The trouble with chemistry is that it is too difficult for chemists.
Einstein
Einstein once said that a theory should be as simple as possible, but no simpler (Ocam's Razor, the Law of Parsimony, or a minimally necessary and maximally sufficient mathematical condition). The same applies to a textbook.
Physical chemistry means physics applied to chemistry. Physics, in turn means mathematics applied to physical objects. The reductionist paradigm of René Descartes is based on the notion that understanding can be achieved by decomposition. That is, complex systems are comprised of simpler components. Hence identifying the underlying components and their interactions leads to understanding behavior in complex systems. In this model, physical systems are constructed hierarchically from the fundamental particles of physics to the atoms and molecules of chemistry to the organisms of biology to the societies of anthropoplgy.
In 1960 the second edition of Physical Chemistry by E.A. Moewlyn-Hughes came off the press. It was a revolutionary approach to physical chemistry incorporating the discoveries of the previous half-century and presenting the subject from a molecular point of view. Originally, physical chemistry was a macroscopic science limited to the resolution of observing devices. The new basis was the quantum mechanics, the "theory of everything chemical." It was recognized early on in the development of the quantum mechanics that the whole of chemistry could be reduced to the solution of Schrödinger's wave equation (or Heisenberg's equivalent matrix equation). It was also immediately appreciated that the mathematical solutions to the general situation would be extremely difficult if not impossible to obtain for the class of equations involved. In hindsight it should be obvious that according to classical (and quantum) physics, complicated systems do not naturally lend themselves to simple descriptions.
All was not hopeless, however. The advent of computing machines has facilitated sophisticated techniques to obtain numbers from complex formulas like the wave equation. We are not anywhere near describing the structure and behavior of a virus yet, but useful, accurate solutions for simple molecues are routine.
However, the modern approach diffused only slowly into the physical chemistry curriculum. Modern developments recognize the role of synergistic, non additive (nonlinear) effects in compound systems. Thus, water is more than the sum of its parts, hydrogen and oxygen. It has new properties not shared with its components. This book is an attempt to modernize physical chemistry education by incorporating the developments in the past half-century into the subject, principally from dynamical systems theory and information science.
Following exposure to some quantitative courses, students sometimes become discouraged, to the point of changing their major interest. This is usually traced to a lack of mathematical preparation and comprehension. Today, powerful mathematical genies (note the cognate genius) in the form of computer computation programs. Like all computational tools (pencils, calculators, etc.), they facillitate the mechanics of computation. We will invoke one of these genies, called Mathematica to replace the drudgery of mathematical manipulation with the joy of exploration.
It has been common to state that there are only two types of problems, trivial and impossible. It has been said the only systems in physics with known solutions are the Kepler (planetary) system and the harmonic oscillator (spring) system. Although undoubtedly an understatement, the gap between traditional textbook applications and real world applications is essentially due to mathematical limitations. With the aid of powerful computational tools like Mathematica, it is possible to explore a wider range of systems than ever before.