Theoretical Studies On The Encapsulation Of Paracetamol In The

Theoretical studies on the encapsulation of Paracetamol in the α, β and γ Cyclodextrins

A thesis submitted for the partial fulfillment of the M. Sc. (Drug Chemistry) Degree

By

Mr. BALTE ANUP SATISH

Under the guidance of

Prof. Shridhar P. Gejji Department of Chemistry University of Pune Pune 411007

( June 2007 )

CERTIFICATE This is certify that Mr. Balte.Anup Satish has completed the Project work entitled “Theoretical studies on the encapsulation of Paracetamol in the α, β and γ Cyclodextrins,”, under guidance of Prof. Shridhar P. Gejji for the fulfillment of the Master’s Degree in Drug Chemistry during the academic year 2007-08, the report of which submitted to the Department of Chemistry, Ahmednagar College, Ahmednagar.

--------------------- --

--------------------

Prof. Shridhar P. Gejji,

Dr.V.V.KHANNA

Project Guide,

Co-ordinator,

Department of Chemistry,

Department of Drug Chemistry,

University of Pune.

Ahmednagar College, Ahmednagar.

ACKNOWLEDGEMENT It gives me immense pleasure to present my project and I take this opportunity to thank all those who were of great help to me during my project work. I would like to express my sincere gratitude to my guide, Prof. S. P. Gejji for his time-to-time guidance, enthusiastic interest, support and constant encouragement throughout the course. I profess my heart full gratitude to Dr. V.V.Khanna, Coordinator of Drug Chemistry, Ahmednagar College, Ahmednagar for giving me this great chance to complete this project. I am also thankful to Dr.S.R.Thopate and S.V.Rohokale of Ahmednagar college. My sincere thanks to Mr.Rahul Pinjare for his assistance in computations without whom I would not be able to present this work. I would like to thank my co-worker Mr. Thorat Sachin.M for his constant support and co-operation in my work. Finally, I would like to thank my parents who gave me constant moral support and encouragement.

Balte .Anup.S

CONTENTS CHAPTER 1: INTRODUTION 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Preamble Born – Oppenheimer approximations Molecular Mechanics method Schrodinger equation Ab initio methods Hartree –Fock Theory semi – Empirical methods

CHAPTER 2: 2.1 Motivation 2.2 Cyclodextrin as Hosts 2.3 Paracetamol as guest 2.4 Methodology 2.5 Computational method

CHAPTER 3: 3.1 Results and Discussion 3.2 Conclusion 3.3 References

Chapter : 1

CHAPTER-1

Introduction 1.1 Preamble Modern computational chemistry has proven to be a useful tool in a variety of chemical problems and have gained popularity to an extent such that the inherent empirical nature of chemistry seemed to be lost in the recent years. These computational chemical methods find a variety of applications in structure, spectroscopy and dynamics. These methods are classified as (a) Molecular mechanics methods (b) ab initio methods (c) Semi-empirical methods and (d) density functional methods. The basis principles and the approximations underlying these theories are given in the following subsection.

1.2 Born – Oppenheimer approximation In 1927, Born and Oppenheimer (BO) proposed an approximation that led to a major leap towards a practical solution to the Schrödinger equation. The Born–Oppenheimer approximation is based on the notion that the nuclear and electronic motions take place at different time scales the latter being much smaller than the former. Hence an electron in motion sees relatively static nuclei while a moving nucleus feels averaged electronic motion. This enables one to separate the electronic and nuclear Hamiltonians and the corresponding wavefunctions as well. The molecular wavefunction can then be represented as a product of electronic and nuclear counterparts.

Ψ ({ri };{R A }) = Φ elec ({ri };{R A }) Φ nuc ({R A })

(1.1)

Here {ri} and {RA} are the positions of electrons and nuclei respectively. The eigenvalue equation for the electronic case is then written as

H elec Φ elec ({ri };{R A }) = E elec Φ elec ({ri };{R A })

(1.2)

The electronic Hamiltonian depends explicitly on the electronic coordinates and parametrically on nuclear coordinates. Since the chemical phenomena occur primarily due to various interactions between electrons of the systems, explicit treatment of the electronic Hamiltonian generally suffices to investigate chemical properties and reactions. However, probing the vibrational, rotational and translational motions of molecules would further require an explicit treatment using the nuclear Hamiltonian. Simplified and convenient electronic Hamiltonian (excluding the internuclear repulsion) in atomic units is as shown below. N N M N N ZA 1 1 H elec = −∑ ∇ i2 − ∑∑ + ∑∑ i =1 2 i =1 A =1 ri − R A i =1 j> i ri − r j

(1.3)

The first term is the electronic kinetic energy operator summed over the number of electrons ‘N’ while the second term represents coulombic attraction between electrons {i} and M nuclei {A}, where {Z A} are the nuclear charges. The last term attributes to the Coulombic repulsion between electrons. Once the wavefunction Ψ is obtained by solving the Schrödinger equation, any experimental observable can be computed as the expectation value of appropriate operator, Ψ Ο Ψ . In the case of total electronic energy, the operator is electronic Hamiltonian.

