The Acidity of Weak NH Acids: Expanding the pK_a Scale in Acetonitrile

Abstract

Nitrogen heterocycles and aromatic amines are well-known and widely used compounds that are usually not seen as acids, although in organic solvents like acetonitrile (MeCN) or dimethyl sulfoxide (DMSO) their acidic properties can be observed. In this work, the acidities (pK_a values) of 37 such weak NH acids were determined in acetonitrile and presented together with computational gas-phase acidities and literature pK_a values in DMSO. In the course of the work the weakest acids range (from pK_a 29 upward) of the MeCN acidity scale has been revised and expanded to around 33.5 by adding 31 compounds in that specific region and the span of experimental pK_a values in MeCN is now more than 30 orders of magnitude. The relations between the structure and acidity of a selection of the studied compounds have been investigated in MeCN and DMSO. The measured pK_a values in MeCN and the gathered pK_a values in DMSO were used for a correlation analysis between the two solvents and for assessing the quality of pK_a conversion equations. A number of pK_a values have been predicted in MeCN from pK_a values in DMSO via the correlation analysis and pK_a conversion equations.

Introduction

In most chemical processes, the acidities or basicities of the involved compounds are essential, particularly when charged species are involved. The most widely used representation of the acidity of a molecule in the liquid phase is based on the Brønsted theory¹ and is quantitatively expressed by the equilibrium constant K_a of the acid dissociation reaction in solvent S (eq 1) or, more often, its negative logarithm pK_a (eq 2).

1

2

When dealing with chemical reactions in the presence of strong bases, in order to control the reaction path and outcomes it is important to understand which of the solution components can get deprotonated by the chosen base. For that, knowing the pK_a values of even very weak acids is crucial. As the majority of such reactions are carried out in nonaqueous media, it is the pK_a values in organic solvents such as acetonitrile (MeCN) and dimethyl sulfoxide (DMSO) that are relevant.

One significant type of acids are NH acids, in which the acidic proton is directly attached to the nitrogen atom. NH acids cover a wide range of pK_a values, from superacidic catalysts² to the weakly acidic indole and its derivatives.³⁻⁵ In MeCN, the pK_a values of numerous superacidic NH have been reported,⁶ and the Bordwell group has published the pK_a values of numerous weak NH acids in DMSO.^3,7 However, to the best of our knowledge, only very limited information is available regarding the acidities of very weak acids (pK_a > 30) in MeCN.

Prominent classes of weak acids lacking experimental pK_a data are conjugated nitrogen heterocycles and aromatic amines - compounds that are usually better known as bases. Compounds such as benzimidazole, benzotriazole, indazole, carbazole, azaindoles and especially their derivatives have numerous applications: these moieties are found in pharmaceuticals,⁸ pesticides, bioactive compounds,⁹ etc. Nitrogen heterocycles are one of the most significant structural fragments in pharmaceuticals¹⁰ as their derivatives exhibit significant anti-inflammatory, antiviral, antihistaminic, antiparasitic, antifungal and anticancer activity.¹¹⁻¹³ Despite the available acidities in DMSO, their pK_a values in a less basic solvent like MeCN are also of interest. Yet, no such data have been published. Some acids of interest also have no pK_a values in DMSO. For instance, to the best of our knowledge, the acidities of azaindoles and benzocarbazoles have not been measured in any nonaqueous solvents before.

Besides the above-mentioned fields of application, weak NH acids are well-suited additions to the previously published comprehensive self-consistent acidity scale in acetonitrile, which contains pK_a values of 231 acids and covers close to 30 orders of magnitude of acidity.⁶ Despite the substantial number of acids in it, the pK_a scale in MeCN is scarce in compounds in the region of the weakest acids. It contains only five acids with pK_a values between 29 and 32.57 (the highest pK_a value on the scale). For comparison, between pK_a values of 25.4 and 29, there are 34 acids on the scale. The available acidity data in MeCN show that the pK_a values of aromatic amines, such as substituted diphenylamines and anilines, can vary over a wide range depending on the number and properties of the substituents.⁶ Thus, aromatic amines with a suitable structure and substituent groups should have pK_a values in the desired region.

MeCN as a solvent is generally not considered as suitable as DMSO for studying very weak acids because of its lower basicity.¹⁴ Nevertheless, numerous acids are expected to have pK_a values above 29 in MeCN, enabling supplementing and expanding the current acidity scale in MeCN. As the highest pK_aH (pK_a value of the conjugated acid of a base)¹⁴ value of the MeCN basicity scale is 33.14,¹⁵ extending the acidity scale to at least a similarly high pK_a value should be possible.

The aim of this study was to present a number of new previously unavailable pK_a values of weak NH acids in MeCN and to expand the pK_a scale in MeCN. In addition, this study aims to evaluate the previously published simple conversion equations for pK_a estimations between DMSO and MeCN,⁶ specifically for weak NH acids, and to predict a number of additional pK_a values in MeCN. Also, computational gas-phase acidity (GA) values were calculated for all the compounds studied in this work.

Results and Discussion

Expanded pK_a Scale in Acetonitrile

The pK_a values of 37 weak NH acids, mainly conjugated nitrogen heterocycles and aromatic amines, were determined in MeCN by 141 relative acidity measurements. As a result, the least acidic section of the MeCN pK_a scale,⁶ with pK_a values over 29, was rebuilt and expanded by adding 31 new compounds. Consequently, the highest pK_a value on the scale is now 33.51 belonging to 2,3,5,6-Cl₄-aniline. The previously published pK_a values for indole (32.57 → 32.78), 3-MeCOO-indole (29.97 → 30.2) and 7-NO₂-indole (29.99 → 30.12) were revised. The results are presented in Table 1. The pK_a values of the aromatic amines presented in this work include some of the highest ever experimentally determined pK_a values of neutral NH acids in MeCN. In addition to the results in Table 1, the pK_a value of benzotriazole in MeCN was determined to be 22.98 (see Table S1 in the SI).

