Joseph J. Stephanos

Drug-protein interactions: Two-site binding of heterocyclic ligands to a monomeric hemoglobin

The reactivity response of the heme proteins to the heterotropic effectors, purine, caffeine, theophylline, and (C2H5)4N+, have been examined. The heterotropic effectors influence the heme ligation affinities. The heme axial ligation of pyridine and pyrazole have not influenced the hemoglobins affinity for caffeine and theophylline. The imidazole ligation indicates a mutual interaction between the heme active site and the noncoordinate binding site.

Particle Wave Duality

This chapter is intended to develop an understanding of the dual wave-particle nature of electrons, photons, and other particles of small mass. The particle nature of the electrons had been confirmed by cathode rays, Millikans capacitor, and Thomsons experimentation. Models for atomic structures were proposed by Thomson and Rutherford. Studies of black-body radiation shows that energy emits in a small, specific quantity called quanta. Also, hydrogen emission spectrum indicates that electrons in atoms exist only in very specific energy states. Quantum has been concluded as the smallest amount of energy that can be lost or gained by an atom. Bohrs and Bohr-Sommerfelds atomic models are presented and discussed. Bohr in his atomic models used quantum theory, not quantum. Wave interference and diffraction are used as evidence to confirm the wave properties of the electrons. Einsteins relationships are explored to describe and clarify the interdependence of mass and energy. Furthermore, the corpuscular nature of light is revealed in the photoelectric effect and the Compton Effect. de Broglie shows that the dual wave-particle nature is true not only for photons but for any other material particles as well. Heisenberg in his uncertainty principle points out that only the probability of finding an electron in a particular volume of space can be determined. This probability of finding an electron is proportional to the square of the absolute value of the wave function. Subatomic particles are examined and classified as fundamental particles (fermions) and force particle (bosons) that mediate interactions among fermions.

Valence Bond Theory and Orbital Hybridization

The concept of valence bond theory is explained; we then investigate how to predict the shapes and geometry of simple molecules using the valence shell electron-pair repulsion (VSEPR) method. The process of predicting the molecules structure is reviewed. In addition, the relationships between the chemical bonds in molecules and its geometry using orbital hybridization theory are addressed. Special attention is devoted to the angles between the bonds formed by a given atom, the aspects of multiple bonding, and σ/π hybridization of atomic orbitals. An adapted linear combination of molecular wave functions, SALC-MO, is composed and explained in detailed, then used to compute the contribution of each atomic orbit in the hybrid orbital.

Vibrational Rotational Spectroscopy

Molecular vibrations are explained by classical mechanics using a simple ball and spring model, whereas vibrational energy levels and transitions between them are concepts taken from quantum mechanics. The quantum mechanics of the translation, vibration, and rotation motions are explored in detail. In addition, the expression for the vibration-rotation energies of diatomic molecule for the harmonic and anharmonic oscillator models is introduced. We then identify the Schrodinger equation for the vibration system of n-atom molecules. We elucidate how to obtain, monitor, and explain the vibrational-rotational excitations, find the quantum mechanical expression of the vibrational and rotational energy levels, predict the frequency of the bands, and compare between harmonic and anharmonic oscillation and between rigid and nonrigid rotor models for the possible excitations. Lagrange’s equation is used to show the change in the amplitude of displacement with time. We also examine how to calculate the relative amplitudes of motion, and the kinetic and potential energies for the vibrational motions of N-atom molecule. The significance of the force constants and how to calculate the force constants using GF-matrix method are discussed. The general steps to determine the normal modes of vibration, and the symmetry representation of these modes, are outlined. We examine the relationship and the differences among the Cartesian, internal, and normal coordinates used to characterize the stretching vibrations. We then show why the normal coordinates are used to calculate the vibrational energy of the polyatomic molecules. In this part, we also focus on how the molecules interact with the radiation and the chemical information obtainable by the measurement of the infrared and Raman spectroscopy. Only the electric waves interact significantly with molecules and are important in explaining infrared absorption and Raman stretching. The requirements and the selection rules for the allowed vibrational and rotational excitations are explored. We investigate the relationship between the center of symmetry and mutual exclusion rule, how to distinguish among isomers, binding modes, and define the forms of the normal modes of vibration, and which of these modes are infrared and/or Raman active.

