c3710 bonding theories

• Properties of Coordination Compounds

  • Often brightly coloured and colour may change with changing ligands and oxidation state of the metal centre
  • Temperature dependence of magnetic properties
  • Complexes with d3 and d6 electron configurations can show remarkable stability
  • Certain ions with d8 configuration, e.g. Pd(II) and Pt(II), prefer square planar geometry to Td and Oh

  
• There are three theories of metal-to-ligand bonding in coordination compounds:

  
• Precursor: Electrostatic Theory
• Electrostatic Theory


  • Assumes that only anionic ligands approach the positively charged metal centre
  • Ligands and central ion attract each other while the ligands repel one another
  • The electrostatic repulsion between the ligands lead to a prediction of molecular geometry depending on the number of coordinated ligands (VSEPR model)

  
• Limitations of Electrostatic Theory


  • Can not account for the existence of square planar complexes
  • Can not explain the existence of complexes with neutral ligands or positively charged ligands such as NH2NH3+ and NO+
  • Says nothing about the magnetic properties of coordination complexes
  • Says nothing about the electronic energy levels in coordination complexes as revealed by their colors and spectra

  
• Valence Bond Theory (VBT)

  • Introduced by Heitler & London in 1927 and extended by Pauling & Slater in 1931
  • Regards bonding as overlap of atomic or hybrid orbitals on individual atoms
  • Treats electrons in a quantum mechanical fashion (unlike in the Lewis Theory which treats electrons as dots in space)
  • Atomic orbitals are regions on space where an electron is likely to spend its time within a certain probability (90%)
  • Standard atomic orbitals are s, p, d and f orbitals

  
• Pauling showed that a set of 6 s, p and d orbitals could be hybridized to form an octahedral geometry (similar to s and p orbitals sp3, sp2, etc. hybrid orbitals)

  
• Coordination compounds contain complex ions, in which ligands form coordinate covalent bonds to the metal


  The ligand must have a lone pair of electrons, the metal must have an empty orbital of suitable energy available for bonding

  
• Postulates of VBT


  • Overlap between two half-filled valence orbitals of two different atoms results in the formation of the covalent bond
  • When atomic orbitals posses more than one unpaired electron, multiple bonds can be formed (σ-, π-bonds)
  • A covalent bond is directional and is parallel to the region of overlapping atomic orbitals

  
• VBT: Linkages in Coordination Compounds


  • The metal atom or ion under the influence of ligands can use its (n-1)d, ns, np and nd orbitals for hybridization to yield a set of equivalent orbitals of definite geometry (e.g. Oh, Td, Sq. pl., etc.)
  • Bonding arises from overlap of filled ligand orbitals and vacant metal orbitals, resulting in a coordinate covalent bond

  
• Formation of a Coordination Complex

  1. The appropriate metal ion is taken

  2. A ligand orbital containing a lone pair of electrons forms a coordinate covalent bond by overlapping with an empty hybrid orbital on the metal ion

  3. Each of the hybrid orbitals can combine with an orbital from a ligand to make a bonding and an anti-bonding orbital, each with sigma symmetry around the metal-ligand bond axis

  4. Pauling proposed that two types of complexes can be prepared: outer-orbital sp3d2 complexes and inner-orbital d2sp3 complexes

  
• Outer-orbital sp3d2 complexes


  • The d-orbitals lie above the s and p orbitals
  • The electrons in the 3d orbitals remain undisturbed, resulting in a paramagnetic complex

  
• Inner-orbital d2sp3 complexes


  • The d-orbitals lie below the s and p orbitals
  • The 3d electrons originally in the metal ion are accommodated in three of the d orbitals and the remaining two 3d orbitals are used in hybridization and accommodate two electron pairs donated by the ligands, resulting in a diamagnetic complex

  
• Octahedral sp3d2 Geometry


  • [CoF6]3–
• Octahedral d2sp3 Geometry


  • [Fe(CN)6]3–
• The difference between sp3d2 and d2sp3 hybrids lies in the principal quantum number of the d orbital
• Experimental data indicates that some d5 complexes such as [MnF6]4- have five unpaired electrons (i.e. outer-orbital complex) while others such as [Mn(CN)6]4- have one unpaired electron

  
• Ligands such as CN- and CO tend to form inner-orbital complexes while ligands such as F-, Cl-, Br- and I- usually form outer-orbital complexes

  
• Limitations of VBT (Re: Coordination Compounds)