1.3 Molecular Mechanics Methods

The molecular mechanics (MM) methods treat molecules as classical objects made of hard-sphere atoms and spring-like elastic bonds. The calculation of energies and properties involve empirical parameters and employ classical equations of motion. A force constant obtained from existing empirical data or from accurate ab initio treatment defines the behavior of bonds between specific pairs of atoms. Similarly, several empirical parameters are used to arrive at the energy of the system as contributions due to bonds, angles, torsions, van der Waal type interactions and electrostatic interactions as shown below. Etotal = El + Eθ + Ew + Enb

(1.4)

where El = bond length energy Eθ = angle bond energy Ew = dihedral bond energy Enb = non bonded energy Contribution from bond stretching is given by Morse function El = ∑ De [1 – exp {- α (l – lo)} 2

(1.5)

where De = dissociation energy α = force constant lo = equilibrium bond length In the simplest form of simple harmonic function is given as El = ∑ kl ( l – lo )2

(1.6)

where kl is mathematical parameter Bond angle has been treated similar to bond length. Contribution of bond angle is given by harmonic function.

Eθ = ∑ kθ ( θ – θo )2

(1.7)

where θo = equilibrium value kθ = mathematical parameter. The functional form if the dihedral angle is given in terms of Fourier series Eω = ∑ Vn (1 + s cosnω )

(1.8)

where Vn = is rotational barrier height n = periodicity of rotation Non-bonded interaction – Non-bonded interaction has two components. van der Waal Electrostatic Functional form of van der Waal interaction is Evdw = Σ∈[(rm/r)12 –2(rmB/r)-6]

(1.9)

where

∈ rm

=

well depth = minimum energy insulation distance

r -12 = short range repulsion r –6 = London dispersion attractive force It is commonly called as 6 – 12 or Lennard – Jones potential. For sterically crowded structures the equation 1.13 rewritten as Evdw = A exp (-Br) - Cr6

(1.10)

The second component of non-bonded interaction is the electrostatic. In this case energy is calculated using coulomb’s law. Eel = ∑ qiqj

(1.11)

Drij where D = Dielectric constant rij = distance between two charges In some cases all the above terms constitute and describe the energy function but in many situations, it is necessary to include the additional term like hydrogen bonding, planarity of isolated unsaturated center. The contribution of hydrogen bonding is  c ij E hb = ∑  12 r  ij

  E ij  −    r 10    ij 

(1.12)

Planarity is maintained by a simple restraining force. Eopl=∑kχ . χ2

(1.13)

where kχ = mathematical parameter χ = height above the plane formed by other 3 atoms There are several sets of force fields (FF) that define these parameters for a given atom and atom-pair. The MM method does not treat electrons explicitly and the FF implicitly includes the electronic contributions. The MM method is an inexpensive computational method and hence can be used to study chemical systems with several thousands of atoms. However, there is a compromise in the accuracy of results from such calculations that are solely dependent on the FFs used. Reliable energies can be only obtained by using extensive parameterization over a class of compounds. The currently popular FFs include AMBER, OPLS, CHARMm, Dreiding, UFF etc. The FFs are obtained by fitting the experimental or ab initio results and hence suffer from transferability to other systems.

Further, MM methods cannot be employed to investigate chemical problems where electronic effects dominate.

1.4 Schrödinger equation The eigenvalue equation proposed by Erwin Schrödinger is the basis of quantum chemistry. The time independent Schrödinger equation can be expressed as HΨ=EΨ This is a second order linear equation homogeneous differential equation. H is the Hamiltonian operator comprising of the nuclear and electronic kinetic energy operators and the potential energy operators corresponding to the nuclear-nuclear, nuclear-electron and electron-electron interactions. The many-particle wavefunction Ψ describes the system. Ψ is the mathematical function of the coordinates of all electrons and nuclei constituting the molecule. The wavefunction should be well-behaved i.e. it should be continuous, single valued, finite, gradient of Ψ should be continuous and it should be square integrable. E is the eigenvalue that is the energy of the system.

1.5 Ab initio methods The goal of our calculations on a particular molecular system is to solve the n-particle timeindependent Schrödinger equation. Many-body problems of this kind cannot be solved exactly. As a simplification the independent particle model is introduced and thereby the problem reduces to solving an n-single particle equation. Thus an effective one electron Hamiltonian is applied to a set of singleparticle wavefunctions, expanded in a suitable basis, and the total energy is minimized using variation principle, which is precisely what is done in Hartree-Fock formulation. Other ab initio methods include Configuration Interaction (CI), Multi configuration Self-Consistent Field (MC-SCF), Coupled Cluster (CC) etc.

