Diffusion and structural behaviour of the dl -2-aminobutyric acid

J. Chem. Thermodynamics 135 (2019) 60–67

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Diffusion and structural behaviour of the

DL-2-aminobutyric

acid

M.M. Rodrigo a, M.A. Esteso a,⇑, L.M.P. Veríssimo a,c, C.M. Romero b, M.L. Ramos c, L.L.G. Justino c, H.D. Burrows c, A.C.F. Ribeiro c,⇑ a

U.D. Química Física, Universidad de Alcalá, 28871 Alcalá de Henares, Madrid, Spain Departamento de Química, Facultad de Ciencias, Universidad Nacional de Colombia, Bogota, Colombia c Coimbra Chemistry Centre, Department of Chemistry, University of Coimbra, P3004-535 Coimbra, Portugal b

a r t i c l e

i n f o

a b s t r a c t DL-2-Aminobutyric acid (a-aminobutyric acid or AABA) is a non-protein amino acid with important physiological properties, and with considerable relevance in different areas, such as fundamental research and pharmaceutical industry. In this paper, the binary mutual diffusion coefficients of AABA in non-buffered aqueous solutions (0.001–0.100) mol
dm3 at 298.15 K were measured. From these diffusion data, limiting values at infinitesimal concentration, D0, as well as those of the thermodynamic factors, FT, and activity coefficients, c, were estimated. These data for AABA were compared with the data previously obtained for DL-4-aminobutyric acid (GABA). The difference of the behaviour of these transport properties for both amino-acids was explained based on the structural differences for the monomeric zwitterionic species of AABA and GABA. Such structural differences are supported by both 1H and 13C NMR spectroscopy and theoretical calculations, which indicate that the predominant species of AABA in these solutions is the extended zwitterionic form in contrast with the curled one of GABA. Ó 2019 Elsevier Ltd.

Article history: Received 25 January 2019 Received in revised form 8 March 2019 Accepted 9 March 2019 Available online 11 March 2019 Keywords: Diffusion coefficient DL-2-Aminobutyric acid Solutions Taylor dispersion technique NMR

1. Introduction Amino acids and their derivatives are biologically important compounds which enjoy nutritional, cosmetic, biomedical and pharmaceutical relevance [1]. Moreover, their solutions give relevant information related to both the proteins behaviour as well as the role of the solvent structure in the understanding of their folding and denaturation processes [1]. Although there is extensive research dedicated to these compounds in aqueous solutions, the investigation of multicomponent mutual diffusion in these systems was scarce and frequently poorly understood. We have already started a comprehensive study of the diffusion of these compounds in aqueous solutions [2–6] at 298.15 K over the concentration range from (0.001 to 0.100) mol
dm3, using the Taylor dispersion technique [7–12]. Now, we are particularly interested in linear hydrocarbon-chain. a-Amino acids have the amine and the carboxylate groups on adjacent carbon atoms. Among them, DL-2-aminobutyric acid (aaminobutyric acid or AABA), a four carbon non-protein amino acid, was selected due to the fact that it is relevant in several biological systems. In aqueous solutions, AABA can exist in three different ⇑ Corresponding authors. E-mail addresses: (A.C.F. Ribeiro).

[email protected]

https://doi.org/10.1016/j.jct.2019.03.009 0021-9614/Ó 2019 Elsevier Ltd.

(M.A.

Esteso),

[email protected]

protonated forms (Scheme 1). At pH of dissolution, the dominant species is the electrically neutral, but under a dipolar (zwitterionic) structure, where both carboxyl and amino groups are electrically charged. Values for some thermodynamic properties of this amino acid have been published in aqueous solutions [14]. Limiting mutual diffusion coefficient values for this amino acid, by using the Taylor dispersion technique, in both aqueous solutions (at various temperatures but injecting only samples at the concentration 0.01 mol
dm3 of the amino acid) [15] and in the presence of 0.015 mol
kg1 NaCl [16] have also been published. Therefore, having in mind these facts, we proposed an experimental study of the binary diffusion for system containing water and AABA over the concentration range from (0.001 to 0.100) mol
dm3, by using Taylor’s dispersion technique at 298.15 K. The experimental interdiffusion coefficients thus obtained for AABA were compared with the respective data for GABA [6]. Furthermore, from these experimental diffusion results, the diffusion coefficient at infinitesimal concentration, D0, the thermodynamic factors, FT, and the activity coefficients by using the Nernst and Onsager–Fuoss equations [17–19], respectively, were estimated, permitting us to have a better understanding of its thermodynamics in aqueous solutions. These studies were complemented by structural information obtained from NMR spectroscopy and DFT calculations.

M.M. Rodrigo et al. / J. Chem. Thermodynamics 135 (2019) 60–67

61

Scheme 1. Structure of the various protonated forms of AABA (DL-2-aminobutyric acid): AH+ ? AH+ (pKa1 = 2.55); AH+ ? A (pKa2 = 9.60) [13].

