The Universe Within: Quantum Chemistry

Halfway there after today, folks. Hang in there.

The topic for this morning is a continuation of the periodic table, particularly the chemical properties of the major elements and the subatomic structure of the atomic nucleus.

The main topic to consider in mastering the modern periodic table in its relationship to quantum mechanics is how to describe electrons in the nucleus. Each electron has a unique address in the electron cloud, a position in an orbital. Each orbital, or shell, is a wave function describing the likely location of electrons based on the lowest possible energy state of the nucleus. We cannot know precisely where any given electron is in an orbital as stated in the Heisenberg uncertainty principle, but we can still describe it numerically. Modern quantum theory holds that each electron orbits the nucleus in a specific shell and sub-shell with a given orientation. Thus, each electron has a unique “address” composed of four quantum numbers.

The principal quantum number, n, defines the shell in which the electron resides. Values of n are positive, non-zero integers. The shells with n = 1, n = 2, and n = 3 are called the first shell (also called the K shell, for no particular reason), second shell (L shell), and third shell (M shell). The secondary quantum number, l, divides each shell into sub-shells of slightly different energies. For a given orbital n, the l values can range from 0 to (n – 1). Thus, for the first shell (n = 1), the only value of l is 0, and only one sub-shell exists; for the second shell (n = 2), values of l can be 0 or 1, and two sub-shells are present; and so on. The sub-shells are designated by a letter code, where the first (l = 0) is labeled “s”, the second (l = 1) is “p”, the third (l = 2) is d, the fourth (l = 3) is “f”. To designate a particular sub-shell, we write the principal quantum number followed by the letter code for the sub-shell. The lower the sub-shell number, the lower the energy. The third quantum number is known as the magnetic quantum number and is designated m_l. It divides each shell into individual orbitals. Values for m_l can range from +l to –l. Thus, the s sub-shell (l = 0) has a single orbital since +0 and -0 are still just 0, while the p sub-shell (l = 1) has three orbitals (+1, 0, -1). All the orbitals of a given sub-shell have the same energy. The fourth quantum number is the spin quantum number, m_s, which is either + ½ or - ½. The Pauli exclusion principle states that no two electrons in the same atom can have identical values for all four quantum numbers.

Atoms are built from the inside out, by adding electrons to the lowest possible orbital because this is the lowest and therefore most favored energy state. This concept is termed the aufbau principle (German for “building up”). When added to a specific orbital, Hund’s rule states that electrons will spread out as much as possible, avoiding pairing within an orbital for as long as possible.

The interaction of atoms in chemical reactions is dictated by the electron configuration in the outer (or valence) shell. Elements in the same group (column) of the periodic table have similar arrangements of electrons in their valence shell. The valence shells fill as one progresses from left to right in the periodic table, until all positions are occupied in the VIIIA group (noble gases) located farthest to the right. The completely filled valence shell of the noble gases renders them quite unreactive. Many other elements undergo chemical reactions in such a way that their electron configuration tends to assume the same configuration as the nearest noble gas.

Rest well until tomorrow – in body, if not in mind.