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Journal of the Chilean Chemical Society

versión On-line ISSN 0717-9707

J. Chil. Chem. Soc. vol.65 no.2 Concepción jun. 2020

http://dx.doi.org/10.4067/S0717-97072020000204759 

Article

THE THEORETICAL CALCULATIONS AND EXPERIMENTAL MEASUREMENTS OF ACID DISSOCIATION CONSTANT AND THERMODYNAMIC PROPERTIES OF GLYCYL-ASPARTIC ACID IN AQUEOUS SOLUTION AT DIFFERENT TEMPERATURES

Fatemeh Zabihi1 

Farhoush Kiani2  * 

Mojtaba Yaghobi1 

Seyed Ahmad Shahidi3 

Fardad Koohyar4  5  * 

1Department of Physic, Faculty of Science, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

2Department of Chemistry, Faculty of Science, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

3Department of Food Science and Technology, College of Agriculture and Food Science, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

4Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

5Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

ABSTRACT

In this research work, a potentiometric technic was used to measure the acidic dissociate constants (pKa,s) for glycyl aspartic acid (GLY-ASP) at temperatures (298.15, 303.15, 313.15, and 318.15) K and in 0.1 mol/l ionic strength of chloride sodium. Using this data, we calculated the thermodynamic properties (changes of enthalpy, ΔH, changes of entropy, ΔS, and changes of Gibbs free energy, ΔG) for acidic dissociation reaction of GLY-ASP. All analyses of data were studied in pH = 1.5-11 and in the aqueous solution. In addition, the value of the acid dissociation constants (pKa1, pKa2, and pKa3), the optimized structure, and the thermodynamic properties of GLY-ASP were calculated in aqueous solution at various temperatures by ab initio and DFT methods. Density function theory (DFT) has been used based on the B3LYP/6-31+G(d) theory to explain the obtained acid dissociation constants of GLY-ASP as well as interactions between solvent and solvated cation, anion, and neutral species of GLY-ASP. Thomasi's method was used to analyze the formation of intermolecular hydrogen bonding between the water molecule and various species of GLY-ASP. In addition, the energy gap of anionic, cationic, and neutral species of GLY-ASP were obtained for dissociation reactions of GLY-ASP. Finally, for GLY-ASP, the theoretically calculated and experimentally determined pKa,s were compared together and a good agreement was observed between them in the first, second, and third ionization constant of GLY-ASP.

Keywords: Glycyl aspartic acid; acid dissociation constant; thermodynamic properties; density function theory; Ab initio

1. INTRODUCTION

Amino acids are molecules which have an amine group (-NH2), and a carboxylic group (-CO2H). Whenever two or more amino acids are connected together, they make a peptide. Peptides are identified from proteins based on the size [1,2]. The difference among peptides is based on the residuals of amino acids in each molecule. According to this fact, they are classified as a dipeptide, tripeptide, and so on.

In the last decade, the structural properties of different peptides have been investigated by many researchers. These data are used in biotechnology, medicine, drug synthesis, food supplements, and analgesic toxins [3,4]. The shortest peptides are dipeptides, including two amino acids that are joined together by one simple peptide bonding. As it can be seen in Figure 1, GLY-ASP is a dipeptide which has one carboxyl group, in low pH in acidic status, one another carboxyl group, in ordinary pH between acid and alkaline status, and an amine group in high pH in alkaline status.

Figure 1 Suggested protonation processes of GLY-ASP. 

Acidic dissociation constant (pKa) for different species of amino acids and dipeptides were studied in the recent years [5,6]. The pKa is used for determining solubility and permeability of solutions in the environmental and pharmaceutical fields [79]. There are various experimental techniques to measure acidic dissociation constant such as HPLC, potentiometer, and spectrophotometry [1014]. To determine the physiochemical properties of a substance, first it must be solved in a solvent. Therefore, it is essential to measure the solubility of a substance in special solvent at different temperatures and various ionic strengths which can describe the thermodynamic system of solution, such as enthalpy and entropy changes of dissolving processes.

One of the most important physical and chemical factors of micro- and macro-molecules is the acid dissociation constant, generally known as pKa. In the present study, the acid dissociation constant was determined for GLY-ASP, in water, by a potentiometric technique. Potentiometric technique is useful and reliable method to measure auto-proteolysis and dissociation constant of various solvents and solutions. In this technique, a glass electrode is used to measure pH and reaction potential in each step. In potentiometry, information about a sample composition is obtained through the appeared potential between two electrodes. Nowadays, selected potentiometric electrodes are used in many fields of clinical diagnosis, industrial processes control, environmental studies, and physiology. This technique is quick, cheap, and accurate [15]. In recent years, many researchers have tried to theoretically calculate the acid dissociate constant of different molecules by Ab initio and DFT methods [16,17]. Considerable research has been carried out to calculate the acid dissociation constants in the gas phase, but there is lack of research in the calculation of acidity in the solution phase [18].

