triplet splittings are given in Tab. 2.



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Tab. 1. The relative energy (∆ ) as well as total energy ( ) with their components from Eq. 1. 1

2

3

4

5

hartree

-0.92126

-0.90924

-0.92170

-0.93739

-0.93884

hartree

-0.09007

-0.08962

-0.09073

-0.09013

-0.09020

hartree

-0.11372

-0.11357

-0.11383

-0.11428

-0.11423

hartree

0.00028

0.00011

0.00051

-0.00005

-0.00012

,"# !

hartree

-205.68047

-205.67160

-205.63194

-205.60633

-205.59883

, $

hartree

-0.11891

-0.11885

-0.11877

-0.11886

-0.11886

% , ∆

hartree

0.00802

0.00801

0.00799

0.00806

0.00806

hartree

0.02626

0.02596

0.02623

0.02490

0.02427

hartree

-206.88988

-206.86881

-206.84224

-206.83408

-206.82875

∆

kJ/mol

0

55

125

146

160

kJ/mol

0

79

118

135

Isomer:

,

,

, − , , −

,

, −

&,

∆

∆

for

sulfur

bearing analogues a

a

Ref 9

Selected singlet-triplet separations are collected in Tab. 2. The five lowest-energy isomers all have triplet states above their singlet states in energy. For isomers 4 and 5 this energy difference is extremely small. In the course of our computations, we did not see any obvious signs of spectroscopic parameters heavily influenced by another state, although such interactions cannot be excluded. For this reason and due to the low singlet-triplet splitting for 4 and 5, spectroscopic parameters for these isomers should be treated with caution. Surprisingly, the largest singlet-triplet splitting is predicted for 2.


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Tab. 2. Selected singlet-triplet splitting in eV. The numbers in the first two columns correspond to structures from Fig. 1. Singlet 1

Triplet 15

Singlet-triplet energy difference 2.6

2

a

3.1

3

13

1.3

4

6

0.2

5

6

0.02

7

8

0.01

9

14

0.6

10

14

0.5

a

This state not pictured in Fig. 1 as its energy is very high with respect to 1

Tab. 1 also presents relative energies for sulfur-bearing analogues9. Sulfur bearing species were included as there are similarities between the sulphur and oxygen bearing families. Cyanoformaldehyde 1, is the most stable compound in the C2HNO family of isomers, even taking into account the likely accuracy of the B3LYP/aug-cc-pVTZ energetic separations. This chemical, as well as species 2, 3, and 4, all have sulfur bearing analogues with similar relative energies separating them from one another. The sulfur containing equivalent of 1, cyanothioformaldehyde, is also the most stable isomer in its family. The energetic isocyanide-cyanide (2/1) separation, 55 kJ/mol, is smaller than

that

of

the

sulphur-bearing

analog

(also

2/1)9,

79

kJ/mol.

While

the

cyanoformaldehyde/isocyanoformaldehyde energy difference is similar to some previously calculated values which lie in the range of 50-55 kJ/mol10-11, 72, the separation is often larger for small organic molecules. Some examples include an energy difference of 112 kJ/mol for methylcyanoacetylene/methylisocyanoacetylene, 97.5 kJ/mol for allenyl cyanide/allenyl isocyanide, 93.2

kJ/mol

for

propargyl

cyanide/propargyl

isocyanide73

and

110

kJ/mol

for

cyanodiacetylene/isocyanodiacetylene71. From our own experience, a small cyanide/iscocanide energy separation is observed for pairs of molecules in which the charge distribution on the atom



