Determination of Ionization Constant

Materials, Methods and Instrumentations

2.0. Introduction

2.3.2. Determination of Ionization Constant

The acid dissociation constant or pKa is a measure of the strength of an acid or a base.

The pKa measurements are useful parameters for understanding the behavior of probe molecules. Different ionic species of a molecule differ in physical, chemical and biological properties and so it is important to find which ionic form of the molecule is present at the site of action. The most familiar Hammette equation used for the determination of ionization constant (pKa) of the dissociation reaction of an acid in water is given below:

BH

⁺

+ H

₂

O B + H

₃

O

⁺ _(2.3)

0 a +

H pK + log [B]

[BH ]

= (2.4)

where [BH⁺] and [B] are the molar concentration of conjugate acid and base, respectively as described by the reaction given in Equation 2.3. H0 is called the Hammette acidity function, which is given by the following Equation 2.5

0 log ^{H B}

BH

a f

H f

+ +

= − (2.5)

where fB and fBH+

are the acidity co-efficients of conjugate base and acid, respectively. aH+

is the activity of the proton. For dilute solution, H0 can be replaced by pH. A plot of pH versus

+

log [B]

[BH ] gives a straight line with unit slope and the pH is equal to pKa when [B] = [BH⁺].

The factor [B]₊

[BH ]can be determined from following relation.

[ ]

[ ]

[ ] [ ]

B BH

A A

B

BH+ A A +

= −

− (2.6)

where A_BH+ and A_B are the absorbances (at the analytical wavelength) of pure BH⁺ and B, respectively and A is the absorbance (at same wavelength) of any solution in which BH⁺

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is partially ionized. The factor [B]₊

[BH ] can also be expressed as

[ ] [ ]

[ ] [ ] [ ]

B B

BH⁺ = C B

− (2.7)

where [C] = molar concentration of the compound in the experimental solution.

The concentration of the conjugate base is given by

1 2 2 1

1 2 2 1

( ) ( ) ( ) ( )

[ ] ( ) ( ) ( ) ( )

BH BH

B BH B BH

A A

B λ ε λ λ ε λ

ε λ ε λ ε λ ε λ

+ +

+ +

= −

− (2.8)

ε is the molar extinction coefficient. Generally, two wavelengths (λ1 and λ2) are chosen on both side of the isosbestic point.

2.3.3. Quantum Mechanical Calculations

Density functional theory (DFT) methods for solving molecular parameters in the electronic ground state have gained rapid momentum in modern computational chemistry due to their accuracy and lower computational cost. Density functional calculations are based on electron probability density function or electron density function unlike ab initio methods which are based on solving wavefunctions. The basic principles on developing the methods and solving the electronic structure of a molecule are discussed in details by Lewar,¹⁹⁴ Cramer¹⁹⁵ and Szabo et al¹⁹⁶ and Gaussian Manuals^197,198 in their books.

However, calculating molecular parameters for an electronic excited complex molecular system is difficult in terms of accuracy and computational cost and time.

Configuration interaction singles (CIS)¹⁹⁹ is a common method for calculations of excited state parameters.^96,200 CIS is an analytic gradient method which allows optimization of the excited state geometries and is less expensive. The geometries obtained at the CIS level are quite reasonable and correct at least as a first approximation for a variety of molecules.^201-204 But CIS has certain limitations such as significant difference of the calculated energies from the experimental data, and incorrect order of the excited states.199,204,205

To be more specific, CIS overestimates the energy barrier for PT and fail to describe the breaking of bond.^206-210 The multireference complete active space self consistent field (CASSCF)²¹¹ method gives better accuracy and optimization in the electronic excited state is also possible with the method. The nondynamic electron correlation effects due to degenerate configurations are also taken into account in CASSCF. However, in this method only selected few orbitals can be included in the molecular orbital (MO) active space.^62,212-215 The active orbitals in the active space can change during geometry optimization.⁶² Therefore, extreme caution should TH-1151_07612201

