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Handout-6 Course 201N 1st Semester 2006-2007 Inorganic Chemistry Instructor: Jitendra K. Bera Contents 2. Coordination Complexes of Transition Metal Ions Magnetic properties of coordination complexes Molecular Orbital Theory of Coordination Complexes Magnetization and Magnetic Susceptibility If a body is placed in a homogeneous field, H0, the field within the body varies from the free space value. The scheme below defines some of the terms that are often used in the field of magnetochemistry. Chemists often prefer to measure mass rather than volume, and to use moles rather than grams. Hence, molar magnetic susceptibility χM is usually reported. The sign of the induced magnetization (M) defines two basic types of magnetic behavior. If M (or χ) is negative, it is Diamagnetism; if M (or χ) is positive, it is Paramagnetism. In a field gradient, diamagnet moves out of field to lower energy (χ < 0) and paramagnet moves in to field to lower energy. Compounds with only paired electrons are diamagnetic and compounds with unpaired electrons are paramagnetic. The ferromagnetism, anti-ferromagnetism and ferrimagnetism are special forms of paramagnetism that are outside the scope of this course. Typically χpara values are higher than χdia. The χM values of diamagnetic N2 and paramagnetic O2 illustrate this fact. All substances have a diamagnetic component to the susceptibility. The observed χobs includes the contribution from both χpara and χdia. Paramagnetism: It arises from the interaction between H0 and the magnetic field of the unpaired e’s associated with their spin and orbital angular momenta. In a hypothetical free ion or atom, both the orbital and spin angular momenta give rise to a magnetic moment and contribute to paramagnetism. When the atom or the ion is part of a complex, orbital angular momentum may be eliminated (or quenched). We shall discuss the quenching of the orbital contribution later. However, the spin angular momentum survives and gives rise to spin-only paramagnetism which is characteristic of many d-metal complexes. The magnitude of the spin magnetic moment of an electron is provided in the right. Curie Law: The Curie law relates the molar magnetic susceptibility χM as a function of temperature. In Curie equation, N is Avogardro’s number, k is Boltzmann constant, g is the gyromagnetic ratio, and β is Bohr magneton. A simplified form of Curie Law: χM = C/T which describe the inverse dependence of χM with temperature T. Here C is a constant that is characteristic of the substance and known as Curie constant. The values of C for different ‘S’ values can be calculated from the Curie equation. For S=½, 1, 3/2, 2 and 5/2, the calculated values of C are 0.375, 1.0, 1.88, 3.0 and 4.375 emu K/mol. Experimentally, if we measure χM of a substance at different temperature and plot χMT values against T, we shall obtain a straight line that would intersects the y-axis at the value C. The experimental C value would provide information on the number of unpaired electrons in the system. Effective magnetic moment: It is a convenient parameter (µeff) (hugely popular among inorganic chemists) that is related to χM. The ‘µeff’ is defined as: (µ µeff)2 = g2 S(S+1) β2 If g=2, It can also be expressed in terms of number of unpaired electrons: The µeff is related to the χMT values: To recapitulate, one first makes a direct measurement of the volume susceptibility of a substance from which χM is calculated, and the above equation allows one to deduce the magnetic moment of the ion, atom or molecule responsible for the paramagnetism. The µeff, however, can be calculated very easily if we know the number of unpaired electrons in the system. Ion Ti3+ V3+ Cr3+ Mn3+ Fe3+ # of unpaired electrons (n) 1 2 3 4 5 S ½ 1 3/2 2 5/2 Predicted µeff values √3 = 1.73 √8 = 2.83 √15 = 3.87 √24 = 4.90 √35 = 5.92 Inferring electron configuration from magnetic moment: 1. The magnetic moment of an octahedral co(II) complex is 4.0 BM. What is its electron configuration? Answer: A Co(II) complex is d7 system. The two possible configurations are t2g5eg2 (high-spin) with three unpaired electrons or t2g6eg1 (low-spin) with one unpaired electron. The spin-only values would be 3.87 and 1.73 BM. Therefore, the only consistent assignment is the configuration t2g5eg2, which means a high-spin complex. 2. The magnetic moment of the complex [Mn(NCS)6]4- is 6.06 BM. What is its electron configuration? - A Mn(II) complex is d5 system. The magnetic moment value suggests an electron configuration t2g3eg2, that means it is a high-spin complex. 3. The anion [Ni(SPh)4]2- is tetrahedral. Explain why it is paramagnetic. – The Ni(II) is d8 system. In a tetrahedral environment the electron configuration should be e4t24 containing two unpaired electrons. Hence it is paramagnetic. On contrary, [Ni(CN)4]2- is diamagnetic as it adopts a square planar geometry and all eight d-electrons are paired up. 4. The complexes NiCl2(PPh3)2 and PdCl2(PPh3)2 are paramagnetic and diamagnetic respectively. The structure of these two complexes can be assigned from the magnetic data. Both the Ni(II) and Pd(II) are d8 ions. The PdCl2(PPh3)2 should have a square-planar geometry and NiCl2(PPh3)2 have a tetrahedral structure with two unpaired electrons. 