Tautomerization, acidity, basicity, and stability of cyanoform: a computational study
 Shaaban A. Elroby^{1, 2}Email author
Received: 3 December 2015
Accepted: 28 March 2016
Published: 11 April 2016
Abstract
Background
Cyanoform is long known as one of the strongest acid. Cyanoform is only stable below −40 °C. The issue of the stability and tautomeric equilibria of cyanoform (CF) are investigated at the DFT and MP2 levels of theory. The present work presents a detailed study of structural tautomer interconversion in three different media, namely, in the gas phase, in a solvent continuum, and in a microhydrated environment where the first solvation layer is described explicitly by one or two water molecule. In all cases, the transition state has been localized and identified. Proton affinities, deprotonation energies and the Raman spectra are reported analyzed and discussed.
Results
The 1 tautomer of cyanoform is shown to be more stable than 2 form by only 1.8 and 14.1 kcal/mol in the gas phase using B3LYP/6311 ++G** and MP2/6311 ++G** level of theory, respectively. This energy difference is reduced to 0.7 and 13.4 kcal/mol in water as a solvent using CPCM model using B3LYP/6311 ++G** and MP2/6311 ++G** level of theory, respectively. The potential energy barrier for this proton transfer process in the gas phase is 77.5 kcal/mol at MP2/6311 ++G** level of theory. NBO analysis, analysis of the electrostatic potential (ESP) of the charge distribution, donor–acceptor interactions and charge transfer interactions in 1 and 2 are performed and discussed.
Conclusions
Gross solvent continuum effects have but negligible effect on this barrier. Inclusion of one and two water molecules to describe explicitly the first solvation layer, within the supermolecule model, lowers the barrier considerably (29.0 and 7.6 kcal/mol, respectively). Natural bond orbital (NBO) analysis indicated that the stability of the cyanoform arising from charge delocalization. A very good agreement between experimental and theoretical data has been found at MP2/6311 ++G** for the energies. On other hand, B3LYP/6311 ++G** level of theory has good agreement with experimental spectra for CF compound.
Keywords
Cyanoform Tautomerization Waterassisted proton transfer B3LYP MP2 PCM Raman spectraBackground
Tricyanomethane or cyanoform is long known as one of the strongest acid with pKa = −5.1 in water and 5.1 in acetonitrile [1], however, its relative stability have been and still is a controversial subject. The molecule has previously only been identified by microwave spectroscopy in the gas phase at very low pressures [2–4].
The stability and structure of 1 in the gas phase were investigated by quantum chemical calculations [7–13]. Results of these computational studies revealed that 1 is more stable than 2 by about 7–10 kcal/mole in the gas phase. In the present work, the issue of the stability and tautomeric equilibria of 1 are revisited. Computations at high level of theory and in the gas as well as in solution are performed. Waterassisted proton transfer is investigated for the first time where transition states, a barrier energies and thermodynamic parameters are computed. The ground state geometries, proton affinities, deprotonation energies and
the Raman spectra are reported. NBO analysis of the charge distribution, donor–acceptor interactions and charge transfer interactions in 1 and 2 are performed and discussed.
Computational methods
All quantum chemical calculations are carried out using the Gaussian 09 [14] suite of programs. Full geometry optimizations for each and every species studied have been carried out using two DFT functionals namely, the B3LYP [15–17], and MP2 [18–20] methods using the 6311 ++G** basis set. The frequency calculations carried out confirm that all the optimized structures correspond to true minima as no negative vibration frequency was observed. Number of imaginary frequencies are zero for minima and one for transition states. Zero point energy (ZPE) was enclosed in all energetic data.
Among all DFT methods, B3LYP often gives geometries and vibration frequencies, which are closest to those obtained from the MP2 method. Natural bond orbital (NBO) population analysis on optimized structures is accomplished at the B3LYP/6311 ++G** level [21]. NBO calculations were performed using NBO 5.0 program as implemented in the gaussian 09 W package. The effect of solvent (water) is taken in consider using the selfconsistent reaction field polarisable continuum model (SCRF/PCM) and SMD models [22–24]. Results were visualized using chemcraft program [25].
Results and discussion
Due to the 1 → 2 intramolecularproton transfer, a number of structural parameters of the 1 form have changed. Going from the 1 to the 2 tautomer, the C–C bonds length decreases from 1.475 to 1.430 and 1.342 Å, whereas the C–N bond length enlarges from 1.175 to 1.178 Å. In the optimized geometry of the TS, breaking of the C–H1 bond together with the formation of N8–H1 bond is clear. In 1 tautomer, The C1–H1 and C–C distances vary from 1.098 and 1.474 Å for the 1 tautomer to 1.862 and 1.426 Å for the TS, respectively. The N1–H1 is 1.539Å in TS. This distance is 1.019 Å for the 2 tautomer. The analysis of the normal modes of TS imaginary frequencies (−1588.00) revealed the displacements of N6–H2 and C1–H2 bond lengths of 1.
Tautomerization 1⇄2
Proton transfer reactions are very important in chemistry and biology as it underlie several technological and biological processes.
Some investigations [6] have suggested that the tautomeric form 2 may exist and underlies the strong acidity of cyanoform. In the present section, the possibility of 1, 3 proton transfer in 1 will be explored.
Total and relative energies for the studied species using two methods (B3LYP and MP2) at 6311 ++G** basis set in the gas phase and in the solution
Structure  Gas phase  Solvent  

