Structural Chemistry

, Volume 28, Issue 2, pp 371–378

How weak an acid can be? Variations of H-bond and/or van der Waals Interaction of Weak Acids

  • Szebasztián Szaniszló
  • Imre G. Csizmadia
  • András Perczel
Original Research

DOI: 10.1007/s11224-016-0888-5

Cite this article as:
Szaniszló, S., Csizmadia, I.G. & Perczel, A. Struct Chem (2017) 28: 371. doi:10.1007/s11224-016-0888-5
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Abstract

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”.

Graphical abstract

Selected NBOs of the complexes formed between NC-CH2-H (Lewis acid) with dioxolane as well as NC-O-H (Brønsted acid) and dioxolane.

Keywords

Acids super-weak acids C-H hydrogen bond Lewis acid and complex Brønsted acid and complex 

Introduction

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 [1]. 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 [2]. 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 [3]. The wide range of criteria of H-bond properties as proton donors, acceptors, energies, distances are clearly summarized in work of Arunan et al. [4]. 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 [5]. The suggestion of C-H..O hydrogen bonding has been first proposed by Glasstone as a logical extension of the X-H..Y concept [6]. 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 [5].

An extreme hydrogen bonded complex was shown between H2O and CH4, where the H2O is the proton donor and CH4 is the proton acceptor [7]. 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 [8].

Recently, the focus of attraction has been extended to the area of super-weak acids and their complexing ability. Interaction concluding to C-H bond breakage was first considered significant in reactions such as the one described for example by Stanislao Cannizzaron, namely Cannizzaro reaction. However, this kind of C-H bond dissociation requests a strong base (beside additional structural prerequisites). By now the arsenal of well characterized organic reactions involving the dissociation of selected C-H covalent bonds fertilized many areas of modern synthetic organic chemistry [9, 10, 11, 12, 13, 14]. Numerous X-ray structures have clearly indicated the existence of C-H..O interactions (Fig. 1) even for cases where the acceptor O-atom is not a strong base [15]. Although such interactions are very weak, the sum of many of such contacts could lead to substantial stabilizations, holding even an entire crystal structure together. The magnitude of C-H..O interactions strongly depends on the actual molecular interaction type, geometrical properties, etc.
Fig. 1

Three C-H..O weak bonds, formed between -CH3 of acetonitrile and 4,4'-Oxydianilinium bis(1,4,7,10,13,16-hexaoxacyclooctadecane) diperchlorate (FECFAW) hold the crystal structure together [15]. (Note that additional weak interactions e.g. C-H..N are present.)

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.

Scope

The aim of the presented study is to better understand the qualitative background of different behavior of the C-H and O-H proton sources (in addition to the well-known difference in their electronegativities: χ(C) = 2.55, χ(O) = 3.44 [16]). The systematic change of substituents (Q) of the proton donors (Q-CH2-H or Q-O-H) is a plausible approach to discover the main differences between these proton sources. In this study in the line of the Hammett-Taft concept, for the structure – reactivity relationship we used the σi values of the substituents to characterize their acidity or basicity [17, 18, 19, 20, 21]. For proton acceptors the oxygen of the substituted (Q’) 1,3-dioxolane was chosen as the proper partner for both Q–CH2-H and Q-O-H proton-donors (Fig. 2). Caused by different substituents (Q’) the oxygen of the 1,3-dioxolane ring has different basicity.
Fig. 2

Schematic molecular structures of substituted (Q’) 1,3-dioxolanes

For proton carrier two different types of molecule were selected, namely both a C-H and O-H type donor, however the same type of substituents (Q) were attached to central carbon atoms and oxygen in both cases. Substituents (Q) selected for this study of increasing electron donating and withdrawing effects are characterized here by their σi values [22, 23, 24]. The two species of proton carriers act indeed as two different types of acids (Fig. 3).
Fig. 3

Different interactions of Q-CH2-H and Q-O-H acids

Methods

It has been shown that the acidity is predictable by using G3 computational scheme [25]. 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 [27]. 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 [26]. 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. 13). For the above reasons the herein applied level of theory and associated computational method can be used with confidence.

