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Density Functional Exploration of CHN Isomers Thomas Gage Custer, Urszula Szczepaniak, Marcin Gronowski, Emilia Fabisiewicz, Isabelle Couturier-Tamburelli, and Robert Kolos J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b03922 • Publication Date (Web): 24 Jun 2016 Downloaded from http://pubs.acs.org on June 27, 2016

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The Journal of Physical Chemistry

Density Functional Exploration of C4H3N Isomers Thomas Custer*a, Urszula Szczepaniaka,b, Marcin Gronowskia, Emilia Fabisiewicza Isabelle Couturier-Tamburellic, Robert Kołosa a

Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland

b

Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS, Univ. Paris-Sud, Université Paris-Saclay, F-91405 Orsay (France) c

UMR CNRS 6633, Physique des Interactions Ioniques et Moléculaires, Equipe de

Spectrométries et Dynamique Moléculaires, Aix-Marseille Université, Case 252, Centre de St-Jérôme, 13397 Marseille cedex 20, France

1 ACS Paragon Plus Environment


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ABSTRACT

Molecules having C4H3N stoichiometry are of astrophysical interest. Two of these, methylcyanoacetylene (CH3C3N) and its structural isomer allenyl cyanide (H2CCCHN), have been observed in interstellar space, while several more have been examined in laboratories. Here we describe, for a broad range of C4H3N isomers, density functional calculations (B3LYP/aug-cc-pVTZ) of molecular parameters including the energetics, geometries, rotational constants, electric dipole moments, polarizabilities, vibrational IR frequencies, IR absorption intensities, and Raman activities. Singlet-triplet splittings as well as singlet vertical electronic excitation energies are given for selected species. The identification of less stable C4H3N molecules, generated in ongoing spectroscopic experiments, relies heavily on these quantum chemical predictions.


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1. INTRODUCTION Substituted carbon chain molecules, CH3(CC)nCN (n=0, 1, 2...), are important for astrochemistry. One of these, methylcyanoacetylene (CH3CCCN, 1, where n=1), has been confirmed in both inter-1,

2

and circumstellar environments3. This species may also

participate in the atmospheric chemistry of Titan4-7. For each value of n, there also exists a family of structural isomers that may be stable and conceivably form in space (referred to in this work by a number according to predicted stability as described in Chart 1 and Supplemental Material).

As of 2005, around one third of all confirmed interstellar

molecules observed also had at least one other observable isomer8, 9. This figure remains the same today, even as the number of astrochemical molecules identified has grown. The interstellar formation of various family members might involve isolated, gas-phase molecules. It might also involve molecules on the surface of or incorporated within ice and dust particles.

Once formed, disparate structural isomers add complexity to

astrochemical models. Although a number of C4H3N species are well known, no comprehensive accounting of the structural variety and spectroscopic properties of this large family of isomers has been published. We aim at providing this information here. Aside from 1, the only additional isomer to have been identified in the interstellar medium is allenyl cyanide (H2CCCHCN, 2)2,

10

. A search for methylisocyanoacetylene (CH3CCNC, 9)11 conducted in the

interstellar cloud TMC-1 failed to detect the molecule, although an upper bound on the 9 : 1 abundance ratio could be determined.



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Within a given family of structural isomers, it is still an active question as to which members might reasonably be expected to be found in space and therefore should be considered as high priority in astro-spectroscopic searches or in laboratory measurements. Thermodynamic12 and kinetic stability13, as well as availability of synthetic pathways under relevant astrochemical or experimental conditions should all be taken into account. Due to the high reactivity of many isomers, special experimental techniques are often needed to prepare them and characterize their spectroscopic properties.

Photolysis of precursors isolated in inert cryogenic matrices can, in

conjunction with IR absorption, Raman scattering, UV-Visible absorption, and luminescence spectroscopy, aid in understanding the chemistry of individual isomers and may provide spectroscopic information of value to future astronomical measurements. Fragments produced by photolysis of a pure chemical confined in an inert matrix cage can often rearrange and recombine in novel, high-energy configurations which remain stable for sufficient time that accurate measurements can be made. In essence, these experiments serve as a form of chemical synthesis for exotic species that cannot be easily accessed in any other way. Unless experimental data is somehow already available, identification of these new, energetic species initially relies heavily on quantum chemical calculations to predict their spectroscopic properties, especially since multiple products often form, each having unique but sometimes overlapping signals. A number of computational methods have been developed to aid in searching potential energy surfaces for all stable structural isomers of a given molecular formula14-16. Such methods are indispensible where there are numerous shallow minima on a potential energy surface, such as for molecular clusters, for determining photolysis pathways, or


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for determining isomers of molecules of modest size where chemical intuition is generally insufficient to predict every stable permutation.

In order to choose

configurations of atoms for optimization using quantum chemical methods, some algorithms rely on stochastic processes while others use properties of potential surfaces to lead the user to the proper minima. In addition to producing lists of structural isomers and their thermodynamic ordering, searching algorithms of either sort may also be able to provide information concerning transition states between optimized structures, barriers leading to breakdown products, and even information on triplet or other excited states and conical intersections. Such techniques, in addition to simple use of chemical intuition, have already been applied to significant or potentially significant astrochemical molecules, a small selection of which includes formaldehyde17, pyrrole18, furan18, thiophene18, acetonitrile19, cyanoacetylene20, C4H2+ isomers21, and C2HNS isomers22. A variety of synthetic and experimental efforts as well as quantum chemical calculations provide a foundation of knowledge for a limited selection of C4H3N family members including 1, 2, propargyl cyanide (HCCCH2CN, 3), allenyl isocyanide (H2CCCHNC, 6), 1-cyanocyclopropene (c-C3H3CN, 7), 3-cyanocyclopropene (cC3H3CN, 8), 9, and propargyl isocyanide (HCCCH2NC, 10), as well as 3-isocyano cyclopropene (c-C3H3NC, 13), 3-ethynyl-2H-azirine (c-C3H3CN, 14), 2-ethynyl-2Hazirine (c-C3H3CN, 17), and N-ethynyl ethynamine (HCCNHCCH, 22). These studies span diverse experimental techniques including purely synthetic efforts, microwave, photoelectron, UV-Visible, and IR spectroscopies, crossed molecular beam experiments, and laboratory simulations of planetary atmospheres potentially leading to isomeric C4H3N species as products. For the purpose of brevity, we limit our literature focus