MP2  B3LYP  MP2  B3LYP  
E_{t}/au  kcal/mol  E_{t/au}  kcal/mol  kcal/mol  
1  −316.40004  0.0  −317.27785  0.000  0.0  0.0  
2  −316.37761  E_{re}  14.1  −317.27506  E_{re}  1.8  E_{re}  13.4  0.7 
TS  −316.28143  E_{a}  77.5  −316.79868  E_{a}  68.7  E_{a}  74.4  68.4 
CF^{−}  −315.91668  DP  303.3  −317.16841  DP  300.7  DP  272.7  262.6 
(CFH)^{+}  −316.70615  PA(H)  −46.8  −317.54566  PA(H)  −168.1  PA(H)  −230.1  −231.4 
Table 1 compiles also relative energies in water as a solvent computed using the solvent continuum model CPCM, where the 1 tautomer is found to be the more stable. Solvent dielectric constant seems to have marked effect on the stability of 1. This is in agreement with a previous experimental study [6].
The lower relative stability of the 2 tautomer may be due to the close proximity of the lone pairs of electrons on the N8 atom and the adjacent triple bond in 2 forms, in 2 form H–N–C angle is bent. On the other hand, the lone pairs of electrons on all N atoms in 1 tautomer are projected in opposite directions collinear with triple bonds. This will minimize the repulsive force in the 1 tautomer as compared to that in the 2.
The 1, 3 proton transfer process takes place via the transfer of the H atom from the central carbon atom to N8. We have been able to localize and identify the transition state (TS) for this process, which is displayed in Fig. 1. Some selected structural parameters of the TS are collected together with the corresponding values for 1 and 2 tautomers for comparison (Additional file 1: Tables 1S and 2S and Figure 1S.
The barrier energy computed for this tautomerization reaction is 68.7 and 74.4 kcal/mol at B3LYP/6311 ++G** and MP2/6311 ++G** level of theory in the gas phase, respectively.
The Gibbs free energy difference between the tautomers is in favor of the 1 tautomer by 13.0 kcal/mol using MP2/6311 ++G** level of theory. By using the Eq. (1), K equal about 3.14 × 10^{−10}.
The relative energies and relative free energies for the two tautomer’s using SMD and CPCM models at MP2/6311 ++G** level of theory in water solution
Structure  SMD  CPCM  

E_{re}  ΔG  E_{re}  ΔG  
1  0.0  0  0.0  0.0 
2  14.6  26.8  14.1  26.4 
Waterassisted proton transfer
Thermal energy parameters for the studied species using B3LYP/6311 ++G** level of theory in solution at 260 and 300 K
T = 260 K  T = 300 K  

H/au  G/au  S/Cal/Mol.K  H/au  G/au  S/Cal/Mol.K  
1  −317.2288  −317.260935  77.565  −317.22743  −317.265745  80.639 
2  −317.22652  −317.25843  77.013  −317.22514  −317.263208  80.121 
Protonation and deprotonation
The proton affinity (PA) values help in understanding fragmentation patterns in mass spectroscopy influenced by protonation and other proton transfer reactions, the basicity of molecules and susceptibility toward electrophilic substitution. Knowledge of preferred site of protonation is also of significance for structure elucidation of polyfunctional molecules [33].
For each protonation and deprotonation site, the structure with the lowest energy was identified as the most stable and with respect to this, the relative energies are calculated.
Vibration Raman spectrum analysis
Observed [6] and calculated Raman frequencies (cm^{−1}) (scaled by an empirical factor of 0.96) for 1 using B3LYP and MP2 methods at two basis sets 6311 ++G** and augccpVQZ
B3LYP  MP2  PBE1PBE  