1.6 Hartree-Fock Theory The Hartree-Fock approximation forms the crux of computational and quantum chemistry. For defining an electron completely, in addition to the spatial coordinates the spin of electron is also required. The notion of electronic spin is introduced in the one-electron wave function (orbital) by means of the spin functions α(ω) and β(ω) that correspond to the up and down spin electrons respectively. This leads to the spin orbitals, { χ j } defined below.

χ 2i −1 (x) = ψ iα (r )α(ω)

(1.14)

χ 2i (x) = ψ βi (r )β(ω)

(1.15)

where each electron is defined in terms of combined spatial and spin coordinates, x. To satisfy the Pauli’s exclusion principle and the principle of antisymmetry, a Slater determinant is used. An N-electron wavefunction (Slater determinant) is given by

χ i ( x 1 ) χ j ( x 1 ) ... χ N ( x 1 ) Ψ HF ( x 1 , x 2 ,...., x N ) =

where 1

1 χ i ( x 2 ) χ j ( x 2 )... χ N ( x 2 ) . ... . N! . χ i ( x N ) χ j ( x N )... χ N ( x N )

(1.16)

N! is the normalization constant. The normalized Slater determinant can also be represented

in a shorter notation as

Ψ( x 1 , x 2 ....., x N ) = χ i χ j .....χ k

(1.17)

The expectation value for the total electronic energy of a system written in bra-ket notation is given by

E 0 = Ψ H Ψ = ∑ a h a + ∑∑ ab ab a

a

b
(1.18)

In the above equation, the first term corresponds to one-electron integrals comprising of nuclearelectron attraction energy and kinetic energy of electrons. The second term is the electron-electron repulsion integral. The indices a and b refer to occupied molecular orbitals (MOs). Using bra-ket notations introduced by Dirac the above one- and two-electron integrals can be expressed as

i j = ∫ dx1χ *i (x1 )h1 (r1 )χ j (x1 )

(1.19)

ij kl = ∫ dx1dx 2 χ*i (x1 )χ*j (x 2 )r12−1 (r1 )χ k (x1 )χ l (x 2 ) ij kl = ij kl − ij lk

(1.20)

(1.21)

The essence of HF theory in its simplest form is in finding the best approximation to the ground sate of a many electron system in the form of a Slater determinant, which minimizes energy of the system given in Eq. (1.9). The minimization is carried out within the framework of variation principle i.e. the expectation value of energy for a well-behaved trial function, obeying appropriate boundary conditions, is never lower than the corresponding energy obtained from an exact wavefunction.

E=

Ψtrial H Ψtrial Ψtrial Ψtrial

≥ E0 =

Ψ0 H Ψ0

(1.22)

Ψ0 Ψ0

Here Ψtrial and Ψ0 are the trial and exact wavefunctions respectively of the system while E is the expectation value for Ψtrial and E0 the corresponding exact HF energy. Thus the best possible estimate for energy has been obtained by minimizing E with respect to the spin orbitals {χi} with a constraint of orthonormality

χ a χ b = δ ab

(1.23)

Such a minimization leads to the HF equations:

f (i)χ(x i ) = εχ(x i ) .

(1.24)

where f(i) is the effective one-electron operator called the Fock operator and ε is its eigenvalue (energies of spin orbitals). The success of HF method is in replacing the exact electron-electron interaction by an effective electron repulsion potential υeff, which is essentially a one-electron operator. The Fock operator is defined as

f (i) = h(i) + υ eff (i) = h(i) + ∑ [ J a (i) − K a (i)]

(1.25)

a

The first term is the one-electron operator, called the core-Hamiltonian and is a sum of kinetic energy and nuclear-electron attraction energy operators, while Ja and Ka are the Coulomb and exchange operators, respectively. The Coulomb operator gives the electron-electron repulsion energy and the exchange operator provides lowering of energy due to correlation between electrons of same spin, an artifact of the determinantal wavefunction. The operators J and K are defined by their operation on one-electron functions.

[

]

J a (1)χ b (1) = ∫ dx 2 χ *a (2)r12−1χ a (2) χ b (1)

[

(1.26)

]

K a (1)χ b (1) = ∫ dx 2 χ *a (2)r12−1χ b (2) χ a (1)

(1.27)

It may be seen that the operators, J and K, themselves are dependent on the eigenfunctions, the spin orbitals {χi}. Hence, the HF equation is termed as pseudo-eigenvalue equation. In the matrix notation it is written as

f χi = εi χi

(1.28)

Here, {εi}, the eigenvalues of Fock operator and denote the energies of spin molecular orbitals. Solving the equation results in a set of canonical spin orbitals that are delocalized and reflect the molecular symmetry

For computational calculations, the MOs are expanded as linear combinations of suitable basis functions. The equation f χ i = ε i χ i takes the form of Roothaan-Hall equation, which is

FC = SCε

(1.29)

Moving from spin orbitals to MOs represented by basis functions, the elements of the Fock Matrix F are given by N/2

f (1) = h(1) + ∑ [ 2J a (1) − K a (1)]

