Exotic isomers of dicyanoacetylene : A density functional theory and ab initio study

Prospects for the existence and detection of yet unknown dicyanoacetylene ~NCCCCN! isomers are discussed, based on quantum-chemical calculations for linear, hexagonal and branched C 4N2 structural variants. It is concluded that apart from dicyanoacetylene itself and its two already discovered isomers, NCCCNC and CNCCNC, at least two other species are of importance: linear CCCNCN and Y-shaped CC ~ N!CN ~dicyanovinylidene!. Combined CCSD~T! and MP4 calculations predict CC ~CN!CN and CCCNCN to be 57 kcal/mol and 66 kcal/mol less stable than dicyanoacetylene, respectively. The height of the energy barrier for dicyanoacetylene ←dicyanovinylidene isomerization is about 5 kcal/mol. Density functional theory calculations indicate that CCCNCN should give rise to prominent IR absorption bands, two orders of magnitude stronger than those of dicyanoacetylene. © 2002 American Institute of Physics. @DOI: 10.1063/1.1489992 #


I. INTRODUCTION
Dicyanoacetylene ͑butynedinitrile; NCCCCN͒, first characterized in 1909 by Moureu and Bongrand, 1,2 was tentatively identified, eight decades later, in Titan's atmosphere. 3,4Its detection in clouds of interstellar matter ͑along with strikingly abundant cyanoacetylene 5 ͒ was not feasible due to the centrosymmetric structure of the molecule, resulting in the absence of rotational microwave spectra.However, interstellar dicyanoacetylene may eventually be discovered due to the rapid development of the astronomical infrared spectroscopy.The existence of such bare carbon-nitrogen chains in space was recently postulated, 6 and it seems important to explore, both theoretically and experimentally, the entire C 4 N 2 potential energy hypersurface, including the ''exotic'' isomers, highly unstable at normal conditions.These studies, pioneered by Smith et al. 7,8 and backed with accurate ab initio calculations by Botschwina et al., 9,10,11 so far resulted in the identification of NCCCNC ͑cyano-iso-cyanoacetylene͒ and CNCCNC ͑diiso-cyanoacetylene͒, created through the in situ ultraviolet photolysis of NCCCCN in solid argon.Present work deals with a range of C 4 N 2 molecules, supplying the theoretical predictions for their equilibrium structures, energies, electric dipole moments, and infrared transitions.

II. DETAILS OF CALCULATIONS
All calculations reported in this study were accomplished with GAUSSIAN 98 suite of programs. 12Hartree-Fock ͑HF͒ method and the 6-31 G* basis set 13 were used for some preliminary geometry optimizations.Density functional theory 14,15,16 ͑DFT͒ calculations, aimed at the reproduction of molecular geometries and harmonic vibrational frequencies ͑normal modes of molecular vibrations being obtained through analytical second derivatives of the total energy, with respect to nuclear positions͒ were accomplished with the Becke's three parameter hybrid exchange functional method 17 and the correlation functional of Lee, Yang, and Parr 18 ͑B3LYP͒.The Dunning's correlation-consistent polarized valence triple-zeta basis set, augmented by s, p, d, and f functions ͑aug-cc-pVTZ͒ ͑Ref.19͒ was used in final DFT calculations.Additionally, for selected species, the equilibrium geometries were found at the Møller-Plesset 20 fourth order perturbation theory level, MP4͑SDTQ͒, involving single, double, triple, and quadruple excitations with frozen core electrons, and the Dunning's cc-pVTZ basis set. 21The single, double, and perturbative triple excitation coupled-clusters 22 calculations, CCSD͑T͒/cc-pVTZ, served exclusively to obtain ''single point'' energies for fixed MP4derived geometries.͓This corresponds to CCSD͑T͒//MP4 according to the notation adopted throughout the article.͔The search for the transition state geometry was carried out with the synchronous transit-guided quasi-Newton ͑STQN͒ method 23 in conjunction with B3LYP/aug-cc-pVTZ; the transition state nature was further verified by tracing the reaction paths in both directions from the saddle point with the method of Gonzalez and Schlegel. 24The ab initio energies of the transition state and relevant stable structures were compared at the uniform CCSD͑T͒/cc-pVTZ//MP4͑SDQ͒/cc-pVTZ level.Post SCF ab initio dipole moment calculations were limited to the MP4͑SDQ͒/cc-pVTZ.Standard convergence criteria were applied in all computations.

III. RESULTS AND DISCUSSION
Formally, dicyanodiacetylene has as many as 9 nonbranched chain isomers, hereafter named 1-9 ͑see Fig. 1  The first stage of this project consisted in calculations of preliminary structures ͑in particular, in finding out what symmetries of chain species 1-9 are to be expected͒.Then, the geometries and IR spectra were obtained at the reliable DFT level.Finally, the geometry optimizations were repeated for selected species with ab initio methods, to improve the predictions on energies and dipole moments.