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connected to the CN group does not change significantly upon isomerization. This trend can be clearly observed by comparing different cyano/isocyano pairs. At one extreme is the hydromagnesium cyanide/hydromagnesium isocyanide pair in which the charge on the atom adjacent to CN does not change at all74 and for which hydromagnesium isocyanide is more stable by a few kJ/mol. In the case of the cyanoformaldehyde/isocyanoformaldehyde pair (Fig. 2), the partial charge on the carbonyl carbon changes by 0.2 with an energy difference of 55 kJ/mol between them. This change is lower than that for the cyanothioformaldehyde/isocyanothioformaldehyde pair which exhibits a change of 0.25 and relative energy of 79 kJ/mol 9. At the other end of the scale is the cyanoacetylene/isocyanoacetylene pair with a change in charge of 0.27 9 and relative energy of 111 kJ/mol9. Kuangsen Sung calculated isomerization energies for sets of various nitriles,72 treating the moiety attached to the nitrile or isonitrile as a functional group. They pointed out that isonitriles connected to σ-donating or π-accepting substituents tend to have a lower nitrile/isonitrile energy separation. Reconciling our results with picture of Kuangsen Sung, we consider the occupation of the π* orbital of C=O or C=S as an indicator of π-accepting properties. The group with smaller π* occupation can be thought of as more able to accept electrons and would therefore be more πaccepting according the picture of Sung. NBO calculations indicate that the occupancy of the π* orbital of C=O is smaller than for C=S (Tab. 3). As consequence, the C=O bond order is larger than C=S bond order (Fig. 2) and the C=O bond of cyanoformaldehyde has more π-accepting nature than C=S. Returning to the observations of Sung et al72, the isonitrile group, with its lone pair formally located on a terminal carbon, can be stabilized through sharing of its electrons (charge delocalization) through π bonds with any good acceptor. This matches with our observation that the smaller the change in charge on the C atom adjacent to the nitrile/isonitrile, the higher the stabilization of the isonitrile (lower energy difference). The electrons of the isonitrile are more easily accommodated by a π acceptor and changes the charge of this acceptor less.


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Fig. 2. Bond orders and atomic charges (in parentheses) represent the result of NBO analysis at B3LYP/aug-cc-pVTZ level.

Tab. 3. Occupation of π and π* orbitals related to C=O bonds of 1 and 2. In parentheses the analogous value for C=S bonds of cyanothioformaldehyde and isocyanothioformaldehyde are given

π π*

1 1.975(1.945) 0.058(0.082)

2 1.982(1.958) 0.109(0.115)

Isomers 4 and 5 can be treated as two conformers. For the family of sulfur bearing molecules, the NC-C-S skeleton is more nearly linear and only one energy minimum can be found (e.g., no equivalent of structure 5 exists for the sulfur species). The singlet-triplet splittings for both 4 and 5 are small and both have the same triplet state: 6. The same small singlet-triplet splitting is observed for the sulfur analogue of 4. Species 9/10 and 11/12 can also be considered as pairs of conformers on the C2HNO potential energy surface. We have not presented some species which have been postulated to exist previously on Fig. 1, because they have relative energies higher than 300 kJ/mol. For example, cyanatomethylene75 and nitrosoethyne15-16 are less stable than 1 by 327 kJ/mol and 337 kJ/mol, respectively. In general, 1, 2, and 3 are quite stable from a thermodynamic point of view (Tab. 4). However the standard enthalpy of decomposition of 1 into HCN and CO is negative (-37.4 kJ/mol). Taking into account the standard enthalpy of formation of HCN (-135.14 kJ/mol)


76

and CO (-110.53 kJ/mol) 76,


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the standard enthalpy of formation of 1 is about -208 kJ/mol. Some reported values for other “interstellar” molecules are: H2C2O (-47.7 kJ/mol)77, HCOOH (-378.8 kJ/mol)78, and CH4 (-74.6 kJ/mol)78. Some enthalpies of formation are much greater and some much less than 1. The standard enthalpies of decomposition of 1 and 2 are not sensitive to changes in temperature. However, the high temperature values reported here are not very precise as we applied a harmonic approximation during calculation of the partition function. The Gibbs energy is obviously much more sensitive to temperature. From a thermodynamic point of view, a low temperature will stabilize 1 and 2. A decrease in pressure also generally shifts the equilibrium toward products of decomposition. The relative energy for members of C2HNO family of isomers can be compared with those for the cyanocetylene (HCCCN) family. In addition to HCCCN, the most stable member of the cyanoacetylene family, two other members (HNCCC79 and HCCNC13) have been detected in space. HNCCC is less stable than the lowest energy isomer by more than 200 kJ/mol 80. This energy is much higher than the separation between 1 and 3. The abundance of molecules in interstellar clouds are mostly determined by synthesis and decompositions pathways of a particular species and energies of transition states separating the various species involved. The geometries, together with relative energies and displacement vectors corresponding to the imaginary frequency of different transition states on the singlet C2HNO potential energy surface, are presented in Fig. 3. The transition state ts2 links structures 4 and 5. The energy of ts2 is only higher than the energy of 5 by 1.5 kJ/mol (130 cm-1). This strongly suggests that 5 may be a very unstable species or that the potential energy surface around the minimum is strongly anharmonic. The same is true for 4, whose dissociation barrier (ts1) is rather low. Isomerization of 1 to 2 and the reverse proceed via ts3. This transition state is not planar. The C≡N bond is nearly perpendicular to the O=C-H plane. The energetic barriers for those reactions are 170 and 130 kJ/mol, respectively. The analogous values for HCN/HNC are 187 and 126 kJ/mol

