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Chapter

Cover Molecular Quantum Mechanics

The electric properties of molecules  

This chapter examines the complexity of the electronic spectra of molecules, which occur in the visible and ultraviolet regions of the electromagnetic spectrum and arise in part from the stimulation of simultaneous vibrational and rotational transitions. It mentions electronic transition that changes the distribution of the electrons, and the nuclei respond to the new force field by breaking into vibration. In turn, the stimulation of vibration results in rotational transitions, just as ice skaters change the speed of their rotation by pulling in or throwing out their arms. The chapter deals with diatomic molecules, reviewing how the concepts generalize to polyatomic molecules. Computational chemistry has a considerable role to play in the prediction and interpretation of electronic absorption spectra.

Chapter

Cover Atkins’ Physical Chemistry

Molecular orbital theory: polyatomic molecules  

This chapter covers the concept of polyatomic molecules while considering molecular orbital theory. Polyatomic molecular orbitals spread over the entire molecule and the electrons that occupy them spread like a web over the atoms to bind them all together. Moreover, symmetry considerations play a central role in the construction of the molecular orbitals of polyatomic molecules, because only atomic orbitals of matching symmetry have non-zero overlap and contribute to a molecular orbital. The chapter introduces the Hückel approximation in relation to the construction of π molecular orbital energy level diagrams of conjugated molecules. It also considers the power and speed of computational chemistry.

Chapter

Cover Elements of Physical Chemistry

Vibration  

This chapter introduces the harmonic oscillator, which is a simple but very important model for the description of molecular vibrations. It shows how energies of vibration are restricted to certain values and covers acceptable wavefunctions that show that the oscillator may be found at extensions and compressions that are forbidden by classical physics. It also talks about the energy of a harmonic oscillator which is quantized and may be found at extensions not allowed classically. The chapter considers vibration as a very important type of motion of a molecule when bonds stretch, compress, and bend. It highlights polyatomic molecules with more than one mode of vibration and explores the consequences of the vibration not being harmonic.

Chapter

Cover Making the Transition to University Chemistry

States of Matter  

This chapter explains the states of matter. It notes how a dipole exists if a positive charge is separated from a negative charge by a distance. The bond's polarity and the shape of the molecule are needed to figure out whether polyatomic molecules have a dipole moment. The molecule's polarizability is in proportion with the induced dipole moment. The chapter also notes that intermolecular forces are forces between molecules that can be classified as dipole-dipole forces, dispersion forces, or hydrogen bonding. The chapter also looks at particles and definitions of solids, liquids, and gases. Finally, it lists the four main types of crystalline solids: simple molecular, giant covalent, ionic, and metallic.

Chapter

Cover Atkins’ Physical Chemistry

Vibrational spectroscopy of polyatomic molecules  

This chapter looks into the vibrational spectroscopy of polyatomic molecules. Due to the range of bond lengths and angles that can change in polyatomic molecules, the vibrational motion of the molecule is very complex. However, some orders can be brought to the complexity through normal modes. The chapter also considers that a normal mode is infrared active if it is accompanied by a change of electric dipole moment, while A normal mode is Raman active if it is accompanied by a change in polarizability. The chapter notes the exclusion rule that no mode can be either of the active normal modes if the molecule has a centre of inversion.

Chapter

Cover Physical Chemistry for the Life Sciences

Valence Bond Theory  

This chapter explains valence bond (VB) theory. In VB theory, a bond is regarded as forming when an electron in an atomic orbital on one atom pairs its spin with that of an electron in an atomic orbital on another atom. To understand why this pairing leads to bonding, the chapter examines the wavefunction for the two electrons that form the bond. It begins by discussing diatomic molecules, as the bonding in these molecules determines their physical and chemical properties and hence their biological function. The chapter then extends the ideas introduced so far to accommodate molecules containing more than two atoms — the polyatomic molecules.