2. Experimental

2.4. Diffusion measurements

2.1. Materials

In a general way, the Taylor dispersion method for measuring diffusion coefficients consists in dispersing a very small amount of a given solution (at a concentration within the range

Table 1 contains all the chemicals used in this work. DL-2aminobutyric acid (a-aminobutyric acid or AABA) (Sigma-Aldrich, mass fraction purity >0.99; molar mass = 103.120 g
mol1) was used as received without further purification, but it was kept in vacuo into a desiccator over silica gel. The solutions for the diffusion measurements were prepared by using Millipore Milli-Q water (specific resistance = 1.82  105 X m, at 25 °C). The solutions for the NMR measurements were prepared by using D2O (Sigma-Aldrich, mass fraction purity >0.99). To perform these measurements, the value of the pH was adjusted by the addition of DCl (Sigma-Aldrich, mass fraction purity >0.99) or NaOD (SigmaAldrich, mass fraction purity >0.99). All solutions were freshly prepared at 298.15 K before each experiment. The pH* values mentioned here are those directly read at the pH-meter at room temperature, after its standardization by using aqueous buffers [13]. 2.2. NMR experiments The 1H and 13C NMR spectra were acquired on a Bruker NMR spectrometer, model Avance III HD 500 MHz. The 13C spectra were obtained by using proton decoupling techniques taking advantage of the nuclear Overhauser effect. As internal reference we made use of the methyl-signal of the tert-butyl alcohol {d = (1.3 and 31.2) 106 for 1H and 13C shifts, respectively}.

Molecular structure calculations were carried out at the secondorder Møller-Plesset perturbation theory (MP2) level using the GAMESS-US code [20] and employing the 6-311++G(d,p) basis set for all atoms. The molecular geometries were optimized without symmetry constrains and the bulk solvent effects of water were taken into account in the molecular structure optimizations by using the polarizable continuum model (PCM) of Tomasi and coworkers [21,22]. In PCM, default van der Waals radii were used for all atoms. The gradient threshold for geometry optimization was taken as 1.0  105 Hartree
Bohr1. Table 1 Sample description.

a

Chemical name

Source

Mass fraction Puritya

DL-2-aminobutyric acid H2O

Sigma-Aldrich Millipore Milli-Q water (1.82  105 O m at 25.0 °C) Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

> 0.99

As stated by the supplier.



(at concentration c ), flowing through a long capillary tube whose dimensions are accurately known. In our case, the diffusion tube was 3.2799 (±0.0001)  103 cm length with a radius of (0.05570 ± 0.00003) cm [7–12]. Various solutions of different concentration were injected into each carrier solution to confirm the independence of the injection concentration on the D value obtained for the carrier solution studied. At the start of each run, 0.063 cm3 of the solution under study were injected through a 6-port Teflon injection valve (Rheodyne, model 5020) into the laminar carrier stream moving at a controlled flow rate of 0.23 cm3
min1 (corresponding to 3.5 rotations per minute of the peristaltic pump head) by using a metering pump (Gilson model Miniplus 3) which gives retention times of about 8  103 s. The dispersion tube and the injection valve were kept into an air thermostat at the temperature of 298.15 K (±0.01 K). Dispersion of the injected samples was monitored at the dispersion tube outlet by a differential refractometer (Waters model 2410). The refractometer output voltages were measured at accurately timed intervals using a digital voltmeter (Agilent 34401 A) with the help of an IEEE interface. Binary diffusion coefficients, D, were calculated by fitting the dispersion equation

V ðtÞ ¼ V 0 þ V 1 t þ V max ðt R =t Þ1=2 exp½12Dðt  t R Þ2 =r 2 t

2.3. Computational details

D2O DCl NaOD



(c  0:150) mol
dm3) into a laminar carrier stream either of pure solvent or the same solution, but of a slightly different composition

>0.99 >0.99 >0.99

ð1Þ

where V0 and V1 are the baseline voltage and the baseline slope, respectively; Vmax the peak height; tR is the mean sample retention time and r is the radius of the dispersion tube. 3. Results and discussion 3.1. Analysis of the experimental diffusion coefficients of AABA in aqueous solutions Table 2 shows the average values of mutual diffusion coefficients, D, of aqueous solutions of AABA at 298.15 K obtained from at least four independent runs together with their respective uncertainties (1–2%). Using a least-squares procedure (with a confidence interval of 98%), our D values of AABA were fitted, to the linear equation (2), with a good correlation coefficient, R2, and a low percentage of standard deviation (<1%). That is,

    D= 109 m2 s1 ¼ 0:843  0:036 m R2 ¼ 0:993

ð2Þ

The limiting diffusion coefficient value, found by extrapolating the experimental data to c ? 0 (D0 = 0.843  109 m2
s1), is in acceptable agreement with the literature value obtained by

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Table 2 Mutual diffusion coefficients, D, of a-aminobutyric acid (AABA) in aqueous solutions at various molar concentrations, c, at 298.15 K and P = 101.3 kPa. c/(mol
dm3)

ma/(mol
kg1)

Db ± SDc/(109 m2
s1) AABA

DD%d

0.00100 0.00500 0.0100 0.0200 0.0500 0.100

0.001003 0.005014 0.01003 0.02005 0.05008 0.1000

0.842 ± 0.009 0.841 ± 0.005 0.839 ± 0.005 0.838 ± 0.005 0.835 ± 0.010 0.832 ± 0.009

7.9 8.0 7.8 7.8 8.2 8.8

a Molalities were calculated from our molarities and density measurements obtained by Romero et al. [14]. b D is the mean diffusion coefficient value from 4 to 6 experiments. c SD is the standard deviation of that mean. d DD% represents the deviations between values of D of AABA and GABA [6] at different concentrations, m. Standard uncertainties are ur(m) = 0.01; u(T) = 0.01 K and u(P) = 2.03 kPa.