5. Take two examples of K3[CoF6] and [Co(NH3)6]Cl3. The first one is a high-spin complex with ground state electron configuration t2g4eg2 and the complex is paramagnetic. The second complex is diamagnetic indicating it as a low-spin complex with electron configuration t2g6eg0. Orbital contribution to magnetic moments: From a quantum mechanics viewpoint, the magnetic moment is dependent on both spin and orbital angular momentum contributions. The spin-only formula used is given as: µs.o. = √{4S(S+1)} and this can be modified to include the orbital angular momentum as follows: For orbital angular momentum to contribute, and hence for the paramagnetism to differ significantly from the spin-only value, the orbital in which electron resides must be able to transform the orbital it occupies into an equivalent and degenerate orbital by a simple rotation (it is the rotation of the electrons which induces the orbital contribution). In a free ion, the five d-orbitals are degenerate and some orbitals can be transformed into others by rotations. The figure at right illustrates that a 90° or 45° rotation about z-axis transform dxz↔dyz and dxy↔dx2-y2 orbitals respectively. In an octahedral complex, due to crystal field splitting, the degeneracy between the dxy and dx2-y2 orbitals is lifted. It causes the partial quenching of the orbital contribution. There is a further factor that needs to be taken into consideration: if all the t2g orbitals are singly occupied, an electron in, say, dxz orbital cannot be transferred into dyz orbital because it already contains an electron having the same spin quantum number as the incoming electron; if all the t2g orbitals are doubly occupied the transfer is not possible. Thus only configurations which have t2g electron other than three or six electrons make orbital contributions to the magnetic moments of octahedral complexes: for high-spin complexes, only the configurations t2g1, t2g2, t2g4eg2 and t2g5eg2. Note that eg electrons do not contribute to orbital moment. For tetrahedral geometry it is easily shown that the configurations giving rise to an orbital contribution are e2t21, e2t22, e4t24 and e4t25. It is evident from this discussion that in most cases the orbital moments are quenched in metal complexes and magnetic moments are close to the spin-only value. The tables below give a list of spin-only and spin+orbital magnetic moments with experimental data for d1 to d9 configurations. An example helps to understand the quenching of orbital moment in different metal complexes. Lets consider Ni(II) (d8) complex. As a free ion, the total magnetic moment µs+o is calculated to be 4.47. In octahedral d8 complex, the orbital contribution is zero. On the contrary, d8 tetrahedral complex will have contribution from the orbital magnetic moment. Hence, although both complexes have two unpaired electrons, the [Ni(H2O)6]2+ has magnetic moment close to the spin-only value but the magnetic moment in [NiCl4]2is higher than the spin-only value. Orbital contribution zero. Magnetic moment is close to the spin-only value. Magnetic moment is higher than the spin-only value as there is positive orbital contribution Molecular Orbital Theory of Coordination Complexes Limitations of Crystal Field Theory. Although Crystal Field theory accounts for many features of complexes including their color it still leaves some facts unexplained. The color of compounds like KMnO4 (Mn7+ has no d electrons) cannot be explained. One of the important experimental facts is the spectrochemical series where many anionic ligands turn out to be quite weak field ligands (H2O > OH-). Also quite strangely neutral ligands and very weak or even poor Lewis bases (for example CO) turn out to be extremely strong field ligands. The above is quite contrary to the Crystal field theory assumption of an electrostatic interaction between the metal ion and the ligand. In addition there is direct experimental evidence that suggests quite strongly that in fact the metal orbitals overlap with the ligand orbitals. One such evidence is found from EPR (Electron Paramagnetic Resonance) experiments. EPR is very similar to NMR except that instead of the nuclear spin the electron spin is the focus of investigation. Thus a species with one unpaired electron would behave in a very similar way as nucleus with a spin of ½. If the crystal field theory is correct, an unpaired electron present on a metal should be localized on it (remember that CFT does not permit overlap between metal and ligand orbitals) and a single absorption should be seen. If however, the electron is delocalized (even partly) into the ligand orbitals also, and if the ligand atoms can couple with the electron spin, a hyperfine structure should be seen in the EPR spectrum. In fact this is what is observed in a number of cases. This means that it is important to look into the overlap between the metal and the ligand orbitals. This can be done by looking at the molecular orbital picture of metal complexes. Complexes in which metal-ligand σ-bonding is involved. As an example for the above type of situation let us choose the complex [Co(NH3)6]3+. This