The pKa is a criterion for measuring the strength of an acid or alkaline. The pKa equals to negative logarithm of equilibrium constant (Ka) of a neutral or charged form of a molecule by which the various species charge across various pH,s. A weak acid has a relative pKa between 2 and 12. Acids with pKa values lower than 2 are strong acids [19]. Acid equilibrium constants (Ka, pKa = -log Ka) are an important property of organic compounds with extensive effects on many biological and chemical systems. This parameter is an important factor in the pharmacokinetics of drugs and the interactions of proteins with other molecules [20].

In this research work, the values of the acid dissociation constant (pKa1, pKa2, and pKa3), the thermodynamic properties (ΔH, ΔS, and ΔG) and optimized structure of GLY-ASP have been calculated in the aqueous solution at various temperatures by potentiometric, Ab initio and DFT methods. Density function theory (DFT) was used based on the B3LYP/6-31+G(d) theory to explain the obtained acid dissociation constants of GLY-ASP and also interactions between solvent and dissolved cationic, anionic, and neutral species of GLY-ASP.

Thomasi's method was used to analyze the formation of intermolecular hydrogen bonding (IHB) between the water molecule and various species of GLY-ASP. In addition, the energy gap of anionic, cationic, and neutral species of GLY-ASP were obtained for the dissociation reactions of GLY-ASP. Finally, the ionization potential was calculated from I = −EHOMO while the electron affinity was determined from A = −ELUMO [21].

2. RESEARCH METHODOLOGY

2.1. Experimental process

2.1.1. Chemicals

GLY-ASP (C6H10N2O5) was purchased from Sigma-Aldrich. NaCl, NaOH, and HCl were purchased from Merck Company. The purity of GLY-ASP was 99%. Also, the purity of NaCl, NaOH, and HCl was 98%. These components were used without further purification. Double distilled water was used to prepare samples for this research.

2.1.2. Apparatus

The electromotive force, E, was measured using a Metrohm model 781 pH ion-meter research potentiometer equipped with a combined pH electrode which consisted of a glass electrode and a reference Ag/AgCl electrode built into a single chamber. The combined glass-pH electrode (model 6.0258.000) was modified by replacing its aqueous KCl solution with 0.01 mol.dm−3 NaCl and 0.09 mol.dm−3 NaClO4 saturated with AgCl. The electrode was soaked for 15 to 20 minutes in a water–alcohol mixture before the potentiometric measurements.

2.1.3. Procedure

All titrations were carried out in an 80 cm3 thermostated, double walled glass vessel. Potentiometric titration method (with 1M NaOH and 0.1M HCl) was used to determine the protonation constants. All tests were conducted in 0.1 mol/l ionic strength of NaCl at T = 298.15 K to 318.15 K. Analyte and titrant solutions were prepared to calculate protonation constants in the following manner:

Analyte solution: 2 ml HCl 0.1M with 2 ml NaCl 1M was reached 20 ml volume using distilled water; a certain amount of the weighted GLY-ASP was added to it later.

Alkaline titrant solution: 2 ml NaOH 1M with 2 ml NaCl 1M was reached 20 ml by distilled water.

NaCl was used for titration in certain ionic strength. The titration was done in pH = 1.5 to 11. A magnet was put in the dish for better homogenization and then the glass electrode was calibrated by the present buffers and put in the solution. After taht, we added the titrant solution to the analyte solution (0.05 to 0.05) for calibration. The calibration of the instrument was done by the Nernst eq in Excel program. An amount of the weighted GLY-ASP was added to the analyte solution and titration was continued by adding a certain amount of titrant by micropipette. Potential was read each time by the Metrohm model 781 pH ion-meter. All tests were individually conducted at T = 298.15 K to 318.15 K.

2.2. Theoretical calculations

Figure 2 shows the optimized structure of cation specie of GLY-ASP. This structure was drawn by the semi-experimental PM3 method using program Hyperchem version 8.0.8 for Windows. All calculations and optimization about studied species of GLY-ASP were done using the GAUSSIAN 98 program. DFT calculations were done using the hybrid exchange-correlation function and the Gaussian B3LYP/6-31+G(d) basis set [2224]. The Polar Constellation Model (PMC) was used to analyze solvent (water) effects on all the involved samples in ionization reaction which generate hydrogen bonds with water molecules [2527]. All reactions of various species of GLY-ASP were examined in an excel file and reactions with more errors, in pKa values, were deleted. Finally, the suitable reactions for the first, second, and third ionization processes of GLY-ASP were selected. All calculations were carried out at T = 298.15 K to 318.15 K.