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mostly to computational studies. Certain experimental data have been included where comparisons with our calculations were possible. Reported quantum chemical calculations have provided energetic and reaction path information as well as ionization energies, thermodynamic properties, electric dipole moments, polarizabilities, and IR frequencies. For the most stable isomer 1, the earliest computations were performed in 196423 and many more accurate and comprehensive studies have followed. Calculations from 1974 produced the electric dipole moment derivatives24 for species 3. Semi-empirical methods (PM3, AM1, MNDO, MINDO3) were tested on carbon chains including 1 as a quick and easy way to obtain fundamental vibrational frequencies25, mostly with a view towards cost effective calculations of much larger molecules formed upon processing of astrochemical species.

Electric field

gradients and quadrupole coupling constants were calculated for 10 and compared to experimental values26 in 1992. Calculations in 1994 at the HF/6-31G* level gave the enthalpy of the isodesmic reaction converting 2 to 8, as well as the energy difference between 2 and 6, along with selected vibrational frequencies27. A number of calculations of excited states have been made in support of photoelectron spectroscopy studies to determine ionization potentials28-32. Recent work has also included calculations at the RCCSD(T)/aug-cc-pVTZ level33 which give dipole moments, polarizabilities, bond distances, and selected bond angles for the most stable C4H3N family members: 1, 2, and 3. IR frequencies and rotational constants have been reported at the B3LYP/aug-cc-pVTZ level for species 2 and 334. Very recently, vibrational frequencies of ground state 1 and various excited states of its molecular cation, CH3C3N+, were published at the B97-1/augcc-pVTZ level of theory31. SCF calculations using double-zeta-type basis were used in


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combination with results from microwave spectroscopy35 to refine the structure of 3. The IR frequencies of 8 were calculated at the B3LYP/6-31(g,d) level36. The same work also gave experimental values for the species isolated in an argon matrix.

Interatomic

distances for 8 have been reported37, apparently at the STO-3G/3-21G level of theory, to support an X-ray crystallographic study of substituent effects on double bond length. Gas phase enthalpies of formation and adiabatic ionization energies of 3 and 22 are also available38. Many other theoretical studies concern C4H3N species as reaction products, starting from various reactive precursors and their respective potential energy surfaces. This includes reactions between CN radical and the unsaturated hydrocarbons CH2CCH, CH2CCH2, or CH3CCCH339-41. The reaction between CN and CH2CCH has also been extensively analyzed experimentally using crossed molecular beams and chirped-pulse microwave spectroscopy in a supersonic flow7,

40, 42

.

Reactions between C(3P) and

CH2C(H)CN (X1A') were investigated theoretically and provide triplet energies and structures of a variety of potential C4H3N products43. Theoretical studies of reactions between 1-butyne, 2-butyne, or 1,2-butadiene and CN radical have also indicated that C4H3N isomers might be formed as a product44. Calculations have been performed in the framework of nucleophilic substitution reactions for the synthetic formation of isonitriles45 and report the energy difference between species 1 and 9. The energetics of another nitrile-isonitrile pair, 8-13 has been investigated in a B3LYP/6-31G** study46. A similar energy difference was reported at the 3-21G level in the context of calculating the ring strain energy of cyclopropene derivatives47.

CAM-B3LYP/6-311g(d,p)-based

predictions for the isocyanides 6 and 10 have been reported recently in support of IR



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measurements and include bond distance and angle information48. Ionization energies of these latter species were calculated49 in support of photoelectron spectroscopy measurements. Here we report the results of a systematic quantum chemical study for the C4H3N family of isomers, including information on relative energies, harmonic fundamental vibrational modes, vibrational intensities, Raman activities, electric dipole moments, polarizabilities, singlet-triplet splittings, and vertical singlet-singlet electronic excitation energies. Anharmonic vibrational frequencies are also provided for selected species. These values are compared with measured values and calculations taken from the literature where available, and should aid in interpretation of the growing body of work concerning photolysis and transformations of newly synthesized C4H3N isomers. For the calculations concerning the C4H3N family given here, the balance between the cost, speed, and accuracy of density functional methods seem to be acceptable. 2. COMPUTATIONAL DETAILS A search for different structural isomers on the C4H3N singlet potential energy surface was performed using the B3LYP functional50 and small basis sets (4-31G and 3-21G51-54) using two complementary methods. This combination was used in an effort to produce as complete a set of isomers as possible. The first method was inspired by the stochastic "Kick" method of Saunders15 and was written in house. In this method, atoms are seeded randomly into a gridded cube having dimensions of 7.15 Å on each side with grid nodes every 0.65 Å. No more than one atom can be placed at each node during random seeding.

All of these structures were considered as starting points for geometry

optimization with density functional calculations (B3LYP/3-21G). Optimization starting


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from randomly placed atoms sometimes resulted in identical structures. Of a total of about 2 × 105 random configurations produced, approximately 2% converged to bound structures. From these, around 100 were unique structures. As a compromise between computational time and generation of a "complete" set of isomers, an energy cut-off value of 207.63 Hartree was used for these B3LYP/3-21G calculations.

