Crystal Field Theory

Crystal Field Theory

Crystal Field Theory Bonding model explaining many important properties of transition-metal complexes: colors, magnetism, structures, stability, and reactivity cannot be explained using valence bond theory.

Crystal Field Theory Central assumption of CFT: metal-ligand connections are electrostatic interactions btwn a central metal ion and a set of negatively charged ligands (or ligand dipoles) arranged around metal ion.

d-Orbital Splittings five d orbitals are initially degenerate (same energy). When the 6 (-) charges are distributed uniformly over surface of a sphere, d orbitals remain degenerate. But! Their energy will be higher due to repulsive electrostatic interactions btwn spherical shell of (-) charge & e-’s in d orbitals

d-Orbital Splittings If the 6 (-) charges are placed at vertices of an octahedron, avg energy of d orbitals does not change. But! It does remove their degeneracy and the five d orbitals split into two groups (eg & t2g) whose energies depend on their orientations to the ligands.

d-Orbital Splittings The dx2 – y2and dz2orbitals (eg orbitals) point directly at the six (-) charges, which increase their Energy compared with a spherical distribution of negative charge.

The dxy, dxz, & dyz (t2g orbitals) are all oriented at a 45º angle to the coordinate axes and point between the six (-) charges, which decreases their Energy compared with a spherical distribution of charge

d-Orbital Splittings Difference in energy btwn the two sets of d orbitals is the crystal field splitting energy. Given the symbol o, where the subscript “o” stands for “octahedral”

d-Orbital Splittings Magnitude of the splitting depends on: charge on metal ion position of metal in the periodic table nature of the ligands Splitting of d orbitals in a crystal field does not change total energy of the five d orbitals

Electronic Structures of Metal Complexes Using d-orbital energy-level diagram: electronic structures & some properties of transition-metal complexes can be predicted. Start with Ti3+ ion, (contains a single d electron), proceed across first row of transition metals by adding a single e- at a time.

Additional e-’s placed in lowest-E orbital available while keeping their spins parallel

For d1-d3 systems, e-’s successively occupy the 3 degenerate t2g orbitals with their spins parallel, giving one, two, and three unpaired electrons.

Electronic Structures of Metal Complexes d4 configuration: two possible choices for 4th e-: enter one of the empty eg orbitals or enter one of the singly occupied t2g orbitals

Spin Pairing Energy (P) is an increase in Energy (due to electrostatic repulsions) when an e- is put into an occupied orbital. If o is < P, then lowest-energy arrangement has 4th e- in an empty eg orbital. results in 4 unpaired e-’s and is called a high-spin configuration: a complex w/ this configuration is a high-spin complex

Electronic Structures of Metal Complexes If ois > P, lowest-energy arrangement has 4th e- in one of the occupied t2g orbitals, results in two unpaired electrons and is called a low-spin configuration. A complex with this e- configuration is called a low-spin complex.

Metal ions with d5, d6, or d7 e- configurations can be either high spin or low spin, depending on magnitudeof o

Factors That Affect the Magnitude of o • magnitude of o dictates whether a complex • with 4, 5, 6, or 7 d electrons is high spin or low spin: • Which affects its: • Magnetic properties • Structure • Reactivity

Factors That Affect the Magnitude of o Nature of the ligands For a series of chemically similar ligands, magnitude of o decreases as size of donor atom increases because smaller, more localized charges interact more strongly with d orbitals of the metal ion. A small neutral ligand with a highly localized lone pair results in larger o values

Nature of the ligands experimentally observed order of the crystal field splitting energies produced by different ligands is called: the spectrochemical series Strong-fieldligands interact strongly with the d orbitals of the metal ions and give a large o Weak-fieldligands interact more weakly and give a smaller o

Factors That Affect the Magnitude of o Charge on the metal ion Increasing charge on a metal ion has 2 effects: Both factors decrease metal-ligand distance, which causes (-) charged ligands to interact more strongly with the d orbitals. magnitude of o increases as charge on metal ion increases