Figure 2 Optimized structure of GLY-ASP cation for performing the calculations. 

3. RESULTS AND DISCUSSION

3.1. Experimental results and discussion

In this article, the values of Ea andK were obtained using potentiometric calibration. The electric electrodes potential, E, can be written as the eq:

E=E°+klog[H+]+klogγH++ELJ (1)

In eq 1, E°, ELJ, k, and γH+ show standard potentials, liquid bonding potential, Nernst slope, and proton activity coefficient, respectively.

In addition, γH+ and ELJ remain in the fixed ionic strength. In this case, eq 1 can be rewritten as:

E=Eakp[H+] (2)

Where, Ea isE°cell + klogγH+ + ELJ.

Consequently, the values of K and Ea were calculated in calibration step using E linear regression on [H+]. Results of calibration step are shown in Table 1.

Table 1 Calibration parameters of GLY-ASP in aqueous solution at temperatures 298.15 K to 318.15 K and NaCl 0.1 M. 

T (K) E′a (mV) K(mV)
298.15 410.45 59.13
303.15 416.76 59.17
308.15 421.32 59.46
313.15 426.28 59.24
318.15 431.65 59.51

Calibration parameters were used to determine concentration of hydrogen ions during titration in the second step for determining protonation constant.

Depending on pH of the solution, the GLY-ASP can exist in four different microforms which are (H3L+), (H2L), (HL), and (L2−) species. These constants are expressed by eqs 6 to 8:

K1=[H3L+][H2L][H+] (3)
K2=[H2L][HL][H+] (4)
K3=[HL][L2][H+] (5)

Based on Bjerrum's method, the fraction of protons bound to a ligand, n¯ , is given by eq 6 [28]:

n¯cal=CH[H+]CL (6)

where CH and CL are the total concentrations of protons and the GLY-ASP, respectively. Substituting, CL= [H2L+] + [H2L] + [HL] + [L2−] and CH= [H+] + [HL] + 2[H2L] + 3[H3L+].

Therefore, eq 6 can be rewritten as the eq 7.

n¯cal=[H3L+]+2[H2L]+3[HL][H3L+]+[H2L]+[HL]+[L2] (7)

We can reach eq 8 using comparison eqs 3-5 and 7:

n¯cal=K1[H+]+2K1K2[H+]2+3K1K2K3[H+]3K1[H+]+K1K2[H+]2+K1K2K3[H+]3+1 (8)

Where, K1 and K2 represent the protonation constants of tow carboxylic acid groups and K3 represents the protonation constant of the amino groups of the GLY-ASP. On the other hand, electrical neutrality demands that the concentration of the cations should equal the concentration of the anions at all times during a titration, and hence:

n¯exp=CL+[Cl][Na+][H+]+[OH]CL (9)

In eq 9, [H+]=10(EcellEa)/k and [OH] was determined as Kap/[H+] by knowing water auto-proteolysis constant, Kap, from available literature [29,30]. Finally, using a suitable computer program (Microsoft Excel Solver) [31,32] the data from eqs 8 and 9 were fitted to estimate the protonation constants of GLY-ASP in the aqueous solution at different temperatures. We used the Gauss-Newton nonlinear least-squares method in the computer program to refine the n¯ values by minimizing the sum of error squares:

U=(n¯expn¯cal)2 (10)

Where, n¯exp is an experimental n¯ value and n¯cal is the calculated one.

Figure 3 shows the mole fraction diagrams versus pH of solution for various species in the aqueous solution of GLY-ASP at different temperatures. This figure helps us find out the values of pKa,s (pKa1, pKa2, and pKa3) for GLY-ASP in water at various temperatures. a, b, and c are the isoelectric points in Figure 3. In these points, the concentrations of the acid and the base are equal together. For an acid (HA), the following eq shows the relationship between pKa and pH in the aqueous solutions:

Figure 3 Mole fraction diagrams obtained from titration in aqueous solution and ionic strength of 0.1M and temperatures (A) T = 298.15 K; (B) 303.15 K; (C) 308.15 K; (D) 313.15 K; (E) 318.15 K. 

pKa=pH+log[A][HA] (11)

In eq 11, [A] and [HA] are the concentrations of acid HA and base A. At isoelectric points (a, b, and c), [A] = [HA] and pH = pKa.

The experimentally determined pKa,s of GLY-ASP, in aqueous solution, at various temperatures are listed in Table 2. It can be seen in this table that the experimental pKa1 and pKa2 increase with temperature growth during the deprotonation process of GLY-ASP while the experimental and pKa3 decreases by temperature increasing.