81

, and

slightly larger values were reported for HCCCN/HCCNC (273 and 155 kJ/mol) 82 or for CH3CN/CH3NC (259 and 160 kJ/mol)

83

. Dissociation into carbon monoxide and hydrogen cyanide (or hydrogen


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isocyanide) is an important decomposition channel. The dissociation of 1 into CO and HCN has been studied previously84 at the MP2 level of theory and ts8 found here has a structure similar to what was reported previously84 but with an energy approximately 29 kJ/mol smaller. This difference in energies is acceptable, if we take into account the precision of B3LYP and MP2 methods. Species 1 can also dissociate into CO and HNC. The transition state for this reaction (ts5) has practically the same energy as ts8 and ts7, the last of which describes dissociation of 2 into HNC and CO. We searched for a transition state which links 3 with 1. Although ts9 seems like a good candidate, IRC calculations show that ts9 also links 1 with the dissociation products HCN and CO. We did not find any transition state that directly linked 3 with 2, but this isomerization can still proceed via a path through ts5, 7, and ts10 (Fig. 4). The activation barrier for the first step (from 3 to 7) is 102 kJ/mol, while for the second step (from 7 to 2) it is 130 kJ/mol. The decomposition of 3 into HCN and CO is also a two-step process. Ring opening (from 3 to 7) is followed by dissociation of 7 into HCN and CO. This second step has a small activation energy: 38 kJ/mol. We did not find any other transition state linking 3 with another minimum on the potential energy surface. From this point of view, we expect 3 to be stable enough to survive in appropriate experimental conditions (noble gas matrix or supersonic jet) or in dense molecular clouds. In general, even taking into account the precision of density functional theory calculations, we conclude that 1, 2, and 3 are moderately stable. While the heights of energetic barriers in the system studied here can be substantial, they are still slightly smaller than for other high energy molecules detected in space82, 85. While species 4 seems to be a true minimum on the potential energy surface, its barrier for dissociation is quite low. The low-lying triplet state predicted for this molecule may significantly alter its spectroscopic properties. The precise estimation of such small singlet-triplet splittings requires more precise multireference quantum chemical calculations. In general (including information about relative energy and height of barrier), only 2 or 3 , if formed, would survive in an extraterrestrial environment with a low flux of UV radiation (for example in a dense molecular cloud). The postulated mechanism for formation of 1 in space includes the reaction



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Page 16 of 37

between CN and H2CO 3-4. It seems likely that 2 might also be formed as a product of this reaction. The protonation of 1, 2, or 3, followed by dissociative recombination, are also processes likely to occur in space. The balance between formation and further transformations affects the relative abundance of isomers that might be found in space. However, a complete discussion of the formation and potential processing of 2 and 3 require their own dedicated quantum chemical and/or experimental studies.

