THE BONDING IN VANADYL ION COMPLEXES

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1 THE BONDING IN VANADYL ION COMPLEXES

2 Abstract This chapter describes how the degeneracy of a d ion is split in octahedral crystal field. The energy levels of a vanadyl ion water complex have further been explained on the basis of ligand field theory. It has further been shown, how the electrons fill the different molecular orbitals, leading to an unpaired electron in the non-bonding b level and observance of EPR and optical absorption in such a complex. 43

3 3.1 The Vanadyl ion Vanadyl ion (VO + ) is the most stable cation among a few molecular paramagnetic metal ions and is used extensively as an impurity probe for electron paramagnetic resonance studies. Vanadyl complexes have been the subject of interest to a number of workers over recent years [1-5]. A vanadium ion has the electronic configuration of 3d 3 4s.In vanadyl ion, V + shares its two electrons with the oxygen, and the resulting configuration is therefore of 3d type and the VO + ion is equivalent to a V 4+ ion. The behaviour of unpaired electron in vanadyl complexes is dominated by strong V=O bonding as a result most of the complexes possess near octahedral, pyramidal symmetry. 3. d 1 ion in an octahedral field The vanadyl ion usually occurs in octahedral coordination with its surrounding atoms or ligands. This situation presents a configuration wherein a 3d ion is perturbed by a crystal field of O h symmetry. The five d orbitals involved in the coordination are given below : 44

4 1 d xy = (Ø Ø - ) 15 = R 3d (r). xy 1 d yz = (Ø 1 Ø -1 ) 15 = R 3d (r). yz 1 d zx = (Ø 1 + Ø -1 ) 15 = R 3d (r). zx 1 d x -y = (Ø + Ø - ) 15 = R 3d (r). (x -y ) 4 d zz = Ø 0 15 = R 3d (r). (z - x - y ) 4 45

5 where R 3d (r) is the radial wave function of a 3d electrons and m (m=,1,0,-1,-) are the spherical harmonics. These are illustrated graphically in Fig The unperturbed Hamiltonian H 0 relating to the free electron has complete spherical symmetry. However, if an entity of 3d 1 electron is placed in an electric field of symmetry O h then from the character table of O h point group [6], given in Table 3.1, the 3d z and 3d x -y orbitals transform according to E g representation and the trio d xy, d yz and d zx according to T g representation. The d z and d x -y point along the Cartesian axes, while d xy, d yz & d zx are directed between the axes. If the field of ligands is due to point negative charges, then the electrons in d xy, d yz, and d zx, will have a lower energy than those in d z and d x -y. The five d-orbitals which were degenerate before application of crystalline electric field as above are now split in O h symmetry, as per Fig.3.. Henderson and Imbusch [7] have further given the quantum mechanical treatment for energy splitting of 3d electrons under O h field, using the points ion model; and it is seen that five fold orbitally degenerate level splits into a two-fold degenerate E g level 46

6 and a three-fold degenerate T g level. The splitting between E g and T g levels equals 10 Dq with D and q defined as: D = 1 35Ze 0 4a 5 q = r d a being the identical distance of the six point charges of the octahedron from the 3d electron site. The crystal field transition T g E g can now occur, if all five d orbitals are not filled. This is a common feature among the hexa coordinated transition metal complexes. The agreement between the experimental values of Dq and those calculated as per formulae given, is however not satisfactory and reflects the crudeness of the point charge approximation in explaining the splitting of 3d-levels. A more rigorous model involving extended ligands is therefore necessary. Nevertheless, the point charge model describes the symmetry of the crystal field quite correctly. The three p- orbitals p x, p y and p z, however, remain degenerate under O h field, because these have exactly equivalent positions with 47

7 respect to the ligands of the octahedron. These p orbitals accordingly belong to the T 1u representation and the crystal field transitions involving individual p-orbitals, in a complex of O h symmetry, can not be observed. 3.3 The complex of vanadyl ion with water In VO (H O) 5 complex of vanadyl ion with water, the V 4+ is surrounded firstly by the oxygen of the vanadyl itself and five other oxygens of water groups. The situation is depicted in Fig. 3.3 [8, 9]. Such a complex has C 4V site symmetry. The corresponding character table is shown in Table 3.. In the above complex, out of the six V-O bonds, five are almost equal in length in the range.3 to.4 A o, the sixth V-O bond being however, quite short with a value around 1.67 A o. The transformation scheme under O h C 4V for various metal and ligand orbitals is given in Table 3.3. The two hybrid combinations of 3d z and 4s orbitals and p z orbital behave like the a 1 - representation of C 4V point group. The orbitals d zx, d yz and p x, p y behave like e - representation. The d x y behaves like b 1 - representation and d xy is of b type. Among the orbitals of ligands, the different combinations with required symmetry are also given in 48