Table 2 Experimental and calculated protonation constants of GLY-ASP in aqueous solution at temperatures 298.15 K to 318.15 K, in NaCl 0.1 M. 

Specie T (K) pKa1
(Exp)
pKa1
(Calcu)
pKa2
(Exp)
pKa2
(Calcu)
pKa3
(Exp)
pKa3
(Calcu)
298.15 2.83a 2.84 4.73a 4.72 8.47a 8.46
303.15 2.84b 2.85 4.75 4.73 8.35 8.33
GLY-ASP 308.15 2.85 2.86 4.76 4.74 8.24 8.24
313.15 2.86 2.86 4.77 4.75 8.11 8.12
318.15 2.87 2.87 4.78 4.76 7.99 7.98

aRef. [32]

bThis work

3.2. Theoretical results and discussion

The pKa quantity is a molecular tendency to lose a proton (H+). GLY-ASP loses proton from two carboxyl groups, in the first and second steps of the ionization reaction, and loses proton from the ammonium group in the third step of the ionization reaction. The microscopic ionization constants k1, k2, and k3 can be applied, wherein k1 and k2 involve two carboxyl groups and k3 involves the ammonium group [33].

k1=[H+][NH3+CH2CONHCH(COOH)CH2COO][NH3+CH2CONHCH(COOH)CH2COOH] (12)
k2=[H+][NH3+CH2CONHCH(COO)CH2COO][NH3+CH2CONHCH(COOH)CH2COO] (13)
k3=[H+][NH2+CH2CONHCH(COO)CH2COO][NH3+CH2CONHCH(COO)CH2COO] (14)

The total free energies for cation, anion, and neutral species of GLY-ASP, in water, were calculated using B3LYP/6-31+G(d) theory by Thomasi's method. Table 3 shows the values of the total free energy (G°sol) for selected species of GLY-ASP at 298.15 K.

Table 3 Thecalculated total free energy using Thomasi's method at the B3LYP/6-31+G(d) level of theory for cation, neutral, and anion species of GLY-ASP at 298.15 K. 

Specie sol sol/molecule Specie sol sol/molecule
Hartree Kj.mol-1 Hartree Kj.mol-1
H3L+ -720.834.828 -1.892.551.659 HL -719.920.077 -1.890.149.981
H3L+(H2O) -797.277.515 -1.046.625.957 HL(H2O) -796.358.213 -1.045.419.144
H3L+(H2O)2 -873.724.961 -7.646.548.883 HL(H2O)2 -872.806.288 -7.638.508.964
H3L+(H2O)3 -950.167.261 -6.236.659.761 HL(H2O)3 -949.248.804 -6.230.631.239
H3L+(H2O)4 -102.660.636 -5.390.709.479 HL(H2O)4 -102.570.158 -538.595.848
H2L -720.367.585 -1.891.324.913 L2- -7.194.688 -1.888.965.153
H2L(H2O) -796.815.803 -1.046.019.845 L2-(H2O) -795.910.757 -1.044.831.746
H2L(H2O)2 -873.267.474 -764.254.511 L2-(H2O)2 -872.352.787 -7.634.540.075
H2L(H2O)3 -949.694.754 -6.233.558.343 L2-(H2O)3 -948.800.422 -6.227.688.172
H2L(H2O)4 -1.026.156.069 -5.388.345.001 L2-(H2O)4 -1.025.243.322 -5.383.552.167
H2O -7.643.735 -2.006.862.432 OH -7.594.893 -1.994.038.966
2H2O -1.528.798 -4.013.858.764 OH(H20) -15.239.712 -2.000.593.001
3H2O -229.321.345 -6.020.831.335 OH(H2O)2 -22.884.536 -2.002.778.117
4H2O -30.572.828 -8.026.895.221 OH(H2O)3 -30.522.555 -2.003.424.012
5H2O -38.218.675 -1.003.431.216 - - -

It can be seen in Table 3 and Figure 4 that the values of total free energy (Kj.mol-1) increase for all species of GLY-ASP as the number of water molecules involved in solvation increases. This subject shows that the solvation process for all species of GLY-ASP has endothermic nature.

Figure 4 Plot of the total free energy (kJ mol-1) of solvated species of GLY-ASP per water molecule against the total number of solvation water molecules at 298.15 K. 

3.2.1 The first dissociation constant of the GLY-ASP

In aqueous solution, the cation specie of GLY-ASP can involve in the below reaction:

H3L+(H2O)4+OH(H2O)3H2L(H2O)3+5H2OKc1 (15)

In which H3L+(H2O)4 (Figure5-A) and H2L(H2O)3 (Figure5-B) show the cation species of GLY-ASP solvated with four water molecules and neutral species of GLY-ASP solvated with three water molecules, respectively. Kc1 indicates the equilibrium constant of eq 15. This constant was theoretically calculated.