Quantum Mechanical Calculations 41

be taken in choosing the active space. Moreover, the method is computationally expensive for large systems.^78,216-217 During the past decade, there has been significant rise in development of time-dependent density functional theory (TDDFT) methods which are DFT based for calculations of excited state properties.^218,219 TDDFT proves good for electronic structure calculations in the excited states including proton transfer even for large molecular system due to its moderate efficiency and accuracy.^220-226 Lately, excited state gradients have been implemented in TDDFT,^224,227 but it is reported that optimization by TDDFT method gives incorrect ordering of energies in few cases.²²⁸ TDDFT calculations over CIS optimized geometries have been proven to be an efficient approach in predicting energy parameters for various systems.202,229-232

Moreover, TDDFT method employing B3LYP functional is shown to be reliable in treating vertical excitation energies even for charge transfer states.²²¹ Therefore, the hybrid method TDDFT//CIS for energy calculations in the excited state was implemented in the entire work. The excited S1 state geometries were optimized using ab initio restricted configuration interaction singles RCIS/6-31G(d) approach.

In all the cases for optimization, the 6-31G(d) basis set was used but the molecular energies and other properties were obtained using 6-31+G(d,p) basis set. The minimum energy nature of the geometries was confirmed by vibration frequency calculations performed on the optimized stationary point geometries and first-order transition states using the same basis set 6-31G(d) used during the geometry optimization.^196,197 Vertical excitation energy calculations were performed on the optimized ground and S1 state geometries by TDDFT/B3LYP/6-31+G(d,p) for the assignment of excitation and emission energies, respectively. The convergence threshold for the energies and residual forces on the atoms during geometry optimization (both the ground and the excited states) were 10⁻⁸ hartree and 4.5 × 10⁻⁴ hartree/bohr, respectively.

Solvent stabilization effects were also studied in cyclohexane, 1,4-dioxane, acetonitrile, methanol and ethylene glycol using the integral equation formalism-polarizable continuum model (IEF-PCM).^233,234 The dielectric constants available from the literature,¹⁹¹ were used for these calculations. In all the cases for optimization, the 6-31G(d,p) basis set was used but the molecular energies and other properties were obtained using 6-31+G(d,p) basis set.

Theoretical calculations were performed using Gaussian 03W program²³⁵ throughout the work to obtain the molecular parameters. Molecular modeling software GaussView 4.1²³⁶ was used for drawing the molecules to obtain the coordinates and to give inputs for the calculations. The flowchart for a typical quantum chemical calculation employed in this work TH-1151_07612201

Quantum Mechanical Calculations 42

is schematically described in Figure 2.3. The ground state geometries of the molecules were obtained by full optimization of structural parameters employing Berny optimization algorithm by DFT utilizing Pople's split-valence polarized basis set²³⁷ 6-31G(d) in a spin restricted shell wavefunction manner.^238,239 The calculations in the ground state were carried out using the hybrid functional B3LYP containing Becke's gradient corrected three-parameter exchange functional B3 with 20% of Hartree-Fock exchange,²⁴⁰ and nonlocal correlation functional of Lee, Yang, and Parr (LYP),²⁴¹ given by the expression below.

(1 )

Slater HF Becke VWN LYP

X X X C C

aE + −a E + ∆b E +E + ∆c E (2.9)

The constants a, b and c are semiempirical coefficients with values 0.8, 0.72 and 0.81, respectively.

Figure 2.3. Flowchart for quantum chemical calculations.

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2.4.0. Instruments 2.4.1. pH Meter

The pH of different solutions was measured using Jenway pH Meter (Model No 3510). The pH meter was calibrated by using three different standard buffer solutions (pH 4.0, pH 7.0 and pH 10.0) within a range of ± 0.01-0.02 pH units before a measurement was performed.

2.4.2. Absorption Spectrometer

Absorption spectroscopy is the most widely used spectroscopic tool which provides the wavelength of a transition and the corresponding molar extinction coefficient (ελ) of a chromophore under investigation. The modern Ultra Violet-Visible (UV-Vis) spectrometer consists of light source, monochromator, detector, amplifier and recording devices. Quartz cells to hold the sample are used for the measurement of the absorption spectra.

In the present work, the absorption spectra were recorded on a double beam UV-Vis spectrometer Cary 100 from Varian. Deuterium and tungsten lamps are used as UV and visible sources, respectively. In the Cary 100, a photomultiplier tube (PMT) is used as detector. The error limits in absorption maximum wavelength were ± 1 nm