Table 1. Acidity Measurements and Assigned pK_a Values of Weak NH Acids in MeCN^a.

^aCompounds with a gray background serve as anchor compounds with fixed pK_a values from ref (6) Previously published pK_a values (from ref (6)) are given for indole, 3-MeCOO-indole and 7-NO₂-indole in parentheses for comparison. Black, brown and red arrows denote high-, medium- and low-reliabiliy ΔpK_a measurements, respectively, depending on the type of acids. See text for more details.

The pK_a scale in Table 1 was built by performing relative acidity (relative pK_a or ΔpK_a) measurements. Each double-headed arrow corresponds to a ΔpK_a determination between a pair of acids (described in more detail in the Experimental Section and SI). Absolute pK_a values of the analyzed acids were assigned using the “ladder” approach,^6,16 i.e. the following least-squares minimization procedure with the experimentally determined relative acidities.

3

According to eq 3, the sum of squares of the differences between all the experimentally determined relative acidities ΔpK_a and the differences between the assigned absolute pK_a values of acids HA₂ and HA₁ over all the relative acidity determination series n_m was minimized. If absolute pK_a values are desired as a result of the minimization then the ladder has to contain at least one reference acid (anchor acid) with a previously known and reliable pK_a value. This pK_a value is kept constant while the pK_a values of the remaining compounds are varied until the minimal SSD is reached. The acids tBu₄Box₂CH₂,¹⁷ 4–CN–2,3,5,6–F₄–aniline, 9–C₆F₅–fluorene, C₆H₅–CH₂–SO₂CF₃ and (4–Me–C₆F₄)(C₆H₅)CHCN have known reliable pK_a values⁶ and were used as reference acids in the least-squares minimization process.

Before the minimization, the analyzed acids were divided into two groups – “backbone” and “secondary” acids–according to the reliability of the relative acidity measurements conducted with them. The acids with the most convenient properties that enable high-quality ΔpK_a measurements were used as the backbone acids. As described in a previous publication, the reliability of the measurements was evaluated by considering the spectral properties of the acids, consistency of values obtained within a measurement series, self-consistency of the ΔpK_a values obtained for a given compound against different reference compounds and the possibility of unwanted side processes.⁶ Aromatic amines were chosen as the “backbone” acids because of their very suitable spectral properties, good within-series agreement, and good consistency of measurements. As a rule, nitrogen heterocycles displayed somewhat worse performance in pK_a measurements and were categorized as “secondary” acids. The third category consists of indolo[2,3-a]carbazole and 3-MeCOO-indole. Even after additional purification, the relative acidity measurements of these compounds were found to be less reliable than those of the other studied compounds. This could be caused by possible side reactions or the presence of impurities, which influenced the UV–vis spectra of these compounds during the spectrophotometric titration in such a way that the self-consistency and accuracy of the experimental results were lowered.

In total, three minimization steps were performed to assign pK_a values for all analyzed compounds. All ΔpK_a measurements involving “backbone” acids are presented as black-colored double-sided arrows in Table 1. The arrows of “secondary” acids are brown, and those involving indolo[2,3-a]carbazole or 3-MeCOO-indole are red.

For the first minimization step, only the relative pK_a values between aromatic amines and relative pK_a values between aromatic amines and the above-mentioned reference acids were used. As a result of this minimization, pK_a values for the “backbone” acids were assigned. In the second minimization step the acidities of the “backbone” acids were kept constant and used as reference to obtain the pK_a values for the “secondary” acids. The third minimization was performed to obtain the pK_a values of 3-MeCOO-indole and indolo[2,3-a]carbazole using all other compounds, which had pK_a values assigned in the previous steps, as reference acids.

The quality of a pK_a scale formed by the relative pK_a determination approach can be evaluated using the consistency standard deviation s of the scale, according to the following equation:

4

In eq 4, SSD is the sum of squares found in eq 3, n_m is the number of measurement series, and n_c is the number of compounds for which an absolute pK_a value was assigned. Strictly speaking, the parameter s is not interpretable as the uncertainty of an individual pK_a value in the scale. However, it serves as a general estimate of the quality of the pK_a values forming the acidity scale, can be loosely interpreted as the average standard uncertainty of the pK_a values with respect to the scale, and can be used for comparing the strengths of the acids belonging to the scale. The consistency standard deviation of the ΔpK_a measurements involving aromatic amines (“backbone” acids) is 0.03. It is the same consistency as that of the “backbone” acids forming the overall pK_a scale in MeCN spanning almost 30 orders of magnitude and can be rated as good.⁶ The s value of the ΔpK_a measurements involving the “secondary” acids is 0.06 and the s value of the ΔpK_a measurements involving indolo[2,3-a]carbazole or 3-MeCOO-indole is 0.09, which can both be considered satisfactory.

The acidity scale published in 2021 by Kütt et al.⁶ was scarce in compounds with pK_a values over 30. The compounds indole, 3-MeCOO-indole and 7-NO₂-indole were already present in that scale. However, because of the lack of other compounds with similar pK_a values, measurements of considerable pK_a differences (ΔpK_a values around or above 2) were used to assign pK_a values for these compounds. Usually, experimental ΔpK_a values higher than 1.5 are less accurate than lower ΔpK_a values because of the narrow (or nonexistent) range within which both measured acids have accurately measurable degrees of dissociation (i.e., degrees of dissociation between 0.1 and 0.9). Thus, such results need confirmatory measurements. The present work adds a large number of acids to the pK_a range of 30 to 33, completely eliminating the need for measuring large ΔpK_a values. The results from the present work indicate that such higher than recommended ΔpK_a measurements caused a contraction of the upper part of the acidity scale. The following four earlier experimental relative acidity measurements⁶ seem to be the main cause of this effect (directly measured ΔpK_a values in parentheses): 3-MeCOO-indole vs 5-NO₂-indole (ΔpK_a = 1.82), 7-NO₂-indole vs 9-C₆F₅-fluorene (ΔpK_a = 1.88), 7-NO₂-indole vs 6-NO₂-indole (ΔpK_a = 2.21) and 7-NO₂-indole vs 5-NO₂-indole (ΔpK_a = 1.74). The corresponding ΔpK_a values calculated from the results of this work (Table 1) are systematically higher by 0.1–0.2 pK_a units. Thus, these four ΔpK_a measurements were considered unreliable and were excluded from the data analysis. The previous⁶ directly measured ΔpK_a values for the acid pairs indole vs 3-MeCOO-indole (ΔpK_a = 2.58) and indole vs 7-NO₂-indole (ΔpK_a = 2.61) are in agreement with the absolute pK_a values in the scale presented in Table 1. Nevertheless, these two previous ΔpK_a measurements were also considered doubtful (in part because of the very high ΔpK_a value–far above the reliable directly measured ΔpK_a range of the used method of up to approximately 1.5 pK_a units) and excluded from the data analysis.