A. Preliminary structures
The rudimentary search for equilibrium geometries of chain molecules 1-9 was accomplished with simple HF/6-31G* optimizations.Planar starting geometries, with uniform bond lengths and all combinations of ϩ133°and Ϫ133°angles between consecutive bonds were systematically tried.The nature of obtained stationary points on the potential energy surface was disclosed by the normal modes of molecular vibrations, saddle points being indicated by the appearance of imaginary frequencies.Energy minima corresponding to linear molecules were found for species 1-5 and 7-9.The linear arrangement of molecule 6 was a second order saddle point; a bent structure was found as the local energy minimum.Some starting geometries led also to bent molecules 3, 5, and 7. Bent 3 was 1.6 kcal/mol less stable than linear 3, bent 5 had virtually the same energy as linear 5, while bent 7 turned out to be a saddle point.
Preliminary calculations for the branched and hexagonal species consisted in geometry optimizations at the B3LYP/ 6-31G* level.The hexagon with adjacent nitrogen atoms ͑ortho structure͒ converged to dicyanoacetylene ͑1͒ and was rejected from further analysis.
It was checked that the ground states of all molecules under study were of singlet multiplicity.The UB3LYP/ 6-31G* scheme was used to find the geometries of triplet species for branched and cyclic isomers, while the combination of UHF/6-31G* and UB3LYP/6-31G* served to optimize diverse starting geometries of chain molecules.The potential energy minima of triplets (E T ) were compared to those of singlets (E S ) at the uniform DFT level.The E T ϪE S differences were at least 19 kcal/mol, with the exception of isomer 11, for which the triplet equilibrium structure was just 1.5 kcal/mol above the singlet.

B. Geometries and vibrational frequencies
In the second phase of the study, the B3LYP/aug-cc-pVTZ calculations were performed for singlet isomers 1-12.This was aimed at producing the realistic predictions for geometries and corresponding harmonic vibrational frequencies, and at selecting the energetically favorable species.For molecules 1-5 and 7-9 the arbitrarily chosen zigzag starting geometries converged to linearity.Bent initial structures 3, 5, and 7 ͑yielded by HF calculations͒ were also subjected to B3LYP/aug-cc-pVTZ geometry optimizations; bent 3 was 1.2 kcal/mol higher in energy than linear 3, whereas bent 5 and 7 ceased to be stationary points, at this level of theory, and evolved towards linear structures.For molecule 6, similarly as in the HF study, the linear conformation was in fact a saddle point, and the energy minimum was found for a bent arrangement.
Table II  The most intense bands for each isomer are listed; transitions predicted as relatively weak are included for 1 and 9 to ease the comparison with available experimental and theoretical data ͑cf.Table I͒; complete listings of vibrational transitions for species 4 and 10 are given in Table III.d Scaled down with the factor 0.96.and 9 generally agree well with former experimental and theoretical data collected in Table I.As expected, however, when compared with advanced ab initio treatment of anharmonic vibrations, DFT is much worse in reproducing IR intensities.
The most important predictions of the DFT study concern species 10, CC͑CN͒CN, and 4, CCCNCN.It appears that the energy of 4, corrected for the zero-point energy ͑ZPE͒, is just several kcal/mol above that of the known centrosymmetric isomer 9. Isomer 4 is remarkable due to the outstanding strength of its infrared bands, approaching 1700 and 900 km/mol-which may facilitate their detection in forthcoming laboratory experiments and astronomical searches.Isomer 10, of the similar energy, is expected to have medium intensity IR bands.The complete listings of predicted fundamental modes for species 4 and 10, given in Table III, can serve as guidelines in the spectroscopic work.Frequency values were scaled down with a uniform factor to account for the anharmonicity, incomplete inclusion of electron correlation, and deficiencies in the basis set.The factor 0.96 was chosen after comparing the calculated values with available experimental frequencies for species 1, 2, and 9. Similar scaling factors were shown to work well for B3LYP calculations with basis sets 6-31G* ͑0.9613; huge selection of arbitrarily chosen molecules 27 ͒ and 6-311ϩG* ͑0.956; recent work on cyanoacetylene isomers 28 ͒.