Tab. 4. Thermodynamic functions (in kJ/mol) for selected reactions occurring on the C2HNO potential energy surface together with ZPE-corrected energy. Results based on harmonic fc-CCSD(T)/cc-pVTZ 1→HCN+CO

1→HNC+CO

2→HNC+CO

1→2

2→3

ΔE

-42.2

19.3

-34.7

54.0

77.0

ΔHo298.15

-37.4

24.8

-29.7

54.5

74.9

ΔHo970.5

-37.4

26.1

-28.5

54.6

74.8

ΔH10K(14 × 10-17 atm)

-41.9

19.5

-34.4

54.0

77.0

ΔH298.15K(14 × 10-17 atm)

-37.4

26.1

-29.7

54.5

74.9

ΔH970.5K(14 × 10-17 atm)

-37.4

26.1

-28.5

54.6

74.8

ΔGo298.15

-75.5

-14.4

-67.6

53.3

79.5

ΔGo970.5

-163.1

-105.7

-156.1

50.4

90.4

ΔG10K(14 × 10-17 atm)

-45.6

15.9

-38.1

54.0

77.0

ΔG298.15K(14 × 10-17 atm)

-166.0

-400.3

-158.1

53.3

79.5

ΔG970.5K(14 × 10-17 atm)

-457.7

-400.3

-450.6

50.4

90.4


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Fig. 3. Structures corresponding to the selected transition states linking deepest minima on singlet potential energy surface (energies relative to 1) calculated using B3LYP/aug-cc-pVTZ. Displacement vectors corresponding to the imaginary frequencies are presented as green arrows.



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Fig. 4. Energetic profile of the singlet potential energy surface for C2HNO. Results of B3LYP/aug-cc-pVTZ calculations.

Information concerning the vibrational spectroscopy of 1-3 are collected in Tab. 5-7 and that of 4 and 5 in the Supporting Info. Experimental data for comparison with our theoretical results exist only for seven modes of 1. The frequencies calculated by the VPT2/CCSD(T) method for nearly all modes are larger than what was measured with a mean difference of about 10 cm-1 and mean absolute difference of about 15 cm-1. A particularly large discrepancy was observed for mode ν6, which, in contrast to all other modes, has a calculated value smaller than the experimental. On the other hand, our calculations predict that the frequency of 2 ν9 (Tab. S2 in Supporting Info) should match well with the measured position of this v6 line and has a predicted intensity larger than the fundamental. This suggests that the infrared spectrum of 1 should be experimentally revisited. The mean difference between experimental frequencies and the results of VMP2/fc-CCSD(T) calculations are small (only -1 cm-1). It is interesting that both methods produce, in most cases, similar anharmonic corrections (i.e. the difference between anharmonic and harmonic frequencies). For only two fundamental modes, ν6 and ν3, the anharmonic corrections for VPT2 calculations differ significantly from those of VMP2 calculations. Mode ν6 has a similar frequency to 2 ν9. Modes ν6 and ν9 are localized in the same part of


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molecule with the ν6 mode corresponding to in-plane N≡C-C bending while ν9 is out-of-plane N≡C-C bending. In the case of ν7, the calculated anhamonic frequency is always bigger than the harmonic one, even though anhamonic frequencies are generally expected to be lower than harmonic. This is true even using software that treats anhamonicity differently and has tight convergence criteria. Because the agreement between anharmonic frequencies and experimental values is good for this system and ν7 is the lowest vibrational frequency in the system, this effect is likely not related to any type of resonance. It is more likely related to an unphysical shape of the calculated potential energy surface or is evidence of some extremely unusual properties of 1. The difference in harmonic frequencies calculated by CCSD(T) and fc-CCSD(T) are much more significant than differences related to the method by which anharmonicities are treated. A particularly large difference of harmonic frequencies was observed for the ν2 mode which is related to C≡N stretching. The C≡N bond is one of the shortest bonds between carbon and elements of second period. The C≡N bond of 1 has a length of only 1.158 Å, much shorter than sum of covalent radius of carbon and nitrogen. In this situation, any improvement of core correlation is important. We do not include a core-valence basis set in vibrational calculations mostly due to computational cost, hoverer we believe that this will improve results, especially for the C≡N stretching mode. No experimental data are available for comparison with other vibrational spectroscopy predictions. The largest predicted infrared intensity of a mode of cyanoformaldehyde is on the order of 100 km×mol-1. For select modes of isomers 2-3, infrared intensities can be up to 5 times larger than this, suggesting that laboratory photolysis of 1 in a rare gas cryogenic matrix experiment may provide the opportunity to detect their signatures in the IR with good sensitivity. For nearly all vibrations of 2 and 3, the anharmonic correction from VPT2 and VMP2 calculations are similar. This is also true for the ν2 mode of 3, for which VPT2 calculations predict a strong increase in IR intensities. The effect is likely artificial, as we did not observe a similar change of intensity in VSCF calculations.



