Quantum molecular basic theory

Molecular orbitals were one of the first molecular features that could be visualized with simple graphical hardware. The reason for this early representation is found in the complex theory of quantum chemistry. Basically, a structure is more attractive and easier to understand when orbitals are displayed, rather than numerical orbital coefficients. The molecular orbitals, calculated by semi-empirical or ab initio quantum mechanical methods, are represented by isosurfaces, corresponding to the electron density surfeces Figure 2-125a). 

Presents the basic theory of quantum mechanics, particularly, semi-empirical molecular orbital theory. The authors detail and justify the approximations inherent in the semi-empirical Hamiltonians. Includes useful discussions of the applications of these methods to specific research problems. 

The basic theories of physics - classical mechanics and electromagnetism, relativity theory, quantum mechanics, statistical mechanics, quantum electrodynamics - support the theoretical apparatus which is used in molecular sciences. Quantum mechanics plays a particular role in theoretical chemistry, providing the basis for the valence theories which allow to interpret the structure of molecules and for the spectroscopic models employed in the determination of structural information from spectral patterns. Indeed, Quantum Chemistry often appears synonymous with Theoretical Chemistry it will, therefore, constitute a major part of this book series. However, the scope of the series will also include other areas of theoretical chemistry, such as mathematical chemistry (which involves the use of algebra and topology in the analysis of molecular structures and reactions) molecular mechanics, molecular dynamics and chemical thermodynamics, which play an important role in rationalizing the geometric and electronic structures of molecular assemblies and polymers, clusters and crystals surface, interface, solvent and solid-state effects excited-state dynamics, reactive collisions, and chemical reactions. 

Most of biological chemistry can be understood in terms of simple ball and stick models. The chemistry of nitric oxide and related oxides is more intimidating because its patterns of bonding depend strongly on quantum mechanics and molecular orbital theory. But the basics can be grasped by comparison to other molecules and a simple consideration of where nitrogen sits in the periodic table. 

To introduce some of the basic ideas of molecular orbital theory, let s look again at orbitals. The concept of an orbital derives from the quantum mechanical wave equation, in which the square of the wave function gives the probability of finding an electron within a given region of space. The kinds of orbitals that we ve been concerned with up to this point are called atomic orbitals because they are characteristic of individual atoms. Atomic orbitals on the same atom can combine to form hybrids, and atomic orbitals on different atoms can overlap to form covalent bonds, but the orbitals and the electrons in them remain localized on specific atoms. 

In order to improve MD simulations, a number of specific areas should be addressed in the area of basic molecular dynamics theory. These include (1) development of full quantum mechanical calculations on complex molecules and more robust ways to incorporate quantum mechanical calculations within larger-scale classical mechanics or statistical mechanics approaches (2) development and refinement of transferable force fields between arbitrary atoms and molecules, which are necessary building blocks for MD simulations of general systems and (3) development of multiscale theories and techniques for understanding systems. Moreover, the community must develop toolkits that allow general users to perform such simulations. 

Modern chemistry owes a great deal to two fundamental concepts, energy and probability, usually coupled to each other. One of the main examples of such a fruitful convergence is the field of quantum chemistry and orbital theory. The orbital concept provides the basic preparation in atomic and molecular structure theory needed for the understanding and interpretation of organic chemistry, inorganic chemistry and spectroscopy. 

I ll touch briefly on these issues in a later section on molecular structure and quantum mechanics. To set the scene, however, let me stress that Primas (1991) is absolutely right when he says that if reduction is used in the sense of "higher-level theory together with its interpretation can be deduced from the basic theory" then it is a brute fact that "... 

The United States is currently a leader in most areas of theoretical/ computational chemistry. In basic theory, Europe has many talented young investigators. Within the next 10 years, given these demographics, the U.S. leadership will be challenged by Europe in electronic structure and basic theory development. This trend does not characterize the entire field of theoretical chemistry. For example, Monte Carlo and molecular dynamics simulation methods were invented in the United States, and to this day, the United States maintains a strong position, especially in quantum Monte Carlo calculations. 

An analogy to molecular orbital (MO) theory may help to clarify further what is needed. Chemists prefer to discuss chemical problems in terms of localized MOs rather than in terms of (canonical) delocalized MOs resulting from Hartree-Fock (HF) based quantum chemical calculations. The localized MOs are obtained from the delocalized ones by a transformation ("localization"), which in most cases yields MOs directly related to the bonds of a molecule. The same should be true with regard to localized modes associated with a particular internal coordinate q. The question is only How can we transform from delocalized normal modes to localized internal modes To answer this question we will first summarize the basic theory of vibrational spectroscopy. 

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