Umecky et al., (D0 = 0.839  109 m2
s1) [23] being the deviation of 1.5%, within the uncertainty of our method. Similarly, this D0 value is also in good agreement with that obtained by Ellerton et al., (D° = 0.8305  109 m2
s1) [24], despite the different technique they used (a modified Spinco electrophoresis-diffusion apparatus); as it can be appreciated, in this case the deviation with respect to our value is also lesser than 1.5%. In addition, from Table 2, despite the experimental diffusion coefficients are fairly constant in the concentration range studied (variations less than 1.5%), it can be seen that they differ systematically and significantly from the respective D values obtained for GABA, in the same concentration range [6], in approximately 8%.

3.2. NMR measurements and density functional theory (DFT) calculations As in earlier studies [6,25], 1H and 13C NMR spectra were carried out to obtain information about the conformation of the AABA species present in aqueous solution. The 1H NMR spectra, for solutions with concentrations (0.089 and 0.0089) mol
kg1, prepared at pH* of dissolution, represented in Fig. 1, show the absence of the aggre-

gation, giving evidence that AABA, in neutral solutions, behaving as a single lone molecular entity. Moreover, the proton and carbon chemical shifts, as well as the proton-proton coupling constants, have been obtained for four pH values, 1.4, 4.6, 6.8 and 12.2 (Figs. 2 and 3) to provide a characterization of the conformation of AABA as a function of its protonation/deprotonation equilibria over the pH range 1–13 and the 1H and 13C chemical shifts are plotted as functions of the pH* in Figs. 4 and 5 to visualize their comparative variation. The 1H and 13C NMR chemical shifts were found to change with pH*, indicating differences in the degree of protonation/ deprotonation of the two acidic functions present in the molecule, the carboxylic group, RCO2H ? RCO 2 , (pKa1 = 2.55), and the adjacent amino group, R0 NH+3 ? R0 NH2 (pKa2 = 9.60), at 298.15 K, respectively [13]. Three pH ranges were studied, corresponding to the monoprotonated AABA, AH+, below pKa1 (2.55), pKa1 < pH < pKa2 and above pKa2. The first RCO2H ? RCO 2, (pKa1 = 2.55) and second R0 NH+3 ? R0 NH2 (pKa2 = 9.60) deprotonation steps is expected to lead to a protection on the 1H NMR signals, which should shift to lower frequencies due to the decreasing positive charge. In contrast, the 13C NMR spectra should show a general tendency of de-shielding with increasing pH. Changes in the chemical shift are mainly related to changes in electron density and other contributions to rp, as recently noted for other nitrogen bases on deprotonation, such as 8-hydroxyquinoline-5-sulfonate [26]. These spectral parameters for 1H and 13C are collected in Tables 3 and 4, respectively. + 0 0 Both deprotonation steps (RCO2H ? RCO 2 and R NH3 ? R NH2) 1 must cause a shifting of the H NMR signals towards lower frequencies because of the decrease of the positive charge on the amino acid molecule. On the contrary, the 13C NMR signals should show a general trend of de-shielding with increasing pH, mainly due to the change in the electron density as well as in other contributions to rp, as it has been shown in the case of the deprotonation of other nitrogen bases, such as 8-hydroxyquinoline-5-sulfonate [26]. Due to its three-carbon chain, AABA is a very flexible molecule, the conformations rationalized primarily by the stabilizing effects of the intramolecular hydrogen bonds between the polar moieties of the amino acid skeleton. NMR parameters suggest relatively

Fig. 1. 1H NMR spectra of a D2O solution of AABA (a) 0.0089 mol kg1 and (b) 0.089 mol kg1, at pH* = 6.8, 298.15 K and P = 101.3 kPa.

M.M. Rodrigo et al. / J. Chem. Thermodynamics 135 (2019) 60–67

Fig. 2. 1H NMR spectra of a D2O solution of AABA 0.089 mol kg1, (a) pH* = 1.4, (b) pH* = 4.6, (c) pH* = 6.8 and (d) pH* = 12.2, at 298.15 K and P = 101.3 kPa.

Fig. 3.

13

C NMR spectra of a D2O solution of AABA 0.089 mol kg1, (a) pH* = 1.4, (b) pH* = 4.6, (c) pH* = 6.8 and (d) pH* = 12.2, at 298.15 K and P = 101.3 kPa.

