1. 1Chemistry 2C Lecture 12: April 26 st, 2010 Lecture 12:Transition Metals I.Spectroscopy II.Crystal Field Theory (CFT) III.High Spin and Low Spin Configurations IV.Spectrochemical Series (strong and weak ligands) V. Absorption Spectra

2. 2Chemistry 2C Lecture 12: April 26 st, 2010 Optical isomers are identical with respect to ordinary chemical reactions, but differences arise when they are in the presence of other chiral molecules. For example, spearmint leaves and caraway seeds respectively contain L-carvone and D-carvone - enantiomers of carvone. These smell different to most people because our taste receptors also contain chiral molecules which behave differently in the presence of different enantiomers. Optical isomers are called this because of their ability to rotate linear polarized light in opposite directions. Optical Isomers

3. 3Chemistry 2C Lecture 12: April 26 st, 2010 The brilliant array of colors observed in transition metal complexes can explained with a rather simple “bonding theory” called Crystal Field Theory, which is based on electrostatic rather than covalent bonding, but it works well to explain colors and magnetism. Colors and Magnetism Other bonding theories exist, e.g. valence bond (VB) theory, ligand field (LF) theory, molecular orbital (MO) theory etc. Empirically, different ligands cause different colors, as mentioned before, [Cu(H 2 O) 4 ] 2+ is a pale blue and [Cu(H 2 O) 4 ] 2+ is a dark blue. So why?

4. 4Chemistry 2C Lecture 12: April 26 st, 2010 For a compound to have a color, it must absorb visible light! Spectroscopy R White light consist of all visible colors. These can be separated with dispersive elements like prisms or diffraction gratings. OYGBIV Red Orange Yellow Green Blue Indigo Violet

5. 5Chemistry 2C Lecture 12: April 26 st, 2010 Visible light is just a small part of the Electromagnetic Spectrum The Electromagnetic Spectrum

6. 6Chemistry 2C Lecture 12: April 26 st, 2010 Quantum Mechanics A compound absorbs light when radiation had the right energy to move electron from a low energy level to a higher lower one. Its energy is given by the resonance condition: Spectroscopy and quantum mechanics are intimately related! Transition up Transition down The higher energy photons are blue, the lower energy photons are red

7. 7Chemistry 2C Lecture 12: April 26 st, 2010 Quantum Mechanics The color we perceive is the sum of the remaining colors (those not absorbed). 490 430 800400 580 620 560 y v g b r o If a compound absorbs all wavelengths of visible light, it appears black. If a compound absorbs no wavelengths of visible light, it appears white. If a compound absorbs blue of visible light, it appears orange. If a compound absorbs X color of visible light, it appears the complimentary color (via color wheel). Complimentary colors are opposites. If a compound absorbs violet @ 420 nm of visible light, it appears yellow.

8. 8Chemistry 2C Lecture 12: April 26 st, 2010 Quantum Mechanics The amount of light absorbed as a function of wavelength is called the “absorption spectrum” of the sample. Plants are green because of the absorption of red by chlorophyll molecules

9. 9Chemistry 2C Lecture 12: April 26 st, 2010 Magnetism Related directly to number of unpaired electrons in sample!! [Co(CN) 6 ] 3- Is diamagnetic (repulsed from magnets), thus, no unpaired e- [CoF 6 ] 3- This complex has four unpair e- and is paramagnetic (attractive to magnets) Contrast two Co complexes: Both complexes have Co(III) ions, and thus a [Ar]3d 6 electronic configuration How to explain?

10. 10Chemistry 2C Lecture 12: April 26 st, 2010 d-orbitals d z2 Orbitald x2-y2 Orbitald xy Orbital d xz Orbitald yz Orbital http://www.chemsoc.org/viselements/orbital/orbital_d.html

11. 11Chemistry 2C Lecture 12: April 26 st, 2010 Let’s talk about d-orbitals The d orbitals are very complex. There are five orbitals in total and each orbital can take two electrons which means that the d manifold can take 10 electrons. d xy Orbital d xz Orbital d yz Orbital They are all equal in 5-D space, but can be represented in many ways in 3-D space. Chemistry always use this designation. These three orbitals are mutually perpendicular and look just the same (but not the coordinate system). The lobes are either given signs (+ or -) or different colors (black or grey) to signify the sign of the “wavefunction” in that region.

12. 12Chemistry 2C Lecture 12: April 26 st, 2010 Let’s talk about d-orbitals d xy Orbital d xz Orbital d yz Orbital The orbitals represent the probability of finding an electron in the region observed (ignore the phase or color of orbital in this matter). The orbitals may have a zero probability as points, or lines, which are called nodes!

13. 13Chemistry 2C Lecture 12: April 26 st, 2010 Let’s talk about d-orbitals The last two are slightly funny. d z2 Orbital d x2-y2 Orbital These last two have lobes that are pointed along the X, Y, and Z axis. This is in contrast to the previous three d orbitals!