Comparison of Acidities between Different Solvents and the Gas Phase

The experimental pK_a values in DMSO and H₂O, as well as the gas-phase acidity (GA) values (found in literature and/or calculated) are presented in Table 2 together with the pK_a values determined in this work. The pK_a values in DMSO and H₂O have been published for less than half of the compounds of the present work. In the case of water, the obvious reason for the scarcity is that the aqueous pK_a values of the majority of the investigated compounds are outside the common aqueous pK_a range. In the case of DMSO, all the values are well within the experimentally achievable pK_a range in this solvent. Data from the Bordwell^3,7 group were preferred if pK_a values from multiple sources were available. The available experimental gas-phase acidity (GA) data was even more scarce than in either of the two solvents. The GA values of only seven studied compounds were found in the NIST Chemistry WebBook,¹⁸ so computational GA values are also provided in Table 2. The root-mean-square difference between the available experimental GA values and their computational counterparts is 10 kJ mol^–1 and the maximum difference is 15 kJ mol^–1 (for comparison, a typical uncertainty of GA values reported in the NIST database is ±8.4 kJ mol^–1). Most of the computational values are higher than the experimental values, displaying an average bias of 8 kJ mol^–1. The possible reason for these comparatively high discrepancies could be a compound class-specific bias that some methods exhibit, method-specific systematic bias (which, in turn, could originate from overestimation of vibrational frequencies),¹⁹ or the interplay between the two.

Table 2. Acidities in Different Solvents and the Gas Phase.

Compound	CAS RN	pKa (MeCN)a	pKa (DMSO)	pKa (H2O)	Exp. GA,b kJ mol-1	Calc. GA,c kJ mol-1
2,3,5,6-Cl4-Aniline	3481–20–7	33.51	21.020	19.2221		1426
4-CF3SO2-Aniline	473–27–8	33.11	21.87			1400
2,3,4,5,6-Cl5-Aniline	527–20–8	32.79				1415
Indole	120–72–9	32.78	20.953	16.9722	1431;23 144024	1441
2-NO2-Aniline	88–74–4	32.63		17.725		1436
N-Me-4-NO2-Aniline	100–15–2	32.62		18.225		1421
4-NO2-Aniline	100–01–6	32.58	20.97	18.225	140726	1421
(2-NO2–C6H4)(Ph)NHg	119–75–5	31.79	19.2d (17.727)	18.025		1421
2-MeO-Carbazole	6933–49–9	31.78				1417
Carbazole	86–74–8	31.74	19.93	16.728	141223	1420
2-NH2-4-NO2-Aniline	99–56–9	31.75				1416
3-Cl-4-NO2-Aniline	825–41–2	31.53				1403
4-Cl-2-NO2-Aniline	89–63–4	31.06	18.93	17.121		1412
5-Cl-2-NO2-Aniline	1635–61–6	31.03				1411
1,3-Ph2-Urea	102–07–8	30.96	19.63			1396
(2-NO2–C6H4)(4–Cl-C6H4)NH	23008–56–2	30.92				1402
2-Cl-6-NO2-Aniline	769–11–9	30.84				1423
7-Azaindole	271–63–6	30.79		12.129,f		1437
4-Azaindolee	272–49–1	30.49		15.530,e; 16.1,30,e		1422
2-Cl-4-NO2-Aniline	121–87–9	30.38		18.0631		1398
Benzo[c]carbazole	205–25–4	30.33				1401
3-MeCOO-Indole	608–08–2	30.2				1427
Benzo[a]carbazole	239–01–0	30.20				1400
7-NO2–Indole	6960–42–5	30.12				1415
4-NH2–C5F4N	1682–20–8	30.12	18.7d (19.232)		139233	1407
5-Azaindole	271–34–1	30.06				1414
Indolo[2,3-a]carbazole	60511–85–5	29.9				1387
(5-Cl-2-NO2–C6H3)(Ph)NH	25781–92–4	29.88				1397
Indazole	271–44–3	29.79	18.228	13.8628	142534	1433
6-Azaindole	271–29–4	29.75				1413
2,3-Cl2-6-NO2-Aniline	65078–77–5	29.43				1403
Norharman	244–63–3	29.33		14.5335		1398
2,4-Cl2-6-NO2-Aniline	2683–43–4	29.26		16.3931		1401
2,5-Cl2-4-NO2-Aniline	6627–34–5	29.20	17.47	16.0536		1380
(4-NO2–C6H4)(Ph)NHg	836–30–6	28.87	16.857	15.625	137433,g	1384
4-NO2-1-Naphthalenamine	776–34–1	28.85	17.4d (18.037)			1385
2,6-Cl2-4-NO2-aniline	99–30–9	28.30		15.5536		1387
Benzimidazole	51–17–2	27.92	16.43	12.8638		1403
2,4-(NO2)2-Aniline	97–02–9	27.64	15.97	15.036		1367
1H-Benzotriazole	95–14–7	22.98	11.923	8.5739	138434	1383

^apK_a values from this work (Table 1).

^bExperimental GA values.

^cComputational GA values (this work).