63

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M.M. Rodrigo et al. / J. Chem. Thermodynamics 135 (2019) 60–67 Table 4 C NMR parametersa for AABA (d values/106), as a function of pH* at 298.15 K and P = 101.3 kPa. 13

AABAb

C-1

C-2

C-3

C-4

pH* = 1.4 pH* = 4.6 pH* = 6.8 pH* = 12.2

172.29 174.80 174.82 183.71

54.06 55.81 55.82 57.16

23.20 23.65 23.65 27.65

8.36 8.47 8.48 9.21

a d values, in ppm, relative to Me4Si, using tert-butyl alcohol (dC = 31.2) as internal reference. b 0.089 mol
kg1 AABA solution. Standard uncertainties are u(T) = 0.01 K and u (P) = 2.03 kPa.

Fig. 4. 1H NMR chemical shifts as a function of pH*, of a D2O solution of AABA 0.089 mol kg1 at 298.15 K and P = 101.3 kPa. Literature pKa values from Ref. [13] are indicated by arrows.

Fig. 5. 13C NMR chemical shifts as a function of pH*, of a D2O solution of AABA 0.089 mol kg1 at 298.15 K and P = 101.3 kPa. Literature pKa values from Ref. [13] are indicated by arrows.

Table 3 H NMR parametersa for AABA (d values/106), as a function of pH* at 298.15 K and P = 101.3 kPa. 1

AABAb

H-2

H-3

H-4

J2,3a

J2,3b

J3,4

*

3.76 3.76 3.76 3.24

1.95 1.95 1.95 1.65

1.03 1.03 1.03 0.93

5.50 5.66 5.65 6.24

6.31 6.21 6.26 6.24

7.54 7.55 7.56 7.50

pH = 1.4 pH* = 4.6 pH* = 6.8 pH* = 12.2

a d values, in ppm, relative to Me4Si, using tert-butyl alcohol (dH = 1.3) as internal reference; J values in Hz. b 0.089 mol
kg1 AABA solution. Standard uncertainties are u(T) = 0.01 K and u (P) = 2.03 kPa.

extended structures for the three forms, AH+ (pH < pKa1), the zwitterionic form, AH+ (pKa1 < pH < pKa2) and A (pH > pKa2). The 1H and 13C chemical shifts measured as function of the pH* (Figs. 4 and 5) suggest slight conformational changes near pKa1, as a result of the RCO2H ? RCO 2 deprotonation and more pronounced changes near pKa2, because of the deprotonation step of R0 NH+3 ? R0 NH2, suggesting some local conformational changes around C-1-C-2, giving rise to a fully extended structure.

It is interesting to compare the results obtained in this study for AABA with the previously obtained for GABA [6], for which we have evidenced of a curled structure for the zwitterionic form. Structural differences for the zwitterionic forms of AABA and GABA should be important to explain the thermodynamic and transport properties of the two amino acids, in aqueous solution. The partial molar volume at infinite dilution and the viscosity coefficient measured for the zwitterionic forms of both amino acids indicate to be lower for the gamma amino acid (GABA), which is in agreement with the results of the mutual diffusion coefficients. Concerning our results for the mutual diffusion coefficients, also the different structures lead to differences of behaviour of diffusion of the two cited amino acids. That is, the D values for AABA are higher than the values obtained for GABA at infinitesimal (D0) and finite (D) concentrations. In this last situation, the deviations increase with increasing the concentration, reaching a maximum value of 10%. The interpretation of the diffusion behaviour of these aqueous systems can be made by using the Onsager–Fuoss model [18,27] (Eq. (5)), which suggests that D is a product of two factors: a kinetic one, FM (or molar mobility coefficient of a diffusing substance) and a thermodynamic one, FT. That is, considering our experimental conditions (i.e., dilute solutions) we can conclude that the variation in D is mainly due to the variation of the thermodynamic factor (attributed to the nonideality in the thermodynamic behaviour). Further details on the conformation of AABA in aqueous solution were obtained from quantum chemical calculations. The conformation of AABA in the neutral un-ionized form was studied in the gas phase by MP2 calculations and laser-ablation molecularbeam Fourier transform microwave spectroscopy [28]. However, in aqueous solution, the neutral non-ionized form of AABA is present only in trace amounts, since in these conditions the proton from the carboxylic group is readily transferred to the amino group, yielding the zwitterionic form. To the best of our knowledge, there are no computational studies in the literature on the structure of AABA in aqueous solution. As the NMR results presented above have shown, the protonation state of AABA changes with the solution pH. The protonation state has a strong influence on the geometry and strength of the intramolecular interactions that can be established in AABA. These interactions, together with the steric effects resulting from the rotation of the ethyl group around the C2-C3 bond, will determine AABA conformation in the various pH regimes in aqueous solution. In the low pH regime we considered twelve possible initial conformations for AABA. These differ on the chain conformation (having the different groups in anti or gauche positions) and on the geometry of the H-bonding system, which can involve a) one or two hydrogen atoms from NH+3 and the carbonyl oxygen or b) one or two hydrogen atoms from NH+3 and the oxygen atom from the hydroxyl group in CO2H. For the moderate pH regime, in which AABA is in the zwitterionic form, we considered six possible initial conformations. These have different chain conformations and can

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M.M. Rodrigo et al. / J. Chem. Thermodynamics 135 (2019) 60–67

either have a single H-bond between one hydrogen atom from NH+3 and one oxygen atom from CO 2 or can gave a bifurcated H-bond involving two hydrogen atoms from NH+3 and one carboxylate oxygen. Finally, above pKa2, AABA has a NH2 group and a CO 2 group which can establish either single H-bonds or bifurcated H-bonds involving the hydrogen atoms from NH2 and one carboxylate oxygen atom. Therefore, for the high pH regime we have also considered 6 possible initial conformations. These geometries were optimized at the MP2 level of theory considering the bulk solvent effects of water and the lowest energy structures are shown in Fig. 6.