(1.30)

a

The coefficient matrix has the form shown below

 C11C12 C1k     C 21C 22  C 2 k  C =         C C C   k1 k 2 kk 

(1.31)

where k denotes the number of basis functions in the system. The overlap matrix S (between different functions of the basis) has elements Sμν defined by

Sµν = ∫ φ*µ (1)φν (1)d 3 r1

(1.32)

Since the Roothaan-Hall equation is also a set of pseudo eigenvalue equations, it needs to be solved iteratively. Initially spin orbitals have been chosen using a proper basis set. Solving the HF equation with the corresponding Fock matrix generates a new set of orbitals. The iterations are continued until the orbitals are converged and the electronic energies in two successive iterations do not vary above a predefined threshold, i.e. a self-consistency in the field is achieved and hence this process is termed self-consistent (SCF) procedure.

1.8 Semi-Empirical Methods

Many semi-empirical methods work within the framework of HF theory except that the laborious integral evaluations involved in the HF theory are not solved rigorously. Instead, the two electron integrals are obtained in terms of atomic parameters generated through fitting the results with experimental data such as heats of formation, atomization energies etc. The Pariser-Parr-Pople (PPP) method is one such semi-empirical method used for treating π-electron models. For solving the twoelectron integrals generally the neglect of differential overlap (NDO) approximation is employed, using different conditions to ignore orbital overlaps. The overlap (Eq. 1.33) and two electron (Eq. 1.34) integrals within Zero Differential Overlap (ZDO) are given as

φ*µ (r )φ ν (r )dv = δ µν

(1.33)

µν λσ = δ µλ δ νσ µν µν

(1.34)

The NDO methods use extensive Parameterization. The core electrons are not treated explicitly; instead a core-core repulsion function is used to represent them. The complete and intermediate (CNDO61and INDO62) NDO methods and their variations were able to produce accurate orbitals and properties like charge densities and dipole moments. The currently popular semi-empirical methods such as MNDO, AM1 and PM3 have minimal neglect of differential overlap and differ primarily in the parameters used i.e. on the set of compounds used for fitting the parameters. In these models, the differential overlap is ignored only if the orbitals are on neighboring atoms. They are very efficient and the molecular geometries and properties produced by them are comparable with low-level ab initio calculations. Within MNDO framework, the Fock operator in the Roothaan-Hall equation becomes core Fµµ = H µµ +



1



∑  Pµν (µµ | νν ) − 2 (µν | µν ) + ∑ λ∑ σ∑ Pλσ (µµ | λσ ) ν B ≠ A on B

on A

core where H µµ = U µµ − ∑ VµµB B≠ A

on A

(1.35)

core Fµν = H µν +

3 1 Pµν ( µν | µν ) − Pµν ( µµ | νν ) + ∑ ∑ ∑ Pλσ ( µµ | λσ ) 2 2 B ≠ A λ on B σ on A

(1.36)

core where H µν = − ∑ VµνB B≠ A

core Fµν = H µν −

core where H µν =

1 ∑ ∑ Pλσ (µσ | νλ ) 2 λ on B σ on B

(1.37)

1 S µν ( β µ + βν ) 2

These Roothaan-Hall equations are solved self-consistently. In 1985, Dewar developed the Austin Model1 (AM1), which is a modified form of MNDO. Here, the core-core term was modified using Gaussian functions, which were of both attractive and repulsive type. In 1989, J. J. P. Stewart developed the Parameterization Method 3 (PM3), another modified version of MNDO. Despite the use of more parameters, the accuracy level of AM1 and PM3 are almost same. A semi-empirical method ‘PM5’ - Parametric Model Number 5, has been employed in this study. It is a simplified version of Hartree Fock theory that uses the empirical data to enhance the performance. It is based on Neglect of Differential Diatomic Overlap (NDDO) wherein all the two-electron integrals involving two-center charge distributions are neglected. A number of parameterization corrections are made in these semi-empirical methods using experimental data such as heat of atomization, atomic mass of most abundant isotope, etc. PM5 is a reparameterization of PM3 and uses atomic as well as diatomic parameters while PM3 uses only single atom parameter. PM5 is accurate enough to have useful predictive powers and fast enough to be employed for large systems.

Chapter : 2

Chapter : 2 Defining the system: The Cyclodextrins has a specific coupling of glucose monomers in cyclic manner giving a rigid conical molecular structure with a hydrophilic exterior and hollow hydrophobic interior of a specific volume. This internal cavity is capable of accommodating wide range of guest molecules including polar as well as non-polar aliphatic and aromatic compounds. The inside cavity of appropriate dimension is conducive to binding to various guest molecules to form an inclusion complexes. The paracetamol is a polar molecule. The width of molecule is 0.43nm and height is around 0.78nm. The molecule can be accommodated in all the three CDs. The complex of Paracetamol and CDs is stable due to hydrogen bonding and hydrophobic interactions.