Chapter 7 – Crystal Field Theory

In this chapter, we start by considering why there is a need for another theory, and the bases of the crystal field theory, then look at how the theory differs from the ligand field theory. The effect of a cubic crystal field on d- and f-electrons is introduced, then the expressions of the Hamiltonian to find the crystal field potential that is experienced by electrons in octahedral, square planar, tetragonally distorted octahedral, and tetrahedral ligand arrangements are computed. The perturbation theory for degenerate systems is used to explain how the crystal field potential of the surrounding ligands perturbs the degeneracy of d-orbitals of the central ion. The energies of the perturbed d-orbitals are calculated by solving the secular determinant. The obtained energies are fed back into secular equations that are derived from the secular determinant, to yield wave functions appropriate for the presence of the potential. The variation in the potential energy of each d-electron due to their crystal field is determined and the splitting of d-orbitals thus deduced in octahedral, tetrahedral, and tetragonally distorted D4h, in terms of Dq, Dt, and Ds. For free ions in weak crystal fields, problems and the required approximations are discussed. We then study the influence of a weak field on polyelectronic configuration of free ion terms, and find the splitting in each term and the wave function for each state. In a strong field approach, the first concern is how the strong field differs from the weak field approach; we define the determinantal, symmetry, and energy of each basis state. We compute the appropriate Hamiltonian, the diagonal and nondiagonal interelectronic repulsion in terms of the Racah parameters A, B, and C.

Chapter 8 – Ligand Field Theory

In this chapter, we show firstly, how it is possible to use the symmetry and group theory to find what states will be obtained when an ion of any electronic configuration is located into a crystalline environment of definite symmetry. Secondly, the relative energies of these states is investigated. Thirdly, we show how the energies of the various states into which the free ion term are split depend on the strength of the interaction of the ion with its environment. The relationship between the energy of the excited states and Dq are discussed using the correlation, Orgel, and Tanabe-Sugano diagrams.

Chapter 2 – Electrons in Atoms

First, we present how Schrodinger derived his wave mechanics equation that deals with the wave-particle duality of matter and energy, and presented the main postulates of this equation. The appropriate considerations for Schrodingers equation of the hydrogen atom and transformation of the Cartesian form of the equation into the corresponding spherical polar form are detailed. The spherical wave function is factored into Θ- and Φ-angular and R -radial wave functions. The solutions of these equations have been meticulously analyzed using Legendre and Laguerre polynomial differential equations. As a result, the physical meaning of the four quantum numbers n , l , m , and s are the relation among angular momentum, moment of inertia, energy of the electron, the final solution for the full wave function, and how it relates to the atomic orbital are clarified. The real wave functions that represent the atomic orbitals have been constructed in polar and Cartesian coordinates. The orthonormal properties are used to verify the reality of the wave functions. The wave functions of s-, p-, and d-orbitals are used to draw graphically the boundary surface of the corresponding orbitals and to evaluate atomic radius, kinetic, potential energy, and the orbital angular momentum. We then demonstrate how to calculate most probable radius and the mean radius, and how to find out the number radial nodes of the orbitals. Secondly, we examined the taken procedures in order to apply Schrodinger equations for many-electron atoms. The Pauli Exclusion Principle, fermions and bosons exchange, and the Slater determinant are used to express acceptable wave functions. Orbital degeneracy in each shell and why it has been removed are laid out. Slaters empirical rules for electron shielding are considered and used to calculate the ionization potential and the energy of atomic electrons. The building-up principle and the empirical rules concerning the order of filling the orbitals are discussed. Thirdly, we examine how to identify the term symbols of the ground state and the different terms of the excited microstates of polyelectronic atoms, and how many subterms arise when spin-orbit coupling is taken into consideration. The term wave functions and the corresponding single-electron wave functions are described in order to understand the effect of the ligand field on terms of the free electron in the following chapters. Finally, we investigate the splitting and the energy of the Russell–Saunders terms due to the interaction between the spin and orbital angular momentums. The energy difference between two adjacent spin-orbital states is also defined. The coupling of the orbital and the spin angular momentums with external magnetic field are examined, and potential energy is assigned. The effect of an external magnetic field and the splitting of each Russell–Saunders term into microstates and the energy of the microstate are identified.

Molecular Orbital Theory

A brief representation of molecular orbital theory is developed, along with understanding the electronic distribution of some elected small molecules, and considerable thoughts of the relative energies of the molecular orbitals are studied. An explanation is given of how the electron distribution changes upon going to some low-lying excited electronic states. The theory is employed to obtain the energy change in chemical reactions, study stability, reactivity, find the delocalization energy, electron density, formal charge, bond order, ionization energy, equilibrium constant, and configuration interaction. The chapter introduces the band theory concept that makes it possible to rationalize conductivity, insulation, and semiconducting.