Fig. 6. MP2/6-311++G(d,p) optimized geometries of the lowest energy conformers of AABA at low, medium and high pH, respectively. Bulk solvent effects of water were considered through PCM [21,22]. Relative Gibbs free energies are given in kJ/mol. Conformers are labelled ‘‘n” for negative, ‘‘zw” for zwitterionic, ‘‘p” for positive, ‘‘g” for gauche and ‘‘a” for anti. Gauche and anti labels refer to the C1-C2-C3C4 and N-C2-C3-C4 dihedral angles.

Table 5 includes the calculated relative Gibbs free energies and selected structural parameters of the optimized structures. As it can be ascertained, in the low pH regime (AH+), the three most stable conformers are p-ag, p-ga and p-ag0 , with approximate populations of 55, 39 and 6%, respectively. In the two most stable conformers the H-bonds are approximately bifurcated, as shown by the N–H


Ocis and N–H0


Ocis distances, which are very similar. Conformers p-ag and p-ga have C1-C2-C3-C4 dihedral angles of (174.92 and 64.59) degrees and N-C2-C3-C4 dihedral angles of (66.04 and 179.5) degrees, indicating that these conformers have extended chain conformations. For the zwitterionic form of AABA (AH+), the two most stable conformers show hydrogen bonds between the NH+3 and CO 2 groups involving only one hydrogen atom in each case, as indicated by the N–H


Ocis distances (0.18 nm) compared to the N–H0


Ocis distances (0.3 nm). The hydrogen bond established in the zwitterionic conformers is stronger than the ones established in the protonated AH+ form, leading to planarization of the Ocis-C1-C2-N unit, as indicated by the decrease of the Ocis-C1-C2-N dihedral angle. The three most stable conformers, zw-gg, zw-ag and zw-ga (approximate populations of 47, 42 and 11%, respectively), have C1-C2-C3-C4 dihedral angles of (55.22, 175.45 and 69.72) degrees and N-C2-C3-C4 dihedral angles of (64.46, 66.69 and 174.36) degrees. Considering the three major conformers, the conformers with extended conformation account for 53% of the population of the zwitterionic form of AABA. In the high pH regime (A), the two most stable conformers are almost isoenergetic and have essentially bifurcated weak Hbonds between the NH2 and CO 2 groups, as indicated by the N– H


Ocis and N–H0


Ocis distances. Large conformational changes are observed in the Ocis-C1-C2-N unit upon deprotonation, with a significant increase of the torsion angle in this unit in the major conformers of the negative form A (16.60 and 49.50) degrees compared to an almost planar Ocis-C1-C2-N unit (dihedral angles of 0.70 and 6.56) degrees in the zwitterionic form. For the A form of AABA in aqueous solution the conformers with extended conformations (n-ga and n-ag) account for approximately 53% of the population. In conclusion, the results obtained from the quantum chemical calculations indicate the prevalence of extended conformations throughout the whole pH range considered, and also indicate significant conformational changes in the Ocis-C1-C2-N unit as a consequence of changes on the protonation state of AABA. These findings are in accordance with the NMR results. To investigate the structural differences between the zwitterionic forms of AABA and GABA in aqueous solution, we have also optimized the structure of this amino acid. A previous computa-

Table 5 Relative Gibbs energies, DG, approximate population at 298.15 K, P298, and selected structural parameters for the lowest energy conformers of AABA calculated at the MP2/6-311+ +G(d,p) level of theory in aqueous solution. Bulk solvent effects of water were considered through PCM. [13,19].

DG/(kJ
mol1)

Approx.P298/(%)

\(Ocis-C1-C2-N)a/(°)

108 d(NH


Ocis)b/cm

108 d(NH0


Ocis)/cm

\(C1-C2-C3-C4)/(°)

\(N-C2-C3-C4)/(°)

A n-gg n-ga n-ag

0.0 0.1 4.9

47 46 7

16.60 49.50 18.83

2.457 2.477 2.466

2.923 3.123 2.874

63.47 59.6 166.77

64.13 176.67 66.51

A H + zw-gg zw-ag zw-ga

0.0 0.3 3.5

47 42 11

0.70 6.56 25.86

1.821 1.756 1.971

3.112 3.138 2.927

55.22 175.45 69.72

64.46 66.69 174.36

AH+ p-ag p-ga p-ag0

0.0 0.9 5.5

55 39 6

7.26 23.59 7.67

2.523 2.387 2.034

2.635 2.678 3.267

174.92 64.59 176.09

66.04 179.5 65.29



a

Ocis refers to the carboxylic oxygen which is cis to the nitrogen atom. In the zwitterionic and protonated structures, in which the amine group is present in the form NH+3, the distances NH