^dOriginal values from the respective publications (shown in parentheses) were corrected in ref (20)

^eIn the abstract and the main text of ref (30) two different pK_a(H₂O) values were presented for 4-azaindole and it was not possible to tell which one is the correct one.

^fDoubtful value.

^gThe GA value of 1374 kJ mol^–1, actually belonging to (4-NO₂–C₆H₄)(Ph)NH, is erroneously assigned to (2-NO₂–C₆H₄)(Ph)NH in the NIST Webbook.

Fifteen compounds studied in this work had pK_a(DMSO) values available in the literature (ten aromatic amines, four nitrogen heterocycles and 1,3-diphenylurea). Using these values and the respective pK_a(MeCN) values determined in the present work, a correlation between acidities in the two solvents was composed (Figure 1). Benzotriazole was excluded from the correlation because of its almost 5 orders of magnitude higher acidity compared to the other compounds. The following correlation equation was obtained:

5

Figure 1.

Correlation between pK_a values in MeCN and DMSO.

Figure 1 shows that the acidities of the selection of NH acids correlate reasonably well between DMSO and MeCN without any strongly deviating compounds. Solvent–solvent correlations are expected to be good if the solvents have sufficiently similar properties and the involved acids are of a similar nature.¹⁴ Both requirements are fulfilled in this case. Better correlations could be obtained for heterocycles and aromatic amines separately. The adequacy of the regression equation is evidenced by the fact that if the pK_a of benzotriazole in MeCN is predicted from it, the value will be 23.6, which is approximately 0.5 pK_a units different from the experiment. Considering the significant extrapolation involved, the agreement can be considered good.

Equations for pK_a Conversions between Solvents

Kütt et al.⁶ developed several equations to predict the pK_a values of acids in different nonaqueous solvents based on pK_a values in MeCN and simple structure-based descriptors. Equations 6 (eq 2.3 in Table 2 in ref (6)) and 7 (eq 2.1 in Table 2 in ref (6)) are the universal and NH acid-specific equations, respectively, to convert pK_a(MeCN) values to pK_a(DMSO) values. These equations have a root-mean-square error (RMSE) of prediction of 0.5 and 1.2, respectively.

6

7

The pK_a values measured in this work offer a convenient possibility to assess the quality of these equations, as most compounds in this work (a) were not used in the training data set for developing the equations and (b) have higher pK_a values than the majority of the training set compounds. Thus, they serve as a good and demanding test set. The accuracy of pK_a(DMSO) values from the literature was critically evaluated, and the corrected pK_a(DMSO) values of (2-NO₂–Ph)(Ph)NH, 4-NH₂–C₅F₄N, 4-NO₂-1-Naphthalenamine were used (see Table 2).

The descriptors used in eqs 6 and 7 are the number of hydrogen bond donors (nHBD), the number of hydrogen atoms or sulfonyl groups attached directly to the acidity center (X-H, X-SO₂), and the number of nitrogen atoms in the molecule (nN). The equations were rearranged in such a way as to predict the pK_a values in MeCN from values in DMSO and the predicted values were compared to the experimental pK_a values determined in this paper. The results are presented in Table 3.

Table 3. pK_a(MeCN) Values Predicted Using Conversion Equations (Eqs 6 and 7)^a.

		Prediction from pKa(DMSO)
Compound	pKa(MeCN)d	NHb	Difference	Allc	Difference
2,3,5,6-Cl4-Aniline	33.51	33.30	–0.21	33.09	–0.42
4-CF3SO2-Aniline	33.11	34.10	0.99	33.94	0.83
4-NO2-Aniline	32.58	32.90	0.32	32.98	0.40
(2-NO2–C6H4)(Ph)NH	31.79	31.20	–0.59	31.49	–0.30
Carbazole	31.74	32.20	0.46	32.23	0.49
4-Cl-2-NO2-Aniline	31.06	30.90	–0.16	30.85	–0.21
1,3-Ph2-Urea	30.96	31.60	0.64	30.74	–0.22
4-NH2–C5F4N	30.12	30.70	0.58	30.64	0.52
Indazole	29.79	30.20	0.41	30.43	0.64
2,5-Cl2-4-NO2-Aniline	29.20	29.40	0.20	29.26	0.06
(4-NO2–C6H4)(Ph)NH	28.87	28.85	–0.02	28.99	0.12
4-NO2-1-Naphthalenamine	28.85	29.40	0.55	29.26	0.41
Benzimidazole	27.92	28.40	0.48	28.51	0.59
2,4-(NO2)2-Aniline	27.64	27.60	–0.04	27.66	0.02
Benzotriazole	22.98	23.62	0.64	23.74	0.76
		RMSEe	0.49		0.46

^aConversion equations taken from ref (6).

^bpK_a(MeCN) values predicted from pK_a(DMSO) using eq 6.

^cpK_a(MeCN) values predicted from pK_a(DMSO) using eq 7

^dExperimental values from this work.

^eRoot mean square error.

The RMSE of the pK_a(MeCN) prediction of the selection of weak acids is 0.49 when using the NH acid-specific and 0.46 when using the universal equation suitable for all types of acids. These RMSE values are equal to or lower than the RMSE values of pK_a(MeCN) to pK_a(DMSO) conversion equations in the original publication (0.5 and 1.2, respectively). This result is made even more noteworthy by considering that these equations were created using different compound classes (mainly sulfonamides and diarylamines), which are typically stronger acids than the aromatic amines and nitrogen heterocycles studied in this work.

Although similar pK_a conversion equations were published in ref (6) for the water-MeCN pair, these almost always yield less accurate results than conversions between DMSO and MeCN. Aqueous pK_a values from Table 2 were used to predict the pK_a values of the respective acids in MeCN, but the obtained RMSE was significantly over 2, which shows that the conversion equations between water and MeCN from ref (6) are unusable for such weak acids. One reason for this large discrepancy is the much different nature of both solvents. MeCN is an aprotic solvent with very weak hydrogen bond donor (HBD) and hydrogen bond acceptor (HBA) properties, whereas water is a protic solvent with strong HBD and HBA properties, thus having the ability to specifically solvate anions. Usually, better correlations of acidities are obtained between solvents with similar properties.¹⁴ Another reason is that the majority of the aqueous pK_a values of the compounds studied in this paper are outside the conventional aqueous pH scale (0–14). This means that certain approximations (regarding transferability of pK_a values from highly concentrated aqueous alkali solutions or aqueous organic mixtures into dilute aqueous solutions)²⁵ have been involved in obtaining these values, which invariably make the values less reliable.