Motivation: Paracetamol is widely studied as an analgesic & antipyretic drug. But they are not studied as a guest molecule in a cyclodextrin cavity. In present work we are addressing the following questions. 1) How the guest (paracetamol) molecule orients itself in the cavity of α,β and γ cyclodextrins? 2) Which types of interactions govern the encapsulation of guest in the cavity of CD? 3) How the hydroxyl groups of CD and amide, hydroxyl group of Paracetamol interact to give stable inclusion

complex. 4) What are the binding energies of guest? 5) what are the energies associated with the inclusion?

Cyclodextrins as Hosts Cyclodextrins are the cyclic oligosaccharides made up of 6 or more α – D glucopyranose units linked by 1→ 4 glycosidic linkages. These were firstly described by A .Villers in 1891.

There are mainly three types of cyclodextrines.

1) α cyclodextrines = made of six glucose molecules linked in ring. 2) β cyclodextrines = made of seven glucose molecules linked in ring. 3) γ cyclodextrines = made of eight glucose molecules linked in ring.

α, β, and γ cyclodextirnes Cyclodextrin consist of 6,7,or 8 (α, β, and γ ) D – glucopyranose units connected by alpha (1 → 4) glycosidic linkages. The most stable three-dimensional molecular configuration for these non –

reducing cyclic oligosaccharides takes the form of a toroid with the upper (larger) and lower (smaller) opening of the toroid presenting secondary and primary hydroxyl groups respectively to solvent environment. The interior of the toroid is hydrophobic as a result of the electron rich environment provided in large part of the glycosidic oxygen atom.

Each glucose unit contain two secondary hydroxyl groups at C 2 and C 3 position and primary hydroxyl group at C 6 position produces 18 to 24 sites for chemical modification and derivatisation. Cyclodextines are synthesized from starch by easily available enzymes. Enzyme used is cyclodextrin glucosytransferase (CGT ), along with α amylases. Starch is liquefied by heat treatment or using α – amylase, then CGT is added for the enzymatic conversion. The product gives the mixture of three main types of cyclic molecule.

 Properties 1) Formation of host – guest inclusion compounds with lipophilic compounds. 2) Solubility: - soluble in water (low), DMF, DMSO, Pyridine. 3) Low toxicity. 4) Biodegradable.

Properties No. Of glucose units Molecular wt Solubility in water (g/cc)

Alpha 6 972 14.5

Beta 7 1135 1.85

Gamma 8 1297 23.2

pKa at 25°C Inner diameter (nm) Outer diameter (nm) Height (nm) Cavity volume Crystal form

12.33 0.45 – 0.57 1.37 7.9 0.174 Hexagonal plate

12.2 0.62 – 0.78 1.53 7.9 0.262 Monoclinic parallelogram

12.08 0.79 – 0.95 1.69 7.9 0.472 Quadratic prism

Complex formation is in stoichemtric ratio ( 1:1,1:2,2:1).complexation is Substrate unspecific. Complexes with lower alcohols, amines or with compound contating heteroatom is easy. Complex is stable in water solution. Compounds suitable for complexation are with low solubility and boiling point < 250 ºC. Complexation improves molecules solubility and stability.

The ability of cyclodextrin to form inclusion complex with a guest molecule is a function of two key factors:-

1) Steric Relative size of cyclodextrin to guest molecule molecule should be comparable. If the guest is wrong size, it will not fit to cyclodextrin. 2) Thermodynamic interaction There must be favorable net energetic driving force that pulls the guest into the cyclodextrin.

3) α cyclodextrin can from low molecular complex with aliphatic side chain, β will complex with aromatic and heteorcycles, γ cyclodextrin can accommodate larger molecules such as macrocycles and steroids. Inclusion complexation with cyclodextrin is like a “host-guest interaction”. In this interaction cyclodextrin act as host molecule and the drug molecule to be entrapped in host cavity act as guest molecule. Comparing to other encapsulation methods, which involve entrapment of more than one

guest, cyclodextrin complexation involve entrapment of one molecule of guest in cyclodextrin cavity. For formation of complex with cyclodextrin, variety of non-covalent forces like Vander wall forces, hydrophobic interaction, and dipole movement are responsible. In majority of cases only a single guest molecules is entrapped in the cavity. For High molecular weight molecules, more than one molecule of cyclodextrins can bind to the guest.

 Bonding in cyclodextrines Cyclodextrins binds to guest molecule with bonding other than covalent bond. It is the interplay of atomic (van der waals forces), thermodynamic (hydrogen bonding), and solvent (hydrophobic) forces that count for the stable complexes, which may be formed with chemical substances in the apolar environment of the cyclodextrin cavity. The complex exists in equilibrium dependent upon the concentration of the cyclodextrin, the guest and water. The bonding may break up with change in pH, temperature of solution, leading to cleavage of hydrogen or ionic bonds between host and guest. Cyclodextrin has vast applications in various fields. Cyclodextrins can release the drug in the body (acts as a drug carrier). Cyclodextrin can be employed for environment protection; they are used in food industry for preparation of cholesterol free products. They have ability to stabilize, the volatile or unstable compounds and the reduction of unwanted taste and odour. It has strong ability to complex with fragrances i.e. used to eliminate bad smell. It is used to solubilization of hydrophobic compounds. Separation of compound in the form of complexes can also be done. Controlled release of compound (drugs, fragrances) is also possible. Stabilization of reactive compounds.