Ocis refer to the two shorter of the three NH


Ocis distances. b

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M.M. Rodrigo et al. / J. Chem. Thermodynamics 135 (2019) 60–67

tional study by Crittenden et al. [29] has shown that the most stable form for the zwitterion of GABA in aqueous solution is a folded structure involving an intramolecular hydrogen bond. We have optimized this structure using the same theoretical method that was used for AABA and the optimized structure is presented in Fig. 7a). More recently, Allouche et al. [30], reported that this curved structure is neutral due to an intramolecular proton transfer (7.b). We have optimized both structures at the MP2/6-311++G (d,p) level in aqueous solution and, in fact, the neutral folded structure 7.b) is 9.3 kJ
mol1 (DG) lower in energy compared to 7.a). Both structures present folded conformations with OOC-C–C–C and N-C–C–C dihedral angles close to gauche (74.61 and  73.65) degrees for 7.a and (86.79 and 67.23) degrees for 7.b, respectively. In conclusion, these studies show that the zwitterions of AABA in aqueous solution adopt conformations which are more extended than those adopted by GABA. 3.3. Interpretation of the dependence of concentration on the diffusion coefficients of AABA The interpretation of the dependence of the diffusion coefficients in dilute aqueous solutions can be made by using the Onsager–Fuoss model [17–19] (Eq. (3)), suggesting that D is a product of two factors: a kinetic one, FM (or molar mobility coefficient of a diffusing substance) and a thermodynamic one, FT. That is,

D ¼ FMFT

ð3Þ

  being F M ¼ D0 þ D1 þ D2

ð4Þ

and

Fig. 7. (a) MP2/6-311++G(d,p) optimized geometry of the lowest energy zwitterion of GABA. The dihedral angles OOC-C-C-C and N-C-C-C are 74.61 and 73.65 degrees, respectively, and the bond length of the hydrogen bond, d(O


H), is 1.411 Å (the complete study was reported in Ref. [30]). (b) MP2/6-311++G(d,p) optimized geometry of the neutral form of the zwitterion of GABA, after proton transfer The dihedral angles OOC-C-C-C and N-C-C-C are 86.79 and 67.23 degrees, respectively, and the bond length of the hydrogen bond, d(N


H), is 1.564 Å (structure similar to the one reported in Ref. [30]). The bulk solvent effects of water were considered through PCM [21,22].

  @ ln c FT 1 þ c @c

ð5Þ

where D0 and D represent the diffusion coefficients of AABA at infinitesimal and finite concentrations, respectively; D1 and D2, the first and second-order electrophoretic terms [17–19], respectively; and c, the mean molar activity coefficient of the solute. Due to the fact that both the values found for the binary diffusion coefficients (Table 2), into the concentration range studied, are fairly constant, and AABA molecules are in the charge compensated zwitterionic form (what is supported by NMR data), this Eq. (3) can be simplified to Eq. (6):

  @ ln c D ¼ D 1 þ c @c

ð6Þ

(the Nernst-Hartley equation) which, in general, is applicable to non-electrolytes only. In other words, from this approach, FM = D0, the effect of the electrophoretic terms on the diffusion coefficient is considered negligible. Based on Eq. (6), the thermodynamic factor, FT, was estimated at the concentrations studied, the values being collected in Table 6. As it can be ascertained, the gradient of the Gibbs energy (FT) slightly decreases when the AABA concentration increases. Moreover, by replacing Eq. (2) into the Nernst–Hartley equation (Eq. (6)), a very simple relation (Eq. (7)) is obtained between the activity coefficient and concentration [31]:

ln c ¼ Bc

ð7Þ 3

1

B being a constant (B = 0.043 dm
mol ) and c, the molar concentration. From this Eq. (7), the values for the activity coefficient, in the concentration range studied, were determined (they are collected in Table 6). From the analysis of Table 6, it can be seen that the thermodynamic factor (FT) as well as the activity coefficient (c) of AABA decrease when its concentration increases. In addition, it is verified that these values are very close to the corresponding values obtained for GABA (deviations <1%), contrarily to what happens with the diffusion coefficient values at both infinitesimal and finite concentration, (D0) and (D) respectively, which present differences of 8% between both amino acids. Thus, despite the approaches used (i.e., the motion of the solvent and the change of parameters such as viscosity, dielectric constant and degree of hydration with concentration are neglected), the difference of the behaviour of diffusion for both amino acids can be mainly attributed to the ionic mobility (8%) and, secondarily, to the gradient of the Gibbs energy (DFT < 1% and Dc < 1%). Structural differences for the zwitterionic forms of AABA and GABA (that is, extended and curled structures, respectively) can be responsible for the different behaviour of their diffusion rates, fact supported by NMR measurements (Section 3.2).

