Chemistry Team 2011-12

Quantum & Electron Configuration

Chris Seok

Vocab + Review: Conventional Classification and their Quantum Number notation: Principal Energy Levels: n = 1, 2, 3, 4.... (Ex.: 1s2) Energy Sublevels: l = 0, 1, 2, 3 (s, p, d, and f sublevels, respectively)...(Ex.: 1s2) Orbitals: The actual orbitals in the sublevels; denoted by -l ml l (Ex.: the px orbital) Electrons: may have up or down spin (either is ½); denoted by ms = ½. Example quantum number for an electron in 1px orbital with up-spin would be 1, 1, -1, +½. Basic List of Electron Config. Rules: Aufbau (“Building up”) Principle: lowest energy sublevels ⇒ highest energy sublevels; to find out, draw a diagram like so and follow the arrows:

Pauli Exclusion Principle: No two electrons may occupy the same quantum state simultaneously (same quantum numbers) ⇒ 2 electrons in an orbital must have opposite spins. Hund’s Rule (Hund’s 1st Rule): The electron configuration that maximizes ms is the one with the lowest energy. Thus, when filling each sublevel, do it such that if maximizes ms. ***Exceptions and Ionization*** There are some elements that form exceptions (via experimentation) to Hund’s Rule/Aufbau Principle; most notable are Chromium ([Ar] 4s13d5 NOT [Ar] 4s23d4) and Copper ([Ar] 4s13d10 NOT [Ar] 4s23d9); justified weakly by the “fact” that “half-filled” and “fully-filled” sublevels are much more stable than any other amt. of filled sublevels. In TRANSITION METALS (the large block of elements in the middle of the periodic table containing Iron), although Aufbau declares Energy4s < Energy3d, during ionization, the 4s electrons are ionized first instead of the higher-energy 3d electrons. (e.g.: Mn is [Ar] 4s23d5 while Mn(II) is [Ar] 3d5) Basic Classification of Elements Definitions via AVEE (Average Valence Electron Energy) Metals: 13 eV; good electron acceptors (more so to the top and right of pd. table) [email protected]

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Chemistry Team 2011-12

Quantum & Electron Configuration

Chris Seok

Metalloids: between metals and nonmetals in terms of AVEE *hydrogen is a nonmetal Bonding Types and Lewis Diagrams Metallic Bonds: Between two metals; many of the valence electrons are freed from the metals and form a “sea” of electrons around the metal cations (delocalization of electrons), which then clump around each other. Little benefit in drawing rows of metal atoms for qualitative analysis. Ionic Bonds: Between a metal and a nonmetal; a metal cation and a nonmetal anion (both usually satisfying the octet rule) are attracted because of opposite charges. Creates unsaturated compounds - theoretically a cation could bond with a huge number of anions. Usually drawn in Lewis diagram like so:

Covalent Bonds: Between 2 nonmetals; nonmetals share a pair of electrons which forms an electrostatic bond. If one nonmetal donates BOTH of the electrons, then it is a dative or coordinate covalent bond. Can be polar or non-polar (if one nonmetal has stronger pull of electrons than the other). Creates saturated compounds. Usually indicated in Lewis structures (not dot diagrams) with lines. Example is shown here:

Can have more than one ‘layer’ of bond; the first bond is a single/sigma bond; the second and third layers (each 2 electrons) are double and triple bonds (or pi bonds) Basic rules for drawing a covalent Lewis structure: 1) Count up all the valence electrons available and subtract/add electrons for ions 2) Place hydrogen/nonmetals preferably on the outside (the more “non-metallic” the farther they are on the outside) and vice versa with metals (but more centred the more metallic it is) 3) Draw single bonds from each atom to the adjacent ones in a reasonable manner; do not exceed the octet rule. 4) Fill in valence electrons as needed to follow the octet rule for each outside atom. 5) With the electrons “left over”, consider the central atom(s); if they have an electron deficiency, create double/triple bonds with other atoms for octet stability. If there is a surplus, then just put them as lone pairs/single electrons (AKA radicals) around the central atom(s). If more than 8, it is considered to be an expanded octet (which only period 3 and below can do). [email protected]

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Chemistry Team 2011-12

Quantum & Electron Configuration

Chris Seok

The Octet Rule Hydrogen/Helium is most stable with 2 electrons in its outer shell; most non-transition metal elements are stable with 8 electrons in its outer shell (the standard octet rule; but can theoretically have more if period 3 or lower in the pd. table); transition metals can have up to (and is stable at) 18 electrons. Why? G. N. Lewis found this out experimentally (through thermodynamics); modern quantum theory verifies the octet rule to hold for the most part because of how electron wave functions work, NOT due to some weird AP Chem-level justification. Exceptions: The most common are Groups I, II, and IIIA (Boron Group). Hybridization (SINGLE BONDS ONLY) - People experimentally realize that predicted bond lengths and angles are off. They theorize that s, p, and d orbitals can be mixed together when the need arises (for example, when exactly 4 orbitals are needed) and turned into unique hybridized orbitals. - For example, Carbon with [He] 2s22p2 may need to bond with 4 different atoms ⇒ take the s orbital and all 3 of the p orbitals to create sp3 hybridized orbitals (75% “barbell” p-character, 25% “sperical end” s-character - looks like baseball bat) - Double and triple bonds may ONLY use spare p or d orbitals. Thus if Carbon created sp2 orbitals, it would have a p orbital remaining that could join with another atom’s p orbital to make a double/triple bond. - For reference: sp orbitals have 180o between each hybridized orbital; sp2, 120o; sp3, 109.5o (tetrahedral). - This system makes sense because it allows for bond homogeneity Resonance - Sometimes electrons can be differently spread amongst the entire molecule. See nitrate:

