PAPER No.7 : Inorganic Chemistry-II MODULE No.1 : Crystal Field Theory

Transcription

1 Subject Chemistry Paper No and Title Module No and Title Module Tag 7, Inorganic Chemistry II 1, Crystal Field Theory CHE_P7_M1

2 TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction to Crystal Field Theory 3. Octahedral Crystal Field Splitting 3.1 Crystal Field 3.2 Octahedral Crystal Field 3.3 Electrons in Orbitals 4. Spectrochemical Series 4.1 Role of Spectrochemical series in Crystal Field Splitting 5. Summary

3 1. Learning Outcomes After studying this module, you shall be able to Know the splitting pattern of d orbitals in octahedral crystal field. Learn why splitting takes place. Identify the strong and weak field ligands. Evaluate the extent of splitting in octahedral complexes. 2. Introduction Crystal field theory was developed by Hans Bethe and Van Vleck in the year 1929 and 1935, respectively. It was developed since the earlier Valence Bond Theory can only rationalize geometry and magnetic properties of the coordination metal complexes on a simple level but cannot say anything about their electronic spectra (color), why some ligands lead to high spin and some to low spin complexes and why low spin d 6 complexes are kinetically inert etc Octahedral Crystal Field Splitting 3.1 Crystal field For a given coordination metal complex having d or f electrons, the overall energy can be represented in the form of Hamiltonian operator as H = H 1+H 2+H 3, where H 1 represents the ligand field term, H 2 is the inter-electronic repulsion and H 3 is the spin-orbit coupling parameter. The crystal field theory suggests that most appropriate value for the above Hamiltonian can be calculated, byassuming the metal ion and all the surrounding ligands aspoint charges so that theterm H 1 will purely be of columbic nature taking care of the electric field gradient interacting with the central metal cation. The H 2 term is for the columbic repulsions between the electrons, as well as their exchange parameters. The term H 3 in general accounts for spin and orbital coupling of the angular momentum of the d or f electrons. The name, crystal field, has been given since it was originally developed for studying the optical properties of crystalline solids.

4 In an isolated gaseous free metal ion all the five d orbitals have same energy and are called degenerate orbitals since the probability of electron occupying any of these orbitals is the same (Figure 2) During complex formation, the approach of ligands towards the metal ion perturbs its electric field, due to electron cloud on the ligands itself (columbic repulsive forces between two set of electrons), which tends to alter the energy level of the d orbitals. If all the ligands approaching the metal ion are equidistant, these generated symmetrical or spherical field, it raises the energy level for all the d orbitals to the same extent but degeneracy of the orbitals is maintained. However, if the metal ion is placed under asymmetrical field due to different orientations of the d orbitals their degeneracy is lifted and these split into two sets. Considering the shape of various d-orbitals it can be seen that the orbitals having lobes directed along the direction of approach of the ligands, will be repelled to greater extent relative to those directed away from the ligand. Thus the energies of all the five d orbitals will not be same, rather it splits up and the splitting of five degenerate orbitals into two sets of orbitals having different energy is known ascfs or crystal field splitting. 3.2 Octahedral Crystal Field Figure 1 In an octahedral ligand field, six ligands approach the central metal ion from all the six directions of the three coordinate axis. The d x2-y2 and d z2 orbitals are directed along the axis while d xy, d xz and d yz lies in between x,y and z axes.. In this field, the greater repulsion between electrons in a metal d x2-y2 or d z2 orbital and the electron pair from ligand, raises the energy of metal orbitals than other three. Thus the d orbitals split up into t 2g and e g where t 2g comprises of three orbitals of lower energy namely d xy, d xz and d yz and e g set having d x2-y2 and d z2 of higher energy (Figure 2).

5 Figure 2 It is also noticeable that the splitting of orbitals occurs in such a way that the overall energy of the system remains constant, since the total increase in the energy of e g orbitals and decrease in energy of the t 2g orbitals from the Barry centre is same. The crystal field energy is represented by the symbol Δ o or 10D qand it defines the crystal field strength of ligands. It means higher the strength of the ligand greater will be the value of this splitting energy. Now it can also be noted that in case of the octahedral complexes the energy of t 2g level goes down by 0.6 Δ o and the value of e g level goes up by 0.4 Δ o, thus making overall energy again equal to zero (Figure 3).