Table 6 Comparison of thermodynamic parameters, (FT, F0 T and c), of a-aminobutyric acid and c-aminobutyric acid aqueous solutions, at 298.15 K and P = 101.3 kPa.

a

c/(mol
dm3)

FT/(109 m2
s1)a

DFT/(%)b

F0 T/(109 m2
s1)c

DF0 T/(%)d

ce

Dc/(%)f

0.00100 0.00500 0.0100 0.0200 0.0500 0.100

0.999 0.998 0.995 0.994 0.990 0.987

0.1 0.1 0.2 0.2 0.0 0.6

1.002 0.999 0.998 1.000 1.005 1.017

0.2 0.2 0.3 0.2 0.0 0.6

1.000 0.999 0.999 0.999 0.998 0.996

0.1 0.0 0.0 0.1 0.4 0.8

FT = Dexp/FM, where Dexp, FT, FM represent our data, thermodynamic and molar mobility factors, respectively. DFT/(%) represents the deviations between the FT values of both AABA and GABA at different concentrations, c. c F0 T = Dexp gr /FM, with gr being the relative viscosities measured by Romero et al. [14]. d DF0 T/(%) represents the deviations between the F0 T values of both AABA and GABA at different concentrations, c. e Activity coefficients, c, estimated from Eqs. (3) to (6), where B/D0 = 0.042, representing B and D0 the thermodynamic coefficient and the limiting D0 value (D0 = 0.843  109 m2
s1), respectively. f Dc/(%) represents the deviations between the c values of both AABA and GABA at different concentrations, c. b

M.M. Rodrigo et al. / J. Chem. Thermodynamics 135 (2019) 60–67

3.4. Hydrodynamic radius, Rh, of AABA From the Stokes–Einstein equation [27] and, having in mind their limitations, the hydrodynamic radius, Rh , of AABA in these aqueous solutions can be estimated, by the equation,

D0 ¼ kB T= 6pg0 Rh




ð8Þ 0

where kB is the Boltzmann’s constant and g is the viscosity of the solvent (water) at temperature T. The value found in this way is lower than that obtained for GABA (Rh = 0.314  1010 m), what leads us to conclude that the entities of AABA would offer less frictional resistance to motion through the liquid, and, consequently, that the diffusion coefficient of this aqueous system becomes larger. Moreover, this behaviour can be also justified considering that the electrostrictive effect of charged groups in AABA is less strong when compared to that of GABA, thus promoting an increase of its diffusion coefficient in these aqueous systems. 4. Conclusions Binary mutual diffusion coefficients of AABA in non-buffered aqueous solutions (0.001–0.100 mol dm3) at 298.15 K were measured by using the Taylor dispersion technique and compared with the data obtained for c-aminobutyric acid (GABA). These measurements indicate that the predominant species of AABA in these solutions is the zwitterionic form, similar to what obtained for GABA. However, we verified that there are differences in the behaviour of some properties of these two amino acids, such as diffusion, mobility, activity coefficient and hydrodynamic radii. The structural differences for the zwitterionic forms of AABA and GABA (extended and curled structures, respectively) can be responsible for these phenomena, fact that was supported by NMR measurements. Acknowledgements The authors in Coimbra are grateful for funding from ‘‘The Coimbra Chemistry Centre” which is supported by the Fundação para a Ciência e a Tecnologia (FCT), Portuguese Agency for Scientific Research, through the programmes UID/QUI/UI0313/2019 and COMPETE. NMR data were obtained at the UC-NMR facility which is supported in part by FEDER – European Regional Development Fund through the COMPETE Programme and by National Funds by FCT, through grants REEQ/481/QUI/2006, RECI/QEQQFI/0168/2012, CENTRO-07-CT62-FEDER-002012, and the Rede Nacional de Ressonância Magnética Nuclear (RNRMN). The authors also thank the Laboratory for Advanced Computing at the University of Coimbra (URL: http://www.lca.uc.pt) for providing computing resources. M.M.R. is thankful to the University of Alcalá (Spain) for the financial assistance (Mobility Grants for Researchers-2016). L.L.G.J. thanks FCT for the SFRH/BPD/97026/2013 postdoctoral grant.

