D. A. Evans The H2 Molecular Orbitals Antibonds Chem 206 The H2 Molecule(again!!) Linear Combination of Atomic Orbitals(LCAO): Orbital Coefficients Let's combine two hydrogen atoms to form the hydrogen molecule ■ Rule two Mathematically, linear combinations of the 2 atomic 1s states create two new orbitals, one is bonding, and one antibonding Each MO is constructed by taking a linear combination of the individual atomic orbitals(AO) Bonding mo Rule one: a linear combination of n atomic states will create n Mos Antibonding MO 0*=C 1V+C2Y2 1s ■ Rule three(c12+(c2 The squares of the C-values are a measure of the electron population AE in neighborhood of atoms in question I Rule Four: bonding(C-+ antibonding(C1=1 In lCao method, both wave functions must each contribute one net orbital Let's now add the two electrons to the new mo, one from each h atom Consider the pi-bond of a C=o function: In the ground state pi-C-0 o*(antibonding is polarized toward Oxygen. Note(Rule 4) that the antibonding MO is polarized in the opposite direction 1s G(bonal Note that△E1 is greater than△E2.WhyD. A. Evans Chem 206 The H2 Molecule (again!!) Let's combine two hydrogen atoms to form the hydrogen molecule. Mathematically, linear combinations of the 2 atomic 1s states create two new orbitals, one is bonding, and one antibonding: Energy 1s 1s s* (antibonding) ■ Rule one: A linear combination of n atomic states will create n MOs. DE DE Let's now add the two electrons to the new MO, one from each H atom: Note that DE1 is greater than DE2 . Why? s (bonding) s (bonding) DE2 DE1 s* (antibonding) 1s 1s y2 y2 y1 y1 Energy s = C1y1 + C2y2 Linear Combination of Atomic Orbitals (LCAO): Orbital Coefficients Each MO is constructed by taking a linear combination of the individual atomic orbitals (AO): Bonding MO Antibonding MO C* s* =C*1y1– 2y2 The coefficients, C1 and C2, represent the contribution of each AO. ■ Rule Three: (C1 )2 + (C2 )2 = 1 antibonding(C*1 ) = 1 2 bonding(C + 1 )2 ■ Rule Four: Energy p* (antibonding) p (bonding) Consider the pi -bond of a C=O function: In the ground state pi-C–O is polarized toward Oxygen. Note (Rule 4) that the antibonding MO is polarized in the opposite direction. C C O C O The H2 Molecular Orbitals & Antibonds The squares of the C-values are a measure of the electron population in neighborhood of atoms in question In LCAO method, both wave functions must each contribute one net orbital ■ Rule Two: H H H H O