These are called resonance forms. This degree of freedom makes the molecule constantly switch between the 3 structures and thus spread the electron density around. This uniformity (seen below) is called resonance stability and makes a molecule more stable than without resonance.

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Chemistry Team 2011-12

Quantum & Electron Configuration

Chris Seok

VESPR (Valence shell electron pair repulsion) Model/Theory A system based on the principle that orbitals containing lone pairs of electrons and those bonded to other atoms (ESPECIALLY those with lone pairs) should be separated as far away from each other as possible. Creates a fairly accurate qualitative model of the molecular structure. Steric number: the total (bonding and non-bonding) number of electron pairs held by the central atom. To see the table of structures, go to http://en.wikipedia.org/wiki/VSEPR_theory. Tip: Think of the central atom as the center of a wheel with a spoke going through it perpendicularly. Then put atoms/lone pairs at the edges of the wheel and the ends of the spoke as symmetrically and as stably (remember the PRINCIPLE behind VESPR) as possible. See below:

MO Theory - Problem with VESPR ⇒ May tell structure, but doesn’t have quantitative aspects to analyze; also, are we just assuming that we’re sticking a random sp3 orbital into an s-orbital and calling it a bond? How does that work? - After quantum theory was popularized and electron densities/probabilities could be described as wavefunctions along a bond’s length, we realized that Linear Combination of Atomic Orbitals (LCAO) was possible - namely, a different, unique molecular bond or orbital was created when atomic orbitals + their electron wavefunctions piled on top of each other and added up (just like regular waves). These molecular orbitals are the basis of MO theory. Simple example: 2 atoms (of element A) bond together ⇒ forms 8 MOs from its valence electron orbitals: , , , (x2), (x2), and , in order of ascending energy. The bonds are signified by their level, sublevel, the type of bond that they create, and finally whether they are bonding or anti-bonding (characterized by the asterisk) orbitals. Bonding orbitals create a mutually attractive electrostatic field in the middle, whereas the anti-bonding orbitals are forced to curve away from the bonding orbitals and from each other. Why are so many orbitals created/prepared? Theoretically we could have 16 electrons total (8 from each atom). But then by Pauli’s Exclusion Principle we are FORCED to ready 8 orbitals in [email protected]

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Chemistry Team 2011-12

Quantum & Electron Configuration

Chris Seok

order to avail a unique quantum/energy state for any electron that might come along. We cannot simply destroy the previously existent atomic orbitals. What’s the difference between bonding and anti-bonding orbitals? Nothing except for the energetics. When each atomic orbital splits into a bonding part + and anti-bonding part, the bonding part is usually lower in energy than the original atomic orbital and vice versa with the anti-bonding orbital. This increase in “orbital energy level” means that putting an electron in an A-B MO is unfavorable for the most part ⇒ destabilizes molecule ⇒ anti-bonding. By drawing MOs on an ascending energy diagram, we can analyze the energetics qualitatively and compare it to other compounds. The notation is similar to electron config. diagrams:

MO theory is immensely useful in qualitative comparison - for example, Band Gap Theory: - Given a molecule/aggregate, there is always an energy gap (the band gap) between the bonding and the anti-bonding molecules...EXCEPT for metallic bonds. This is how you can immediately tell the different types of bonds with an MO diagram. Furthermore... - Why is metallic bonding an exception? Assume that metallic aggregation can be represented by AN, or N number of A metal atoms clumped together. Then by Pauli Exclusion Principle, all of the orbitals are forced to have unique energy levels. Then as we take N to infinity, we can keep drawing orbitals closer and closer in energy level to each other until not only is the band gap gone, but there is a seamless continuum from the lowest bonding orbital to the highest A-B orbital, which means that with a minimum delta energy, electrons can go anywhere they want in the aggregation. This explains why metals have delocalized electrons. - Other properties such as transparency, luster, conductivity can also be explained by MO and the band gap theory. [email protected]

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Chemistry Team 2011-12

Quantum & Electron Configuration

Chris Seok

Last Notes on Diagrams - No one model is “better” than the others; use the simplest diagram necessary for the occasion. - VESPR/Lewis models help with qualitative/first principle problems

- MO theory and energy diagrams help with understanding quantitative/qualitative behavior, esp. in relation to OTHER compounds.

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