[2] A.C.F. Ribeiro, M.C.F. Barros, L.M.P. Verissimo, V.M.M. Lobo, A.J.M. Valente, J. Solution Chem. 43 (2014) 83–92, https://doi.org/10.1007/s10953-013-0034-6. [3] A.C.F. Ribeiro, M.M. Rodrigo, M.C.F. Barros, L.M.P. Verissimo, C. Romero, A.J.M. Valente, M.A. Esteso, J. Chem. Thermodyn. 74 (2014) 133–137, https://doi.org/ 10.1016/j.jct.2014.01.017. [4] M.M. Rodrigo, A.J.M. Valente, M.C.F. Barros, L.M.P. Verissimo, C. Romero, M.A. Esteso, A.C.F. Ribeiro, J. Chem. Thermodyn. 74 (2014) 227–230, https://doi.org/ 10.1016/j.jct.2014.02.008. [5] M.C.F. Barros, A.C.F. Ribeiro, M.A. Esteso, V.M.M. Lobo, D.G. Leaist, J. Chem. Thermodyn. 72 (2014) 44–47, https://doi.org/10.1016/j.jct.2013.12.010. [6] M.M. Rodrigo, M.A. Esteso, M.F. Barros, L.M.P. Verissimo, C. Romero, A.F. Suarez, M.L. Ramos, A.J.M. Valente, H.D. Burrows, A.C.F. Ribeiro, J. Chem. Thermodyn. 104 (2017) 110–117, https://doi.org/10.1016/j.jct.2016.09.014. [7] J. Barthel, H.J. Gores, C.M. Lohr, J.J. Seidl, J. Solution Chem. 25 (1996) 921–935, https://doi.org/10.1007/BF00972589. [8] R. Callendar, D.G. Leaist, J. Solution Chem. 35 (2006) 353–379, https://doi.org/ 10.1007/s10953-005-9000-2. [9] A.C.F. Ribeiro, V.M.M. Lobo, D.G. Leaist, J.J.S. Natividade, L.M.P. Veríssimo, M.C. F. Barros, A.M.T.D.P.V. Cabral, J. Solution Chem. 34 (2005) 1009–1016, https:// doi.org/10.1007/s10953-005-6987-3. [10] H.J.V. Tyrrell, K.R. Harris, Diffusion in Liquids: A Theoretical and Experimental Study, Butterworth’s Monographs in Chemistry, London, 1984. [11] W. Loh, Quim. Nova 20 (1997) 541–545, https://doi.org/10.1590/S010040421997000500015. [12] I.M.S. Lampreia, A.F.S. Santos, M.J.A. Barbas, F.J.V. Santos, M.L.S.M. Lopes, J. Chem. Eng. 52 (2007) 2388–2394, https://doi.org/10.1021/je700350b. [13] R.M.C. Dawson, Data for Biochemical Research, second ed., Repr. with corrections., Oxford University Press, Oxford [Oxfordshire], 1982. [14] C.M. Romero, D.M. Rodríguez, A.C.F. Ribeiro, M.A. Esteso, J. Chem. Thermodyn. 104 (2017) 274–280, https://doi.org/10.1016/j.jct.2017.07.037. [15] T. Umecky, T. Kuga, T. Funazukuri, J. Chem. Eng. Data 5 (2006) 1705–1710, https://doi.org/10.1021/je060149b. [16] D.M. Rodriguez, L.M.P. Verissimo, M.C.F. Barros, D.F.S.L. Rodrigues, M.M. Rodrigo, M.A. Esteso, C.M. Romero, A.C.F. Ribeiro, Eur. Phys. J. E 40 (2017) 21– 25, https://doi.org/10.1140/epje/i2017-11511-y. [17] H.S. Harned, B.B. Owen, The Physical Chemistry of Electrolytic Solutions, third ed., Reinhold Publ. Corp., New York, 1967. [18] R.A. Robinson, R.H. Stokes, Electrolyte Solutions, Dover Publications, Inc., New York, 2002. [19] V.M.M. Lobo, A.C.F. Ribeiro, S.G.C.S. Andrade, Ber. Bunsenges Phys. Chem. 99 (1995) 713–720, https://doi.org/10.1002/bbpc.19950990504. [20] W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14 (1993) 1347–1363, https://doi.org/10.1002/ jcc.540141112. [21] S. Miertus, E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981) 117–129, https://doi. org/10.1016/0301-0104(81)85090-2. [22] J. Tomasi, B. Mennucci, R. Cammi, Chem. Rev. 105 (2005) 2999–3093, https:// doi.org/10.1021/cr9904009. [23] T. Umecky, K. Ehara, S. Omori, T. Kuga, K. Yui, T. Funazukuri, J. Chem. Eng. Data 58 (2013) 1909–1917, https://doi.org/10.1021/je3012698. [24] H.D. Ellerton, G. Reinfelds, D.E. Mulcahy, P.J. Dunlop, J. Phys. Chem. 68 (2) (1964) 403–408, https://doi.org/10.1021/j100784a035. [25] L.M.P. Veríssimo, M.L. Ramos, L.L.G. Justino, H.D. Burrows, A.M.T.D.P.V. Cabral, D.G. Leaist, A.C.F. Ribeiro, J. Chem. Thermodyn. 90 (2015) 140–146, https://doi. org/10.1016/j.jct.2015.06.018. [26] M.L. Ramos, L.L.G. Justino, A. Branco, C.M.G. Duarte, P.E. Abreu, S.M. Fonseca, H. D. Burrows, Dalton Trans. 40 (2011) 11732–11741, https://doi.org/10.1039/ C1DT10978B. [27] T. Erdey-Grúz, Transport Phenomena in Aqueous Solutions, second ed., Halsted Press (Division of John Wiley & Sons), London, 1974. [28] E.J. Cocinero, A. Lesarri, M.E. Sanz, J.C. López, J.L. Alonso, Chem. Phys. Chem. 7 (2006) 1481–1487, https://doi.org/10.1002/cphc.200600091. [29] D.L. Crittenden, M. Chebib, M.J.T. Jordan, J. Phys. Chem. A 108 (2004) 203–211, https://doi.org/10.1021/jp036700i. [30] A.R. Allouche, M. Aubert-Frécon, D. Graveron-Demilly, PCCP 9 (2007) 3098– 3103, https://doi.org/10.1039/b700631d. [31] K. Miyajima, M. Sawada, M. Nakagaki, Bull. Chem. Soc. Jpn. 56 (1983) 827–830, https://doi.org/10.1246/bcsj.56.827.

References [1] R. Elango, R.O. Ball, P.B. Pencharz, Amino Acids 37 (2009) 19–27, https://doi. org/10.1007/s00726-009-0234-y.

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