Gas-phase reactions of the H-bonding thermodynamic parameters were calculated from the following equations:
$$ \varDelta E={\mathrm{E}}_{zp\left(\mathrm{Complex}\right)}{\textstyle \hbox{-}}\left[{\mathrm{E}}_{zp\left(\mathrm{Ax}\kern.2em \mathrm{or}\kern.2em Bx\right)}+{\mathrm{E}}_{zp(Cy)}\right] $$
(1)
$$ \varDelta H={\mathrm{H}}_{\left(\mathrm{Complex}\right)}{\textstyle \hbox{-}}\left[{\mathrm{H}}_{\left(\mathrm{Ax}\kern.2em \mathrm{or}\kern.2em Bx\right)}+{\mathrm{H}}_{(Cy)}\right] $$
(2)
$$ \varDelta G={\mathrm{G}}_{\left(\mathrm{Complex}\right)}{\textstyle \hbox{-}}\left[{\mathrm{G}}_{\left(\mathrm{Ax}\kern.2em \mathrm{or}\kern.2em Bx\right)}+{\mathrm{G}}_{(Cy)}\right] $$
(3)

Results and discussion

In the present in silico structure elucidation the stability values of the complexes (Ax..Cy and Bx..Cy) of proton carrier (Ax and Bx) and proton acceptor (Cy) molecules (Scheme 1) were calculated by suitable QM methods.
Scheme 1

Complex formations between selected C-H and O-H acids with 1,3-dioxolane derivatives as suitable base

The σi values of the used substituents (Q and Q’) are covering a large range of inductive effects from σi(CH3) = −0.01 to σi(N2O) = 0.67 [24]. It has to be added that substituents -C(O)CH3, -CN and -NO2 exhibit also resonance effect, σr, but these values are significantly smaller than their σi values. These proton donors and acceptors are summarized in Table 1, together with the σi values of the substituents. The derived thermodynamic parameters from equation 13 are summarized in Table 2.
Table 1

Characteristic σi values of various proton carriers (Ax and Bx) and acceptors (Cy) (Scheme 1)

Table 2

Computed relative Stability* (Energy( ΔEzp), Enthalpy (ΔH), and Gibbs free Energy (ΔG)) of the different 54 Ax.Cy and/or Bx.Cy complexes

codes

ΔEzp(kcal mol−1)

ΔH(kcal mol−1)

ΔG(kcal mol−1)

Cy

C1

C2

C3

C1

C2

C3

C1

C2

C3

Ax

A1

0.163

0.257

0.178

0.852

1.029

0.971

4.233

3.779

3.377

A2

−0.060

−0.100

−0.063

0.820

0.275

0.319

5.981

6.940

6.992

A3

−0.210

−0.045

−0.081

0.171

0.284

−0.275

6.877

7.819

9.112

A4

−0.705

−0.531

−0.638

−0.497

0.234

0.198

7.958

6.273

6.710

A5

−1.322

−1.182

−0.940

−1.056

−0.936

−0.603

7.385

8.097

7.435

A6

−0.949

−0.817

−0.727

−0.740

−0.639

−0.457

6.376

7.578

6.451

A7

−0.623

−0.701

−0.402

−0.402

−0.468

0.465

6.241

6.113

4.265

A8

−1.683

−1.317

−1.007

−1.543

−1.178

−0.198

6.211

7.276

5.021

A9

−1.879

−2.107

−1.404

−1.775

−1.387

−1.194

7.349

5.112

6.842

Bx

B1

−3.283

−3.134

−1.743

−3.406

−3.264

−2.200

4.036

4.251

5.921

B2

−5.198

−5.279

−3.374

−4.842

−4.898

−2.843

3.195

3.226

4.064

B3

−3.734

−3.396

−2.436

−3.341

−3.960

−2.313

5.413

7.472

6.006

B4

−6.112

−6.046

−4.840

−5.614

−5.565

−4.251

2.632

3.129

3.794

B5

−8.370

−8.583

−5.993

−7.984

−8.206

−5.495

−0.093

0.575

2.614

B6

−5.872

−6.026

−3.955

−5.718

−5.863

−3.672

2.300

2.178

3.735

B7

−6.610

−6.710

−4.418

−7.073

−7.162

−4.679

2.920

2.732

4.133

B8

−10.194

−10.466

−7.175

−10.211

−11.025

−7.576

−1.595

−0.493

2.403

B9

−8.199

−8.364

−5.969

−7.808

−7.992

−5.472

0.683

0.892

2.985

*Stabilization energies

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 relationship of the different stability terms (ΔEzp, ΔH and ΔG) of Table 2 are graphically presented in Fig. 4.
Fig. 4

Variations of the relative stabilities (ΔEzp, ΔH and ΔG) correlated with inductive effects, for Ax..C1 and Bx..C1 (a), Ax..C2 and Bx..C2 (b) Ax..C3 and Bx..C3 (c) complexes

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.

