Lectures 5-6 Molecular Bonding Theories 1) Lewis structures and octet rule According to the Lewis theory, a single covalent bond between two atoms forms when they share one electron pair. A double bonds means two shared electron pairs etc. Formation of an ionic bond assumes that one atom loses an electron and another adds it to its shell. The octet rule. For the elements with unavailable d-orbitals (Li … Ne), there is a maximum of 8 electrons in their valence shell. If this number is not reached (BH3, BeH2 etc.), a compound tends to react with electron pair donors (OH2, NH3 etc) to get more shared electrons. Based on the number of electrons in the valence shell, each atom in a chemical species can be assigned a formal charge (the difference in the number of electrons in the element’s valence shell before and after formation of bonds; see + and – signs in the formula above). For the elements with available d orbitals the valence shell can include more than 8 electrons (AlF63-, SiF62-, PCl5, SF4, ClF5, IF7). In some cases atoms can share less (H2+, B2H6) or more (NO) than one electron pair per one bond. Sometimes a configuration with unpaired electrons is more stable than that with paired electrons (O2).

2) Valence Bond (VB) theory One of two major theories describing orbital structure of polyatomic species. Used in modern quantum chemical calculations along with Molecular Orbital (MO) theory. VB theory assumes that covalent bonds are formed when atomic orbitals on two adjacent atoms overlap and electrons on these orbitals are shared. Thus, as a rule, the bonds are two electron, two-center. VB theory gives rise to the concepts of hybridization and resonance. Allows for more exact calculation of bond energies than MO theory. Used extensively in organic chemistry on a qualitative level.

3) Valence bond theory. Origin of bonding in H2+ molecule ion When two nuclei approach each other, electron density decreases at the nuclei which is the region of the strongest nucleus – electron attraction. The overall potential energy Vg of the system increases (becomes more positive) so destabilizing the system. At the same time the kinetic energy Tg of the electron decreases in a much greater extent and stabilizes the system. In quantum mechanics, kinetic energy T of an electron is a function of the square of the gradient of its wavefunction y, T = f(grad(y)2). Good overlap of atomic orbitals leads to lower gradients and thus to lower T what is critical to make a strong bond.

4) Valence bond theory. H2 molecule Consider the wavefunction ycov, g of a system of two hydrogen atoms A and B with electrons 1 and 2 of opposite spin. There are two ways of distributing the electrons, one per atoms, which correspond to y’ and y”. Combining y’ and y” (exchanging electrons by their location) we increase the space each of the electrons 1 and 2 can move within what leads finally to an extra energy gain (exchange energy). When two hydrogen atoms approach each other, their atomic orbitals overlap and the total energy of the system decreases mainly as a result of sharing (exchanging) electrons between two atoms. The H-H bond energy calculated with ycov, g is 72.4 kcal/mol vs 5.7 kcal/mol with either y’ or y” only.

5) Valence bond theory. H2 molecule The experimental value of H-H bond energy is 109.5 kcal/mol. The H-H bond energy of 72.4 kcal/mol calculated with the wavefunction ycov, g can be improved to 87.2 kcal/mol if Z* is used instead of Z to account for the electron shielding. Another way to improve the description of the bonding in the dihydrogen molecule with the resulting H-H bond energy of 92.7 kcal/mol is to consider the ionic contribution (H+H-) with a weight factor l: The covalent and ionic structures are said to be in a resonance with each other:

6) Valence bond vs MO theory In contrast to MO theory, in VB theory electron pairs are localized in a restricted space near two atoms. This leads to smaller error related to accounting for electron correlation and more exact value of bond energies. At the same time in the case of polyatomic molecules with many resonance structures possible application of VB theory becomes quite complicated. MO theory which is simpler is used instead.

7) Resonance A concept suggested to overcome some limitations of Lewis and VB theories and to complement them. Uses multiple canonical (Lewis) structures to describe bonding when a single structure does not allow to account for some features of a species. 1) A favorable resonance structure should have maximum number of covalent bonds.

8) Resonance 2) In resonance structures atoms should not change their connectivity. 3) Structures with separated charges contribute less than those without them. 4) A resonance structure contributes more if sign of a developing charge matches elements’ electronegativity (see above). 5) All resonance structures should have the same number of unpaired electrons.