This is

approximately 340 kJ/mol with respect to the lowest energy isomer uncorrected for zero point energy. A second method for exploring the potential energy surface was to identify 14 possible molecular skeletons featuring 4 carbon atoms and 1 nitrogen atom. Around these skeletons, 3 hydrogen atoms were placed in all possible positions with the assumption that each carbon or nitrogen atom has sp3 hybridization. These structures were then subjected to geometry optimizations at both B3LYP/3-21G and B3LYP/4-31G levels of theory. The same 207.63 Hartree energy cut-off value applied earlier was again used for the B3LYP/3-21G level of theory and a cut-off of 208.5 Hartree was used for the B3LYP/4-31G level of theory. Some additional structures (no more than two per heavy atom arrangement), with relative energies less than 370 kJ/mol, were also selected for higher level calculations. The skeletal method produced essentially equivalent results to the grid-based method. Lists of molecules from the grid method and from the skeletal method were merged and subjected to further optimization at the B3LYP/aug-cc-pVTZ55-58 level. These calculations yielded equilibrium electric dipole moment, polarizability, harmonic vibrational frequencies (with corresponding IR transition intensities and Raman activities), and anharmonic vibrational frequencies for selected isomers59. All harmonic



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IR frequencies were corrected using a factor of 0.9660. Energies of the lowest triplet electronic states were also obtained at the same level of theory for the first thirty isomers and select isomers thereafter. Vertical electronic transition energies and oscillator strengths were derived using time-dependent DFT61-63 maintaining the previous functional and basis set. Most of the calculations were performed using Gaussian 0964, while some preliminary studies were made using Gaussian 0365. The programs Jmol66 and Avogadro67 were used for visualization of our results and for producing tables of bond lengths, angles, and dihedral angles which are found in the Supplemental Material. 3. RESULTS AND DISCUSSION A. Thermodynamic stability of isomers A total of 54 different bound C4H3N isomers were optimized at the B3LYP/aug-ccpVTZ level of theory. Although this is a large list, due to the energetic constraints put on the calculation, certain exotic species and individual members of isoenergetic pairs may be missing from this catalogue (see below). Only those structures with energies relative to the lowest energy isomer of less than 340 kJ/mol (without ZPE correction) were chosen for further calculations. This cut-off is based on preliminary calculations whose error in energy can be substantial. Comparing the relative energies of isomers 2-12 computed using B3LYP/4-31G to those calculated using B3LYP/aug-cc-pVTZ, the mean absolute difference is 22 kJ/mol or 27%. Extrapolating this to the higher energy cut-off of 340 kJ/mol, it is possible that species with energies as low as ~250 kJ/mol (energies 27% lower than 340 kJ/mol as calculated at the lower level of theory) failed to make the cutoff for higher level calculations and will therefore not appear in our catalogue. Beyond isomer 30, the list may be incomplete. A second energetic constraint on these calculations


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is that any isomers with identical energies and rotational constants (parameters reflecting chemical structure) were considered as the same species. This generally only poses a problem for certain chiral molecules. Once one conformation has been found, the second will have the same energy and rotational constant and will therefore be discarded, even though its non-superimposable structure formally constitutes a separate isomer. The first example of such a chiral species arises with isomer 17. At the lowest relative energies, there should be no missing structural isomers. These low energy species are discussed with the greatest detail here. Species up to isomer 12 are depicted in Chart 1 along with bond orders calculated using results of natural bond orbital analysis, natural atomic charges, point group, and energy relative to the lowest energy isomer 1. Figure 1 is a plot of both singlet and triplet energies of these isomers. Singlet methylcyanoacetylene, 1, is the global energy minimum for all structures and all energies are given with respect to this species. Similar information can be found in Table 1 which lists the species in order of total, ZPE-corrected singlet energy. Table 1 also indicates singlet energies relative to 1, ZPE-corrected triplet energies for numerous species, singlet-triplet energy differences where available, and a list of

frequencies and IR

intensities for each singlet for which intensities are greater than 100 km/mol. Considering the higher level calculation, energies that lie within about 26 kJ/mol68 of one another fall within the uncertainty of the calculation and too great a significance should not be attributed to their exact ordering. Nevertheless, spacing between isomers 12 and 13 is significantly larger than this uncertainty, indicating that the 12 lowest energy isomers are definitively more stable than those above. In addition, the energies of each of these isomers are smaller than the global energy minimum on the triplet potential energy



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surface (Fig. 1). Of the triplet structures considered here, only triplet species 19 (for which there are two distinct corresponding singlet structures, 19 and 20) is expected, together with triplet 30, to be a ground triplet state. The majority of the predicted lowest energy triplet states have high energies and need not be considered. For species 1 to 18, the average difference between the singlet and triplet state is 232 kJ/mol with the triplet always higher in energy. Relative energies of triplets obtained here match with results for the triplet surfaces calculated previously43.


