Metal-Ligand bonding in transition metal complexes

Valence Bond Theory A covalent bond forms between two atoms when an orbital on one atom overlaps with the orbital on another atom Total number of electrons on both orbitals is no more than two.

In transition metal complexes, covalent bonds are formed via overlap of a completely filled ligand orbital and a vacant hybrid orbital on metal ion. Hybridization determines the geometry of the molecule If geometry is known, the hybrid orbitals of the metal ion used in the bonding is known.

Hybrid orbitals for common geometries in complexes CN Geometry Hybrid orbitals 2 linear sp 4 tetrahedral sp3 4 square planar dsp2 6 octahedral d2sp3, sp3d2

                                                                           

                                                                           

                                                                           

                                                                           

Color and Magnetism Color of a complex depends on; (i) the metal, (ii) its oxidation state & (iii) ligands (i.e., everything) For example, pale blue [Cu(H2O)6]2+ versus dark blue [Cu(NH3)6]2+. Partially filled d orbitals usually give rise to colored complexes because they can absorb light from the visible region of the spectrum. The color of the complex is the sum of the light not absorbed (reflected) by the complex.

A plot of absorption intensity of light versus wavelength is called an absorption spectrum for the complex or compound. Since the spectrum for [Ti(H2O)6]3+ has a maximum absorption at 510 nm (green & yellow), & transmits all other wavelengths, the complex is purple.

Transition metal complexes that are paramagnetic have unpaired e-’s & those that are diamagnetic have no unpaired e-’s. Consider the d6 Co metal ion: [Co(NH3)6]3+ has no unpaired electrons, but [CoF6]3- has four unpaired electrons per ion. (note, s e-’s are lost first before d e-’s in a metal cation) We need to develop a bonding theory to account for both color and magnetism in transition metal complexes.

Crystal field theory (CFT) describes bonding & can account for many of the color and magnetic properties in transition metal complexes. Lewis A/B model assumes bonding results from ligand e-’s donated into hybridized d metal orbital. CFT assumes that the interaction between ligand & metal is electrostatic (pos. nuclei & neg. e-’s). Complex has lower E

Crystal-Field Theory An octehedral array of negative ligands shown as small (blue) dots approaching the five different d orbitals of a metal ion.

Crystal-Field Theory Although there is an overall reduction in E, the negative ligands repel d e-’s giving rise to a slight increase in E. The E gap is called D or the CF splitting E. Two of the five d orbitals are higher in E.

Crystal-Field Theory [Ti(H2O)6]3+

Cl- < F- < H2O < NH3 < en < NO2- (N-bonded) < CN- A Spectrochemical series is a listing of ligands in order of their ability to increase : Cl- < F- < H2O < NH3 < en < NO2- (N-bonded) < CN- Weak field ligands (Cl- & F-) lie on the low end of the spectrochemical series. Strong field ligands (CN-) lie on the high end of the spectrochemical series.

2 As Cr3+ goes from complexes with weak field ligands to strong field ligands,  increases and the color of the complex changes from green to yellow.

Octahedral Complexes Recall that the s e-’s are lost first for the metal ion. So, Ti3+ is d1, V3+ is a d?? and Cr3+ is a d?? ion. We apply Hund’s rule to the 2 sets of 5 d-orbitals. The first three e-’s go into different d orbitals with their spins parallel. We have a choice for the placement of the fourth electron: if it goes into a higher energy orbital, then there is an energy cost associated with promotion (); if it goes into a lower energy orbital, then there is an energy cost associated with e- spin pairing.

Weak-field ligands (which have a small D) tend to favor adding electrons to the higher-energy orbitals (high-spin complexes) because D is less than the spin-pairing energy. Strong-field ligands (which have a large D) tend to favor adding electrons to lower-energy orbitals (low-spin complexes) because D is greater than the spin-pairing energy.

Tetrahedral & Square-Planar In a tetrahedral field the dxy, dyz, & dxz orbitals are of higher E than the dx2-y2 and the dz2 orbitals. Because there are only 4 ligands,  for a tetrahedral field is smaller than  for an octahedral field. This causes all tetrahedral complexes to be high spin (unless told otherwise).

Figure 23.24A Splitting of d-orbital energies by a tetrahedral field of ligands. The splitting of d-orbital energies is less in a tetrahedral than an octahedral complex, and the relative d-orbital energies are reversed. Only high-spin tetrahedral complexes are known because Δ is small.

Square planar complexes can be thought of as octahedral complexes with the two ligands along the z-axis removed. As a consequence the four planar ligands are drawn in closer towards the metal. Relative to the octahedral field, the dz2 orbital is greatly lowered in energy, the dyz, and dxz orbitals lowered in energy, the dxy, and dx2-y2 orbitals are raised in energy.

Most d8 metal ions form square planar complexes. The majority of complexes are low spin (i.e. diamagnetic). Examples: Pd2+, Pt2+, Ir+, and Au3+.

Figure 23.24B Splitting of d-orbital energies by a square planar field of ligands. Square planar complexes are low-spin and usually diamagnetic because the four pairs of d electrons fill the four lowest-energy orbitals.

The Magnetic Properties of Transition Metal Complexes Magnetic properties are determined by the number of unpaired electrons in the d orbitals of the metal ion. Hund’s rule states that e- occupy orbitals of equal energy one at a time. When all lower energy orbitals are half-filled: - The next e- can enter a half-filled orbital and pair up by overcoming a repulsive pairing energy, (Epairing). - The next e- can enter an empty, higher, energy orbital by overcoming Δ. The number of unpaired e- will depend on the relative sizes of Epairing and Δ.

Figure 23.22 High-spin and low-spin octahedral complex ions of Mn2+.

Figure 23.23 Orbital occupancy for high-spin and low-spin octahedral complexes of d4 through d7 metal ions. high spin: weak-field ligand low spin: strong-field ligand high spin: weak-field ligand low spin: strong-field ligand

Sample Problem 23.6 Identifying High-Spin or Low-Spin Complex Ions PROBLEM: Iron (II) forms a complex in hemoglobin. For each of the two octahedral complex ions [Fe(H2O)6]2+ and [Fe(CN)6]4, draw an energy diagram showing orbital splitting, predict the number of unpaired electrons, and identify the ion as low spin or high spin. PLAN: Fe2+ electron configuration shows the number of d electrons, and the spectrochemical series shows the relative ligand strengths. We draw energy diagrams and separate the t2g and eg orbital sets more for the strong-field ligand. Then we add electrons, noting that a weak-field ligand gives the maximum number of unpaired electrons and a high-spin complex, whereas the strong-field ligand will give the minimum number of unpaired electrons and a low-spin complex.

Sample Problem 23.6 SOLUTION: t2g eg ↑↓ [Fe(CN)6]4- low-spin t2g eg ↑ Potential energy ↑↓ [Fe(CN)6]4- low-spin t2g eg Potential energy ↑ ↑↓ [Fe(H2O)6]2+ high-spin