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  Field Theories, Chemistry tutorial

Ligand and Crystal Field theory:

Linus Pauling considered the formation of a complex as an outcome of coordinate bond formation between the metal ion (that is, Lewis acid) and the ligand (that is, Lewis base). The metal ion accommodates the electron pairs (from hybridized ligand orbitals) in correctly hybridized orbitals. The hybridization of orbitals on the metal decides the geometric arrangement of the complex.

Valence Bond Theory:

The theory is basically based on the idea that the formation of complexes involves the donor-acceptor reaction. The most significant hypothesizes for the theory is that a pair of electrons from the donor atoms are donated to empty orbital of the metal ion and in order to accept the donated electron the atomic orbitals on the metal should be hybridized to provide a set of equivalent orbitals with the essential symmetry needed. The given assumptions are made in the theory:

1) The metal ion should make available a number of orbitals, equivalent to its coordination number, for accommodating the electrons from the ligands. The metal ion employs hybrid orbitals comprising s, p and d orbitals for accepting the electrons from the ligand, which as well should include the electron pairs in hybrid orbitals, in such a way that a maximum and fruitful overlap of orbitals is possible by the strongly directional metal hybrid orbitals.

2) π-bonding formation by the electron donation filled dxy, dyz and dzx, orbitals of the metal, was incorporated to decrease the accumulated negative charge on metal ions through back donation of electrons to the ligands via π bonding.

3) Hunds rule applies to the electrons in the non bonded orbitals, presence of unpaired electrons in the complexes providing paramagnetism.

Molecular Orbital Theory:

It supposes that electrons move in the molecular orbitals (M.O.) that expands over all the nuclear on the system. Mathematically the molecular orbitals are comprised via a linear combination of atomic orbitals (L.C.A.O.). Therefore if two atomic orbitals overlap they form a molecular orbital that holds a maximum of two electrons and this electron are under the affect of the two nuclear.

A molecular orbital can be symbolized by 4 and they encompass the given characteristics:

1) They are like atomic orbitals encompass definite energy.

2) Nomenclatures s, p. d and so on employed for atomic orbitals are substituted by sigma, pie (π) and delta (δ).

3) Paulis principle applies to molecular orbital, in such a way that no single molecular orbital can have two accurately similar electrons.

4) In filling molecular orbitals Aufbau principle is applied. 

Differences between the valence bond and molecular orbital theories:

1) Dissimilar the molecular orbital theory, the Atom still retains to some extent these distinct characters even whenever chemically bonded. 

2) This introduces the theory of resonance into bonding theory.

3) Instead considering the electrons as been related all the time with both nuclear value bond theory, in the case of molecular orbital theory, an electron is considered to be related first by one nucleus and then by the other nucleus, in such a way that the complete wave function of the electron can be represented as the linear combination of both.

4) The valence bond theory is much simpler to follow whenever treating polyatomic molecules. 

5) Dissimilar to the molecular theory where spin pairing occurs from the application of Pauli Exclusion Principle, in valence bond theory, spin pairing is an essential condition for energy minimum and therefore for bonding.

Crystal Field theory:

The crystal field theory (CFT) introduced by Bethe in the year 1929 and Van Black in the year 1935 considers the electrostatic interactions of the ligands (taken as charges) by the d-orbitals of the metal ions.

In an isolated gaseous metal ion, the 5 d-orbital are degenerate, as dxz, dyz, dxy, dx2- y2 and dz2

The electronic configuration of the metal ions, and therefore the magnetic properties of the complexes can simply be understood from the d orbital splitting in the ligand fields. The electronic configuration of the ion will provided the given considerations:

a) Electrons occupy the orbitals of the lowest energy in ground state.

b) Due to reduced inter-electronic repulsions in different orbitals, in a degenerate level, Hund's rule is always followed or obeyed.

c) The quantum mechanical exchange energy for parallel spins is more than that for the opposite spin.

d) Whenever pairing of electrons occurs, the energy of the system will be increased by P, the pairing energy for the system. 

The effects of the splitting of the inner orbital which the CFT can illustrate are: 

a) Spectra of the coordinate compound.

b) The manganese properties of such compound.

c) Thermodynamic properties of metal ion like lattice energy and ionic radii.

d) The kinetic and method of their reaction.

e) The geometry of complexes.

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