Due to the low RMSE of prediction on the basis of pK_a(DMSO) values, the acidities of a selection of well-known heterocycles were estimated in MeCN using their pK_a values in DMSO. The results are presented in Table 4. To our knowledge, no experimental pK_a values have yet been determined in MeCN for pyrrole, pyrazole, imidazole, 1,2,3-triazole, and 1,2,4-triazole.

Table 4. Estimated pK_a Values of Some Heterocyclic Compounds.

			pKa(MeCN) estimated from pKa(DMSO)
Compound	CAS RN	pKa (DMSO)a	eq 5	eq 6	eq 7	Recommended pKa (MeCN)b	Exp. GAc [kJ mol-1]	Calc. GAd [kJ mol-1]
Pyrrole	109–97–7	23.0	34.9	35.3	35.5	35.2 ± 0.5	1468;40 147241	1482
Pyrazole	288–13–1	19.8	31.6	31.8	32.1	31.8 ± 0.5	144942	1463
Imidazole	288–32–4	18.6	30.4	30.6	30.9	30.6 ± 0.5	143442	1443
1,2,4-Triazole	288–88–0	14.75	26.5	26.5	26.8	26.6 ± 0.5	141018	1419
1H-1,2,3-Triazole	288–36–8	13.9	25.6	25.6	25.9	25.7 ± 0.5	141934	1412

^aAll experimental values from the Bordwell group.³

^bRecommended pK_a values based on the arithmetic mean of estimations from DMSO, uncertainty estimates refer to standard uncertainty.

^cExperimental GA values.

^dComputational GA values from this work.

Structural Effects on Acidity

Scheme 1 shows the effects of structural differences on the pK_a(MeCN) values of nitrogen (N) heterocycles related to indole. The compounds indazole, benzimidazole and benzotriazole can be viewed as indole derivatives with two or three ring nitrogen atoms. Adding N atoms into the 5-membered indole ring has an acidity-enhancing effect, the extent of the effect depending on their position. Indazole (N in position 2) has by 2.99 units lower pK_a value than indole, whereas the pK_a of benzimidazole (N in position 3) is by 4.86 units lower. Similar acidity differences were observed in DMSO, 2.75 and 4.55 pK_a units, respectively.³ The increase in acidity is caused by a combination of the inductive and resonance effects, which stabilize the anion. Although in benzimidazole, the second N is further away from the acidity center, thus having a lower inductive effect, it has a more substantial resonance effect, resulting in a lower pK_a value than in the case of indazole. Benzotriazole has by 9.80 units lower pK_a than indole. The third N in the five-member ring further stabilizes the anion. Interestingly, the ΔpK_a of indole and benzimidazole with 4.86 is almost the same as the ΔpK_a of benzimidazole and benzotriazole with 4.94. In DMSO, the acidity enhancing effect of the two additional N atoms is even larger, amounting to 11.92 units.³

Scheme 1. Relations between Structural Features and Acidities of Indole Derivatives.

Absolute pK_a values (determined in this work) are given below the compound names. pK_a differences between compounds are shown on the arrows.

The acidifying effect of an N atom in the six-membered ring of azaindoles is weaker due to the longer distance from the acidity center. The variation in pK_a values of the azaindoles with an N atom in different positions is small, spanning around 1 pK_a unit. 7-Azaindole is by 1.99, 4-azaindole by 2.29, 5-azaindole by 2.72 and 6-azaindole by 3.03 pK_a units stronger acid than indole. In the case of norharman, which has by 2.41 pK_a units lower pK_a value than carbazole, the extent of this acidifying effect is comparable to that of azaindoles.

Comparing the pK_a values of indole and carbazole reveals that the acidity-enhancing effect of a fused aromatic ring is smaller than the effect of additional N atoms, and carbazole is only by 1.04 pK_a units stronger acid than indole. The effect is almost identical in DMSO with 1.05 units.³ The effect of a fused aromatic ring in 6-azaindole is still lower, and accordingly, the pK_a value of norharman is only 0.42 units lower than the pK_a of 6-azaindole. Somewhat surprisingly, the effect of adding a second fused benzene ring into the carbazole molecule has a slightly higher impact on the pK_a value. Benzo[c]carbazole and benzo[a]carbazole are more acidic than carbazole by 1.41 and 1.54 units, respectively. Although the benzene ring fused to the c side of carbazole is further away from the acidity center than the one fused to the a side, the difference between the pK_a values of these two compounds is marginal. Indolo[2,3-a]carbazole can be viewed as a carbazole with an indole fused to its a side. Indolo[2,3-a]carbazole has by 0.3 units lower pK_a value than benzo[a]carbazole. The NH fragment close to the deprotonated acidity center might have some anion-stabilizing effect.

2-NO₂-Aniline and 4-NO₂-aniline have similar pK_a values in MeCN - 32.63 and 32.58, respectively. Replacing one of the hydrogens in their amino groups with a phenyl group has a drastically different impact on their pK_a values. (2-NO₂–Ph)(Ph)NH is by 0.84 pK_a units stronger acid than 2-NO₂-aniline, but (4-NO₂–Ph)(Ph)NH is by 3.71 units (4.05 units in DMSO) stronger acid than 4-NO₂-aniline. This difference is likely caused by the stabilizing intramolecular hydrogen bond (IMHB) in the neutral (2-NO₂–Ph)(Ph)NH molecule, thus making it less acidic than (4-NO₂–Ph)(Ph)NH where no IMHB is possible. The pK_a of 4-NO₂-1-naphthalenamine is almost identical to the pK_a of (4-NO₂–Ph)(Ph)NH.