Chapter

Cover Molecular Spectroscopy

Vibrational spectroscopy  

This chapter defines vibrational motion, which is a periodic, concerted displacement of the nuclei in a molecule that leaves the centre of mass unaltered in laboratory space. It explains that the appropriate linear combination of the displacements of a nucleus from its equilibrium position is called the vibrational coordinate, which is used to describe a particular vibrational motion. It also mentions the polyatomic molecule. This has several distinct vibrational modes, while the diatomic molecule only has one. The chapter reviews two distinct contributions to energy: the kinetic part that arises from the motion of the nuclei and the potential part that comes from the compression or expansion of the bond from its equilibrium value. It highlights the form of the potential energy curve. This shows that molecular energy increases rapidly as the charged particles in the molecule experience strong repulsive forces.

Book

Cover Chemical Bonding
Chemical Bonding starts off with a chapter on simple bonding schemes. The next chapter considers atomic structure. The third chapter looks at diatomic molecules. There is also a chapter on molecular geometry. The last two chapters cover hybrid orbital bonding and the molecular orbital approach and polyatomic molecules.

Chapter

Cover Chemical Bonding

The molecular orbital approach and polyatomic molecules  

This chapter addresses the molecular orbital approach and polyatomic molecules. The molecular orbital approach involves the identification of groups of orbitals whose symmetries allow overlap to form molecular orbitals. Molecular orbitals may be bonding, antibonding, or non-bonding relative to their component atomic orbitals. Molecular orbitals may hold one or two electrons. Moreover, molecular orbitals may link 1 to n atoms in a molecule, where n is the number of atoms in the molecule. Molecular orbital analysis and Lewis structures may lead to lone pairs but the nature of these lone pairs may differ. The chapter then looks at triatomic molecules EX2 and tetraatomic molecules EX3.

Chapter

Cover Chemistry3

Polyatomic molecules  

This chapter demonstrates how to predict shapes of polyatomic molecules and how to explain the bonding within them, including how the three bonding theories can be extended from diatomic to polyatomic molecules. The Lewis model, valence bond theory, and molecular orbital theory are looked at in turn, as each provides a different insight into structure and bonding. The chapter discusses the formal charges on the atoms in a molecule or ion, which are used to predict which of several possible structures a compound is likely to adopt. It describes bonding in a compound by predicting the hybridization of the central atoms and how the hybrid orbitals interact with the orbitals on other atoms. It also shows how to use resonance forms in describing the bonding in compounds that contain bonds that appear to be different in the Lewis structure but are found to be the same experimentally.

Chapter

Cover Physical Chemistry for the Life Sciences

Molecular orbital theory: polyatomic molecules  

This chapter extends MB theory to polyatomic molecules. Here, all the atoms contribute atomic orbitals to the construction of molecular orbitals. There are two special cases. One consists of molecules with conjugated chains of carbon atoms. Although the Hückel theory used to treat these molecules is very primitive, it generates orbitals and energy levels in a simple way and in fact underlies more sophisticated calculations. The other case consists of d-metal complexes where their high symmetry can be used to establish their spectroscopic and magnetic properties. Modern computational techniques for calculating molecular structure bring together all these features and provide deep insight into the properties of molecules of almost any complexity, with striking graphical displays.

Chapter

Cover Quantum Mechanics 1

Exact solutions  

This chapter evaluates some of the simplified Schrödinger equations obtained in the previous chapter, and presents explicit solutions for the energy levels and the corresponding wavefunctions. It begins by looking at the free particle and the particle in a box. The particle in a box is the simplest example of a confined particle, and enables us to understand the origin of many features of such systems, such as the appearance of discrete energy levels. It is a general feature of particles confined by a potential to some region of space that solutions to the Schrödinger equation can only be found at certain discrete energies. The chapter then considers the harmonic oscillator; angular momentum; rotations of a polyatomic molecule; and the hydrogen atom.

Chapter

Cover Quantum Mechanics 1

Separations  

This chapter examines the separation of variables in quantum mechanics. Although many mathematical methods are available for one-dimensional eigenvalue problems, multi-dimensional partial differential equations are much more difficult to solve, often requiring computational methods. The first step is therefore to search for some means of reducing the problem to a collection of one-dimensional equations, which can be solved separately. The procedure involved is called the separation of variables. The chapter first outlines the method of separation of variables before considering how it is applied to problems in chemistry. It looks at spherical symmetry; the Born–Oppenheimer separation; spin; orbital approximation; the diatomic molecule; and the vibrations of a polyatomic molecule.