Electronic Structure: All the periodic trends (size, ionization energy, electron affinity, electronegativity) can be rationalized by remembering that the nucleus at the center of the atom is attracting or pulling in the electrons. (E.g. as we traverse a row of the periodic table, atoms get smaller because there are more protons in the nucleus to pull in the electrons of that shell; as we go down a column the atoms get larger because we are adding more shells.) For the hydrogen atom, all subshells (orbital types like s and p) in a given shell are degenerate, meaning that they have the same energy. For atoms having more than one electron, however, orbital types are nondegenerate; the s electrons spend more time closer to the nucleus and therefore shield the p electrons, etc. You can read the order in which orbitals are filled off the periodic table. Hunds rules say that we fill up the orbitals from lowest energy to highest energy. The Pauli Exclusion principle states that two electrons in the same orbital must have opposite spin because electrons having the same spin repel each other like two like-polarized magnets. Bonding: Electrons can be visualized as waves. Electron waves can interfere with each other constructively ("in phase") or destructively ("out of phase"). The wave nature of electrons causes us to refer to electron orbitals as "wavefunctions," which are denoted by the Greek letter psi, Y. Y itself doesn’t have physical meaning, but its square indicates where electrons are likely to be found in space, which is why Y2 is called the "probability density distribution." The Y2 typically looks more smeared-out than the orbital itself. Since it is the square of Y, it is positive (same shading) everywhere. When two atomic orbitals come together to form a bond, it is required by quantum mechanical laws that the phases of their electron waves be added constructively and subtracted destructively to create two new molecular orbitals (MO’s). The overlap of two orbitals of different phase (one is shaded and the other is not) is unstable, high-energy, "out of phase." The overlap of two orbitals of the same phase (both are shaded or both are unshaded) is stable, low-energy, "in phase." Hund’s rules and the Pauli Exclusion principle apply to MO’s the same way they apply to atoms.
When constructing MO diagrams remember: 1. Conservation of energy dictates that bonding, antibonding, and nonbonding orbitals be combined so that their energy adds up to that of the atomic orbitals. This means (roughly speaking) that for every bonding orbital there should be an antibonding orbital. 2. The number of MO’s you end up with must equal the number of AO’s (atomic orbitals) from which they are formed. When we started with 2 H 1s orbitals, we got out 2 MO’s. If you start with 3 2p orbitals, you’ll get 3 MO’s out, etc. 3. Atomic orbitals interact with each other only if they have similar energies and the same symmetry about the internuclear axis. The most common symmetries to have about the internuclear axis are C-infinity or "cylindrical symmetry" and C2 antisymmetry. These are the symmetries of sigma and pi bonds, respectively, where sigma bonds are comprised of s and pz orbitals and pi bonds are comprised of parallel p orbitals. The diagram above illustrates the interaction of an s orbital with a pz orbital along the internuclear axis. 4. Interactions only happen if they stabilize the molecule. If all of the bonding and antibonding orbitals are filled, then the molecule is not stabilized because the energy of its electrons is not lowered. 5. Head-on interactions (C-infinity symmetry about the internuclear axis) are "better" than side-on interactions (C2 antisymmetry about the internuclear axis) because the orbital overlap is more effective. Therefore head-on interactions should be shown as lowering the energy of the bonding MO (and increasing the energy of the antibonding MO) more side-on interactions. 6. In the "LCAO-MO" numbering scheme, each MO is named with the Greek letter sigma or pi and then numbered from most stable to least stable. 7. MO’s have the character of the component atomic orbital to which they are closest in energy. This is a consideration only if the component atomic orbitals start out at different energies. In the picture above, the bonding molecular orbital has more s character and the antibonding orbital has more pz character. 8. Although the lobes are shown above with opposite sign, the square of the molecular orbital wavefunction (not shown) has the same sign in both lobes. The square of the wavefunction represents the probability density distribution, or where the electrons are likely to be found. 9. The more nodes a wavefunction has, the higher its energy. Hybrid orbitals: Like molecular orbitals, hybrid orbitals are formed from the combination of atomic orbitals. The atomic orbitals comprising hybrids, however, come from the same atom. This distinction is very important. You will recall that molecular orbitals form in bonding and antibonding combinations; hybrid orbitals have equivalent energies. For example, the wavefunctions for the two sp hybrids are of the form Y = (1/2)1/2(Y2s + Y2p) or Y = (1/2)1/2(Y2s - Y2p). The two orbitals are equivalent. Note the shape and signs of the lobes for the wavefunctions shown below.
Look at the squares of these wavefunctions. Note that all the lobes have a positive sign,
When you follow Hund’s rules and the Pauli Exclusion Principle to put the electrons in their orbitals, you are diagramming the atom in its ground state. The atom can move to an excited state when a photon of light kicks an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). In order for this to occur, the photon must have an energy exactly equal to the energy difference between those two orbitals. You can calculate the energy of a photon from its wavelength by using E=h(nu) = hc/(lambda), where h is Planck’s constant and c is the speed of light in a vacuum. Molecules or atoms having unpaired electrons are paramagnetic (attracted to a magnetic field). Molecules or atoms with no unpaired electrons are diamagnetic (repelled by a magnetic field). The more a bond lowers the energy of a molecule, the more stable that bond is said to be. More stable bonds are associated with smaller atom-atom internuclear distances and greater infrared stretching frequencies. (Infrared spectroscopy will be studied later in the course.) The multiplicity of a molecule is given by two times the total electron spin of the molecule plus one. A molecules total spin S is half the number of unpaired electrons, so we can simplify the definition by saying that the multiplicity of a molecule is the number of unpaired electrons of the molecule plus one. Highest possible multiplicity is lowest energy.
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