14. 14Chemistry 2C Lecture 12: April 26 st, 2010 Field Splitting What happens to the d-orbitals in a Electric field from the ligands? vacuum Energy All five orbitals have the same energy in a vacuum (as you had seen before) d z2 d x2-y2 d xy d xz d yz d z2 d x2-y2 d xy d xz d yz All five orbitals have the same, but higher, energy in a perfectly spherical (isotropic) field. d z2 d x2-y2 d yz All five orbitals have different energies in an octahedral (anisotropic) field of size ligands. d xy d xz oo  o is the “crystal field splitting” due to the anisotropic ligand field

15. 15Chemistry 2C Lecture 12: April 26 st, 2010 Field Splitting  o is the “crystal field splitting” due to the anisotropic ligand field Notice that some are raised relative to the average, and some are lowered. The average energy in the anisotropic field must be the same as the average energy in a isotropic field, so for the octahedral field: d z2 d x2-y2 d xy d xz d yz d z2 d x2-y2 d yz d xy d xz Average 0.6  o 0.4  o These orbitals are destabilized by +0.6  o These orbitals are stabilized by -0.4  o If all the orbitals are filled, the net effect on the energy is (3 orbitals) * (2 electrons per orbital) * (-0.4  o ) + (2 orbitals) * (2 electrons per orbital) * (+0.6  o ) = 0 Isotropic Ligand Field Octahedral Ligand Field

16. 16Chemistry 2C Lecture 12: April 26 st, 2010 Background of Crystal Field Theory We know that the d-orbitals electrons participate in forming chemical bonds, but CFT doesn’t use this information. It’s a “theory” and not necessarily truth, which doesn’t exist in science anyway. Instead, we consider the d-electrons to belong to the metal. They occupy the d- orbitals according to the rules: Hund’s rule: Electrons will fill orbitals of identical energy without pairing first! (It costs energy to pair electrons!) Aufbau principle: Electrons are going to occupy the orbitals in the order that minimizes the overall energy of the atom or molecule! (Build up) CFT works because it gives a rationale for how this usually works in practice.

17. 17Chemistry 2C Lecture 12: April 26 st, 2010 Background of Crystal Field Theory CFT is a model based on electrostatics. To derive this model we must consider the d-orbitals to be filled with electron (although they aren’t necessarily) and the ligands represent a “field” of negative charge (although not necessarily fully ionic). Because electrons are negative, the ligand field is a repulsive situation.

18. 18Chemistry 2C Lecture 12: April 26 st, 2010 Field Splitting What happens to the d-orbitals in a Electric field from the ligands? vacuum Energy All five orbitals have the same energy in a vacuum (as you had seen before) d z2 d x2-y2 d xy d xz d yz d z2 d x2-y2 d xy d xz d yz All five orbitals have the same, but higher, energy in a perfectly spherical (isotropic) field. d z2 d x2-y2 d yz All five orbitals have different energies in an octahedral (anisotropic) field of size ligands. d xy d xz oo  o is the “crystal field splitting” due to the anisotropic ligand field

19. 19Chemistry 2C Lecture 12: April 26 st, 2010 Field Splitting  o is the “crystal field splitting” due to the anisotropic ligand field Notice that some are raised relative to the average, and some are lowered. The average energy in the anisotropic field must be the same as the average energy in a isotropic field, so for the octahedral field: d z2 d x2-y2 d xy d xz d yz d z2 d x2-y2 d yz d xy d xz Average 0.6  o 0.4  o These orbitals are destabilized by +0.6  o These orbitals are stabilized by -0.4  o If all the orbitals are filled, the net effect on the energy is (3 orbitals) * (2 electrons per orbital) * (-0.4  o ) + (2 orbitals) * (2 electrons per orbital) * (+0.6  o ) = 0 Isotropic Ligand Field Octahedral Ligand Field

20. 20Chemistry 2C Lecture 12: April 26 st, 2010 Crystal Field Theory Filling of the d-orbitals will proceed in order to give the lowest possible energy! 21 [Sc][Ar] 4s 2 3d 1 Sc +2 [Ar] 3d 1 (unstable) 22 [Ti][Ar] 4s 2 3d 2 Ti +2 [Ar] 3d 2 23 [V][Ar] 4s 2 3d 3 V +2 [Ar] 3d 3 24 [Cr][Ar] 4s 1 3d 5 Cr +2 [Ar] 3d 4 25 [Mn][Ar] 4s 2 3d 5 Mn +2 [Ar] 3d 5 26 [Fe][Ar] 4s 2 3d 6 Fe +2 [Ar] 3d 6 27 [Co][Ar] 4s 2 3d 7 Co +2 [Ar] 3d 7 28 [Ni][Ar] 4s 2 3d 8 Ni +2 [Ar] 3d 8 29 [Cu][Ar] 4s 1 3d 10 Cu +2 [Ar] 3d 9 30 [Zn][Ar] 4s 2 3d 10 Zn +2 [Ar] 3d 10 Z (nuclear charge)Metals Electronic Configuration+2 ionElectronic Configuration Remember the first 2 electrons come off the 4s orbital before the 3d orbitals! Q: How many d electrons in Ti 3+ ? Q: How many d electrons in Cr 3+ ? Q: How many d electrons in Cu + ? Q: How many d electrons in Fe 3+ ?