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1.97

+0.24

5

8

-0.30 -0.67

+0.23

+0.24

8 7 5

+0.16

-0.19

+0.22

-0.26

4

3

2

1

0.99

2.81

2.87

0.98

6

-0.44

+0.17

1

2

1.97

-0.30

1

0.99 +0.26

-0.02

4

2

2.94

8

0.98

3

0.98

2.95

4

-0.55

-0.40

0.97

3

1.95

5

+0.29

2.92

0.97

7

0.98

1.97 -0.19

7

6

0.96

1.88

+0.27

6

0.97

+0.26

1: 0 kJ/mol, C3v

2: 10.4 kJ/mol, Cs

3: 46.5 kJ/mol, Cs

+0.23

-0.59

1.97

0.95 0.95

+0.23 -0.51 +0.17

8 6 7

1.86

3

4 1.83

+0.38

1

+0.39 -0.59

-0.29

5

+0.29

0.99

+0.46

-0.03

1

2

1.75

+0.38

-0.23

8

2.89

2

1.88

3

0.98

0.97

4

-0.48

0.97

7

1.81

1

8

2

3 0.96

1.88

1.96

7

4: 97.3 kJ/mol, Cs

+0.24

5: 104.1 kJ/mol, C1

+0.23

3 +0.24

1.88

4

-0.08

+0.24

2

3

6

1

0.94

-0.53

3 2.80

+0.31

1

2 0.97

2.86

0.98

1.97

0.94

8 +0.21

+0.23

0.99

6

0.97

+0.10

4 0.99

0.98

7: 108.8 kJ/mol, Cs

8

+0.07

8 5

0.97

8

+0.19

7

1

4 6

0.98

2

1.94

-0.66

2.94

5

-0.35

7

2.90 1.97

0.97

5

-0.27

+0.26

-0.13

+0.23

-0.13

0.96 -0.36

6: 107.9 kJ/mol, Cs 1.97

-0.33

7 0.98

6

0.97

+0.26

4

-0.13

+0.10

-0.42

0.96

2.92

-0.52

+0.23

1.96

1.80

1.80

5

6

5

8: 109.1 kJ/mol, Cs

9: 112.0 kJ/mol, C3v

1.96 +0.29

-0.18

1 2.94

-0.52

-0.03

4

-0.28

2

0.97

3

0.98

7

5 2.96

-0.80 +0.39

7

-0.17

4

6 5 0.99

0.97

6

+0.23 +0.23

-0.08

2

3 2.74

-0.19

0.98

1 2.84

8

+0.24 7 -0.60 +0.45

8 1

0.99

1.89 0.97

0.98

1.87

-0.44

3

4

6

5

0.99 2.86

0.98

1.82 1.72

+0.24

10: 139.7 kJ/mol, Cs

2

+0.23 -0.25 +0.13

11: 140.3 kJ/mol, Cs

12: 143.2 kJ/mol, Cs

Chart 1. Optimized structures for isomers 1-12 calculated at the B3LYP/aug-cc-pVTZ level of theory.

Energies are given with respect to singlet methylcyanoacetylene

(CH3C3N, 1) which is the global energy minimum.

Bond orders (bold italic) and lone

pair occupation (bold italic underlined), as well as natural charges (normal font with a



sign), were calculated or taken directly from natural bond orbital output. For symmetric molecules, duplicate bond orders and atomic charges are left off to improve legibility. Nitrogen atoms are shown in green, carbon in grey, and hydrogen in white with each atom having a unique number. Bond lengths and angles are tabulated using these numbers in the Supplemental Material along with the structures of isomers 13-54.

500

10T

23T

17T

13T

22T

3T 14T

450 Energy Relative to CH3C3N singlet (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 38

9T

16T

400

29T

26T 25T

21T 8T

27T 28T 11T

350

7T

1T

12T

300

24T

18T

6T

15T

5T

31 32

4T

250 2T

200

13

14

15

16

17

18

19

22 20 21

23

24

25

26

27

28

29

33 34

30 30T

19/20T 10

150 4

100

5

6

7

8

11

12

9

3

50 2 1

0 5

10

15

20

25

30

Figure 1. B3LYP/aug-cc-pVTZ energies of singlet C4H3N structural isomers from 1 to 34 (blue) along with the lowest energy triplets from 1T to 30T (green) having structures closest to their respective singlet structures. Singlet methylcyanoacetylene (CH3C3N, 1) is the global minimum and all energy values are given with respect to this species. Singlet numbering corresponds to structures pictured in Chart 1. Remaining structures and energies up to isomer 54 can be found in the Supplemental Material.


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Point Group

Zero-Point Corrected Energy in Hartree

Singlet Energy Relative to Singlet 1 in kJ/mol

Singlet-Triplet Splitting in kJ/mol

Strongest IR transitions Frequency in cm-1

IR Intensity in km/mol

2295

135

1

C3v (Cs)

-208.929107 (-208.805939)

0.0

323.4

2

Cs (C1)

-208.925137 (-208.854785)

10.4

184.7

3

Cs (C1)

-208.911391 (-208.751310)

46.5

420.3

4

Cs (C1)

-208.892031 (-208.837606)

97.3

142.9

2162, 941, 1448

1444, 435, 100

5

C1 (Cs)

-208.889455 (-208.826300)

104.1

165.8

2030, 951

588, 268

6

Cs (C1)

-208.888003 (-208.819441)

107.9

180.0

2110

193

7

Cs (C1)

-208.887678 (-208.804115)

108.8

219.4

8

Cs (C1)

-208.887560 (-208.782471)

109.1

275.9

9

C3v (C1)

-208.886461 (-208.762938)

112.0

324.3

2060

134

10

Cs (C1)

-208.875884 (-208.745456)

139.7

342.4

2139

170

11

Cs (C1)

-208.875661 (-208.795786)

140.3

209.7

2243, 459, 3332

321, 159, 119

12

Cs (C1)

-208.874571 (-208.810894)

143.2

167.2

2039, 3338, 2130

607, 112, 102

Table 1. Energies, point groups, IR frequencies, and IR absorption intensities for the 12 lowest energy structural C4H3N isomers, all of which are singlets. Energy values are given with respect to the singlet methylcyanoacetylene (CH3C3N, 1) global minimum. Only those IR frequencies whose vibrational transitions are stronger than 100 km/mol are listed.

In parentheses are point groups and energies for the lowest energy triplet

electronic states with structures closest to the singlet. Singlet-triplet splittings are given in a separate column. Information for isomers up to 54 can be found in the Supplemental Material along with tables with complete predictions concerning the vibrational spectroscopy of each species.



