Quantum mechanical model electrons

Organic molecules are the easiest to model and the easiest for which to obtain the most accurate results. This is so for a number of reasons. Since the amount of computational resources necessary to run an orbital-based calculation depends on the number of electrons, quantum mechanical calculations run fastest for compounds with few electrons. Organic molecules are also the most heavily studied and thus have the largest number of computational techniques available. 

How are the electrons distributed in an atom You might recall from your general chemistry course that, according to the quantum mechanical model, the behavior of a specific electron in an atom can be described by a mathematical expression called a wave equation—the same sort of expression used to describe the motion of waves in a fluid. The solution to a wave equation is called a wave function, or orbital, and is denoted by the Greek letter psi, i/y. 

Quantum mechanical model, 138-139 Quantum number A number used to describe energy levels available to electrons in atoms there are four such numbers, 140-142,159q electron spin, 141 orbital, 141... 

We are now ready to build a quantum mechanical model of a hydrogen atom. Our task is to combine our knowledge that an electron has wavelike properties and is described by a wavefunction with the nuclear model of the atom, and explain the ladder of energy levels suggested by spectroscopy. 

Whether the Bohr atomic model or the quantum mechanical model is introduced to students, it is inevitable that they have to learn, among other things, that (i) the atomic nucleus is surrounded by electrons and (ii) most of an atom is empty space. Students understanding of the visual representation of the above two statements was explored by Harrison and Treagust (1996). In the study, 48 Grade 8-10... 

PALS is based on the injection of positrons into investigated sample and measurement of their lifetimes before annihilation with the electrons in the sample. After entering the sample, positron thermalizes in very short time, approx. 10"12 s, and in process of diffusion it can either directly annihilate with an electron in the sample or form positronium (para-positronium, p-Ps or orto-positronium, o-Ps, with vacuum lifetimes of 125 ps and 142 ns, respectively) if available space permits. In the porous materials, such as zeolites or their gel precursors, ort/zo-positronium can be localized in the pore and have interactions with the electrons on the pore surface leading to annihilation in two gamma rays in pick-off process, with the lifetime which depends on the pore size. In the simple quantum mechanical model of spherical holes, developed by Tao and Eldrup [18,19], these pick-off lifetimes, up to approx. 10 ns, can be connected with the hole size by the relation ... 

In the early development of the atomic model scientists initially thought that, they could define the sub-atomic particles by the laws of classical physics—that is, they were tiny bits of matter. However, they later discovered that this particle view of the atom could not explain many of the observations that scientists were making. About this time, a model (the quantum mechanical model) that attributed the properties of both matter and waves to particles began to gain favor. This model described the behavior of electrons in terms of waves (electromagnetic radiation). 

In the development of the quantum mechanical model of the atom, scientists found that an electron in an atom could have only certain distinct quantities of energy associated with it and that in order to change its energy it had to absorb or emit a certain distinct amount of energy. The energy that the atom emits or absorbs is really the difference in the two energy states and we can calculate it by the equation ... 

In this chapter, you learned about the electronic structure of the atom in terms of the older Bohr model and the newer quantum mechanical model. You learned about the wave properties of matter, and how to describe each individual electron in terms of its four quantum numbers. You then learned how to write the electron configuration of an atom and some exceptions to the general rules. 

Some aspects of the bonding in molecules are explained by a model called molecular orbital theory. In an analogous manner to that used for atomic orbitals, the quantum mechanical model applied to molecules allows only certain energy states of an electron to exist. These quantised energy states are described by using specific wavefunctions called molecular orbitals. 

The theoretical aspects of electron transfer mechanisms in aqueous solution have received considerable attention in the last two decades. The early successes of Marcus Q, 2), Hush (3, 4), and Levich (5) have stimulated the development of a wide variety of more detailed models, including those based on simple transition state theory, as well as more elaborate semi-clas-sical and quantum mechanical models (6-12). 

In this article, a brief discussion will be given on the relevance of continuum theory in explaining the rate of electron transfer and the activation of species in solution we will concentrate in particular on molecular and quantum mechanical models of ET reactions at the electrode/electrolyte interface that are needed to replace those based on the continuum approach. ... 

Molecular modeling treatments of electron transfer kinetics for reactions involving bond breaking were developed much earlier than the continuum theories originated by Weiss in 1951. Gurney in 193l published a landmark paper (the foundation of quantum electrochemistry) on a molecular and quantum mechanical model of proton and electron transfer... 

Distinguish clearly between an electron orbit, as depicted in Bohr s atomic model, and an electron orbital, as depicted in the quantum mechanical model of the atom. 

In this section, you saw how the ideas of quantum mechanics led to a new, revolutionary atomic model—the quantum mechanical model of the atom. According to this model, electrons have both matter-like and wave-like properties. Their position and momentum cannot both be determined with certainty, so they must be described in terms of probabilities. An orbital represents a mathematical description of the volume of space in which an electron has a high probability of being found. You learned the first three quantum numbers that describe the size, energy, shape, and orientation of an orbital. In the next section, you will use quantum numbers to describe the total number of electrons in an atom and the energy levels in which they are most likely to be found in their ground state. You will also discover how the ideas of quantum mechanics explain the structure and organization of the periodic table. 

In this section, you have seen how a theoretical idea, the quantum mechanical model of the atom, explains the experimentally determined structure of the periodic table, and the properties of its elements. Your understanding of the four quantum numbers enabled you to write electron configurations and draw orbital diagrams for atoms of the elements. You also learned how to read the periodic table to deduce the electron configuration of any element. 

You know that a covalent bond involves the sharing of a pair of electrons between two atoms each atom contributes one electron to the shared pair. In some cases, such as the hydronium ion, HsO", one atom contributes both of the electrons to the shared pair. The bond in these cases is called a co-ordinate covalent bond. In terms of the quantum mechanical model, a co-ordinate covalent bond forms when a filled atomic orbital overlaps with an empty atomic orbital. Once a co-ordinate bond is formed, it behaves in the same way as any other single covalent bond. The next Sample Problem involves a polyatomic ion with a co-ordinate covalent bond. 

The quantum mechanical model and the electron configurations of the elements provide the basis for explaining many aspects of chemistry. Particularly important are the electrons in the outermost orbital of... 

The breakthrough in understanding atomic structure came in 1926, when the Austrian physicist Erwin Schrodinger (1887-1961) proposed what has come to be called the quantum mechanical model of the atom. The fundamental idea behind the model is that it s best to abandon the notion of an electron as a small particle moving around the nucleus in a defined path and to concentrate instead on the electron s wavelike properties. In fact, it was shown in 1927 by Werner Heisenberg (1901-1976) that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle. 

The quantum mechanical model proposed in 1926 by Erwin Schrodinger describes an atom by a mathematical equation similar to that used to describe wave motion. The behavior of each electron in an atom is characterized by a wave function, or orbital, the square of which defines the probability of finding the electron in a given volume of space. Each wave function has a set of three variables, called quantum numbers. The principal quantum number n defines the size of the orbital the angular-momentum quantum number l defines the shape of the orbital and the magnetic quantum number mj defines the spatial orientation of the orbital. In a hydrogen atom, which contains only one electron, the... 

The electron-dot structures described in Sections 7.6 and 7.7 provide a simple way to predict the distribution of valence electrons in a molecule, and the VSEPR model discussed in Section 7.9 provides a simple way to predict molecular shapes. Neither model, however, says anything about the detailed electronic nature of covalent bonds. To describe bonding, a quantum mechanical model called valence bond theory has been developed. 

---