In pharmaceuticals they are used to enhance the rate of dissociation of drug. More complete and faster absorption after oral application is possible. Enhancement in drug absorption independently of the acidity of the gastric juice. Reduced side effects. Reduce skin irritation and, muscular tissue damage. Reduced kidney damage. The activity period of drug is increased.

 Mechanism of drug capture by cyclodextrins Cyclodextrins form a complex with drug rapidly because even the most lipophilic compounds are solvated by water to some extent and these discrete hydrated molecular particles are better able to get part of the hydrophilic hydroxyl group at the entrance of the cyclodextrin cavity.

Drug capture by cyclodextrin The hydrating molecules of water can actively interact with the hydroxyl group on the rim of cyclodextrin toroid or they may simply shield the hydrophobic drug molecule from being repelled by the hydroxyl group. Once, the part of the hydroxyl rim, the hydrating molecule of water is driven from the hydrophobic cavity leaving the drug molecule to find its most stable resting place. In the case of extremely water insoluble substances, the true equilibrium may not be achieved for hours or days because molecular separation due to hydration occurs extremely slowly.

Dissociation is an equally rapid process, most often caused by the sudden increase in the number of water molecules outside the cavity. Even though there may be an initial energy barrier to dissociation, the concentration gradient created becomes excess and the chemical (drug) is displaced. It unable to find relatively scare cyclodextrin molecule to reform the complex, the drug exists free in solution or precipitates depending upon the amount of dilution and concentration of cyclodextrin. Dissociation may also take place due to change in pH or temperature. ------------------------------------------------------------------------------------------------------------

Paracetamol as guest Paracetamol is a minor analgesic that is given orally for relief of mild to moderate pain. It also has anti – pyretic effect and is commonly used in children for this action. It is also known as Acetaminophen.

Fig: paracetamol Paracetamol consists of a benzene ring core, substituted by one hydroxyl group and the nitrogen atom of an amide group in the Para (1,4) pattern. The amide group is acetamide (ethanamide). It is extensively conjugated system, as the lone pair of the hydroxyl oxygen, the benzene pi cloud, the nitrogen lone pair, the p – orbital on the carbonyl carbon and the lone pair on the carbonyl oxygen are all conjugated.

 Physical properties 1) Colour = White. 2) State = Solid, Crystalline. 3) Density = 1.263 g/ cc.

4) Melting point = 169 °C. 5) Solubility in water = 1.4 g/100ml at 20 °C. 6) Solubility in organic solvents = soluble in methanol, ethanol,dimethyl formamide, ethylene dichloride. Insoluble in petroleum ether, pentane,benzene. 7) Mol.wt = 151.17 g/mol 8) Bioavailability = almost 100%. 9) Metabolism = 90 to 95 % Hepatic. 10) Half-life = 1 to 4 hours. 11)Excretion = Renal

Paracetamol is used to relive mild to moderate pain, including instances of tension, headache, muscular aches, joint pain, general pain, and toothache. It is also used as an antipyretic that can reduce fever. It is suitable to most people including the elder and young children because it has low side effects. The recommended adult dose of Paracetamol is two 500mg tablets with four hours between doses and no more than eight tablets in 24 hours.There are no toxic effects even in prolonged or habitual use. It does not accumulate in the body. But overdose affects the liver leading to hepatotoxicity. While the precise mode of action of paracrtamol is unclear, it is thought that like Aspirin its effect is due to inhibition of prostaglandin synthesis.Paracetamol inhibit the enzyme cyclo-oxygenase responsible for the biosynthesis of prostaglandins. By reducing the synthesis of prostaglandin, paracetamol produces analgesia by elevating the pain threshold and reduces fever by resetting the hypothalamic heat-regulating center of the brain.Paracetamol is thought to act almost exclusively on

the central nerves system with little peripheral effect. This explains why paracetamol even in higher doses, has limited anti – inflammatory effect and is associated with fewer gastro intestinal side effects. The plasma half-life of paracetamol ranges from 1 to 4 hours. It is distributed throughout most fluids of the body and is metabolized primarily in the liver. Little unchanged drug is excreted in the urine, but most metabolic products appears in the urine with in 24 hours. Compared with other minor analgesics, such as aspirin, its onset of action is generally slower, since it is only absorbed once it has left the stomach and entered the duodenum.