Figure 5 Calculated structure for GLY-ASP solvated with water molecules at the B3LYP/6-31+G(d) level of theory using Thomasi's method in water at 298.15 K. 

In aqueous solutions, the autoproteolysis process can happen for two, three, four, and five water molecules. In this study, the autoproteolysis process happened for five water molecules according to the below eq:

5H2OH3O++OH(H2O)3KN3 (16)
Kw=KN3[H2O]3 (17)
KN3=KW[H2O]3=6.4149×10-20 (18)

In eq 18, KW = 1.0081 × 10-14 at T = 298.15 K. This shows that only a few water molecules were ionized to H+ and OH- ions [34].

eq 19 is obtained by combining eqs 15 and 16:

H3L+(H2O)4H2L(H2O)3+H3O+     Ka1 (19)

It is clear that the value of constant Ka1 can be calculated according to the following eq:

Ka1=KN3×Kc1 (20)

The reaction of eq 19 shows the first ionization process of GLY-ASP. Ka1 is applied to calculate the first acid dissociation constant (pKa1) of GLY-ASP. For GLY-ASP, the calculated values of pKa1, at various temperatures, are listed in Table 2. Table 2 shows that there is a good agreement between theoretically calculated and experimentally determined values of pKa1 for GLY-ASP at various temperatures.

Table 4 summarizes the optimized values of molecular properties for various species of GLY-ASP, in water, obtained at the B3LYP/6-31+G(d) level of theory with Tomasi's method at 298.15 K. As it can be seen in this table, the negative atomic charge of O10 atom (qO10), in H2L(H2O)3, increases compared to that of in H3L+(H2O)4 specie. It shows that the density of negative atomic charge increases in O10 atom during the first ionization process of GLY-ASP. This indicates that H+ is separated from O10 atom in the first ionization process of GLY-ASP, (pKa1).

Table 4 The calculated structural magnitudes using Thomasi's method at the B3LYP/6-31+G(d) level of theory for the cation, neutral, and anion of GLY-ASP at 298.15 K. 

Calculated magnitudes specie
H3L+(H2O)4 H2L(H2O)2 H2L(H2O)3 HL(H2O) HL(H2O)4 L2-(H2O)3
q: Total atomic charge (Muliken) (au)
qC1 0.651756 0.566695 0.652006 0.665395 0.335896 0.556615
qC2 -0.469916 -0.572008 -0.926321 -0.658725 -0.196794 -0.441520
qC3 -0.857076 -0.537964 -0.059799 -0.372012 -0.154239 -0.457014
qN4 -0.287580 -0.412129 -0.458344 -0.611813 -0.470768 -0.416254
qC5 0.443535 0.617521 0.569309 0.769104 0.279241 0.682373
qC6 -0.199821 -0.313098 -0.200987 -0.404532 0.026503 -0.482376
qN7 -1.047778 -1.158053 -1.174469 -1.036543 -1.133027 -0.944343
qC8 0.913028 0.862267 0.642153 0.674438 0.195161 0.617228
qO9 -0.593115 -0.681269 -0.691673 -0.798784 -0.684806 -0.747558
qO10 -0.665393 -0.718271 -0.786261 -0.720063 -0.687635 -0.747719
qO11 -0.609144 -0.523335 -0.559590 -0.552001 -0.687759 -0.726398
qO12 -0.670961 -0.616937 -0.639145 -0.625117 -0.644641 -0.723690
qO13 -0.609057 -0.671771 -0.630512 -0.647621 -0.639551 -0.687509
d: Distance between the indicated atoms (Å)
dC1-C2 1.522524 1.54387 1.57639 1.56141 1.54276 1.54953
dC1-O9 1.219051 1.25105 1.23201 1.28659 1.26692 1.27954
dC2-H14 1.097349 1.09517 1.09396 1.09236 1.09405 1.09909
dC3-N4 1.458984 1.46046 1.47128 1.45180 1.47906 1.46059
dN4-H17 1.013753 1.02083 1.01673 1.03515 1.03124 1.02568
A: Angles between the indicated atoms (°)
AC2-C1-O9 122.82867 118.32466 116.37500 117.59091 116.87168 116.03662
AO9-C1-O10 124.75031 126.56537 128.01527 126.22749 126.54145 125.82270
AC1-C2-C3 114.63935 107.41386 110.19841 117.94932 109.44702 115.89851
AC1-C2-H14 106.85975 109.72167 109.43062 108.30701 110.07974 107.25619
AH14-C2-H15 108.04726 109.6044 106.85058 107.06760 107.88843 108.33622
AN4-C3-C8 109.87279 111.00077 106.76830 113.11783 110.12963 113.66091
AN4-C3-H16 107.70161 107.80059 107.15360 110.38409 104.04371 108.97040
AN4-C5-O13 124.89052 124.80483 123.00890 125.45978 126.02343 125.87278
AO11-C8-O12 124.65657 123.25751 123.50981 120.49945 126.49487 127.57625
D: dihedral angle between the indicated atoms (°)
DO9C1C2H14 -105.21793 -153.2557 -39.41902 150.62301 11.11925 56.79998
DC1C2C3N4 164.83102 41.60976 89.76473 -48.34314 49.42594 47.48304
DN4C3 O11C8 -179.63306 -166.47574 112.90153 -166.82993 142.15863 37.33348
DH17N4O13C5 162.879 -165.7033 -179.42055 -3.82956 168.25217 24.18107
DO13C5C6N7 -35.49073 62.81359 100.89486 -124.12082 -38.33232 30.77337
DH16C3N4H17 163.50637 140.83215 -178.50844 153.47773 20.44457 114.63236
DC3N4H17C5 158.98503 151.43811 165.76673 154.31781 179.92230 -164.01299