complex contains NH3 as the ligand which can only participate as a σ-donor to the metal ion (The nitrogen atom does not have any low lying orbitals to participate in any additional type of bonding). How do we construct the molecular orbital diagram for this complex? We can use simple symmetry arguments to come out with a picture that would be understandable. Let us first consider the metal orbitals. The valence orbitals available are 3d, 4s, and 4p. So a total of 9 orbitals are available. Which of these orbitals are suitable to be used in σ-bonding? Remember that we are constructing a molecular orbital diagram for an octahedral complex. This means that the orbitals that we can use should have their lobes pointed along the axes (In order to have a positive and head-on overlap with the ligand orbitals). Obviously the 4s orbital is quite suitable. This is labeled a1g (look handout-4 for the interpretation of different representation symbols). All the 4p orbitals are also suitable (px, py, pz are along the x, y and z directions). These are labeled as t1u. Now let us inspect the 3d orbitals. Only two of them are suitable. The orbitals dx2-y2 and dz2 are suitable since they have the lobes along the axes. These are labeled eg ; we have seen them before!!!) However, the orbitals dxz, dyz and dxy are not suitable since ligand orbitals cannot overlap with them to give a positive overlap. These cannot be, therefore, utilized by the metal for σ-bonding. These remain non-bonding and are labeled as t2g. Thus we conclude that of the 9 valence orbitals of the metal six are suitable for forming σbonding (a1g, t1u, eg) and three are non-bonding orbitals (t2g). Let us assume that by a linear combination of the ligand orbitals (one from each ligand) we are able to generate six orbitals of similar symmetry, called as ligand group orbitals (LGO’s) as that of the six metal bonding orbitals . These orbitals on the metal and the ligand now can combine to afford the M. O diagram as shown below. The salient features of the above M. O. diagram can be summarized as follows: The lowest energy orbitals a1g, t1u, eg are closer in energy to the ligand orbitals. The t2g orbitals remain non-bonding and their energy is not changed after forming the M.O.’s The higer energy orbitals a1g*, t1u*, eg* are closer in energy to the metal orbitals. The energy separation between the non-bonding t2g and the eg* orbitals represents the ∆o of the crystal field diagram. As before, if this separation is large, low-spin complexes are formed. If the separation is small, high spin complexes are formed. Thus, [Co(NH3)6]3+ ( Co3+ has six electrons; six ammonia ligands contribute twelve electrons) has the electronic configuration, a1g2, t1u6, eg4, t2g6. In contrast [CoF6]3- has the configuration a1g2, t1u6, eg4, t2g4 eg*2. Notice that the filling of the lower energy orbitals a1g2, t1u6, eg4is reminiscent of the valence bond treatment and the filling of the higher energy orbitals t2g6 (for the cobalt hexammine complex) or t2g4 eg*2 (for the cobalt hexafluoride) is reminiscent of the crystal field treatment. π-bonding involving π-donor ligands Ligands like halides or hydroxide, in spite of being ionic, are found in the lower end of the spectrochemical series. The M. O. theory has a more satisfactory answer to their position. Consider, F-. In addition to acting as a σ-donor this ligand can also act as a πdonor. We have already seen the σ-bonding picture. If we have to utilize the metal orbitals for π-bonding we have seen that only the t2g orbitals are available. These can be utilized for π-bonding by forming LGO’s of the same symmetry. However, note that the t2g set of LGO’s will be lower in energy in comparison with the metal orbitals, because of the greater electronegativity of F- ligands. Consequently, the π-overlap between the metal and ligand orbitals will give rise to an energy diagram where the metal t2g orbitals will be raised in energy (now they will be called t2g*). As a result the gap between these orbitals and the eg* orbitals is decreased compared to the pre π-bonding situation. Because of this, high spin complexes result. π-bonding involving π-acceptor ligands Ligands such as CO, PR3 etc., can form σ-bonds with metals similar to ammonia. Unlike ammonia, which does not have any vacant orbitals to receive electron density, CO and PR3, however have vacant orbitals of the suitable symmetry to form π-bonds with the metal. However, since these orbitals are empty, they will be higher in energy in comparison to the metal t2g orbitals with which they have to overlap to form the π-bonds. Consequently the metal t2g orbitals are lowered in energy after formation of the π-bonds. The result is that the energy separation between the t2g and the eg* orbitals is increased after π-bond formation. Note that although the t2g orbitals (LGO’s) of the ligand are raised after the π-bond formation it does not matter as these remain empty. Thus the formation of the π-bond explains quite readily the intriguing fact that neutral and weakly Lewis Basic ligands such as CO and PR3 are found in the higher end of the spectrochemical series. A single scheme below illustrate the effect of both the π-donor and π-acceptor ligands.