 Features of Paracetamol 1) Its analgesic (pain relief) and antipyretic (fever relief) effects are comparable to those of Aspirin. 2) There is virtually no group of people who should not take it. 3) An interaction with other treatments is not a problem. 4) At the recommended dosage there are no side effects. 5) It is suitable for small children and elders. 6) It can be taken by those sensitive to Aspirin. 7) It is well tolerated by patients with peptic ulcers. -----------------------------------------------------------------------------------------------------------

Methodology: CD complexes were optimized by employing the semi – empirical PM3 (parametric method 3) Hamiltonian in the semi – empirical quantum chemical calculations. A parameterization scheme herein is based on the known data of heats of formation. It may be remarked here that the PM3 method yields good estimates of geometrical parameters of the stationary point geometries and relatively fast which

make it useful for longer molecular systems containing say 50 to few thousand atoms. GAUSSIAN 03 program were used for obtaining the stationary point geometries. The geometries thus derived were confirmed to be local minima on the potential energy surface by calculating the vibrational frequencies. Since no vibrational frequency turns out to be imaginary these are confirmed to be local minima. (one imaginary frequency implies a transition state and more than one imaginary frequencies lead to saddle point of order two or more on the potential energy surface.) A relative stabilization energies along with the free energy change associated with the inclusion phenomenon are reported for all the conformers of α,β and γ CDs.The results obtained using PM3 geometry optimization are reported in the following chapter.

Computational Method Structure drawing by Winmopac

Geometry optimization by PM3 method

Frequency and frontier orbital calculations

Calculation of Stabilization energy of conformers

Chapter : 3

 Calculations Stabilization energy of cyclodextrin complex with paracetamol is calculated as

1) ∆E = Ecomplex – ( Ecd + Eguest ) * 2625.5 kJ mol–1 where, ∆E = stabilized energy. Ecomplex = energy of complex. Ecd = energy of host (cyclodextrin). Eguest = energy of guest (paracetamol)

2) ∆Eref = E most stable complex – Ecomplex ) * 2625.5 kJ mol–1 where, ∆Eref = energy of complex with reference to most stable complex11

Calculated energies of complexes are:-

complex

∆E , kJ mol–1

∆Eref , kJ mol–1

Alpha 1 Alpha 2 Alpha 3 Alpha 4 Alpha 5 Alpha 6 Alpha 7 Alpha 8 Beta 1 Beta 2 Beta 3

–66.7 –64.88 –54.4 –52.0 –53.1 –43.8 –39.1 –39.4 –84.4 –80.1 –70.1

0.00 02.6 11.03 13.1 13.1 23.6 26.3 39.4 0.00 05.3 15.8

No of Hbonding 1 1 2 1 1 0 0 0 1 1 1

No of H-H interactions 3 4 2 4 3 3 3 3 2 2 3

Beta 4 Beta 5 Beta 6 Beta 7 Beta 8 Beta 9 Beta 10 Beta 11

–64.4 –63.72 –61.5 –61.1 –55.6 –49.5 –50.10 +820.3

21.0 21.5 23.6 26.3 31.5 36.8 36.8 905.7

0 2 1 2 0 0 0 2

3 2 3 2 1 2 3 3

complex

∆E , kJ mol–1

∆Eref , kJ mol–1

Gamma 1 Gamma 2 Gamma 3 Gamma 4 Gamma 5 Gamma 6 Gamma 7 Gamma 8 Gamma 9 Gamma 10

–104.5 –97.1 –95.8 –91.8 –91.5 –88.7 –84.5 –82.0 –82.0 –35.2

0.00 07.9 07.9 13.1 13.5 15.8 18.4 21.0 21.0 68.3

No of Hbonding 0 1 1 1 0 1 3 0 1 0

No of H-H interactions 2 2 1 1 1 3 3 1 2 2

 Observation 1) The energy of the complex is less than the sum of energies of host (cyclodextrin) and guest (paracetamol).

2) Complex of α cyclodextrin with paracetamol : The most stable complex is of energy –66.7 kJ mol –1.The paracetamol molecule has width around 0.44nm, and inner diameter of alpha cyclodextrin is about 0.57nm. So paracetamol has to fix itself in guest straight up only. when methyl group is upward the hydrogen bonding may occur with three hydrogen atoms thus leading to more stability, the nitrogen lone pair and carbonyl oxygen may also interact with hydrogen of cyclodextrin. But if hydroxyl group is upward then hydrogen bonding can occur only with one hydrogen and thus complex is not much stable. The Hydrogen – Hydrogen

interactions are much strong in α complex than the hydrogen bonding The extent of hydrogen bonding is less than the H – H interactions.

3) Complex of β cyclodextrin with paracetamol: The most stable complex is of energy –84.4 kJ mol–1.The inner diameter of beta cyclodextrin is 0.78nm.Here the paracetamol molecule can be rotated and can also be kept slightly horizontal. The interaction can occur with primary as well as secondary hydroxyl group of cyclodextrin,leading to more stablilty. Thus the position of hydroxyl or methyl group do not affect stability of complex. The extent of hydrogen bonding is greater in β complexes than H - H interactions.

