Electrons occupy atomic orbitals

We mentioned an electron orbiting a hydrogen nucleus in the last paragraph deliberately, because that is one way of thinking about an atom—as a miniature (10 scale ) solar system with the nucleus as the sun and the electrons as planets. This model breaks down when we look at it in detail (as we shall see shortly), but for the moment we can use it to think about why electrons must exist in quantized energy levels. 

To do this, we need to introduce a concept from nineteenth century physics—the experimentally observable fact that particles such as photons and electrons can also have the character of a wave as well as a particle. It s not obvious why the energy of a particle should be quantized, but it makes sense if you allow yourself to think of an electron as a wave. 

This diagram shows a snapshot of the string we could also represent a blurred image of all the places you might find the string as it vibrates, such as you would get if you took a picture with a slow shutter speed. 

As a consequence, we have to think of electrons in atoms (and in molecules) as having a probability of being in a certain place at a certain time, and the sum of all these probabilities gives a smeared out picture of the electron s habits, a bit like blurred pictures of the vibrating strings. Because an electron is free to move around an atom in three dimensions, not just two, the allowed 

The vibration anaiogy was first seen by the Danish physicist Nieis Bohr, and we hope you can see how it heips to expiain why orbitais can oniy have certain energies. The anaiogy oniy works so far— we wiii have to ieave it behind soon—but it can be used to visuaiize some other aspects of orbitais too, such as nodes and signs of wavefunctions. 

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The electrons occupy atomic orbitals starting with the lowest energy (the orbital closest to the nucleus). 

Minimal basis functions (e.g. STO-LG) contain only minimal required contracted functions for each atom. For example, since electrons occupy atomic orbitals up to the 2p orbital in the carbon atom, five contracted Gaussian-type functions corresponding to Is, 2s, 2p, 2py, and 2p orbitals are necessary at the minimum. The minimal basis functions approximating Slater-type orbitals (STO) corresponding to atomic orbitals with L prinoitive functions are called STO-LG basis functions. 

The electron configuration indicates which atomic orbitals are occupied by electrons. Nitrogen has a total of seven electrons. These electrons occupy atomic orbitals of increasing energy, with two electrons being placed in each orbital ... 

If the orbital energies given by the exact quantum mechanical solution for the H atom held for other atoms, we might expect to see the rows of the Periodic Table contain successively 2, 8,18, 32 elements as orbitals with n = 1, 2, 3,4 were filled with electrons. In reality, the relative energies of atomic orbitals (or the electrons occupying atomic orbitals) vary as the atomic number of the elements increases and, besides the attractive force between the nucleus and the electron in the H atom, there are also repulsive forces between the several electrons in the... 

Quantum theory shows that atoms exist only in discrete states, each of which possesses a characteristic energy, defined by quantum numbers, which characterize the atomic state. Transitions may occur only between these levels, and even then some transitions are unfavorable. Electrons occupy atomic orbitals with characteristic spatial distributions around the nucleus. 

Carbonyl, dinitrogen and cyanide complexes of transition metals are generally not stable unless the metal has lone-pair electrons occupying atomic orbitals that overlap with Ugand n orbitals. In structures (4)-(6), we have indicated two sets of lone-pair electrons. If we assume that these electrons occupy metal and... 

It is essential to keep in mind that all atoms possess excited orbitals that may become involved in bond formation if one or more electrons occupies these orbitals. Whenever aos with principal quantum number one or more unit higher than that of the conventional aos becomes involved in bond formation, Rydberg mos are formed. 

The molecular orbital approach to chemical bonding rests on the notion that as elec trons m atoms occupy atomic orbitals electrons m molecules occupy molecular orbitals Just as our first task m writing the electron configuration of an atom is to identify the atomic orbitals that are available to it so too must we first describe the orbitals avail able to a molecule In the molecular orbital method this is done by representing molec ular orbitals as combinations of atomic orbitals the linear combination of atomic orbitals molecular orbital (LCAO MO) method... 

The lowest energy molecular orbital of singlet methylene looks like a Is atomic orbital on carbon. The electrons occupying this orbital restrict their motion to the immediate region of the carbon nucleus and do not significantly affect bonding. Because of this restriction, and because the orbital s energy is very low (-11 au), this orbital is referred to as a core orbital and its electrons are referred to as core electrons. 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

Recently it was pointed out by Zener7 that the atomic moments, in parallel orientation, might react with the electrons in the conduction band in such a way as to uncouple some of the pairs, producing a set of conduction electrons occupying individual orbitals, and with spins parallel to the spins of the atomic electrons. Zener assumed that the conduction band for the transition metals is formed by the 4.s orbitals of the atoms, and that there is somewhat less than one conduction electron per atom in iron, cobalt, and nickel. Like Slater, he attributed the atomic magnetic moments to the partially filled 3d subshell. 

Application of the Theory to Iron.—We assume, in essential accordance with earlier conclusions,2 8 that six of the eight outer electrons of the iron atom are valence electrons, occupying d3sp2 orbitals, and the remaining two are atomic electrons. 

An atomic orbital is designated by its and / values, such as Is, 4p, 3d, and so on. When / > 0, there is more than one orbital of each designation three p orbitals, five d orbitals, and so on. When an electron occupies any orbital, its spin quantum number, lit, can be either + or -. Thus, there are many sets of valid quantum numbers. An electron in a 3p orbital, for example, has six valid sets of quantum numbers n = 3, / = 1, m =+1, j — -2 / —i — — 1... 

Increasing atomic mass accounts for both these trends. The volume occupied by an individual atom in the metallic lattice varies slowly within the d block, so the more massive the nucleus, the greater the density of the metal. Toward the end of each row, density decreases for the same reason that melting point decreases. The added electrons occupy antibonding orbitals, and this leads to a looser array of atoms, larger atomic volume, and decreased density. 

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