6 3.3 Electrons in Orbitals Figure 3 For the octahedral case, the electrons are filled from lower (d xy,d xz,d yz) to higher (d x2-y2, d z2) energy orbitals according to the Aufbau principle. Following Hund's rule, electrons are filled in order to have the highest possible spin multiplicity as possible which means the arrangement should have maximum number of unpaired electrons. For example, in the case of a d 3 complex, in total there are three unpaired electrons. Now with the addition of one more electron to the system, the electron has an option to occupy a higher energy orbital (d z² or d x2-y2) or to get paired up with an electron residing in the d xy, d xz, or d yz orbitals. This pairing of electrons requires energy (spin pairing energy). If the pairing energy is less than the crystal field splitting energy, o, then the next electron will enter into the d xy, d xz, or d yz orbitals due to higher stability and allows minimum unpaired electrons, and called aslow spin.if pairing energy is more than o, then the next electron will enter into the higher energy d z2 or d x2-y2 orbitals as an unpaired electron. This situation is opposite to last one and called as high spin (Figure 4). The ligands that cause a transition metal to have a small crystal field splitting and leads to high spin are called weak-field ligands, while those producing large CFS and known as strong field ligands. Figure 4 Similarly with d 5, d 6 and d 7 cases we can have either a low spin or a high spin complex as shown below (Figures 5, 6, 7).

7 Figure 5 Figure 6

8 Figure 7 Once we move to the case of d 8, d 9 and d 10 systems, it can be seen that in all these cases electrons can only be filled in only one way which leads to same configuration in high and low spin complexes. It is also notable that in a similar way when we consider d 1, d 2 and d 3 cases, again there is only possibility (single configuration) whether we consider high or low spin complexes. 4. Spectrochemical Series 4.1 Role of the spectrochemical series in crystal field splitting CFT is primarily based on the arrangement of the ligands about the central metal/ion and ligand field effects. Once the electrons of the ligand interact with those of electron of the d-orbitals, electrostatic interactions may cause the energy levels of d-orbitals to alter with orientation. Ligands are classified as strong or weak based on their position in the spectrochemical series: I - < Br - < S 2- < SCN - < Cl - < NO 3- < F - < OH - < C 2O 4 2- < H 2O < NCS - < CH 3CN <NH 3<en<bipy<phen< NO 2- < PPh 3< CN - < CO Table-1 The ligands lying on the left side of the series are called weak field whereas those lying on the right side are known as the strong field ligands. Thus spectrochemical series can be described as the arrangement of ligands in a particular sequence such that the ligands on the left side of the series are those which have low splitting tendency (weak field) and thus form high spin complexes, whereas the ligands on the right side

9 are those which have greater splitting tendency (strong field) and thus form low spin complexes (Table 1). Consider the complexes [Co(NH 3) 6] 3+ and [CoF 6] 3-, based on Co metal in the (+3) oxidation state, both complexes have octahedral geometry but the complex with NH 3 as the ligands forms a low spin diamagnetic complex (where all the electrons are paired up) whereas the one with F forms a high spin complex. This can be explained on the basis of different splitting ability of the coordinated ligands i.e, NH 3 and F - with the same metal ion. Here NH 3 is a strong field ligand that leads to high amount of crystal field splitting and thus leads to low spin complexes, whereas F - is a weak field ligand, creates lower amount of splitting and thus forms high spin paramagnetic complexes. 5. Summary Crystal field theory was developed by Hans Bethe and Van Vleck in year 1929 and 1935 respectively. It was developed because Valence Bond Theory was unable to rationalize the electronic and magnetic properties of the complexes. The name has been given since it was originally developed to account for the optical properties of the crystalline solids. The five d orbitals split up into two sets of orbitals under the influence of ligand field. The d- orbitals split up into two sets of orbitals namely t 2g and e gwhere t 2g comprises of three orbitals of lower energy namely d xy, d xz and d yz and e g set having d x2-y2 and d z2 orbital of higher energy The crystal field energy is represented by the symbol Δ o and it defines the crytal field strength of the ligands. Electrons are filled from lower (d xy, d xz, d yz) to higher (d x2-y2, d z2) energy orbitals according to the Aufbau principle and Hund's rule where electrons are filled in orbitals in accordance with highest spin multiplicity. Ligands are classified as strong or weak based on their position in the spectrochemical series The ligands lying at the extreme left side of the series are called weak field whereas those at the right side of the series are called strong field ligands