6311 ++G**  AugccpVQZ  6311 ++G**  AugccpVQZ  6311G (3df,3dp)  Observed  Assignment 
342 (3)  337 (2)  323 (3)  316 (2)  345  347 (45)  ∂ CCN 
549 (5)  551 (5)  544 (4)  541 (5)  556  567 (16)  ∂ CCN 
555 (2)  553 (1)  559  575 (7)  ∂ CCC  
804 (6)  808 (7)  808 (7)  801 (8)  813  835 (24)  v _{ s } CC 
985 (1)  980 (1)  995 (2)  994 (1)  1002  1022 (7)  v _{ as } CC 
1238 (3)  1239 (3)  1247 (3)  1239 (2)  1232  1253 (5)  ∂ CCH 
2281 (34)  2284 (31)  2093 (82)  2098 (98)  2310  2259 (7)  v _{ as } CN 
2288 (160)  2292 (175)  2101 (18)  2105 (18)  2316  2287 (100)  v _{ s } CN 
2895 (88)  2894 (85)  2960 (85)  2956 (82)  2922  2885 (38)  v CH 
The Raman spectrum of cyanoform was reported recently by Theresa Soltner et al. [6]. Comparison of the of the theoretically computed frequencies and those observed experimentally shows a very good agreement especially with B3LYP/augccpVQZ level of theory.
Most intensive band in Raman spectra, obtained experimentally was observed at 2287 cm^{−1} occurred in calculated spectra at 2288, 2292 and 2316 cm^{−1} in B3LYP/6311 ++G**, B3LYP/augccpVQZ and PBE1PBE/6311G(3df, 3dp) [6] level of theory, respectively.
It should be noted that the B3LYP at the two basis sets gave good band position evaluation, e.g. band appeared at 2285 cm^{−1} (obs), 2895 cm^{−1} (6311 ++G**) and 2894 cm^{−1} (augccpVQZ).
As it can be seen from Table 4, the theoretically calculated values at 2897 and 1228 cm^{−1} showed excellent agreement with the experimental values.
The C–H stretching vibrations is observed experimentally at 2885 cm^{−1} and predicted theoretically at 2895 and 2894 cm^{−1} using the 6311 ++G** and augccpVQZ basis sets, respectively, in excellent agreement.
The γ(CN) stretching is predicted theoretically at 2288 cm^{−1} using 6311 ++G** basis set in a very good agreement with the experimental observed Raman line at 2287 cm^{−1}. No bands for C=C or C=N stretching vibrations are observed in FTRaman of 1. The absence of any band in the 1500–1900 range confirms that the stable form for the studied molecule is 1 tautomer. Full assignment of Raman spectrum of 1 tautomer is given in Table 4.
NBO analysis
Second order perturbation energy (E^{(2)}) in NBO basis for 1 using B3LYP and MP2 methods at 6311 ++G** basis set
Donor  Type  Acceptor  Type  E^{(2)}  