3.2.2. The second ionization constant of GLY-ASP

GLY-ASP can lose the second hydrogen cation when involved in the following reaction:

H2L(H2O)2+OH(H2O)3HL(H2O)+5H2O     Kc2 (21)

In which H2L(H2O)2(Figure5-C) and HL(H2O) (Figure5-D) show the neutral species of GLY-ASP solvated with two water molecules and the anion species of GLY-ASP solvated with one water molecules, respectively. Kc2 indicates the equilibrium constant of eq 21. The value of this constant was theoretically calculated.

The autoproteolysis reaction of five water molecules occurs in the second ionization process of GLY-ASP.

eq 22 is obtained by combining eqs 21 and 16:

H2L(H2O)2HL(H2O)+H3O+Ka2 (22)

It is obvious that the value of the constant Ka2 can be calculated using KN3 and KC2 according to the eq below:

Ka2=KN3×Kc2 (23)

The reaction of eq 22 shows the second ionization process of GLY-ASP. Ka2 is applied to calculate the second acid dissociation constant of GLY-ASP. For GLY-ASP, the calculated values of pKa2, at various temperatures, are listed in Table 2. As it can be seen in Table 2, the theoretically calculated and experimentally determined values of pKa2 are very close together.

Table 4 shows that the negative value of atomic charge for the O12 atom (qO12), in HL(H2O), increases compared to that of in H2L(H2O)2. It shows that the density of negative charge increases in the O12 atom during the second ionization process of GLY-ASP. This subject indicates that H+ is separated from the O12 atom during the second ionization process of GLY-ASP (pKa2).

3.2.3. The third ionization constant of GLY-ASP

In aqueous solutions, anion specie of GLY-ASP can participate in the below reaction:

HL(H2O)4+OH(H2O)3L2(H2O)3+5H2O     Kc3 (24)

In which HL(H2O)4 (Figure5-E) and L2-(H2O)3 (Figure5-F) show the anion species of GLY-ASP solvated with four and three water molecules, respectively. Kc3 indicates the equilibrium constant of eq 24. The value of this constant was theoretically calculated.

The autoproteolysis reaction of five water molecules can happen during the third ionization process of GLY-ASP.

eq 25 is obtained by combining eqs 24 and 16:

HL(H2O)4L2(H2O)3+H3O+     Kc3 (25)

It is obvious that the value of the constant Ka3 can be calculated using KN3 and Kc3 according to the below eq:

Ka3=KN3×Kc3 (26)

The reaction of eq 25 shows the third ionization process of GLY-ASP. Ka3 is applied to calculate the third acid dissociation constant of GLY-ASP. For GLY-ASP, the calculated values of pKa3, at various temperatures, are listed in Table 2. As it can be seen in Table 2, the theoretically calculated value of pKa3 is very close to experimentally determined one at various temperatures.

Table 4 shows that the absolute value atomic charge for N7 atom (qN7), in L2-(H2O)3, decreases compared to that of in HL(H2O)4. It shows that the density of negative charge decreases in the N7 atom during the third ionization process of GLY-ASP. This subject indicates that H+ is separated from the N7 atom during the third ionization process of GLY-ASP (pKa3).

For involving species in the first, second, and third ionization process of GLY-ASP, the values of total free energy were calculated at various temperatures (T = 298.15 K, 303.15 K, 308.15 K, 313.15 K, and 318.15 K) using the B3LYP/6-31+G(d) surface theory by Thomasi's method. The obtained data have been listed in Table 5.