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Tab. 5. The vibrational spectroscopy of 1. The combination modes and overtones are in Tab. S2 in Supporting Info. Frequencies/cm

-1

-1

Intensities / km × mol

CCSD(T) mode

Harmonic

Sym.

fc-CCSD(T) Anharmonic

Harmonic

VPT2

CCSD(T) Anharmonic

Gas

phase

VSCF

VMP2

experiment

Harmonic

fc-CCSD(T)/HF Anharmonic

Anharmonic

VPT2

VSCF

Fundamental modes A’

ν1

3051

2902

3034

2850

2887

2892a

32

33

14

A’

ν2

2282

2246

2258

2215

2219

2230

a

42

43

14

A’

ν3

1765

1729

1752

1723

1741

1716

a

105

97

193

A’

ν4

1433

1401

1416

1385

1382

1383

a

9

8

13

A’’

ν8

1011

992

990

983

974

0

0

0

A’

ν5

933

921

922

907

908

914a

89

87

124

A’

ν6

619

603

612

609

609

626

a

1

1

1

A’’

ν9

314

311

294

305

290

278

b

1

1

1

A’

ν7

226

229

222

235

223

227

b

14

13

19

a) Ref. 84 b) Ref. 1


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Tab. 6. The vibrational spectroscopy of 2. The combination modes and overtones are in Tab. S3 in Supporting Info. Frequencies/cm-1 CCSD(T)

Intensities / km × mol-1 fc-CCSD(T)

CCSD(T)

fcCCSD(T)/HF

Sym.

mode

Harmonic

Anharmonic

Harmonic

VPT2

Anharmonic VSCF

VMP2

Harmonic

Anharmonic

Anharmonic

VPT2

VSCF


ν1

3102

2954

3085

2905

2937

25

26

15

A’

ν2

2147

2112

2123

2077

2083

351

337

541

A’

ν3

1801

1766

1788

1759

1751

214

206

383

A’

ν4

1431

1397

1413

1381

1377

10

9

13

A’’

ν8

1035

1015

1014

1004

995

0

0

1

A’

ν5

978

959

965

946

945

183

188

237

A’

ν6

632

625

624

619

619

10

10

15

A’’

ν9

205

204

190

208

187

0

0

2

A’

ν7

171

176

168

187

169

5

5

5



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Page 22 of 37

Tab. 7. The vibrational spectroscopy of 3. The combination modes and overtones are in Tab. S4 in Supporting Info. Symm. mode

Frequencies/cm-1

Intensities / km × mol-1

CCSD(T)

fc-CCSD(T)

CCSD(T)

Harmonic Anharmonic

Harmonic Anharmonic

Harmonic

VPT2

VSCF

VMP2

2987

3014

fc-CCSD(T)/HF Anharmonic

Anharmonic

VPT2

VSCF

1

2

18 768


ν1

3201

3056

3186

A’

ν2

2026

1997

2008

1975

1977

512

a

A’

ν3

1508

1473

1491

1461

1464

4

2

12

A’

ν4

1227

1199

1216

1198

1188

20

18

33

A’

ν5

926

902

915

904

893

19

19

19

A’’

ν8

863

854

855

847

833

16

16

25

A’

ν6

796

764

785

759

749

48

48

52

A’

ν7

545

537

539

534

532

11

11

17

A’’

ν9

533

528

525

525

509

2

2

6

a) The ν2 and ν4 + ν6 vibrations have a strong anharmonic interaction. The predicted anharmonic intensities are therefore unphysically high (higher than 50 × 103 km × mol-1).


