How weak an acid can be? Variations of H-bond and/or van der Waals Interaction of Weak Acids
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- Szaniszló, S., Csizmadia, I.G. & Perczel, A. Struct Chem (2017) 28: 371. doi:10.1007/s11224-016-0888-5
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Complex formation ability and stability of both weak and super-weak acids was studied by mean of in silico determined thermodynamic data of the complexes. While weak acids act like Brønsted acids forming hydrogen bond type Brønsted complexes, super-weak acids form Lewis complexes via van der Waals interaction. Unlike in the former type, upon complexation, C-H distances changes insignificantly, yet the complex formation is energy driven in the terms of zero-point corrected Energies, ΔEzp < 0 kcal mol−1, which supports the Lewis complex formation, with the exception of CH4, an extremely “weak acid”.
KeywordsAcids super-weak acids C-H hydrogen bond Lewis acid and complex Brønsted acid and complex
From a historic point of view in nineteenth century, the interest of chemistry focused on understanding the formation of chemical bond, the range of this dissociation energy falls in 20–100 kcal mol−1 bond, covering a bond distance (d) between 0.9 and 1.5 Å. The concept of the hydrogen bond was first mentioned by T.F. Winmill, and T.S. Moore in 1912 . By the middle the twentieth century, the discovery and atomic level description of natural products and bio-macromolecules (e.g. DNA, proteins) the significance of hydrogen bond formation emerged due to the fundamental role in the living systems . Based on the X-ray diffraction (Photo 51) of DNA recorded by Rosaline Franklin, discovered not only that the DNA double helix hold together by H-bonds (and π-π stacking), but also that both replication, transcription and translation are driven by correct H-bond pairing mechanisms . The wide range of criteria of H-bond properties as proton donors, acceptors, energies, distances are clearly summarized in work of Arunan et al. . At the end of his report he gives a short definition of hydrogen bond: “The hydrogen bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X–H in which X is more electronegative than H, and an atom or a group of atoms in the same or a different molecule, in which there is evidence of bond formation”. Depending on several factors and on the molecular environment H-bond energy falls in the range of 1–15 kcal mol−1 covering X-H..Y distance between 1.5 and 3 Å . The suggestion of C-H..O hydrogen bonding has been first proposed by Glasstone as a logical extension of the X-H..Y concept . Later Desiraju et al. has defined quantitative criteria of the C-H..O hydrogen bond, as bond distance D(C..O) < 3.80 Å, angle θ(C-H..O) 100° < θ <180°and bond energy E ≤ 4 kcal mol−1 .
An extreme hydrogen bonded complex was shown between H2O and CH4, where the H2O is the proton donor and CH4 is the proton acceptor . This can be considered as one case of CH5+ formation. This interesting species of carbocations was earlier established by George Olah proving that even methane is suitable to be protonated as a base. Extending this concept to various protonated alkanes and explaining their formation, he founded the chemistry of superacids playing a significant role in boosting organic chemistry of the twentieth century .
Even in this example (Fig. 1) the C-H bond in acetonitrile does not behave in a protonic fashion but, the whole group is involved in a van der Waals complex formation, making in fact a Lewis complex. Consequently, the -CH3 group in acetonitrile acts as a super-weak, or rather a Lewis acid and not as a Brønsted one.
The electron withdrawing group(s) in the vicinity of the C-H..O interaction, might enhance the partial positive charge on the hydrogen of the proton donor, while electron donor groups increase the partial negative charge on the proton acceptor side of the complex.
It has been shown that the acidity is predictable by using G3 computational scheme . Vianello and co-workers have used the 6–311 + G(2d,p) basis set to calculate the pKa values of C-H acids for nitrile derivatives in gas phase and in DMSO . All calculations were carried out using the Gaussian 09b01 software using Density Functional Theory (DFT) method with B3LYP functional and standard 6–311++G(d,p) basis set . In some cases the proton donor moiety can interact with the substituent side to form a second (unwanted) interaction. To eliminate this effect, suitable redundant coordinates were chosen to restrict the reaction path. No imaginary frequencies were observed for the fully optimized (closed shell) geometries, except molecules calculated with redundant coordinates. To eliminate the basis set superposition error, Counterpoise Corrected calculations were carried out on all complexes while determining their thermodynamic parameters, namely “Ezp, H and G” (eqs. 1–3). For the above reasons the herein applied level of theory and associated computational method can be used with confidence.