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Page 16 of 38

Setting aside concerns about energetic ordering, it is still instructive to look through the chemical structures and consider where they fall on the relative energy scale. Cyanides 1, 2 and 3 have the lowest energies of all C4H3N isomers. Although compounds 1 and 2 technically fall within the estimated 26 kJ/mol uncertainty, species 3 is unmistakably higher in energy than either of the first two. The isocyano- analogues of these chemicals, 6 and 9, are definitively less stable, although their ordering might be subject to dispute. Our calculations predict practically the same energies for 6 and 9 (108 kJ/mol and 112 kJ/mol, respectively), and a clearly higher value (~140 kJ/mol) for species 10. Almost 50 kJ/mol higher than 3 is an energy plateau spanning approximately 20 kJ/mol and consisting of isomers 4 through 9. This group is comprised of two imines (4 and 5) at the lower energies, and energetically intermixed isocyanide (6 and 9) and cyclopropene species (7 and 8). A second plateau at almost 139 kJ/mol consists of structures 10 through 12. Relative energies rise slowly and smoothly to the highest energies starting with structure 13 at 191 kJ/mol and ending with structure 54 with a relative energy of more than 400 kJ/mol.

Information concerning these high-energy species is given in

Supplemental Material. The energy difference between some of molecules studied here can be compared to those found in other works. Many calculations have employed density functional theory with similar or smaller basis sets and, as might be expected, produce results close to our own. These include energy differences: 1-2, 2-3, 2-7, 2-87, 40; 1-945; and 8-1346, 47. None of these vary from our values by more than 5 kJ/mol. In a few cases, potentially more accurate or completely different methodologies were used for calculation. Values for the energy difference 1-2 of 14.1 kJ/mol were calculated at the CBS-QB3 level of theory42


Page 17 of 38

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and 15.7 kJ/mol at the CCSD(T)/cc-pVQZ level12. A reported 3-22 energy difference of 163.2 kJ/mol was obtained by extrapolation from heats of formation of related chemicals38. With the exception of this last case and calculations at lower levels of theory, previously reported energy differences are within 10 kJ/mol of our own. A few comparisons with species outside of the C4H3N family are also possible. First, there is usually an energetic penalty for formation of isocyanides from cyanides. The 1/9 pair is separated by 112 kJ/mol, a value essentially identical to that previously calculated for the analogous cyanoacetylene/isocyanoacetylene (111 kJ/mol)69 pair.

For the

corresponding allenyl- and propargyl-based pairs (i.e. 2/6 and 3/10) the predicted energy differences

are

87

and

93

kJ/mol,

respectively.

Similarly,

for

the

cyclic

cyanide/isocyanide structures 7/16 and 8/13, this energy difference amounts to 97 kJ/mol and 82 kJ/mol, respectively. Previous calculations have indicated a similar result for the 8/13 pair46 with the additional information that there is a significant barrier for interconversion of between ~146 and 371 kJ/mol depending on the nature of the transition state. Although a full accounting of cyanide/isocyanide conversion is outside the scope of this work, some reported penalties for conversion to the isocyanide for species of astrochemical interest are worth mentioning: 79 kJ/mol for the thioformylcyanide/thioformylisocyanide

pair22,

110

kJ/mol

for

cyanodiacetylene/isocyanodiacetylene70, 100.5 kJ/mol for methyl cyanide/methyl isocyanide, and 142 kJ/mol for thionitrosyl cyanide/thionitrosyl isocyanide pair71. Some of these values are higher than those predicted for the C4H3N family. However, the isocyanide form can also be more stable than the cyanide, as exemplified by the metalcontaining pairs MgCN/MgNC72 or HMgCN/HMgNC73.



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Page 18 of 38

Ranging further afield, the relative energy of CH3CNCC, 39 (296.6 kJ/mol) with respect to 1 is a bit smaller than that of the non-methylated HCNCC (324.7 kJ/mol)69 with respect to its lowest energy isomer, HC3N. In contrast, CH3NCCC, 23 (227.2 kJ/mol) has a slightly higher relative energy than the imine HNCCC (213 kJ/mol)69. While arrangements with the CNCC skeleton are higher in energy than with the NCCC skeleton in both cases, the difference between them is greater for the non-methylated chemicals. It is interesting to note that no structure NH3CCCC was found in our calculations, possibly due to energetic cut-off values built into the algorithm used. Such a structure would have been analogous to NH3CC which has been identified as a high energy isomer of CH3CN and is 469.8 kJ/mol less stable19. Nevertheless, H2CCCCNH (4, 97.3 kJ/mol) can be compared with H2CCNH (99.9 kJ/mol), H2CCCNCH (24, 227.8 kJ/mol) or H2CNCCCH (15, 199.9 kJ/mol) with H2CNCH (221.4 kJ/mol), and finally H2NCCCCH (11, 140.3 kJ/mol) with H2NCCH (169 kJ/mol). The relative energy of imine 24 is not significantly different than that of its shorter cousin H2CNCH. However, comparing 15 with H2CNCH indicates that 15 is better stabilized with respect to its smaller analogue. The same is true for 11 and H2NCCH. One more structural motif worth mentioning in this family of isomers is the occurrence of cyclic structures. A total of 9 structures form a three-membered cyclopropene ring. Four basic cyclopropene isomers consist of the cyanide/isocyanide pairs 7/16 and 8/13. Isomers 27, 32, 35, 43, and 47 deviate from the rest by the position of hydrogen atoms which, for these species, are allowed to leave the three membered ring for outer C or N atoms. Another 6 structures form a three membered ring incorporating the N atom and two C atoms rather than three C atoms. The lowest energy structure of this kind comes