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Rotational constants for 1, 2, and 3 are collected in Tab. 8. The differences between equilibrium rotational constants and ground state rotational constants were estimated by VPT2-CCSD(T) and VMP2-fc-CCSD(T) calculations. The values produced by both methods agree to within a few MHz for B and C rotational constants. Once again, 1 is treated as a “test molecule” as experimental data is available for this chemical. Based on experimental values of rotational constants and predicted A0-Ae, B0-Be, and C0-Ce values we can estimate the equilibrium rotational constants: Ae=66896-67073 MHz, Be=5023-5026 MHz, and Ce=4673-4675 MHz. Surprisingly, values obtained in this way are closer to those obtained with the cc-pVQZ basis set than with the larger cc-pCVQZ basis. This may be the effect of fortuitous error cancelation. The inaccuracy of predicted vibration-rotation interaction constants by CCSD(T)/cc-pVTZ are significant86 and can affect estimated equilibrium rotational constants. The reported mean absolute error in calculated equilibrium rotational constants using frozen core CCSD(T) with a cc-pVQZ basis set is on the order of 0.4% 87 (about 20 MHz in the case of the B and C rotational constants of 1). Inclusion of core correlation should significantly decrease this uncertainty.87 In comparison to previous studies5, the A0 rotational constant is predicted with much higher precision. Some of the distortion constants fit experimental values better as well (Tab. 9). The biggest discrepancy between experiment and theory occurs for δK, although this is still approximately two times smaller than in previous studies 5. Similar problems with predictions of δK were also evident in studies of thioformyl cyanide. Finding the underlying reason for these discrepancies will require a separate, more thorough investigation. The nuclear quadrupole coupling tensor is very sensitive to changes in molecular structure and can even be used for identification of different conformers 88. The predicted components of this tensor for different isomers are collected in Tab. 10. We observed large differences between the nuclear quadrupole coupling tensors of 1 and 2 although their rotational constants and centrifugal distortion constants are similar. All of these differences are much bigger than the uncertainty of our calculations. For isomer 1, we were able to compare the results of our calculations to experimental values2 and determine a mean absolute error on the order of 0.04 MHz. Similar calculations at the



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CCSD(T)/cc-pwCVTZ level for the chlorine atom in 1-chloro-2-fluoroethylene give errors smaller than 1%89. In general, the CCSD method applied here reproduces the results of a full configuration interaction (FCI) calculation with a deviation smaller than 1%.


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Tab. 8. Rotational constants (MHz) and zero-point/equilibrium differences. The numbers 1, 2, and 3 in the top row correspond to isomers in Fig. 1. 1

2

3

Ae

67318

70631

38519

Be

5020

5516

8093

Ce

4672

5116

6688

Ae

67255

70830

38463

Be

5015

5510

8084

Ce

4667

5112

6680

CCSD(T)/cc-pVQZ

CCSD(T)/cc-pCVQZ

VPT2-CCSD(T)/cc-pVTZ A0-Ae

397

374

-201

B0-Be

-13

-11

-37

C0-Ce

-17

-16

-41

VMP2-CCSD(T)/cc-pVTZ A0-Ae

573

556

-162

B0-Be

-16

-15

-34

C0-Ce

-18

-18

-38

CCSD(T)/cc-pCVQZ + VMP2-CCSD(T)/cc-pVTZ A0

67828

71386

38301

B0

4999

5495

8050

C0

4649

5094

6642

Experimental values a) A0

67469.6749

B0

5010.18856

C0

4656.60175

a)

Ref 2



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Tab. 9. A-reduced centrifugal distortion parameter (MHz) in Ir representation and total equilibrium electric dipole moment together with its components (D). isomer

1 Calc.

a)

Pred.

b)

2

3

4

5

0.27× 10-2

0.19× 10-2

0.73× 10-3

0.75× 10-3

c)

Exp.

ΔJ

0.22× 10-2

2.244× 10-2

ΔK

0.71× 10

1

0.8252× 10

ΔJK

-0.14

δJ

0.38× 10

δK

0.26× 10-1

R6

-0.22× 10

R5

0.33× 10

-.

1.21

0.98

-.

Structure and Spectroscopy of C2HNO Isomers

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