Results and discussion
Characteristic σi values of various proton carriers (Ax and Bx) and acceptors (Cy) (Scheme 1)
Computed relative Stability* (Energy( ΔEzp), Enthalpy (ΔH), and Gibbs free Energy (ΔG)) of the different 54 Ax.Cy and/or Bx.Cy complexes
The systematic variation of the above donors and acceptors (Table 1) makes possible the formation of 54 different complexes in total. The associated thermodynamic functions were determined form computed Ezp, H and G values. All changes in ΔEzp ΔH and ΔG values associated with the complex formation are summarized in Table 2. It has to be emphasized that the A1..C1, A1..C2 and A1..C3 complexes have positive of ΔEzp energies which means they are insufficiently stable, consequently, their values were not considered when the thermodynamic function was formulated (values highlighted red in Table 2).
In the case of A4..Cy, A9..Cy, B4..Cy and B9..Cy complexes an extra O..H-C interaction type could have been obtained during complex optimization, where the O-atom of the substituents of the proton carrier might interact with a C-H of the 1,3-dioxolane ring. Redundant coordinates were used to eliminate this secondary (unwanted) interaction type. Furthermore, in the case of the B9..Cy complex even this approach failed and thus, the associated values have to be considered with caution. Due to the highly similar σi values of the substituents of C1 and C2, the formed Ax..C1, Bx..C1, Ax..C2 and Bx..C2 complexes are also similar. These phenomena are easily explained by the nature of their σi values: σi(H) = 0 and σi(CH3) = −0.01, due to the similar inductive effects of-H and -CH3 groups.
The negative values of ΔEzp (Zero-point corrected Energies) show that the complex formation is associated with some stability (energy) gain and thus, complex formation is possible: a spontaneous thermodynamically driven procedure not necessarily manifesting in term of ΔH and/or ΔG. The fact of complex formation can easily be explained by n → σ* (HOMO-LUMO) interaction types, in line with the well-established MO theory.
Linearity (m, b and R2) of selected thermodynamic ΔEzp, ΔH and ΔG and values with substituents
From data tabulated in Table 3 it looks obvious, that while the trends shown in Fig. 4 due exist, the maximum correlating (Pearson) coefficient is limited (Rmax = 0.8). It is more important to compare the slope (m) of the lines as these are the measures to indicate changes in complex stability following the increasing inductive effect, σi, of substituents. As expected most of the slopes are negative signaling that acidity increases by the inductive effect of the substituent. Values are more negative in the cases of Q-O-H family than they are for Q-CH2-H. These differences make the formers (Q-O-H) weak, while the latter’s (Q-CH2-H) super-weak acids.
It seems therefore that the difference between weak acids (R-O-H) and super-weak acids (R-CH2-H) has been manifested in terms of thermodynamic changes as well as in characteristic shifts in bond lengths. Clearly the super-weak acids behave as Lewis acid in spite of the fact that they have hydrogen atoms, of very low “mobility” and thus their pKa (s) are large figures.
The territory of the acids extends from George Olah’s super acids, as the strongest species to the weak acids. Furthermore, the latter’s can be divided to two subtypes: weak acids and super-weak acids, which differ not only in the range of bond energies, but also changes in the bond length (Δd). For better understanding the problem of the difference between weak acids and super-weak acids we performed in silico QM calculations supplemented with an MO-approach. The calculated thermodynamic functions established that in the case of O-H acids the Δd values increase parallel with the σi values, which is typical of Brønsted acids. On the other hand, the Δd values of C-H acids in C-H..O complexes are practically zero, i.e., they behave like Lewis acids as no significant changes are seen. Consequently, super weak acids Q-CH2-H can be regarded as exceptional Lewis acids bearing a proton suitable for C-H..O complex formation. This consideration might help in explaining unexpected cases of organo-catalysis, or organo-inhibition and crystal structure formation.
This work was supported by grants from the Hungarian Scientific Research Fund(OTKA NK101072). We gratefully acknowledge István Pintér and Imre Jákli for their constructive remarks.