Page 19 of 38

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close to that of species 13, at 191.4 kJ/mol, which suggests the instability of this configuration. Only two structures have rings containing 4 atoms. Neither of these incorporates the N atom in the ring and both are quite high in relative energy (>294 kJ/mol). At least 5 structures are possible for five-membered rings. The lowest energy of these might be compared to the highest energy 3-membered cyclic structure at 247 kJ/mol. Structural isomers with the molecular formula C4H5N, an increase of 2 H atoms compared to the C4H3N surface examined here, have been studied computationally18 and indicate that several 5 membered rings have energies lower than about 70 kJ/mol with respect to the lowest energy isomer. It is tempting to associate energetic ordering with stability of a given compound in the laboratory. However, just as for the existence of molecules in space, kinetic stability is also of great importance. Calculations are currently underway to determine transition states and reaction paths for interconversion and decomposition of various isomers. Clues from the literature and our own experimental work with these chemicals hint at the complexity of the system. Many syntheses of 1 begin by first producing 2 and 3 which are then converted to 1 through simple processes such as steam distillation4. The spontaneous conversion of species 2 to 1 in the cell of a microwave spectrometer has also been reported74. Flash vacuum pyrolysis of tetrazolo[1,5-b]pyridazine at 380°C and 0.02 mm Hg results in production of a mixture potentially containing 1, 2, 3, 7, and 875. Attempted purification of 3 and 8 from the mixed products was reportedly impossible using gas-liquid chromatography.

The authors go on to speculate that 3 and 8

spontaneously convert to 1 and 2 and note that lower temperature pyrolysis results in a higher fraction of 3 and 8. From this, it was inferred that 1 and 2 are formed by the



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Page 20 of 38

isomerization of 3 and 8. Further, the possible observation of the CN stretch of 7 following gas-liquid chromatography was reported, a signal that disappeared at higher column temperatures. These collected observations might be taken as support for the general energetic order: 1, 2, and 3 followed by 7 and 8 at somewhat higher energies. The facile decomposition of 3, something we have observed in our laboratory even at temperatures of -78°C, is also indicative of poor kinetic stability and seems to be shared by 7 and 8. Very few references exist in the literature concerning 7, while 8 has been produced in sufficient quantity that its microwave spectrum could be recorded. From experience in the lab, isocyanides 6 and 10 both can be comfortably stored for long periods at -78°C. This hints that the barrier to their decomposition or interconversion is higher than for certain lower energy species like 3. Perhaps the most striking observation is that neither imine 4 nor 5 has been synthesized or observed either in lab or in space, even though both have substantially lower energies than the mentioned isocyanides and in light of the fact that smaller imine analogues including CH2NH, H2CCNH and CH3CHNH have all been characterized and detected in space76. It may be that 4 and 5 are kinetically even less stable than their smaller counterparts, explaining why they have yet to be detected in spite of a growing body of experimental work on C4H3N isomers. B. Electric dipole moment and polarizability Knowledge of electric dipole moments is crucial for astrochemistry. Gas phase ionmolecule reaction rate constants depend on the dipole moments and polarizabilites of the neutral molecules77, 78 and theoretically predicted values can be applied in modeling of the chemical evolution of interstellar gas clouds. The intensities of rotational transitions also depend on dipole moments, so the values given here can be used to estimate


Page 21 of 38

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abundances of molecules in space. Table 2 shows the calculated equilibrium dipole moments of the 12 most stable isomers together with experimentally measured ground state values, where available. Calculated polarizabilities are also given although no experimental values are available for comparison. It is instructive to compare our predicted electric dipole moment values with values from microwave spectroscopy experiments. The mean difference between theoretical and experimental value is 0.2 D with a significantly larger difference of 0.62 D for the isomer 1. Calculations using a variety of density functionals (HFB, CAM-B3LYP, O3LYP, HCTH, X3LYP, B97D, B2PLYP, B2PLYPD, and HFS) produced dipole moments between 5.2 D to 5.4 D. These dipole values are not significantly closer to the only available experimental value of 0.29 D than the B3LYP results. Use of RCCSD(T)/aug-cc-pVTZ (without d functions on H and f functions on heavy atoms)33 predicts a dipole moment of 5.041 D. The difference with respect to the experimental value of 0.29 D (4.8 D) is still larger than that expected (less than 0.2)79 for this combination of theory and basis set. The errors in dipole moments come close to those reported in benchmark calculations on small molecules80 which suggest that the RMSD error in dipole moments should be on the order of 0.12 to 0.13 Debye and for polarizabilities around 0.3 to 0.38 Å3. Further corrections for ground state vibrations81-83 were not performed as the level of accuracy obtained was sufficient for our broad survey of structural isomers. Electric Dipole Moment (D) Polarizability (Å3) Experiment

Calculation

Calculation

4.7584

5.04133, 5.37

8.00833, 8.42

2

4.2874, 4.2885 4.26633, 4.48

8.13633, 8.48

3

3.6186, 3.9985 3.62133, 3.72

7.17533, 7.41

1



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

4

1.46

10.86

5

1.54

9.06

4.03

8.82

4.05

7.77

3.81187

6 7 8

4.4788

4.60

7.22

9

4.1989

4.30

8.80

10

3.7186

3.64

7.67

11

2.66

9.63

12

1.20

9.47

Page 22 of 38

Table 2. Electric dipole moments and polarizabilities of the 12 lowest energy C4H3N isomers. Values from this work (B3LYP/aug-cc-pVTZ) are given without superscript. All other superscripts are references to the original data. A full table including all species is given in the Supplemental Material. C. Geometric parameters and rotational constants The predicted bond distances and angles are presented in tables in the Supplemental Material. The estimated error in calculated interatomic distances is on the order of few pm90. For species 1, 2, and 3 we can compare the results of present calculations to those of a high level ab initio study33. The predicted B3LYP/aug-cc-pVTZ bond distances are shorter on average by 0.009 Å than those calculated using CCSD(T)/aug-cc-pVTZ. Rotational constants generally scale as the square of the bond distance and, based on this, we estimate that equilibrium rotational constants are predicted with precision on the order of one percent. We can also compare our ground vibrational or equilibrium rotational constants with experimental ground state rotational constants for the isomers 191-93, 274, 94, 385, 86, 95, 687, 888, 96, 989, and 1086, 97. The predicted ground vibrational and equilibrium