In MeCN, the pK_a of 4-NO₂-aniline is by 0.53 pK_a units lower than the pK_a of 4-CF₃SO₂-aniline. The same trend can be observed in DMSO, where 4-NO₂-aniline is a stronger acid than 4-CF₃SO₂-aniline by 0.9 pK_a units. To compare the electron-withdrawing nature of both substituents, the resonance and field inductive effect substituent constants can be used. These demonstrate that the SO₂CF₃ substituent (σ_F = 0.83, σ_R = 0.26) is a stronger resonance and induction acceptor than the NO₂ substituent (σ_F = 0.64, σ_R = 0.16),⁴³ at odds with the above-described acidity order. The inversion of acidity order of NO₂ and SO₂CF₃ derivatives, relative to the order of substituent constants, has been described previously for other compounds and seems to depend on the solvent. In the case of the compound pairs Ph–CH₂–NO₂ and Ph–CH₂–SO₂CF₃, the nitro-substituted compound is a stronger acid in DMSO.⁴⁴ Goumont et al.,⁴⁵ on the other hand, have demonstrated that the relative strength of the acidifying effect of the NO₂ and SO₂CF₃ groups can be different in water and DMSO. They have shown on the example of NO₂–CH₂–COOEt and CF₃SO₂–CH₂–COOEt that in water, the former is a stronger acid and in DMSO the latter is a stronger acid.⁴⁵

The Upper Limit of the Acidity Scale in MeCN

In the present work, the MeCN acidity scale was expanded by 0.94 units to a pK_a value of 33.51 (2,3,5,6-Cl₄-aniline). Initial experiments have shown that theoretically it would be possible to expand the MeCN acidity scale even further toward higher pK_a values but there are some experimental limits. First, the anions of the studied acids need to be stable. All the NH acids studied in this work met that requirement. However, this was not valid for two CH acids whose pK_a is expected to be in the studied region. Specifically, it was observed from their UV–vis spectra that the anions of phenylacetonitrile and 4-NO₂-toluene were not stable under the conditions used for pK_a determinations.

Second, a base is needed that is strong enough to deprotonate the acids of interest but not too strong to decompose the solvent. Previously the phosphazene bases t–Bu-N=P₁(pyrr)₃ [pK_aH(MeCN) = 28.42]¹⁵ and Et-N=P₂(dma)₅ [pK_aH(MeCN) = 32.94]⁴⁶ have been used. Neither of them is sufficiently basic to fully deprotonate acids with pK_a values higher than approximately 32.5. Also Et-N=P₂(pyrr)₅ has been used as a deprotonating compound⁴⁶ in MeCN, but due to its commercial unavailability and its only marginally higher pK_a value than Et-N=P₂(dma)₅, it was not considered. t-Bu-N=P₄(dma)₉ would be a suitable deprotonating base in terms of basicity and spectral properties but P₃ and higher phosphazenes cause the self-condensation of acetonitrile and the formation of 4-NH₂-2,6-Me₂-pyrimidine.⁴⁷ Thus, the phosphazene base HN=P₁(tmg)₃ was used in the present work. The pK_aH (pK_a of the conjugate acid) value of HN=P₁(tmg)₃ in MeCN has been estimated to be 37.2.⁴⁶ This work marks the first time HN=P₁(tmg)₃ has been used as a basic titrant to deprotonate acids for the relative pK_a determinations in MeCN. Although HN=P₁(tmg)₃ is strong enough to deprotonate very weak acids and is stable as a free base in MeCN, it has a downside. Differently from the other mentioned strong bases, the protonated form of HN=P₁(tmg)₃ absorbs at wavelengths up to 290 nm (Figure S2 in the SI), meaning that it is a suitable titrant for acids that absorb at longer wavelengths, thus essentially limiting its usage to acids which have in their structure chromophores conjugated to the acidity center, e.g. nitro-substituted aromatic amines. This limitation would be absent in pK_a determinations with NMR, meaning that HN=P₁(tmg)₃ could be used in such pK_a determinations in the future. The phosphazene base t–Bu-N=P₁(pyrr)₃ has already been successfully used in pK_a determinations with NMR.⁴⁸

Conclusion

As a result of this work, the weak acid region of the MeCN acidity scale (from pK_a 29 upward), which previously contained only five acids, has been populated by 31 new compounds and extended to the pK_a value of 33.5. Altogether, 37 new pK_a values have been determined, which were among the highest experimental pK_a values of neutral NH acids in MeCN that have been reported until now. Several of the previously reported pK_a values have been revised. The experimental challenges encountered when measuring the pK_a values of very weak acids in MeCN were described and analyzed. The relations between the structure and acidity of a number of weak NH acids–nitrogen heterocycles and aromatic amines–have been discussed.

The newly determined pK_a values in MeCN were used in correlation with acidity data in DMSO to assess the quality of simple pK_a conversion equations from the literature between pK_a values in MeCN and DMSO. It was found that these equations yield pK_a values with an RMSE of prediction of 0.5, which is accurate enough for many applications. On the basis of the available data and correlation and conversion equations, some pK_a values have been predicted in MeCN. Together with computational gas-phase acidities of more than 40 compounds, this work presents over 90 new experimental or predicted acidity values—pK_a values in MeCN and computational acidity values in the gas phase.

Experimental Section

pK_a Determination Method

The pK_a values in MeCN were determined using the previously developed spectrophotometric titration methodology. This methodology is based on the measurement of relative acidities (ΔpK_a) of two acids (HA and HB). The studied equilibrium is the following:

8

The logarithm of the equilibrium constant of the reaction shown in eq 8 is the difference in pK_a values of compounds HB and HA, i.e. ΔpK_a, as defined in eq 9.