C. Ab initio calculations
In the final stage of the study, geometry optimizations for most important isomers were repeated at the higher level of theory-to refine the energetics.The ab initio calculations were performed on molecules with frozen symmetries ͑either D ϱh , C ϱv or C 2v , as predicted with DFT͒.MP4͑SDTQ͒derived bond lengths and angles for 1, 2, 4, 9, and 10 are listed in Fig. 1.Calculated lengths are expected to be too large by not more than 2%, as exemplified by molecule 2, for which the experimental data are available; 11 the main share of this elongation presumably stems from the neglect of the core electrons correlation.B3LYP/aug-cc-pVTZ geometries seem more accurate.
Conversely, the energies yielded by CCSD͑T͒// MP4͑SDTQ͒ ͑Table IV͒ are more reliable than corresponding DFT values.The relative numbers for species 2 and 9 practically match those found by Botschwina et al. ͑cf.Table I͒; the latter have to be regarded as highly precise.The energies of 4 and 10 suggest, just as precedent DFT results, that these two molecules are potentially detectable C 4 N 2 isomers.It has to be noticed that the reverse-when compared to DFT-energy order for compounds 4 and 10 was obtained.Namely, the ZPE-corrected dicyanovinylidene ͑10͒ potential energy is 5 kcal/mol above that of known species 9, while the energy of 4 is higher by an additional 9 kcal/mol ͑ZPEs calculated with B3LYP/aug-cc-pVTZ͒.
The MP4͑SDQ͒-derived electric dipole moment of 2 ͑Table IV͒ is very close to the more refined CCSD͑T͒ value reported by Horn et al. 9 ͑cf.Table I͒, which enables us to draw reliable conclusions from two other e values delivered by present ab initio calculations.Specifically, rather low ͑though higher than predicted by DFT͒ dipole moments of 4 and 10 mean that the detection of corresponding interstellar rotational microwave spectra would be difficult, if possible.
The barrier height for dicyanoacetylene←dicyanovinylidene (1←10) isomerization, calculated at the CCSD͑T͒//MP4͑SDQ͒ level, amounts to 5.8 kcal/mol classically, and diminishes to 5.1 kcal/mol after the inclusion of ZPE corrections.͓The ZPE of the transition state ͑TS͒ is 14.5 kcal/mol, as predicted by B3LYP/aug-cc-pVTZ.͔At the B3LYP/aug-cc-pVTZ level the ZPE-corrected barrier is 3.5 kcal/mol.The imaginary vibrational mode of TS ͑Fig.2͒ moves the terminal carbon atom towards one of cyano groups, thus distorting the structure in the direction of 1.The vibrational mode of 10, which promotes the 1←10 isomerization, is 9 ͑Table III͒ with corresponding harmonic vibra-   29 who did extensive ab initio calculations on cyanovinylidene, CC͑H͒CN.Their CCSD͑T͒/TZ2P study yielded 47 kcal/mol as the ZPE-corrected energy difference between cyanoacetylene ͑the global minimum on the PES of HC 3 N͒ and cyanovinylidene.The barrier for reverse isomerization ͑towards cyanoacetylene͒ was 2.2 kcal/mol with ZPE ͑roughly two quanta of the cyanovinylidene mode that leads to the transition state͒.These predictions were very quickly followed by the experimental ͑mass-spectrometric͒ evidence for the existence of cyanovinylidene. 30

IV. CONCLUSIONS
Despite relatively high potential energy, the linear species CCCNCN is-considering the strength of its infrared spectrum-the candidate for detection in laboratory samples and in interstellar molecular clouds.It can probably be trapped and isolated, together with its Y-shaped isomer dicyanovinylidene, CC͑CN͒CN, in cryogenic rare gas matrices, after the suitable decomposition and rearrangement of gaseous dicyanoacetylene.The entire C 4 N 2 hypersurface, with transition states linking numerous minima, deserves further exploration in order to adequately evaluate the stabilities of different isomers, including the highly energetic ones.Likewise, the availability of synthetic routes, which could possibly lead to the interstellar formation of polycarbondinitrogen molecules, remains an open issue.

FIG. 1 .
FIG. 1. Equilibrium geometries for selected isomers of C 4 N 2 , as derived by B3LYP/aug-cc-pVTZ calculations.Black balls represent nitrogen atoms.Bond lengths given in angstroms.Values in parentheses result from MP4͑SDTQ͒/cc-pVTZ geometry optimizations.

TABLE II .
Energies, dipole moments, and main IR vibrational transitions of C 4 N 2 molecules, as predicted by the density functional theory ͑B3LYP/aug-cc-pVTZ͒.
a Zero-point correction included.bB e constants for linear species ͑B e multiplied by 0.99 can serve as the prediction for B 0 ; see text͒; A e , B e , and C e for nonlinear species.c
a Scaled down with the factor 0.96.

TABLE IV .
Ab initio potential energy minima, relative energies, and equilibrium electric dipole moments for selected C 4 N 2 isomers.These qualitative considerations suggest dicyanovinylidene to be a well bound species.It is of interest at this point to recall the results of Hu and Schaefer, tional quantum of Ϸ1 kcal/mol.Calculations indicate that it takes several such quanta to climb the barrier towards 1.