Page 23 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


rotational constants for 12 isomers are presented in Table 3 along with available experimental ground state values, while the complete list of calculated ground vibrational and equilibrium rotational constants appears in the Supplemental Material. The mean difference between our calculated value and each of the different experimentally measured rotational constants is 0.9% with a mean absolute difference ~1.2 times larger, in generally good agreement with the accuracy we predict for our calculations. Theory (this work)

Experimental

Point A0(Ae)/GHz

B0(Be)/GHz

C0(Ce)/GHz

A0/GHz

B0/GHz

C0/GHz

Group 2.0657393 1

C3v

158.5 (160.4)

2.082 (2.083)

2.082 (2.083)

2.065738684 (181)92 2.0657383691

2

3

Cs

Cs

27.15 (26.92)

20.43 (20.29)

2.677 (2.684)

2.889 (2.898)

2.474 (2.482)

2.566 (2.576)

4

Cs

285.2 (207.9)

2.144 (2.145)

2.148 (2.135)

5

C1

28.86 (28.52)

2.68 (2.69)

2.466 (2.475)

6

Cs

29.25 (29.07)

2.799 (2.805)

2.595 (2.604)

7

Cs

23.77 (23.97)

3.326 (3.329)

2.972 (2.981)

8

Cs

20.16 (20.27)

3.519 (3.534)

3.403 (3.415)

9

C3v

158.9

2.210

2.210

25.98100(8)74

2.68929(3)74

2.47481(2)74

25.981049(27)94

2.68927577(66)94

2.47482156(65)94

19.81954(50)95

2.90958(13)95

2.57333(12)95

19.82017935(23)85

2.90960528(33)85

2.57321073(35)85

19.8201789(22)

2.90959089 (33)

2.57322455(35)

19.8204418(4)86

2.9095993(1)86

2.5732246(1)86

28.0697626(61)87

2.81363039(49)87

2.59900326(52)87

19.876036(6)88

3.533743(1)88

3.417839(1)88

19.569(29)96

3.483966(4)96

3.363052(52)96

2.1963343(1)89



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(160.8)

(2.211)

(2.211)

3.044 (3.054)

2.701 (2.711)

10

Cs

21.14 (20.99)

11

Cs

324.4 (318.7)

2.099 (2.098)

2.087 (2.087)

12

Cs

51.07 (48.41)

2.581 (2.6)

2.495 (2.51)

Page 24 of 38

20.5279749(3)86

3.07459486

2.7145230(1)86

20.527875(33)97

3.0746060(65)97

2.7145243(62)97

Table 3. Calculated ground vibrational state and equilibrium rotational constants of the 12 lowest energy isomers in GHz (B3LYP/aug-cc-pVTZ) alongside ground vibrational state rotational constants from microwave spectroscopy experiments reported in the literature. Values in parentheses represent uncertainties in the last digits of the number they follow. D. IR vibrational transitions Table 1 lists vibrational frequencies and intensities for vibrational transitions stronger than 100 km/mol. Complete lists of fundamental harmonic vibrational frequencies corrected by 0.96 and anharmonic frequencies are given in Supplemental Material. Our theoretical results can be compared to limited available gas-phase or matrix isolation measurements including species 131, 98-100, 299, 399, 648, 836, 99, 9101, and 1048. Calculated frequencies deviate from gas-phase measurements by up to 100 cm-1 in either direction, depending on the vibration and the chemical being considered. This is true of both anharmonic and scaled harmonic values. For anharmonic results, the deviation between the calculated value and measured value is comparable to that observed for scaled harmonic results. Where experimental values were measured in a rare gas matrix, matrix shifts can cause further deviations from calculations. Ultimately, calculated IR


Page 25 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


absorption intensities are reflective of what is observed but can only be used qualitatively. Based on the results of the calculations, transition intensities for the strongest absorptions can be roughly divided into four intensity categories: greater than 1000 km/mol, between 500 and 1000 km/mol, between 100 and 500 km/mol, and less than 100 km/mol. Intensities serve as a rough proxy for how sensitively a given species might be detected. Species 4, 23, and 47 have the strongest transitions (1444 km/mol at 2162 cm-1; 1763 km/mol at 2290 cm-1; and 1479 km/mol at 2067 cm-1) of all the chemicals. The intense CN vibration combined with the low overall energy of species 4 make it an appealing target for detection, e.g., upon photolysis of 1. Following these three chemicals, the next most intense transition is that of species 24 (722 km/mol at 860 cm-1) followed closely by species 5, 12, 18, 37, 39, 40, 41, and 45 whose most intense IR bands lie between 500 and 722 km/mol. An additional 23 species have intensities between 100 and 500 km/mol with the remaining 18 having intensities below 100 km/mol. It has been noted previously that carbon-nitrogen stretching IR bands often have lower intensities in nitriles (-CN) than in corresponding isonitriles (-NC)102. This has proven to be true for the nitrile/isonitrile pairs 2/6, 7/16, 8/13, whose isonitrile vibrational intensities are 8, 5, and 9 times the nitrile intensities, respectively. For the pair 3/10, the nitrile and isonitrile vibrations are weakly coupled with the CC triple bond. Nevertheless, the isonitrile stretching intensity is 33 times that of the nitrile. In the linear nitrile/isonitrile pair 1/9, the nitrile and isonitrile stretches are strongly coupled with CC triple bond vibrations. Comparisons between absorption intensities no longer make sense for this molecule as no pure nitrile or isonitrile vibration can be said to exist.