For GLY-ASP, the values of pKa1, pKa2, and pKa3, at various temperatures, were calculated using data of Table 5. The obtained results (pKa1, pKa2, and pKa3, at various temperatures) were listed in Table 2. According to Table 2, the pKa1 and pKa2 increase and also, the pKa3 decrease with temperature growth.

4. STUDYING ON HYDROGEN BONDING

In a solution, we can find out the power of the interaction between solute and solvent molecules by calculation of distance between them (in Å). The shorter distance between molecules shows the stronger interaction between them. The water molecules which originated from the acid-base reaction and the hydration water molecule of GLY-ASP can contribute to intermolecular hydrogen bonding (IHBs). The power of hydrogen bond is based on their length, angle, and energy as strong, medium, and weak. In strong, medium, and weak hydrogen bonds the bond lengths are 1.2 to 2.2, 1.5 to 2.2, and 2.2 to 3.2 Angstrom, respectively. Also, the bond angles in weak, moderate, and strong hydrogen bonds are 175° to 180°, 130° to 180°, and 90° to 150°, respectively [35,36]. The data of Tables 4 and Figure 5 show that all species of GLY-ASP generate moderate hydrogen bonding with water molecules. It must be noted that IHB data can be used to design and predict nano drugs. They can be conjugated to biomolecules and have a widespread application in medical science [37,38].

5. THERMODYNAMIC ANALYSIS

The changes of Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) are important thermodynamic parameters. The ΔG is the key parameter, because its value under a particular set of reactant concentrations dictates the direction of biomolecules equilibria in solutions. If its sign is negative, the binding reaction or conformational transition will proceed spontaneously to an extent governed by the magnitude of ΔG. If its sign is positive, the magnitude of ΔG specifies the energy needed to drive the reaction to form product. The free energy is a balance between enthalpy and entropy [3941].

Change of free energy in gas or solution phases can be calculated using the below eq:

 ΔG=RT lnKa2.303RTpKa (30)

In eq 30, R is universal gas constant (8.314 K-1 J mol-1), T is the temperature (K), and Ka is the equilibrium constant process.

The values of ΔH and ΔS can be obtained using Van't Hoff eq (by plotting ln Kaversus 1/T) [42]:

pKa=ΔH/2.303RT ΔS/2.303R (31)

The sign of ΔG, ΔH, and ΔS can show the state of chemical reactions. Chemical reactions can be spontaneous at each temperature when ΔG and ΔH have negative and ΔS has positive values [43,44]. The values of temperature can affect the state of chemical reactions when ΔH and ΔS have the same signs.

In order to calculate ΔH and ΔS, the pKa values, at the different temperature T = 298.15 K, 303.15 K, 308.15 K, 313.15 K, and 318.15 K, were plotted versus 1/T by using Eq. (31) (Figure 6). The experimentally determined and theoretically calculated values of changes of Gibbs free energy, enthalpy, and entropy for GLY-ASP are listed in Table 6. According to this table, ΔG increases with temperature increase, ΔS is negative, and ΔH is negative during the first and second ionization but positive for the third ionization. As a result, the first and second ionization reactions of GLY-ASP are spontaneous at low temperature.

Figure 6 The plotting of calculated (A) and experimentally determined (B) pKa versus 1/T for GLY-ASP. 

Table 6 The experimentally determined and theoretically calculated values of changes of Gibbs free energy, enthalpy, and entropy for GLY-ASP 

Specie ΔH (kJ/mol) ΔS (J/mol.K) ΔG (kJ/mol)
298.15 K 303.15 K 308.15 K 313.15 K 318.15 K
GLY-ASP Exp.
-2.73 -63.45 16.18 16.50 16.82 17.14 17.45
-3.68 -102.96 27.01 27.53 28.04 28.56 29.07
43.47 -16.37 48.35 48.44 48.52 48.60 48.68
Cal.
-2.89 -64.1 16.22 16.54 16.86 17.18 17.50
-3.54 -102.28 26.95 27.46 27.98 28.49 29.00
41.86 -21.52 48.28 48.39 48.49 48.60 48.71

6. MULLIKEN ATOMIC CHARGES

Flux distribution is one of the important factors in molecules. Figure 7 shows the flux distribution of all GLY-ASP species at 298.15 K. It shows that the atoms C1, C5, and C8 have more positive charge among carbon atoms of various species of GLY-ASP. As can be seen in Figure 7, the oxygen atoms are attached to C1, C5, and C8. It is well known that the oxygen atom has high electronegativity. In addition, the atoms N7, O10, and O12, compared to other atoms, have more negative charge.

