Molecular Orbitals of Heteronuclear Diatomics The molecular orbitals of heteronuclear diatomics (HF, CO, CN -, etc.) can be predicted using the same principles that we used to construct the molecular orbitals of homonuclear diatomics: i) Ignore the core electrons ii) Remember that the total number of MOs = total number of AOs iii) Only AOs of similar energy combine. iv) Only AOs of compatible symmetry combine. ie.  -type AOs (s and p z orbitals) make  MOs  -type AOs (p x and p y orbitals) make  MOs

Molecular Orbitals for HF Valence Atomic Orbitals of Isolated H and F

Molecular Orbitals for HF 2pz 2px, 2py Valence Atomic Orbitals of H next to F along the z-axis 1  2  1  3  

Bonding in HF Localized on F Bonding MO Anti-bonding MO Non-bonding 2s(F) 2pz(F) + 1s(H) 2px(F) 2py(F) - 2pz(F) + 1s(H) 1  2  1  3  

Bonding in HF LP BP LP H-F : : : LUMO HOMO NBB LP BP 122214122214 1LP 1BP2LP’s 1  2  1  3  

Molecular Orbitals for CO 2s 2pz 2s 2pxy 2pz 2pxy 2s(O) 11 Core 1s(C) & 1s(O) Not MO’s but AO’s Valence AO’s for C and O aligned along the z-axis

Molecular Orbitals for CO 2s 2pz 2s 2pxy 2pz 2pxy 2s(O) 11 Core 2px(C) + 2 px(O) 2py(C) + 2 py(O) 11 11 1s(C) & 1s(O) Not MO’s but AO’s Valence AO’s for C and O aligned along the z-axis 2px(C) - 2 px(O) 2py(C) - 2 py(O) 22 22

Molecular Orbitals for CO 2s 2pz 2s 2pxy 2pz 2pxy 2s(O) 11 1s(C) & 1s(O) Core 2px(C) + 2 px(O) 2py(C) + 2 py(O) 11 11 2s(C) + 2pz 22 2pz(C) - 2 p z (O) 33 Not MO’s but AO’s Valence AO’s for C and O aligned along the z-axis 2pz(C) + 2 p z (O) 44 2px(C) - 2 px(O) 2py(C) - 2 py(O) 22 22

9 11 22 11 22 33 Molecular Orbitals for CO 2pz 44

10 11 2  11 2  33 4  Molecular Orbitals for CO 2 s 2 p xy 2 p z 2 p xy 2 p z 1222143212221432 LP 2BP 1BP C O ::

Actual Molecular Orbitals for CO from Hyperchem 2s(O) 2s(C)+2pz(O) 2px(C)+2px(O) 2py(C)+2py(O) 2pz(C)-2pz(O) 2px(C)-2px(O) 2py(C)-2py(C) 2pz(C)+2pz(O) Node =   Bond = BMO Bond =  Bond =  Node =   Node =   Bond = 

B AB BB B 122*21432122*21432 C O :: 3 Sets of Bonding Pairs LP 2BP’s BP 1  2   1  3  2   4   B AB Electron Configuration for CO using MO

33 1  4  11 2  11 Electron Configuration of N 2 122*21432122*21432 N :: LP 2BP’s BP

14 Computating MOs Ab initio calculations : “from the beginning” and refers to calculations made from first principles. 1) consider all electrons in a molecule. (core & valence) 2) considers all interactions. (n-e, e-e & n-n) 3) Uses Born-Oppenheimer Approximation. 4) Simplifies e-e interactions to make the equations solvable. Semi-empirical calculations 1) Consider only the valence electrons, replacing the nucleus and core electrons with a “core potential” which represents their effect on the valence electrons. 2) Valence MO’s are calculated just as in Ab-initio methods where the core potential is added along with the Coulombic interactions. Faster than ab initio calculations and give relatively reliable molecular geometries. MO diagrams are less accurate than ab initio, but the MOs are typically in the correct order with the right separations. Predicted geometries can be verified by X-ray crystallography (and other techniques) and the energies can be verified by spectroscopy.