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Page 26 of 38

E. Excited electronic states A combination of measurements including UV-Vis absorption and luminescence, IR absorption, or Raman spectroscopy is often necessary for unambiguous identification of a previously uncharacterized chemical. Strong electronic transitions are sometimes useful molecular fingerprints, providing a sensitive means of detection of certain species. Knowledge of such transitions may also aid in the search for molecules in space103 although relatively few astrochemically relevant species have been identified on the basis of their electronic transitions alone. Table 4 lists the electronic states for the most stable C4H3N isomers. Most of the transitions have a π→π* nature, especially those towards the ෩ and B ෩ electronic states are of a lowest states. For isomers 1 and 9, the transitions to A nature similar to those known for cyanoacetylene and isocyanoacetylene. With the exception of 4, all of the molecules discussed here have electronic transitions confined to the UV range. They are therefore not likely to undergo any transformation on exposure to visible light. The only published electronic spectrum found for this family of isomers4 was for species 1. This spectrum is in qualitatively good agreement with our calculated ෩ state progression starting near 228 nm and a less values and show a more intense B ෩ state progression starting near 244 nm. Our calculations indicate values near intense A 233 nm and 238 nm should be expected for these states, respectively. Molecule

State

Energy/eV

Oscillator strength2)

(CH3CCCN, 1)

෩ A2 A

5.2

0

෩E B

5.3

0.0003

෩ 1A’’ A

5.4

0.0006

෩ 1A’’ B

5.6

0.0002

(H2CCCHCN, 2)


Page 27 of 38

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C෨ 1A’

6.4

0.3

(HCCCH2CN, 3)

෩ 1A’’ A

6.5

0.0001

(HNCCCCH2, 4)

෩ 1A’’ A

2.8

0.0002

෩ 1A’ B

4.4

0.05

C෨ 1A’

5.1

0.005

෩ 1A’’ D

5.1

0

෩ 1A’ E

5.5

0.007

F෨ 1A’’

5.8

0.0009

෩ 1A’’ G

6.1

0

෩ 1A’ H

6.3

0.09

ሚI 1A’

6.3

0.9

෩ 1A A

4.1

0.0004

෩ 1A B

5.1

0.011

C෨ 1A

5.4

0.03

෩ 1A D

5.7

0.013

෩ 1A E

5.8

0.006

F෨ 1A

5.9

0.002

෩ 1A G

6.1

0.07

෩ 1A H

6.1

0.09

෩ 1A’’ A

5.3

0.0008

෩ 1A’’ B

5.8

0.002

C෨ 1A’

6.3

0.4

෩ 1A’’ D

6.4

0.0010

෩ 1A’’ A

5.3

0.0004

෩ 1A’ B

5.4

0.15

(HCCCHCNH, 5)

(H2CCCHNC, 6)

(c-C3H3CN, 7)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

C෨ 1A’’

6.3

0.0004

෩ 1A’’ D

6.4

0.006

(c-C3H3CN, 8)

෩ 1A’’ A

6.0

0.011

(CH3CCNC, 9)

෩ A2 A

5.2

0

5.3

0.0002

6.5

0.0013

෩ 1A’’ (HCCCH2NC, 10) A

6.4

0.0001

෩ 1A’’ (HCCCCNH2, 11) A

4.0

0

෩ 1A’ B

4.6

0.003

C෨ 1A’

4.8

0.010

෩ 1A’’ D

5.4

0

෩ 1A’’ E

5.5

0.0001

F෨ 1A’

5.6

0.003

෩ 1A’’ G

5.7

0.0002

෩ 1A’ H

6.2

0.014

ሚI 1A’’

6.4

0.008

ሚJ 1A’

6.4

0.007

෩ 1A’’ (HCCNCCH2, 12) A

3.7

0.0002

෩ 1A’’ B

5.3

0

C෨ 1A’

5.4

0.05

෩ 1A’ D

5.5

0.02

෩ 1A’ E

6.2

0.017

F෨ 1A’

6.4

0.4

෩ 1A’’ G

6.4

0.0014

෩ 1A’’ H

6.5

0.01

෩E B C෨ 1E

Page 28 of 38


Page 29 of 38

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ሚI 1A’’

6.5

0.005

Table 4. Excited singlet electronic states having vertical energies lower than 6.5 eV (190 nm) for the 12 lowest energy isomers calculated using TD-B3LYP/aug-cc-pVTZ. Oscillator strengths smaller than 0.0001 were treated as 0.

4. CONCLUSIONS The 12 lowest energy isomers of C4H3N were determined and include 5 nitriles, 3 isonitriles, 3 imines, and 1 amine. Many of these species have appreciable IR absorption intensities. Those with the lowest energy and strongest IR bands include species 4, 5, and 12. All of these are imines, none of which have ever been detected experimentally or in space. Only four species have a maximum IR absorption intensity less than 100 km/mol and these include 2, 3, 7, and 8. With the possible exception of 4 which has a low-lying excited state, the other 11 lowest energy species should be resistant to photochemical destruction by visible light. This set of calculations provides a solid starting point for interpretation

of

experiments,

particularly

those

concerning

photochemical

transformations, involving the various C4H3N isomers.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 38

ASSOCIATED CONTENT Supporting Information. Chart including structures, bond orders, and natural charges of all calculated singlet structures in addition to triplets 19 and 30. Tables including all fundamental IR vibrational transitions and their respective intensities, and bond lengths and angles of optimized singlet structures. Also included is a table of dipole moments and equilibrium rotational constants for all singlet molecules. This material is available free of charge via the internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *) corresponding author; Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52 01-224 Warszawa, Poland; Email: [email protected]. Phone: +48 22 343 3353 ACKNOWLEDGMENT Authors acknowledge financial support from the Polish National Science Centre, project number 2011/03/B/ST4/02763.


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