Figure 7 The natural atomic charge distribution for different species of GLY-ASP at T = 298.15 K (cation, neutral, anion) with color range. 

Figure 8 shows the electrostatic-molecular potential distribution of molecular (MEP) charge in 3D for different species of GLY-ASP at T = 298.15 K. The charged areas of the molecule can also be seen in this figure. In a molecule, the information obtained from charge distribution can be applied to describe the reaction between various species. MEP has resulted in the correlation of electronic charges of nuclear and electrons of molecules. Therefore, it gives us useful data to detect various species [45]. MEP has a specific role in the determination of charged molecule areas with neighboring molecules. Actually, these reactive sites are useful in prediction of the reaction between one electrophile and one nucleophile. Various areas of MEP are detected with colors like red, orange, yellow, green, and blue [46]. The negative values (red) in MEP are related to the reactivity of electrophile and the positive areas (blue) are related to nucleophile reactivity [46]. There are several sites for electrophiles to attack oxygen atom in GLY-ASP. In addition, areas with positive charge are usually placed on hydrogen atom. This shows the probability of nucleophile attack on these sites.

Figure 8 The total electron density isosurface mapped with the molecular electrostatic potential (MEP) for different species of GLY-ASP at T = 298.15 K. (red: O; blue: N; gray: C; white: H). 

7. HOMO AND LUMO

Energy gap is the gap between the highest full level in the HOMO (or half-occupied molecular orbital) capacity bar and the lowest empty level in the LUMO conduction bar. HOMO and LUMO are the most important orbitals in a molecule. They are called border molecular orbitals. Examination of border molecular orbitals has a determining role in the chemical stability of molecules. HOMO and LUMO energy estimate the reduction or oxidation characteristics of a molecule [48]. The energy gap between HOMO and LUMO determines the optical reactivity and chemical hardness and softness of the molecule. Energy gap or energy difference between HOMO and LUMO levels is an important stability index for structures. The high difference between these two levels (HOMO and LUMO) shows a high stability. Also, the smaller HOMO-LUMO energy gap indicates that the molecule is the more reactive and more polarizable [49]. High stability of a molecule means low reactivity in chemical reactions.

Based on the provided data in Table 7 (The values of ΔE and EGap), and according to the energy difference between species, it can be stated that the specie L2- has high reactivity. According to Figure 9, HOMO focuses more on carboxyl group and LUMO focuses on the NH3 of a molecule. It can be seen in Table 7 that differences of energy level (ΔE) for GLY-ASP decrease with increasing of negative charge.

Table 7 Calculated chemical reactivity for different species of GLY-ASP at T = 298.15 K. (cation, neutral, anion). 

Parameters H3L+ H2L HL- L2-
ELUMO -0.14 -0.15 -0.15 -0.15
EHOMO -0.36 -0.36 -0.35 -0.34
A 0.14 0.15 0.15 0.15
I 0.36 0.367 0.35 0.34
ΔE 0.22 0.21 0.20 0.19
EGap 6.01 5.70 5.41 5.22

Figure 9 The atomic orbital compositions of the frontier molecular orbitals for different species of GLY-ASP at T = 298.15 K. (cationic, neutral, anionic) (red: O; blue: N; gray: C; white: H) (color figure online). 

8. CONCLUSION

In this research work, the acid dissociation constants of GLY-ASP were experimentally determined and theoretically calculated at various temperatures, T = (298.15, 303.15, 308.15, 313.15, 318.15) K. In calculation section, ab initio and DFT methods were used based on the B3LYP/6-31+G(d) theory. Also, Thomasi's method was used to analyze the formation of intermolecular hydrogen bonds between the water molecule and various species of GLY-ASP. In experimental section, the potentiometric titration technique was used to obtain pKa,s values.

We compared the experimentally determined and theoretically calculated pKa values of GLY-ASP at different temperatures and good agreements were observed for them. It was observed that pKa1 and pKa2 increase and pKa3 decreases by temperature growth. The values of ΔH and ΔS were obtained using Van't Hoff eq (plotting pKa versus 1/T). The values of ΔG were calculated using values of ΔH, ΔS, and T. The results show that ΔG values increase with temperature growth. ΔS has negative values in first, second and third processes of ionization of GLY-ASP. In addition, ΔH has negative values in first and second ionization processes and positive values for the third ionization process. Finally, the theoretical calculations of the HOMO-LUMO gap for GLY-ASP show that the negative charges increase in lower potential.

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*Corresponding author email: fardadkoohyar@tdtu.edu.vn, farhoush_kiani@yahoo.com

CONFLICT OF INTEREST

The authors declare that they have no conflict of interest.

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