Electron populations

Bardeen C J, Yakovlev V V, Wilson K R, Carpenter S D, Weber P M and Warren W S 1997 Feedback quantum control of molecular electronic population transfer Chem. Phys. Lett. 280 151... 

Figure C3.2.14. Electron population difference x(t) = - P (0 for tliree electron transfer reactions in the...

Population anaiysis methods of assigning charges rely on the LCAO approximation and express the numbers of electrons assigned to an atom as the sum of the populations of the AOs centered at its nucleus. The simplest of these methods is the Coulson analysis usually used in semi-empirical MO theory. This analysis assumes that the orbitals are orthogonal, which leads to the very simple expression for the electronic population of atom i that is given by Eq. (53), where Natomic orbitals centered... 

The electron population associated with an atom becomes ... 

You can order the molecular orbitals that are a solution to equation (47) according to their energy. Electrons populate the orbitals, with the lowest energy orbitals first. Anormal, closed-shell, Restricted Hartree Fock (RHF) description has a maximum of two electrons in each molecular orbital, one with electron spin up and one with electron spin down, as shown ... 

Compare the dipole moment and the electrostatic potential map for the ground state of acetone to those of the n to pistar state of acetone. Which molecule is more polar Rationalize the differences by appealing to the shape of the orbitals (in ground-state acetone) whose electron populations are changed by excitation. 

Electronic Population Analysis on LCAO-MO Molecular Wave Functions I... 

The chemistry of the elements we have examined thus far in this chapter is dominated by the special stabilities of the inert gas electron populations. We can expect to see this same factor at work in the chemistry of the elements in other parts of the periodic table. We shall now take an... 

The simple trend in the formulas shown by the third-row elements demonstrates the importance of the inert gas electron populations. The usefulness of the regularities is evident. Merely from the positions of two atoms in the periodic table, it is possible to predict the most likely empirical and molecular formulas. In Chapters 16 and 17 we shall see that the properties of a substance can often be predicted from its molecular formula. Thus, we shall use the periodic table continuously throughout the course as an aid in correlating and in predicting the properties of substances. 

An alkali element produces ions having the same electron population as atoms of the preceding inert gas. In what ways do these ions differ from the inert gases In what ways are they alike ... 

Refer to the halogen column in the periodic table. How many electrons must each halogen atom gain to have an electron population equal that of an atom of the adjacent inert gas What property does this population impart to each ion ... 

In Chapter 6 we saw that the chemistry of sodium can be understood in terms of the special stability of the inert gas electron population of neon. An electron can be pulled away from a sodium atom relatively easily to form a sodium ion, Na+. Chlorine, on the other hand, readily accepts an electron to form chloride ion, Cl-, achieving the inert gas population of argon. When sodium and chlorine react, the product, sodium chloride, is an ionic solid, made up of Na+ ions and Cl- ions packed in a regular lattice. Sodium chloride dissolves in water to give Na+(aq) and C (aq) ions. Sodium chloride is an electrolyte it forms a conducting solution in water. 

This special stability associated with the inert gas electron populations was found to pervade the chemistry of every element of the third row of the periodic table (see Section 6-6.2). Each element forms compounds in which it contrives to reach an inert gas electron population. Elements with a few more electrons than an inert gas are apt to donate one or two electrons to some other more needy atom. Elements with a few less electrons than an inert gas are apt to acquire one or two electrons or to negotiate a... 

REGULARITY AMONG THE ELECTRON POPULATIONS OF THE INERT GASES... 

At last we are ready to return to the periodic table. At last we are able to begin answering those who are wondering why about the special properties of the electron populations in Table 15-1. Let us reproduce Table 15-1 together with the numbers of orbitals of the hydrogen atom. The suggestion of a connection is irresistible, as seen in Table 15-II. 

The hydrogen atom orbitals give us the numbers 2, 8, 18, and 32—the numbers we find separating the specially stable electron populations of the inert gases. It was necessary to multiply n2 by two—an important factor that could not have been anticipated. Furthermore, it will be necessary to find an explanation for the occurrence of eight-electron differences both at neon and at argon and eighteen-electron differences both at krypton and at xenon. 

Table 15-11. stable electron populations and the hydrogen atom... 

Now we can see the development of the entire periodic table. The special stabilities of the inert gases are fixed by the large energy gaps in the energy level diagram, Figure 15-11. The number of orbitals in a cluster, multiplied by two because of our double occupancy assumption, fixes the number of electrons needed to reach the inert gas electron population. The numbers at the... 

Consider these two electron populations for neutral atoms ... 

The neutral fluorine atom has seven valence electrons that is, seven electrons occupy the highest partially filled cluster of energy levels. This cluster of energy levels thus contains one fewer electron than its capacity permits. The electron affinity of fluorine shows that the addition of this last electron is energetically favored. This is in accord with much other experience which shows that there is a special stability to the inert gas electron population. 

What properties do we actually find for the transition elements What kinds of compounds do they form How can the properties be interpreted in terms of the electron populations of the atoms ... 

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