9

Methanesulfonic acid (CAS No. 75–75–2) was used as the acidic titrant during all relative acidity measurements. Phosphazene base P₂-Et (CAS No. 165535–45–5) was used as the basic titrant for deprotonating weak acids with pK_a values under 31. Acids with pK_a values over 31 were deprotonated using the phosphazene base HN=P₁(tmg)₃ (CAS No. 874220–27–6). For some measurements Et-N=P₂(pyrr)₅ (CAS No. 874220–47–0) was used as the basic titrant. The concentrations of the acidic and basic titrant solutions were (2 × 10^–3 – 6 × 10^–3) mol L^–1.

One ΔpK_a measurement series consisted of three experimental steps. As the first step, a solution of acid HA in MeCN with a concentration of (1 × 10^–5 – 2 × 10^–4) mol L^–1 was prepared into a 1 cm optical path length quartz cuvette and its UV–vis spectrum was registered. Then, a drop of an acidic titrant was added to the cuvette with a 100 μL Hamilton gastight syringe and a new spectrum was registered. This was done to make sure acid HA was in its neutral form in the solution. After that, a basic titrant was stepwise added until all of HA in the solution was converted to its anion A^–. This was evidenced by the absence of changes in the absorbance spectrum of the solution after further addition of the titrant. This step yielded the UV–vis spectra of the fully protonated (HA) and deprotonated (A^–) forms of the acid. In total, 5–10 spectra were registered. After the UV–vis spectrum of the fully deprotonated form A^– was recorded, an acidic titrant was stepwise added to the solution to verify the reversibility of deprotonation of HA. Although only the spectra of neutral and anionic forms were used in the calculation of the result, the spectra of the partially deprotonated HA were important for diagnostic reasons. These spectra gave information on whether the compound was pure or the presence of possible side processes (e.g., if it was decomposing during the measurement).

As the second step of the ΔpK_a measurement, the same operations were done with acid HB.

As the third step, a mixture containing both HA and HB was prepared, and the same titration procedure was applied. If it was found during the individual titrations that HA and HB were already initially in their neutral forms, no acidic titrant was added, and the mixture of HA and HB was only titrated with the basic titrant. During the titration of the mixture, 15–30 spectra were recorded. It was important to have more spectra of the mixture where HA and HB are partially deprotonated than during the titration of HA and HB individually. The reason is that a ΔpK_a value was calculated for every solution formed, which in turn was used to assign the final ΔpK_a value for the pair of acids.

After mathematically treating the spectral data obtained from the titration of the mixture, as well as the spectra of the solutions of the individual species HA, A^–, HB and B^– at multiple wavelengths using multilinear regression analysis, the dissociation levels α_HA = [A^–]/([A^–] + [HA]) and α_HB = [B^–]/([B^–] + [HB]) of both acids in all the mixtures formed during titration were obtained and were then in turn used to calculate the ΔpK_a values of HA and HB according to eq 10:

10

A more detailed description of the derivation of equations used to calculate the results of experimental ΔpK_a determinations is provided in the Supporting Information (SI). The UV–vis spectra of all the acids studied in this paper can be found in the SI (Figures S4–S51).

Every weak acid studied in this paper has relative acidity measurements done against at least three other acids. The agreement between these three measurements can be visualized from Table 1 by comparing the directly measured ΔpK_a values with the differences of the assigned pK_a values of the respective acids.

Computational Method

The geometry optimization and vibrational frequency calculations were carried out at DFT BP86/def2-TZVPP level of theory with DFT-D3(BJ) dispersion correction (software: Turbomole V7.8⁴⁹ and V7.7⁵⁰). The absence of imaginary frequencies in the spectra was taken as proof that local energy minimum was reached. For structures with many possible conformers the most stable one was identified and its geometry was used in the further calculations.

The complete basis set (CBS) energy values were determined based on the procedure developed by Helgaker et al.⁵¹ For each structure, DLPNO–CCSD(T)⁵² single-point calculations were carried out using basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ (software: ORCA⁵³ versions 5.0.4 and 6.0.0). For most compounds, the CBS energy value was found as an intercept of energy vs X^–3 plot, where X = 2 for cc-pVDZ, X = 3 for cc-pVTZ and X = 4 for cc-pVQZ. For compound tBu₄Box₂CH₂, due to its size, the CBS energy was found from cc-pVDZ and cc-pVTZ calculations via two parameter expression with integer exponent 4.^54,55

Gas-phase acidity (GA) values were computed as follows:

11

where E_CBS is CBS energy computed as described above, CP_TZVPP is chemical potential obtained from the TZVPP calculation using the freeh module in Turbomole, and G(H⁺) is Gibbs energy of the proton (−6.275 kcal mol^–1). Chemical potential is equal to H – TS, where H is enthalpy, T is temperature and S is entropy.

For comparison, GA values of several compounds were calculated with G4MP2⁵⁶ method (software: Gaussian 16 Rev A.03⁵⁷). The G4MP2 results were very well correlated with CBS results:

12

G4MP2 is one of the most accurate of the relatively computationally affordable methods for GA calculation.¹⁹ Our results suggest that for the studied compounds it does not fall short of the used combination of DLPNO–CCSD(T) and BP86/TZVPP.

The optimized geometries of the lowest-energy conformers and tabulated results of individual single-point calculations are available in the SI.

Instruments

An Agilent Cary 60 spectrophotometer (scanning speed 600 nm/min) connected with optical fiber cables to an external cell compartment inside a commercial MBraun Unilab glovebox filled with 99.999% pure argon (5.0, Linde Gas) was used for the pK_a determinations in MeCN. This setup ensured that the moisture and oxygen contents inside the glovebox were usually under 1 ppm and always under 10 ppm during all titrations. The external cell compartment did not have a built-in thermostat but its temperature was monitored and was in the range of (24.5 ± 1.5) °C.

Chemicals

Solvent

Acetonitrile (Romil 190 SpS far UV/gradient quality) was used as solvent after drying with molecular sieves (3 Å) for at least 12 h, which lowered the water content to under 6 ppm. The water content of the solvent was monitored using coulometric Karl Fischer titration. For all measurements involving aromatic amines, additionally purified MeCN was used. After drying with 3 Å molecular sieves, distillation over CaH₂ under argon was applied. The water content after the distillation process was found to be under 10 ppm and the solvent was stored in the argon glovebox. No molecular sieves were used for further drying the solvent in order to keep it as pure as possible.

