Search Results

This chapter discusses the physics and properties of four types of atomic forces occurring in STM and AFM: the van der Waals force, the hard core repulsion, the ionic bond, and the covalent bond. The general mathematical form of the van der Waals force between a tip and a flat sample is derived. The focus of this chapter is the covalent-bond force, which is a key in the understanding of STM and AFM. The concept of covalent bond is illustrated by the hydrogen molecular ion, the prototypical molecule used by Pauling to illustrate Heisenberg's concept of resonance. The Herring-Landau perturbation theory of the covalent bond, an analytical incarnation of the concept of resonance, is presented in great detail. It is then applied to molecules built from many-electron atoms, to show that the perturbation theory can be applied to practical systems to produce simple analytic results for measurable physical quantities with decent accuracy.

This chapter presents a unified theory of tunneling phenomenon and covalent bond force, as a result of the similarity between the Bardeen theory of tunneling and the Herring-Landau theory of the covalent bond. Three general theoretical treatments are presented, which show that tunneling conductance is proportional to the square of the covalent bond interaction energy, or equivalently, the square of covalent bond force. The constant of proportionality is related to the electronic properties of the materials. For the case of a metal tip and a metal sample, an explicit equation contains only measurable physical quantities is derived. Several experimental verifications are presented. The equivalence of covalent bond energy and tunneling conductance provides a theoretical explanation of the threshold resistance observed in atom-manipulation experiments, and points to a method of predicting the threshold resistance for atom manipulation.

Chemical Bonding I: Basic Concepts examines general ideas of chemical bonding between atoms and ions and how this bonding affects the chemical properties of the elements. An overview of Lewis symbols, Lewis structures and the octet rule is presented including the role of valence electrons in ionic and covalent bonding. The energy changes that accompany ionic bond formation are also discussed with emphasis on lattice energy. The chapter covers guidelines and general procedures for writing Lewis structures or electron dot formulas for molecular compounds and polyatomic ions. The concepts and applications of resonance, formal charge and exceptions to the octet rules are presented, along with coverage of the relationship between bond polarity and electronegativity.

Bohr and his allies in quantum theory made use of chemical data, but without taking chemistry seriously. Conversely, Bohr’s atom theory was received with scepticism by the chemists, who did not find it useful for chemical purposes. To understand the covalent bond they designed static models that worked but were physically inadmissible. As an example, the chapter considers the theory of I. Langmuir. The Bohr theory was applied with some success to molecular spectroscopy, but it was unable to account for the structure of even the simplest molecules such as hydrogen and, as shown by W. Pauli, the even simpler hydrogen ion. Moreover, elaborate attempts to calculate the helium atom failed, which caused much concern. The chapter also deals with other anomalies of the early 1920s, such as the Paschen–Back effect in hydrogen and the Ramsauer effect.

This chapter discusses the physics and properties of four types of atomic forces occurring in STM and AFM: the van der Waals force, the hard core repulsion, the ionic bond, and the covalent bond. The general mathematical form of the van der Waals force between a tip and a flat sample is derived. The focus of this chapter is the covalent-bond force, which is a key in the understanding of STM and AFM. The concept of covalent bond is illustrated by the hydrogen molecular ion, the prototypical molecule used by Pauling to illustrate Heisenberg’s concept of resonance. The Herring-Landau perturbation theory of the covalent bond, an analytical incarnation of the concept of resonance, is presented in great detail. It is then applied to molecules built from many-electron atoms, to show that the perturbation theory can be applied to practical systems to produce simple analytic results for measurable physical quantities with decent accuracy.

This chapter presents a unified theory of tunneling phenomenon and covalent bond force, as a result of the similarity between the Bardeen theory of tunneling and the Herring-Landau theory of the covalent bond. Three general theoretical treatments are presented, which show that tunneling conductance is proportional to the square of the covalent bond interaction energy, or equivalently, the square of covalent bond force. The constant of proportionality is related to the electronic properties of the materials. For the case of a metal tip and a metal sample, an explicit equation contains only measurable physical quantities is derived. Several experimental verifications are presented. The equivalence of covalent bond energy and tunneling conductance provides a theoretical explanation of the threshold resistance observed in atom-manipulation experiments, and points to a method of predicting the threshold resistance for atom manipulation. Theory of imaging wavefunctions with AFM is discussed.

Chapter 9 presents an introductory overview of quantum chemistry and solid state physics. First, the Periodic Table is examined in terms of atomic structure, electron orbitals and the shell model. Simple polar and non-polar molecules are considered in terms of the overlap of atomic orbitals which gives rise to covalent bonding between atoms. Hückel theory is used to analyse the electronic structure of benzene and polyene molecules. These ideas are extended to periodic solids. Bloch’s theorem is used to explain their band structure in terms of molecular orbital theory. Band theory provides an explanation of the distinctions between metals, semi-conductors and insulators. Caesium chloride is used to illustrate how the band structure and properties of an ionic compound arise from its atomic structure. Metals are discussed, with emphasis on copper as an illustrative example, and the significance of the Fermi surface is explained. Ferromagnetism is considered in the transition metals.

This chapter discusses several highly simplified models that have been used historically to discuss crystal bonding. It is customary to divide materials into categories according to the qualitative nature of the chemical or physical bonding existing among the atoms. The ‘dividing line’ between these categories is not always sharp. For instance bonding in transition metals, such as tungsten, may be thought of as both metallic and covalent. The remainder of the chapter discusses simple models of the van der Waals bond, ionic bond, covalent bond, and metallic bond. The chapter also includes some sample problems.

Mechanical properties of bonds are discussed, with the aid of a simple phenomenological model in which the variation of energy as a function of distance between the elements is described in terms of polynomials. The properties of various kinds of bonds (ionic bond, metallic bond, covalent bond, van der Waals bond) are explained with the aid of simple models. Carbon is discussed with two examples: bonds between 60 atoms that lead to the formation of a three-dimensional molecule known as Buckminsterfullerene, and the alternative sheet-shaped configuration known as graphene, that has recently become the centre of interest. A general theory for finding the energy levels is introduced, relying on Feynman’s coupled wave equations. There is a brief reference to nuclear forces, followed by a discussion of the hydrogen molecule. The relationship between coupling and the splitting of the energy levels is discussed with an analogy to coupled resonant circuits.

A new theory of diachronic ontological emergence called transformational emergence is constructed, and its relations with the author’s previous account of fusion emergence are described. They are both shown to satisfy three of the four criteria for emergence. The author shows how problems with existing accounts of synchronic emergence do not apply to transformational emergence. The account is motivated by a simple example from sociology and a more sophisticated example from the Standard Model in physics is given. The distinction between synchronic fundamentality and diachronic fundamentality is explained. Possible objections to fusion emergence are canvassed and shown to fail, the inverse process of defusion is explained, and additional examples, including covalent bonding, are given. It is suggested that a property interaction account of laws is the only feasible option for diachronic emergence.