B3LYP/6311 ++G**  MP2/6311 ++G**  
1  2  1  2  
C1–C3  σ  C4–N7  π*  3.53  5.26  4.25  6.14 
C1–C3  σ  C5–N8  π*  3.53  4.21  2.63  5.31 
C1–C4  σ  C3–N6  π*  3.53  20.34  4.25  5.68 
C1–C4  σ  C4–N7  π*  5.69  7.37  9.19  9.62 
C1–C4  σ  C5–N8  π*  3.53  4.44  4.25  5.68 
C1–C5  σ  C3–N6  π*  3.53  4.21  4.25  5.31 
C1–C5  σ  C4–N7  π*  3.53  5.26  4.25  3.42 
C1–C5  σ  C5–N8  π*  5.69  7.48  9.91  4.27 
C3–N6  π  C1–C3  σ*  5.62  2.64  9.09  
C3–N6  π  C1–H1  σ*  2.76  3.58  
C4–N7  π  C1–C4  σ*  5.62  6.68  8.60  8.62 
C4–N7  π  C1–H1  σ*  2.76  3.85  
C4–N7  π  C1–C3  σ*  2.19  3.57  2.65  4.32 
C5–N8  π  C1–C5  σ*  5.62  7.36  8.60  9.09 
C5–N8  π  C1–H1  σ*  2.76  3.85  
C5–N8  π  C1–C3  σ*  2.19  3.34  2.64  4.12 
C5–N8  π  C1–C4  σ*  2.19  6.46  2.64  5.21 
N6  LP  C1–C3  σ*  12.13  11.67  12.72  12.52 
N7  LP  C1–C4  σ*  12.13  31.61  12.72  78.33 
N8  LP  C1–C5  σ*  12.13  11.67  12.72  12.52 
Natural bond orbital (NBO) [41, 42] analysis gives information about interactions in both filled and virtual orbital spaces that could help to have a detailed analysis of intra and intermolecular interactions. The second order Fock matrix was carried out to evaluate the donor–acceptor interactions in the NBO analysis [43].
In Table 5 the perturbation energies of significant donor–acceptor interactions are comparatively presented for 1 and 2 forms. The larger the E^{(2)} value, the intense is the interaction between electron donors and electron acceptors.
The NBO results show that the specific lone pairs of N atoms with σ∗ of the C–C bonds interactions are the most important interactions in 1 and CF_NH, respectively.
In 1, the interactions initiated by the donor NBOs like σ_{C1–C2}, σ_{C3–C4}, π_{N–C} and NBOs due to lone pairs of N atoms are giving substantial stabilization to the structures in the both MP2 and B3LYP methods. Above all, the interaction between lone pairs namely, N6, N7 and N8 is giving the most possible stabilization to 1 since it has the most E^{(2)} value around 12.81 and 11.5 kcal/mole in 2. The other interaction energy in the 1 and 2 is π electron donating from π _{(C3–N6)}−π*_{(C1–C3)}, π_{(C3–N6)}−π*_{(C1–H2)}, π_{(C4–N7)}−π*_{(C1–C4)}, and π _{(C5–N8)−}π*_{(C1–C5}) resulting stabilization energy of about 5.62, 2.76, 5.69 and 5.89 kcal/mol, respectively. The present study at the two methods (MP2 and B3LYP), shows clearly that the electron density of conjugated triple bond of cyano groups exhibits strong delocalization.
The NBO analysis has revealed that the lone pairs of N atoms and C–C, C–H and C–N bonds interactions give the strongest stabilization to both of the 1 and 2 with an average value of 12.5 kcal/mole.
The 3Ddistribution map for the highestoccupiedmolecular orbital (HOMO) and the lowestunoccupiedmolecular orbital (LUMO) of the 1 and 2 tautomers are shown in Fig. 6. As seen, the HOMO is mainly localized on the cyano groups; while, the LUMO is mainly localized on the CC bonds.
The energy difference between the HOMO and LUMO frontier orbitals is one of the most important characteristics of molecules, which has a determining role in such cases as electric properties, electronic spectra, and photochemical reactions. The gap energy (HOMO–LUMO) is equal to 9.00 and 5.40 eV for the 1 and 2 tautomers, respectively. The large energy gap for 1 tautomer implies that structure of the cyanoform is more stable.
Conclusions

Despite the B3LYP and MP2 methods affording good results which provide a better picture of the geometry and spectra and energetics, respectively, both in the gas phase and in a water solution (PCM–water).

At all levels of theory used, the 1 form is predicted to be more stable than its 2 form, both in the gas phase and in solution.

The potential energy barrier for this proton transfer process in the gas phase is 77.5 kcal/mol using MP2/6311 ++G** level of theory. Gross solvent continuum effects have negligible effect on this barrier.

Inclusion of one and two water molecules to describe explicitly the first solvation layer, within the supermolecule model, lowers the barrier considerably (29.1 and 7.6 kcal/mol).

There is good correspondence between the DFTpredicted and experimentally reported Raman frequencies, confirming suitability of optimized geometry for the 1 as the most stable conformer of the cyanoform. This conformation is characterized also by larger HOMO–LUMO gap of 9.00 eV further confirming its marked stability.

The NBO analysis has revealed that the lone pairs of N atoms and C–C, C–H and C–N bonds interactions give the strongest stabilization to both of the 1 and 2 with an average value of 12.5 kcal/mol.
Declarations
Acknowledgements
The author would like to thank Prof Rifaat H. Hilal for the valuable discussions.
Competing interests
The author declares that he has no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
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