Quantum mechanics basic principles

A quantum mechanical formulation of solute charge density can be pursued in a number of ways. The most accurate treatment is the one that uses quantum mechanical first principle or ab initio approaches. However, the ab initio calculation of the electronic structure of a macromolecule is currently prohibitively expensive due to the large number of degrees of freedom. A variety of elegant theories and algorithms have been developed in the literature to reduce the dimensionality of this many-body problem [165-172]. In earlier work from the Wei group, a density functional theory (DFT) treatment of solute electron distributions was incorporated into our DG-based solvation model [132]. In this work, we review the basic formulation and present an improved DG-DFT model for solvation... 

The purpose of this chapter is to provide an introduction to tlie basic framework of quantum mechanics, with an emphasis on aspects that are most relevant for the study of atoms and molecules. After siumnarizing the basic principles of the subject that represent required knowledge for all students of physical chemistry, the independent-particle approximation so important in molecular quantum mechanics is introduced. A significant effort is made to describe this approach in detail and to coimnunicate how it is used as a foundation for qualitative understanding and as a basis for more accurate treatments. Following this, the basic teclmiques used in accurate calculations that go beyond the independent-particle picture (variational method and perturbation theory) are described, with some attention given to how they are actually used in practical calculations. 

An excellent treatment of molecular quantum mechanics, on a level comparable to that of Szabo and Ostiund. The scope of this book is quite different, however, as it focuses mainly on the basic principles of quantum mechanics and the theoretical treatment of spectroscopy. 

R. E. Christoffersen, Basic Principles and Techniques of Molecular Quantum Mechanics Springer-Verlag, New York (1989). 

Our presentation of the basic principles of quantum mechanics is contained in the first three chapters. Chapter 1 begins with a treatment of plane waves and wave packets, which serves as background material for the subsequent discussion of the wave function for a free particle. Several experiments, which lead to a physical interpretation of the wave function, are also described. In Chapter 2, the Schrodinger differential wave equation is introduced and the wave function concept is extended to include particles in an external potential field. The formal mathematical postulates of quantum theory are presented in Chapter 3. 

In this section we state the postulates of quantum mechanics in terms of the properties of linear operators. By way of an introduction to quantum theory, the basic principles have already been presented in Chapters 1 and 2. The purpose of that introduction is to provide a rationale for the quantum concepts by showing how the particle-wave duality leads to the postulate of a wave function based on the properties of a wave packet. Although this approach, based in part on historical development, helps to explain why certain quantum concepts were proposed, the basic principles of quantum mechanics cannot be obtained by any process of deduction. They must be stated as postulates to be accepted because the conclusions drawn from them agree with experiment without exception. 

This book is intended as a text for a first-year physieal-ehemistry or ehemical-physies graduate eourse in quantum meehanies. Emphasis is plaeed on a rigorous mathematical presentation of the principles of quantum mechanics with applications serving as illustrations of the basic theory. The material is normally covered in the first semester of a two-term sequence and is based on the graduate course that I have taught from time to time at the University of Pennsylvania. The book may also be used for independent study and as a reference throughout and beyond the student s academic program. 

A basic principle in quantum mechanics is the indistinguishability of particles. Thus, as indicated in Section 10.5, two particles of the same type in an ideal gas are characterized by a wavefunction, say f(r, 0j, tp 0%, spherical polar coordinates. If for simplicity this wave-function is written as (1,2), the permutation of the coordinates of the two identical particles can be represented by... 

In this chapter we give a brief review of some of the basic concepts of quantum mechanics with emphasis on salient points of this theory relevant to the central theme of the book. We focus particularly on the electron density because it is the basis of the theory of atoms in molecules (AIM), which is discussed in Chapter 6. The Pauli exclusion principle is also given special attention in view of its role in the VSEPR and LCP models (Chapters 4 and 5). We first revisit the perhaps most characteristic feature of quantum mechanics, which differentiates it from classical mechanics its probabilistic character. For that purpose we go back to the origins of quantum mechanics, a theory that has its roots in attempts to explain the nature of light and its interactions with atoms and molecules. References to more complete and more advanced treatments of quantum mechanics are given at the end of the chapter. 

In the 1920s it was found that electrons do not behave like macroscopic objects that are governed by Newton s laws of motion rather, they obey the laws of quantum mechanics. The application of these laws to atoms and molecules gave rise to orbital-based models of chemical bonding. In Chapter 3 we discuss some of the basic ideas of quantum mechanics, particularly the Pauli principle, the Heisenberg uncertainty principle, and the concept of electronic charge distribution, and we give a brief review of orbital-based models and modem ab initio calculations based on them. 

According to the basic principle of quantum mechanics, any measurable property can be computed ab initio if the total wave function y/ describing the quantum eigenstate of the system is known, since it contains the complete... 

What was the distinction between quantum chemistry and chemical physics After the Journal of Chemical Physics was established, it was easy to say that chemical physics was anything found in the new journal. This included molecular spectroscopy and molecular structures, the quantum mechanical treatment of electronic structure of molecules and crystals and the problem of chemical binding, the kinetics of chemical reactions from the standpoint of basic physical principles, the thermodynamic properties of substances and calculation by statistical mechanical methods, the structure of crystals, and surface phenomena. 

In principle there are three methods of calculation the ab initio molecular orbital (MO) method, the semiempirical MO method, and molecular mechanics. The choice depends on a number of factors such as the size of the molecule, the type of information required, and the budget. Whereas the ab initio method is the most basic and reliable quantum mechanical method,t the time requirement is so... 

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