  • Does not give quantitative interpretation of magnetic properties of TM compounds
  • Fails to account for the colour exhibited by TM compounds
  • Does not give a quantitative interpretation of the thermodynamic and kinetic stabilities of coordination compounds
  • Predications made by VBT regarding the Td and Sq. pl. structures of 4-coordinate complexes are not accurate
  • Fails to distinguish between weak and strong field ligands
• Crystal Field Theory (CFT)


  • Assumes that the interactions between the metal ion and the ligands are purely electrostatic (ionic)
  • A ligand lone pair is regarded as a point negative charge (or as the partial negative charge of an electric dipole) that repels electrons in the d orbitals of the central metal ion
  • The theory focuses the splitting of the d orbitals into groups with different energies and uses that splitting to rationalize the optical spectra, thermodynamic stability and magnetic properties of TM complexes

  
• Coulombic Theory of Electrostatic Interactions


  • Repulsion of like charges and attraction of unlike charges
  • The potential energy of two charges (q1 and q2) separated by a distance r is given by the formula P.E. = q1×q2/r2
• A thorough understanding of the shapes and orientations of d orbitals is essential to the understanding of CFT
• Octahedral Complex and d-Orbital Energies

  1. Stage 1: The metal centre and the 12 ligand electrons are an infinite distance apart, the five d orbitals of the "free" metal ions will not be affected by the ligand electrons and will remain degenerate

  2. Stage 2: The 12 ligand electrons are brought up around the metal centre to form a spherical shell, all the five (5) d-orbitals are equally affected and remain degenerate, but the P.E. of the system will increase

  3. Stage 3: The 12 ligand electrons arrange into an octahedral field, two (2) of the d-orbitals increase in energy w.r.t. the Barycentre, while three (3) decrease in energy

  
• The dx2-y2 and dz2 orbitals are the most affected by the negative charges, which represent the ligands, as they point directly along the Cartesian axes

  
• Electrons in dxy, dyz and dxz are further away from the ligands than they were in stage 2 and so their energy decreases
• Stage 3


  • The 12 ligand e-s arrange into an octahedral field at the same M-L distance (as in stage 2) around the metal centre
  • The distance between the metal centre and the ligand e-s remains constant, the net P.E. of the system remains the same, i.e. the barycentre of the orbitals remains the same
  • Two (2) of the d-orbitals increases in energy w.r.t. the Barycentre, while three (3) decrease in energy

  
• In stage 3, the dx2-y2 and dz2 orbitals are the most affected by the negative charges, which represent the ligands

  
• The dx2-y2 and dz2 orbitals point directly along the Cartesian axes, and therefore at the incoming ligands
• Any electrons in these orbitals will experience greater repulsion from the electrons in the incoming ligands than those in the dxy, dyz and dxz orbitals, which point in between the axes (i.e. between the ligands)

  
• Electrons in dxy, dyz and dxz are further away from the ligands than they were in stage 2 and so their energy, relative to the barycentre, drops

  
• Crystal Field Splitting Energy, Δ

  The difference between the energies of the d-orbitals as a result of the application of a field of ligands
• ΔO


  CFSE due to an octahedral field
• Since the position of the barycentre remains unchanged, the total energy decrease of the three t2g orbitals (dxy, dyz, dxz) is equal to the total increase in the energy of the two eg orbitals (dx2-y2, dz2)

  
• Octahedral Fields - Stage 4


  The electrostatic attraction between the +ve metal cation and the 12 e-s in the ligands result in the decrease of the Barycentre of the system and a complex that is lower in energy than the "free" metal ion located at an infinite distance from the 12 ligand e-s

  
• Δo


  The size of the energy gap between the eg and t2g levels
• Complex [Ti(H2O)6]3+


  • Ti3+:[Ar]3d1
  • In the complex, the one d-electron will occupy the orbital with the lowest energy (i.e. one of the t2g orbitals)
  • The complex absorbs light of the correct wavelength (energy) to promote the electron from the t2g to the eg orbital set

  
• The d-d transition is the single band with a maximum at 20, 300 cm-1
• Δo for [Ti(H2O)6]3+ = 20,300/83.7 = 243 kJmol-1
• The CFSE in [Ti(H2O)6]3+ is 2/5Δo = 2/5 x 243 kJmol-1 = 97kJmol-1
• Solutions containing the hydrated Ti3+ ion are reddish-violet in colour. This is because the yellow and green light are absorbed to excite the electron from the t2g orbital set to the eg orbital set in these complexes