21. 21Chemistry 2C Lecture 12: April 26 st, 2010 Crystal Field Theory d z2 d x2-y2 d xy d xz d yz d z2 d x2-y2 d yz d xy d xz Consider the ion Cr 3+ : Isotropic Ligand Field Assuming an Octahedral Ligand Field, the electronic configuration looks like this (CFT): Its electronic configuration is [Ar] 3d 3 and hence has three d-orbital electrons Each orbital has one electron and no pairing. This is a particularly stable ion since the energy levels are half-filled! Energy= 3 * (-0.4  o ) + 0 * (+0.6  o ) = -1.2  o

22. 22Chemistry 2C Lecture 12: April 26 st, 2010 d z2 d x2-y2 d xy d xz d yz d z2 d x2-y2 d yz d xy d xz Now, consider the ion Cr 2+ or Mn 3+ : Isotropic Ligand Field Its electronic configuration is [Ar] 3d 4 and hence has Four d-orbital electrons Hund’s Rule: It takes energy, P, to pair electrons up in the same orbital! d z2 d x2-y2 d yz d xy d xz or Case 1: Total Energy = 4 * (-0.4  o ) + 0 * (+0.6  o ) + P = -1.6  o +P Case 1:Case 2: Case 2: Total Energy = 3 * (-0.4  o ) + 1 * (+0.6  o ) = -0.6  o

23. 23Chemistry 2C Lecture 12: April 26 st, 2010 d z2 d x2-y2 d yz d xy d xz Now, consider the ion Cr 2+ or Mn 3+ : For the low spin to be favored we must have: d z2 d x2-y2 d yz d xy d xz or -1.6  o +P < -0.6  o P< 1.0  o Case 1: (Low spin)Case 2: (High Spin) The pairing energy must be less than the crystal field splitting energy!

24. 24Chemistry 2C Lecture 12: April 26 st, 2010 Splitting the d-orbitals Strong field There exists a ligand dependence (upon keeping the metal constant), in the amplitude of  o called the “spectrochemical series:” CN - > NO 2 - > … > NH 3 > … > H 2 0 > OH - > F - The CF splitting,  o, is a function of both the metal and the ligands. Weak field d z2 d x2-y2 d yz d xy d xz d z2 d x2-y2 d yz d xy d xz [Fe(CN) 6 ] 3- [Fe(F) 6 ] 3- e.g. Fe +3 : [Ar] 3d 5 Strong Field LigandsWeak Field Ligands P <  o P >  o P is approx. constant in different systems

25. 25Chemistry 2C Lecture 12: April 26 st, 2010 Pretty Colors What makes transition metal complexes colorful is that the value of  o is in the range of visible light! d z2 d x2-y2 d yz d xy d xz For example: What is the splitting for [Ti(H 2 0)] 3+ if it absorbs at 510 nm? oo We can calculate the wavelength that will be absorbed by this complex!  o =h =hc/ c = 2.998 x 10 10 cm/s h = 6.626 x 10 -34 J · s  o =3.90 x 10 -19 J per electron  o =N a x 3.90 x 10 -19 J per mol of electrons  o =2.35 x 10 5 J per mol of electrons

26. 26Chemistry 2C Lecture 12: April 26 st, 2010 Not-so-Pretty Colors That was for Ti 3+, what about Ti 4+ ? d z2 d x2-y2 d yz d xy d xz There are no d-electrons in this transition metal, so visible light does not promote electrons from one d-orbital to another. Thus, it is not colored! It does however, absorb in the Ultraviolet, but our eyes are not good enough to see that! oo What about Zn 2+ ? d z2 d x2-y2 d yz d xy d xz There are no spaced for d-electrons in this transition metal, so visible light cannot not promote electrons from one d-orbital to another. It is colorless! oo

27. 27Chemistry 2C Lecture 12: April 26 st, 2010 Non-octahedral complexes CFT applied to complexes of any anisotropic ligand field, not just octahedral complexes! Tetrahedral case: The d xy-y2 and d z2 orbitals were destabilized because they were pointing directly toward the ligands in an octahedral complex d z2 d x2-y2 d yz d xy d xz oo Octahedral case: The ligands don’t point directly at the d- orbitals and a different splitting pattern is observed. d z2 d x2-y2 d yz d xy d xz tt Because of this, most tetrahedral complexes are high spin (max # of unpaired electrons since P >  t ). You can get five unpaired electrons in this system!