Studied Compounds

The following commercially obtained chemicals were used without further purification: 2,3,5,6–Cl₄–aniline (Dr. Ehrenstorfer GmbH, 99.0%), 4–CF₃SO₂–aniline (Apollo Scientific, 97%), 2,3,4,5,6–Cl₅–aniline (Fluka, 99.1%), indole (Aldrich, ≥ 99%), N–Me–4–NO₂–aniline (Sigma-Aldrich, 97%), (2–NO₂–C₆H₄)(Ph)NH (Aldrich, 98%), 2–MeO–carbazole (BLD Pharmatech, 99.94%), 2–NH₂–4–NO₂–aniline (Aldrich, 98%), 5–Cl–2–NO₂–aniline (Fluka, 99%), 1,3–diphenylurea (Aldrich, 98%), (2–NO₂–C₆H₄)(4–Cl–C₆H₄)NH (BLD Pharmatech, 97%), 2–Cl–6–NO₂–aniline (BLD Pharmatech, 97%), 7–azaindole (Thermo Scientific, 98%), 4–azaindole (Thermo Scientific, 97%), 2–Cl–4–NO₂–aniline (Sigma-Aldrich, 99%), benzo[c]carbazole (BLD Pharmatech, 97%), benzo[a]carbazole (BLD Pharmatech, 98%), 5–azaindole (Thermo Scientific, 98%), (5–Cl–2–NO₂–C₆H₃)(Ph)NH (Alfa Aesar, 98%), indazole (Aldrich, 98%), 6–azaindole (Thermo Scientific, ≥ 97%), 2,3–Cl₂–6–NO₂–aniline (BLD Pharmatech, 97%), norharman (Acros Organics, 98%), 2,4–Cl₂–6–NO₂–aniline (BLD Pharmatech, 98%), 2,5–Cl₂–4–NO₂–aniline (BLD Pharmatech, 98%), (4–NO₂–C₆H₄)(Ph)NH (Sigma-Aldrich, 99%), 4–NO₂–1–Naphthalenamine (BLD Pharmatech, 98.53%), 2,6–Cl₂–4–NO₂–aniline (BLD Pharmatech, 98.32%), benzimidazole (Aldrich, 98%), benzotriazole (Reakhim, “pure for analysis”). The following chemicals were kind gifts and they were used as received: 3–Cl–4–NO₂–aniline (a kind gift from Peeter Talts, University of Tartu) and 4–Cl–2–NO₂–aniline (a kind gift from the late prof. Ilmar Koppel, University of Tartu). The following chemicals were of the same origin as in previous publications and they were used without further purification: 7–NO₂-indole,⁴tBu₄Box₂CH₂,⁵⁸ 4–CN–2,3,5,6–F₄–aniline,⁵⁹ 4–NH₂–C₅F₄N,⁵⁹ 9–C₆F₅–fluorene,⁶⁰ C₆H₅–CH₂–SO₂CF₃,⁶ (4–Me–C₆F₄)(C₆H₅)CHCN,⁶⁰ 2,4–(NO₂)₂–aniline,⁶¹ 4–NO₂–aniline,⁶² 2–NO₂–aniline.⁶² The purity of the chemicals was assessed while observing their UV–vis spectra during titrations and the compounds were declared pure enough if no unknown absorbance changes were seen and if the isosbestic points (if present) were sharp. Carbazole (Aldrich) was recrystallized from ethanol, and 3–MeCOO-indole (Chemapol) was recrystallized twice from 40% methanol before usage. Indolo[2,3-a]carbazole was the same as used in a previous publication⁶⁵ and it was additionally recrystallized from ethanol.

Titrants

Methanesulfonic acid (Aldrich, ≥ 99%) was used to prepare the acidic titrant solution. Phosphazene base P₂-Et (Sigma-Aldrich, ≥ 98%), Et-N=P₂(pyrr)₅ (same as used in a previous publication⁶³) or HN=P₁(tmg)₃ (prepared for this work) were used to prepare the basic titrant solution.

HN=P₁(tmg)₃

HN=P₁(tmg)₃·HBF₃ (2.02 mmol; 963 mg), KHMDS (2.06 mmol; 411 mg) and hexane (12 mL) were added to an oven-dried (140 °C) ACE pressure tube inside a glovebox. The reaction mixture was stirred overnight at 70 °C outside the glovebox under argon. The mixture was then filtered in a glovebox and hexane was removed in vacuo. The raw product was recrystallized from hexane at −30 °C to give HN=P₁(tmg)₃ as colorless crystals (514 mg, 65%). Some of the substrate did not react. It is likely that a finer ground powder compared to what was used is preferred since the starting compound is not soluble in hexane. Or longer reaction time should be used. The obtained spectral data corresponded to that previously reported.⁶³

Data Availability Statement

The data underlying this study are available in the published article and its Supporting Information.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsorginorgau.4c00095.

• Optimized gas-phase geometries as a set of XYZ files (ZIP)

• Computational energies in the gas phase (XLSX)

• Theoretical background of the relative acidity determination method, pK_a measurement results of benzotriazole, computational GA values of reference acids, UV–vis titration spectra of all studied compounds, UV–vis spectrum of HN=P₁(tmg)₃, acetonitrile for pK_a determinations (PDF)

Author Contributions

CRediT: Märt Lõkov investigation, writing–original draft, formal analysis, supervision, data curation; Carmen Kesküla investigation; Sofja Tshepelevitsh investigation, formal analysis, data curation, visualization, writing - review and editing; Marta-Lisette Pikma investigation; Jaan Saame investigation; Dmitri Trubitsõn investigation; Tõnis Kanger funding acquisition, supervision; Ivo Leito: conceptualization, methodology, formal analysis, supervision, resources, writing–review and editing, project administration, funding acquisition.

The authors declare no competing financial interest.