University:
Seattle Pacific University
Course:
CHM 1211 | General Chemistry I
Academic year:

2022
Views:

492

Pages:

16
Author:

ilikemyicons0y5

Molecular orbitals for σ bonding in Td complexes • The set of n A−B σ bonds in ABn (Td n = 4) molecules are often thought of as independent entities. • The concept of MO’s allows us to begin with a very general and nonrestrictive framework that is in accord with all symmetry requirements allowing us to visualize (through computational methods) the physical geometry of the wave functions for different MO’s in a molecule. • First the symmetries of the MO’s are determined followed by the identification of the AO’s on A and B in ABn • The atomic orbitals on the central metal A, together with the corresponding symmetry adapted linear combinations of ligand atomic orbitals (SALCs) on the B atoms (or molecules if appropriate), that can be used to form MO’s will have to form a basis for the representations that contribute to the reducible representation. • Thus we begin by applying all of the symmetry operations in the molecular point group to the set of σ orbitals. Point group Symmetry operations of point group • For this purpose we may represent each σ orbital by a vector pointing from A to a B atom, and number these vectors r1, r2, r3, r4. • Applying the identity operation we obtain: which is a unit matrix with character χ (E) = 4 (all 4 vectors map onto themselves). • If we rotate the set of vectors by 2π/3 about the C3 axis which is coincident with r1 we get χ (C3) = 1 (only r1 maps onto itself): • The character of the matrix of the coefficients here χ (C3) = 1 • Proceeding in the same way for C2, S4 and σd we obtain the ligand AO representation Γtetra . • Reference to the Td character table shows that the Γtetra representation can be reduced to Γtetra = A1 + T2 (….irreducible representations) • This means that the four σ MO’s must be chosen so as to include an orbital of A1 symmetry and a set of three orbitals belonging to the T2 representation. • The character table also tells us that AO’s of the central metal atom falling into these categories are A1 orbitals s (x2 + y2 + z2) • T2 orbitals px, py, pz dxy, dxz, dyz We therefore see that to form a complete set of tetrahedrally directed σ bonds, the central metal atom will have to provide an s orbital, as well as a set of p or d orbitals, or both. Γtetra = A1 + T2 Construction of SALCs for σ bonding in Td complexes • Consider first the A1 SALC. It must have the same symmetry of the s orbital on the central metal atom. This requires that it be everywhere positive and unchanged by all symmetry operations A1 (s) = σ1 + σ2 + σ3 + σ4 • The T2 SALC’s must match the symmetries of the p orbitals, i.e. must have positive amplitude where the p orbital is positive and negative amplitude where the p orbitals are negative σ4 (pz) = σ1 - σ2 - σ3 + σ4 T2 (px) = σ1 - σ2 + σ3 - σ4 pz px σ1 σ3 σ2 (py) = σ1 + σ2 - σ3 - σ4 • Note: A1 has zero nodes whereas T2 has one node. py • We are now in a position to form the MO’s by allowing overlap of the AO’s on A with the SALCs of corresponding symmetry on the four B atoms. • In each case we may bring the central orbital and the SALC together to give positive and negative overlap thus forming bonding and anti-bonding MO’s respectively. Steps for construction of MO correlation diagram for transition metal complexes 1. Firstly determine metal oxidation state and calculate metal and ligand electron counts. 2. Draw the metal valence atomic orbitals, e.g. 3d, 4s and 4p orbitals (coordinates may be chosen arbitrarily but must be kept consistent throughout). Assign Mulliken symbols from point group character table. Check for proper assignments by degeneracy requirements. 3. Draw ligand SALC’s Assign Mulliken symbols from irreducible representations. Check for proper assignments by degeneracy requirements. 4. Match ligand irreducible representations with metal atomic orbitals for σ and π bonding interactions. 5. Check for non-bonding metal/ligand orbitals. 6. Construct MO correlation diagram 7. Fill electrons and check with original metal/ligand electron count in step 1. Character table for the Td point group MO description of σ only bonding in a Td transition metal complex Metal valence orbitals The tetrahedral geometry is electronically favored by d4 or d10 metal complexes where the non-bonding orbitals are either 1/2 or entirely filled, respectively. Symmetry adapted linear combinations (SALCs) of ligand bonding orbitals Character table for the Oh point group X2 + y2 + z2 MO description of σ only bonding in an Oh transition metal complex Metal valence orbitals σ-bonding Symmetry adapted linear combinations (SALCs) of ligand bonding orbitals Summary of π-bonding in Oh complexes π donor ligands result in L→M π bonding, a smaller ∆o favoring high spin configurations and a decreased stability. π acceptor ligands result in M→L π bonding, a larger ∆o favoring low spin configurations with an increased stability. Character table for the D4h point group Γσ = A1g + Eu + B1g MO description of σ only bonding in a square planar D4h transition metal complex Metal valence orbitals σ-bonding Symmetry adapted linear combinations (SALCs) of ligand bonding orbitals

Molecular Orbitals for σ Bonding in Td Complexes

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