Quantum mechanics principles

The introductory treatment of quantum mechanics presented in this textbook is excellent. Particularly appealing is the effort devoted to developing a qualitative understanding of quantum-mechanical principles. 

This venerable book was written in 1935, shortly after the birth of modern quantum mechanics. Nevertheless, it remains one of the best sources for students seeking to gain an understanding of quantum-mechanical principles that are relevant in chemistry and chemical physics. Equally outstanding jobs are done in dealing with both quantitative and qualitative aspects of the subject. More accessible to most chemists than Landau and Lifschitz. 

After the discovery of quantum mechanics in 1925 it became evident that the quantum mechanical equations constitute a reliable basis for the theory of molecular structure. It also soon became evident that these equations, such as the Schrodinger wave equation, cannot be solved rigorously for any but the simplest molecules. The development of the theory of molecular structure and the nature of the chemical bond during the past twenty-five years has been in considerable part empirical — based upon the facts of chemistry — but with the interpretation of these facts greatly influenced by quantum mechanical principles and concepts. 

Group I relies, as said before, on the reductionistic ideal that everything, in the field of chemistry, is amenable to the first principles and that a correct applications of the principles, accompanied by the necessary computational effort, will give the answer one is searching. It is a rigourous approach, based on quantum mechanical principles, in which the elements of the computation have no cognitive status, unless when employed to get numerical values of physical observables or of other quantities having a well defined status in the theory. 

Figure 13.2 Combination of three atomic p orbitals to form three n molecular orbitals in the allyl radical. The bonding n molecular orbital is formed by the combination of the three p orbitals with lobes of the same sign overlapping above and below the plane of the atoms. The nonbonding n molecular orbital has a node at C2. The antibonding n molecular orbital has two nodes between Cl and C2, and between C2 and C3. The shapes of molecular orbitals for the allyl radical calculated using quantum mechanical principles are shown alongside the schematic orbitals.

Figure 13.3 The n molecular orbitals of the allyl cation. The allyl cation, like the allyl radical, is a conjugated unsaturated system. The shapes of molecular orbitals for the allyl cation calculated using quantum mechanical principles are shown alongside the schematic orbitals. 

In previous sections, the basis for applying quantum mechanical principles has been illustrated. Although it is possible to solve exactly several types of problems, it should not be inferred that this is always the case. For example, it is easy to formulate wave equations for numerous systems, but generally they cannot be solved exactly. Consider the case of the helium atom, which is illustrated in Figure 2.7 to show the coordinates of the parts of the system. 

Here again, however, we have neglected the resonance phenomenon for the structure with electron 2 attached to nucleus A and electron 1 to nucleus B is just as stable as the equivalent structure assumed above, and in accordance with quantum-mechanical principles we must consider as a representation of the normal state of the system neither one structure nor the other, but rather a combination to which the two contribute equally that is, we must make the calculation in. such a way as to take into consideration the possibility of the exchange of places of the two electrons ... 

We may now ask why the valence of tin in the metallic form of the element is not 2, corresponding to one metallic orbital per atom and the electron configuration 4d °5 J5pt, but is 2.56. The answer is, I think, given by the quantum-mechanical principle that the actual structure for the normal state of a system is that structure, from among all... 

The purpose of this chapter is to review the recent results obtained in this context over the last decade and, in particular, in our group. The report is organized as follows. In Section II, we summarize the relevant quantum-mechanical principles and the Gutzwiller and Berry-Tabor trace formulas. 

R. McWeeny, Quantum Mechanics Principles and Formalism, Pergamon, Elmsford, NY, 1972. 

Marcelo Alonso and Henry Valk, Quantum Mechanics Principles and Applications, Addison-Wesley, Reading, MA, 1974. 

Werner Kutzelnigg, Quantum Mechanical Principles, Verlag Chemie, Weinheim, 1975. 

Moreover, several mechanisms for the suggested direct displacement of the halide ion from the radical anion by a nucleophile were examined and all were considered unacceptable because of the violation of quantum-mechanical principles or incompatibility with experimental observations64. 

Semi-empirical molecular orbital calculations, which are based on the same or related quantum mechanical principles, but make approximations or assumptions to simplify the computations, or include some empirical parameters based on experimental data [254-259]. 

An effective understanding of electronic spectra does require a basic knowledge of a number of fundamental quantum mechanical principles. This section only briefly highlights, in a descriptive way, some important aspects. More complete and formal treatments are available in a wide range of texts. ... 

Fig.l Scheme showing the structure from quantum mechanical principles to quantum chemical methods... 

The conventional macroscopic Fourier conduction model violates this non-local feature of microscale heat transfer, and alternative approaches are necessary for analysis. The most suitable model to date is the concept of phonon. The thermal energy in a uniform solid material can be jntetpreied as the vibrations of a regular lattice of closely bound atoms inside. These atoms exhibit collective modes of sound waves (phonons) wliich transports energy at tlie speed of sound in a material. Following quantum mechanical principles, phonons exhibit paiticle-like properties of bosons with zero spin (wave-particle duality). Phonons play an important role in many of the physical properties of solids, such as the thermal and the electrical conductivities. In insulating solids, phonons are also (he primary mechanism by which heal conduction takes place. 

The nature of the chemical bond and the principles of molecular structure were formu lated along time ago to systematize an immense body of chemical knowledge. With the advent of quanmm mechanics, it became possible to actually derive the concepts of chemical bonding from more fundamental laws governing matter on the atomic scale. Remarkably, many of the empirical concepts developed by chemists have remained valid when reexpressed in terms of quantum-mechanical principles. 

The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state simultaneously. It is one of tire most important principles in physics, primarily because the three types of particles from which ordinary matter is made—electrons, protons, and neutrons—are all subject to it. The Pauli exclusion principle underlies many of the characteristic properties of matter, from the large-scale stability of matter to the existence of the periodic table of the elements. 

McWeeny, R. (1972). Quantum Mechanics. Principles and Formalism. Pergamon, Oxford. 

All the work developed in our Laboratory concerning QSM is focussed on defining and interpreting a QSM according to quantum mechanical principles and to accompany this by a construction of a QSM theoretical framework as general as possible. Also, our research is concerned with handling the obtained measures by means of results manipulation and visualization within pure geometrical ideas. 

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