General Electronic Considerations of Metal-Ligand Complexes

MIT OpenCourseWarehttp://ocw.mit.edu 5.04 Principles of Inorganic Chemistry II �� Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.04, Principles of Inorganic Chemistry II Prof. Daniel G. Nocera Lecture 10: General Electronic Considerations of Metal-Ligand Complexes Metal complexes are Lewis acid-base adducts formed between metal ions (the acid) and ligands (the base). The interaction of the frontier atomic (for single atom ligands) or molecular (for many atom ligands) orbitals of the ligand and metal lead to bond formation, *L*L * interactions (n+1)p 3 different ligand types: (n+1)s M -only, -donor, -acceptor nd L interactions L L interactions L metal ligand orbitals orbitals More quantitatively, the interaction energy of stabilization and destabilization, εσ and εσ*, respectively, is defined on the following energy level diagram, 5.04, Principles of Inorganic Chemistry II Lecture 10 Prof. Daniel G. Nocera Page 1 of 4 Treating this problem within the LCAO framework comprising metal and ligand orbitals yields, ψ= cMφM + cLφL and solving for the Hamiltonian, Hψ= Eψ H − E ψ = H − Ej cMφM + cLφL = 0 Left-multiplying by φM and φL yields the set of linear homogeneous equations, cM Η− E + cL Η− E = 0φM φM φM φLcMΗ− E + cL Η− E = 0φL φM φL φL which furnishes the secular determinant, HMM − E HML − ESML EM − E HML − ESML= = 0 HML − ESML HLL − E HML − ESML EL − E 1Solving the above secular determinant, using the expansion 1 + x = 1 + x − ...,2 and realizing that HMM = EM and HLL = EL 22( HML − EMSML )( HML − EMSML )E+= EM + E−= EL − ΔEML ΔEML ↓↓ ↓↓ HMM εσ* HLL εσ The Wolfsberg-Hemholz approximation provides a value for HML, defined as HML = SML (EL + EM) Substituting HML in the above expressions for E+ and E– yields, εσ = EM2SML2 εσ = EL2SML2ΔEML * ΔEML5.04, Principles of Inorganic Chemistry II Lecture 10 Prof. Daniel G. Nocera Page 2 of 4 The derivation highlights the following general rules for the construction of MO diagrams, (1) M—L atomic orbital mixing is proportional to the overlap of the metal and ligand orbital, i.e., SML corollary A: only orbitals of correct symmetry can mix and ∴ give a nonzero interaction energy (i.e. SML ≠ 0) corollary B: σ interactions typically give rise to larger interaction energies than those resulting from π interactions and π interactions are greater than δ interactions owing to more directional bonding along the series SML(σ) > SML(π) > SML(δ) (2) M–L atomic orbital mixing is inversely proportional to energy difference of mixing orbitals (i.e. ΔEML). Another issue of interest for the construction of MOs is, (3) The order of the EL and EM energy levels almost always is: σ(L) < π(L) < nd < (n+1)s < (n+1)p π*L depending on the nature of the ligand This energy ordering comes directly from Valence Orbital Ionization Energies (VOIE) of metal and main group atoms and PES spectra of molecular ligands. VOIE’s of metal atoms: 3dn–14s → 3dn–24s 3dn–14s → 3dn–1 3dn–14p → 3dn–1 Atom 3d 4s 4p Sc 4.7 5.7 3.2 Ti 5.6 6.1 3.3 V 6.3 6.3 3.5 Cr 7.2 6.6 3.5 Mn 7.9 6.8 3.6 Fe 8.7 7.1 3.7 Co 9.4 7.3 3.8 Ni 10.0 7.6 3.8 Cu 10.7 7.7 4.0 5.04, Principles of Inorganic Chemistry II Lecture 10 Prof. Daniel G. Nocera Page 3 of 4 VOIE’s of ligand atomic orbitals and PES spectra of selected ligands: Atom 1s 2s 2p 3s 3p 4s 4p H 13.6 C 19.4 10.6 N 25.6 13.2 O 32.3 15.8 F 40.2 18.6 Si 14.9 7.7 P 18.8 10.1 S 20.7 11.6 Br 24.1 12.5 PES energies of ligands are in eVs (note: a VOIE is simply the opposite of the ionization energy) General observations: (1) The s orbitals are generally too low in energy to participate in bonding (ΔEML(σ) is very large) (2) Filled p orbitals are the frontier orbitals, and they have VOIEs that place them below the metal orbitals (3) For molecular ligands, since the frontier orbitals comprise s and p orbitals, here too filled ligand orbitals have energies that are stabilized relative to the metal orbitals 5.04, Principles of Inorganic Chemistry II Lecture 10 Prof. Daniel G. Nocera Page 4 of 4