8 1, 3, & 4 are used. Further p x, p y pair orbitals of oxygen shows up a -type orbital. Ballhausen & Gray [10] have given the C 4V symmetry molecular orbital picture of vanadyl ion bonded with five other oxygens belonging to water ligands. The formation of molecular orbitals is indicated in Fig In the left of this picture, we have the orbitals of vanadium - type s orbital of oxide - type sp hybrid orbitals of water oxygens & the -type (p x and p y ) orbitals of oxide (vanadyl) oxygen. The nature of - type is shown in Fig In view of sufficiently long V to O (water) bond lengths (.4 A o ) and further considering the alignment of water orbitals, the -bonding involving the vanadium orbitals and water oxygen seems unlikely and is thus ignored. The -bonding however, exists between the oxide oxygen and d xz, d yz pair orbitals. It is seen that metal and ligand orbitals of like symmetry ( represented as bonding and anti-bonding (indicated by an asterisk * ) orbitals. The bonding orbitals have lower energy compared to corresponding antibonding orbitals of higher energy. So far filling of orbitals by 49

9 electrons is concerned, the non-degenerate orbitals a 1, b 1 and b can occupy up to two electrons and degenerate e-orbitals up to four electrons. In Fig. 3.4, we have finally three a 1 -type bonding molecular orbitals (MOs) and similarly three anti-bonding MOs too. Coming to other representation, we have one set of b 1 -type bonding and antibonding orbitals and another set of e-type bonding and anti-bonding orbitals. The b type metal orbital, however remains uncombined and is thus called non-bonding MO. There are 17 electrons (5 of vanadium, 10 from five water ligands and from sixth vanadyl oxygen) involved in the process of filling the MOs of Fig In the figure, these electrons are indicated by dots ( ) and it is seen that the filling process leads to an unpaired electron in the b level. It is this electron which is responsible for observed EPR spectrum of vandayl ion complex and also for the optical absorption spectrum originating through the jump of this electron from b to e * and b * 1 levels. 50

10 3.4 References 1. Prem Chand, V.K. Jain & G.C. Upreti, Magn. Res. Rev. 14, 49 (1988).. G. Jayaram & V.G. Krishnan, Phys. Rev. B49, 71(1994). 3. K.V. Narasimhulu & J.Lakshmana Rao, Spectrochim. Acta. Part A, 53, 605 (1997). 4. R. Tapramaz, B. Karabulet & F. Kokoral, J. Phys. Chem. Solids 61, 1367 (000). 5. N.O. Gopal, K.V. Narasimhulu, C.S. Sunandana & J. Lakshmana Rao, Physica B307, 117 (001). 6. F.A. Cotton, Chemical Applications of Group Theory, Wiley Eastern Ltd., New Delhi, B. Henderson & G.F. Imbusch, Optical Spectroscopy of Inorganic Solids, Clarendon Press, Oxford, C.J. Ballhausen, Introduction to Ligand Field Theory, Mc. Graw Hill, New York, K.de Armond, B.B. Garrett & H.B. Gutowsky, J.Chem. Phys. 4, 1019 (1965). 51

11 10. C.J. Ballhausen & H.B. Gray, Inorg. Chem. 1, 111 (196). 11. A.K. Chandra, Introduction to Quantum Chemistry, Tata Mc Graw Hill, New Delhi,

12 Table 3.1 Character table for O h point group O h E 8C 3 6C 6C 4 3S I 6S 4 8S 6 3 h 3 d Simple Examples A 1g x +y +z A g A 1u A u E g z -r, x -y E u T 1g R x, R y, R z T 1u x,y,z T g xy,yz,zx T u Here x, y & z are displacements along x, y & z axes and R x, R y & R z are rotations about x, y & z axes respectively. 53

13 Table 3. Character table of C 4V point group C 4V E C 4 (z) C v d Simple Examples A A B B E z x +y, z R z - - x y - xy x,y yz, zx R x, R y Here x, y & z are displacements along x, y & z axes and R x, R y & R z are rotations about x, y & z axes respectively. 54

14 Table 3.3 Representation of metal and ligand orbitals in C 4V symmetry. Representation Vanadium orbitals Ligand orbitals a 1 3d z + 4s 5 4s 3d z ( ) / 4 p z 6 e 3d xz, 3d yz 5 (p x, p y ) 4p x, 4p y ( 1 3 ) / 4 ) / b 1 3x y ( ) / b 3d xy -- 55

LECTURE 2 DEGENERACY AND DESCENT IN SYMMETRY: LIGAND FIELD SPLITTINGS AND RELATED MATTERS

SYMMETRY II. J. M. GOICOECHEA. LECTURE 2. 1 LECTURE 2 DEGENERACY AND DESCENT IN SYMMETRY: LIGAND FIELD SPLITTINGS AND RELATED MATTERS 2.1 Degeneracy When dealing with non-degenerate symmetry adapted wavefunctions