As was expected the energy level of the complex is always lower than that of non-bonding n orbital of the oxygen atom of the acceptor and that of the σ-bond orbital of the donor moieties. The energy gain (ΔE1 or ΔE2) is the difference between the level of the σ bond (C-H or O-H) and that of the complex bond (C-H..O or O-H..O) in both cases. It is essential this gain is always larger in the O-H..O than in the C-H..O complex (schematically demonstrated in Fig. 5).
Fig. 5

MO scheme of energy gain (ΔE) from the complex formation of either Ax..Cy (G1) or Bx..Cy (G2)

The values of thermodynamic functions (ΔEzp, ΔH as well as ΔG) decreases as the σi values increase (Fig. 4). The slope of these lines clearly indicates that the effect of the σi of the acids is less pronounced if the basicity of the 1,3-dioxolane oxygen is reduced by the fluorine substituent. As it is well known from the Hammett – Taft relationship, a linear correlation is to be observed with increasing values of σi if a uniform and “single interaction” is operative. The parameters of the linear fits are summarized in Table 3.
Table 3

Linearity (m, b and R2) of selected thermodynamic ΔEzp, ΔH and ΔG and values with substituents

Code Bx.Cy

ΔG(Q-OH)

Code Ax.Cy

ΔG(Q-CH2-H)

R2

m

b

R2

m

b

Bx.C1

0.487

−7.151

5.229

Ax.C1

0.212

−2.349

7.849

Bx.C2

0.489

−6.612

4.539

Ax.C2

0.0021

0.1628

6.731

Bx.C3

0.572

−4.275

5.496

Ax.C3

0.372

−4.549

8.44

 

ΔH(Q-OH)

 

ΔH(Q-CH2-H)

R2

m

b

R2

m

b

Bx.C1

0.675

−8.691

−3.318

Ax.C1

0.803

−3.071

0.763

Bx.C2

0.692

−8.228

−3.268

Ax.C2

0.795

−3.872

0.935

Bx.C3

0.657

−6.215

−2.047

Ax.C3

0.233

−1.337

0.322

 

ΔEzp(Q-OH)

 

ΔEzp(Q-CH2-H)

R2

m

b

R2

m

b

Bx.C1

0.672

−8.641

−3.343

Ax.C1

0.777

−3.038

0.376

Bx.C2

0.671

−8.034

−3.513

Ax.C2

0.738

−2.867

0.228

Bx.C3

0.669

−6.331

−2.161

Ax.C3

0.696

−1.965

0.135

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.

One may expect to see some geometrical deviation of the two type of complexes with 1,3-dioxolanes (Q’ = CH3, H, F) due to the differences between Lewis (C-H) and Brønsted (O-H) acids (Fig. 6). The C-H bond length (d) in C-H..O complexes slightly changes (Δd ~ 0) with increasing inductive effects (σi) of the substituents. In contrast to that the O-H bond length (d) in an O-H..O complex exhibits an increase with increasing (σi) values of the substituent.
Fig. 6

Changes of C-H and O-H bond length (Δd) correlated to the inductive effect of Qs

Figure 6 shows the cases in which the anion charge leads to destabilization, marked by arrows, showing downward to a smaller d value. In contrast to that, the substituents where the negative charge of the anion is stabilized either by inductive (F3C-) or inductive and conjugative (NC-) effects are marked by arrows showing upward to a larger than observed values of d. Thus, the deviation from the linear correlations is attributed to the structural possibility of destabilization or stabilization by the substituent on the negative charge: the total anionic structure suggests two classes, proposed on Fig. 7.
Fig. 7

Stabilizing and destabilizing structures of anionic electron pairs

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.

Conclusion

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.

Acknowledgements

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.

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Szebasztián Szaniszló
    • 1
  • Imre G. Csizmadia
    • 2
  • András Perczel
    • 1
    • 3
  1. 1.Laboratory of Structural Chemistry and Biology, Institute of ChemistryEötvös Loránd UniversityBudapestHungary
  2. 2.Department of ChemistryUniversity of TorontoTorontoCanada
  3. 3.MTA-ELTE, Protein Modelling Research GroupBudapestHungary