3) Complex of γ cyclodextrin with paracetamol: The most stable complex is of energy –104.5 kJ mol–1.The inner diameter of gamma cyclodextrin is 0.95nm.Here the paracetamol molecule can be rotated freely. The paracetamol entirely fits in to the of γ cyclodextrin, so the formation of hydrogen bonding and other interaction are easier thus leading to most stable complex of paracetamol. The position of hydroxyl or methyl group do not affect stability of complex. The of γ complex is stable due to balance of both H – bonding and H – H interactions.

 Conclusion 1) All the cyclodextrin i.e. ( α, β & γ ) forms stable inclusion complex with paracetamol. 2) The γ cyclodextrin forms most stable complex while α forms least stable complex.

3) The γ complexes are stable by 40 kJ mol–1energy than α and by 20 kJ mol–1energy than β. 4) The β complexes are stable by 20 kJ mol–1energy than α .

5) The cavity of cyclodextrin and number of possible hydrogen bonding and other interactions determines the stability of the complex. 6) The hydroxyl group of cyclodextrins and hetero atoms in guest are responsible for hydrogen bonding and complex stability. 7) The position of methyl or hydroxyl group affects the α complex stability and not of β & γ complexes. 8) The Hydrogen bonding as well as Hydrogen – Hydrogen interactions strongly govern the stability of complex.

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References

Paracetamol

Alpha cyclodextrin

Beta cyclodextrin

Gamma cyclodextrin

Alpha 1, ∆E = – 66.7 kJ mol–1 (∆Erel = 0 kJ mol–1)

Alpha 2, ∆E = – 64.9 kJ mol–1 (∆Erel = 02.6 kJ mol–1)

Alpha 3, ∆E = – 54.4 kJ mol–1 (∆Erel = 11.0 kJ mol–1)

Alpha 4, ∆E = – 52.0 kJ mol–1 (∆Erel = 13.1 kJ mol–1)

Alpha 5, ∆E = – 53.1 kJ mol–1 (∆Erel = 13.1 kJ mol–1)

Alpha 6, ∆E = – 43.8 kJ mol–1 (∆Erel = 23.6 kJ mol–1)

Alpha 7, ∆E = – 39.1 kJ mol–1 (∆Erel = 26.3 kJ mol–1)

Alpha 8, ∆E = – 27.3 kJ mol–1 (∆Erel = 39.4 kJ mol–1)

Beta 1, ∆E = – 84.4 kJ mol–1 (∆Erel = 0.0 kJ mol– 1 )

Beta 2, ∆E = – 80.1 kJ mol–1 (∆Erel = 05.3 kJ mol–1)

Beta 3, ∆E = – 70.1 kJ mol–1 (∆Erel = 15.8 kJ mol– 1 )

Beta 4, ∆E = – 64.4 kJ mol–1 (∆Erel = 21.0 kJ mol–1)

Beta 5, ∆E = – 63.7 kJ mol–1 (∆Erel = 21.5 kJ mol–1)

Beta 6, ∆E = – 61.5 kJ mol–1 (∆Erel = 23.6 kJ mol–1)

Beta 7, ∆E = – 61.1 kJ mol–1 (∆Erel = 26.3 kJ mol–1)

Beta 8, ∆E = – 55.6 kJ mol–1 (∆Erel = 31.5 kJ mol–1)

Beta 9, ∆E = – 49.5 kJ mol–1 (∆Erel = 36.8 kJ mol–1)

Beta 11, ∆E = +820.3 kJ mol–1 (∆Erel = 905.7 kJ mol–1)

Beta 10, ∆E = – 50.1 kJ mol–1 (∆Erel = 36.8 kJ mol–1)

Gamma 1, ∆E = – 104.5 kJ mol–1 (∆Erel = 00.0 kJ mol–1)

Gamma 2, ∆E = – 97.1 kJ mol–1 (∆Erel = 07.9 kJ mol–1)

Gamma 3, ∆E = – 95.8 kJ mol–1 (∆Erel = 07.9 kJ mol–1)

Gamma 4, ∆E = – 91.8 kJ mol–1 (∆Erel = 13.1 kJ mol–1)

Gamma 5, ∆E = – 91.5 kJ mol–1 (∆Erel = 13.1 kJ mol–1)

Gamma 6, ∆E = – 88.7 kJ mol–1 (∆Erel = 15.8 kJ mol–1)

Gamma 7 , ∆E = – 84.5 kJ mol–1 (∆Erel = 18.4 kJ mol–1)

Gamma 8, ∆E = – 82.0 kJ mol–1 (∆Erel = 21.0 kJ mol–1)

Gamma 9, ∆E = – 82.0 kJ mol–1 (∆Erel = 21.0 kJ mol–1)

Gamma 10, ∆E = – 35.2 kJ mol–1 (∆Erel = 68.3 kJ mol–1)