Factors That Affect the Magnitude of o Principal quantum # of the metal For a series of complexes of metals from same group in periodic table with same charge and same ligands: magnitude of o increases with increasing quantum #:

Factors That Affect the Magnitude of o Principal quantum # of the metal o (3d) << o (4d) < o (5d) Increase in o w/ increasing principal quantum # is due to: larger radius of valence orbitals going down a column. Repulsive ligand-ligand interactions are important for smaller metal ions, which results in shorter M–L distances and stronger d-orbital-ligand interactions

Colors of Transition-MetalComplexes Striking colors exhibited by transition-metal complexes are caused by the excitation of an e- from a lower-lying d orbital to a higher-energy d orbital, which is called a d-d transition

For a photon to affect the d-d transition, its E must be = to the difference in E btwn the two d orbitals, which depends on the magnitude ofo which depends on the structure of the complex.

The energy of a photon of light is inversely proportional to its wavelength E = hc = hu l

Observedcolor is due to transmitted or reflected light that is complementary in color to light that is absorbed

Rubies & Emeralds both contain Cr3+ impurities in octahedral6-oxide environment. Host lattice causes differences in distances of d-orbital-to-ligand lengths. Rubies have a shorter distance, making Do large, so rubies absorb green light & transmit red.

Crystal field stabilization energy(CFSE): additional stability of metal complex by selective population of lower-E d orbitals (t2g orbitals). CFSE of a complex can be calculated by: multiplying # of e-’s in t2g orbitals by energy of those orbitals, and multiplying # of e-’s in eg orbitals by energy of those orbitals, and summing the two. CFSE is highest for low-spin d6 complexes

Tetragonal and Square-Planar Complexes If two trans ligands in an octahedral complex are either chem different from other four or a different distance from the metal than the other four, the result is a tetragonally distorted octahedral complex. Moving 2 axial ligands away from metal ion along z axis gives elongated octahedral complex & eventually produces a square-planar complex

Figure 23.13

Tetragonal and Square-Planar Complexes Axial elongation causes dz2, dxz, & dyz orbitals to decrease in energy and dx2–y2and dxy orbitals to increase in energy. D in energy is not the same for all five d orbitals.

Figure 23.13

Tetrahedral Complexes none of the five d orbitals points directly at or between the ligands. dxy, dxz, and dyzorbitals interact more strongly with ligands than do the dx2 – y2 and dz2orbitals, so order of orbital energies in a tetrahedral complex is opposite the order in an octahedral complex.

Figure 23.14b

Tetrahedral Complexes Splitting of energies of orbitals in tetrahedral complex, o,is smaller than in an octahedral complex for two reasons: d orbitals interact less strongly with ligands in a tetrahedral arrangement. Only four negative charges rather than six, which decreases electrostatic interactions

Figure 23.14a

Transition Metals in Biology

Uptake and Storage of Transition Metals 3 possible dietary levels for any essential element: deficient, optimal, and toxic. 3 distinct steps involved in transition-metal uptake: Mobilization: metal must be “mobilized” from environment & brought into contact with cell in a form that can be absorbed. Transport: metal must be transported across cell membrane into cell. Transfer: element must be transported to its point of utilization within cell or to other cells within the organism.

Process of iron uptake Siderophores: Organic ligands used by bacteria. (Cyclic compounds that use bidentate ligands) Have high affinity for Fe() Are secreted into surrounding medium to increase total concentration of dissolved iron. Otherwise Fe(OH)3is insoluble at higher pH. Look for lone pairs on N, O or, S.

MetalloproteinsandMetalloenzymes Metalloprotein = protein containing one or more metal ions tightly bound to amino acid side chains. Metalloenzyme = metalloprotein that catalyzes a chem rxtn. Important compounds in synthesis, duplication, & repair of DNA & RNA.

Crystal Field Theory