Molecular Orbital Theory (MOT)

Molecular Orbital Theory (MOT)  Molecular orbital theory was given by Hund and Mulliken in 1932. The main ideas of this theory are:  When two atomic orbitals combine or overlap, they lose their identity and form new orbitals. are called molecular orbitals.  Molecular orbitals are the energy state...

Molecular Orbital Theory (MOT)  Molecular orbital theory was given by Hund and Mulliken in 1932. The main ideas of this theory are:  When two atomic orbitals combine or overlap, they lose their identity and form new orbitals. are called molecular orbitals.  Molecular orbitals are the energy states of a molecule in which the electrons of the molecule are filled just as atomic orbitals are the energy states of an atom in which the electrons of the atom are filled.  Only those atomic orbital can combine to form molecular orbital which have comparable same energies and proper orientation.  The number of molecular orbitals formed is equal to the number of combining atomic orbitals.  When two atomic orbitals combine, they form two new orbitals called bonding molecular orbital and antibonding molecular orbital.  The bonding molecular orbital has lower energy and hence greater stability than the corresponding antibonding molecular orbital.  The bonding molecular orbitals are represented by σ, π etc, whereas the corresponding antibonding molecular orbitals are represented by σ* π* etc.  The filling of molecular orbitals in a molecule takes place in accordance with Aufbau principle, Pauli's exclusion principle and Hund's rule.  Electrons are filled in the increasing energy of the MO which is in order  If all the electrons in a molecule are paired then the substance is a diamagnetic on the other hand if there are unpaired electrons in the molecule, then the substance is paramagnetic.  Formation of molecular orbitals OR Linear combination of atomic orbitals LCAO According to LCAO method: The molecular orbital wave function ΨMo is formed by the linear combination of the wave functions of the individual atomic orbitals ΨA and ΨB 1. Molecular orbital is formed by the addition of wave function of atomic orbitals. It can be represented as ΨMo = ΨA + ΨB. This molecular orbital is called Bonding molecular orbital. 2. Molecular orbital is formed by the subtraction of wave function of atomic orbitals. It can be represented as Ψ*Mo = ΨA – ΨB This molecular orbital is called Antibonding molecular orbital. 3. The filling of molecular orbitals in a molecule takes place in accordance with Aufbau principle, Pauli's exclusion principle and Hund's rule. 4. Electrons are filled in the increasing energy of the MO which is in order. 5. Stability of bond are determined by bond order: - Bond Order: Bond order may be defined as half the difference between number of electrons in bonding molecular orbitals and number of electrons in antibonding molecular orbitals. BO = Nb – Na /2 Where, Nb= number of electrons in bonding molecular orbitals Na= number of electrons in antibonding molecular orbitals.  Write the difference between atomic and molecular orbital? Atomic orbital Molecular orbital Atomic orbital is the region having the Molecular orbital is the region having the highest probability of finding an electron in highest probability of finding an electron of an atom a molecule Atomic orbitals are inherent property of anMolecular orbitals are formed by atom. Formed by the electron cloud around combination of atomic orbitals that have the Atom nearly the same energy The shape is determined by the type of The shape is determined by the shapes of atomic orbital(s, p, d or f) atomic orbitals that make the molecule. They have complex shapes Monocentric as it is found around a single Polycentric as it is found around different Reaction nuclei Schrodinger equation is used Linear combination of atomic orbitals (LCAO) is used  Define bonding and anti-bonding molecular orbitals? Bonding Molecular Orbitals:  When addition of wave function takes place, the type of molecular orbitals formed are called Bonding Molecular orbitals and is represented by- ΨMO = ΨA + ΨB.  They have lower energy than atomic orbitals involved. It is similar to constructive interference occurring in phase because of which electron probability density increases resulting in formation of bonding orbital.  Molecular orbital formed by addition of overlapping of two s orbitals.  It is represented by Sigma (σ) called sigma bonding and pai (π) bonding. Anti-Bonding Molecular Orbitals:  When molecular orbital is formed by subtraction of wave function, the type of molecular orbitals formed are called Antibonding Molecular Orbitals and is represented by- ΨMO = ΨA -ΨB.  They have higher energy than atomic orbitals. It is similar to destructive interference occurring out of phase resulting in formation of antibonding orbitals.  Molecular Orbital formed by subtraction of overlapping of two s orbitals.  It is represented by σ* [(Sigma*) and π* is used to represent antibonding molecular orbital) called sigma Antibonding. According to the molecular orbital theory, the filling of orbitals takes place according to the following rules:  Aufbau’s principle: Molecular orbitals are filled in the increasing order of energy levels.  Pauli’s exclusion principle: In an atom or a molecule, no two electrons can have the same set of four quantum numbers.  Hund’s rule of maximum multiplicity: Pairing of electrons doesn’t take place until all the atomic or molecular orbitals are singly occupied.  Molecular orbital energy diagrams of Homo- nuclear diatomic Molecules H2, He2, Li2, Be2, B2, C2, N2, O2 and F2:- 1. Nitrogen Molecule N2: Nitrogen molecule is formed by two nitrogenAtomic number of nitrogen is: 7 Electronic configuration of nitrogen is -1S2 2S2 2P3 In N2 molecule total electrons are 7+7=14 According to molecular orbital approach, the electronic configuration of N2 is- σ 1s2, σ *1s2, σ 2s2, σ *2s2, [π 2px2 = π 2py2], σ 2pz2 [π *2px= π *2py], σ*2pz Bond order of N2: Bond order = ½(Nb-Na) Bond order = ½ (10-4) = 3. Triple bond is present in the molecule. In N2 molecule all the electrons are paired therefore it is diamagnetic. 2. Oxygen Molecule O2 : The atomic number of oxygen is 8 The electronic configuration of oxygen is 1S2 2S2 2P4 According to molecular orbital approach, the electronic configuration of O2 is- σ1s2, σ *1s2, σ 2s2, σ *2s2, σ 2pz2, [π2px2 = π2py2], [π*2px1= π*2py1], σ *2pz  Bond order of O2: Bond order = ½(Nb-Na) Bond order = 1 (10-6) = 2. Double bond is present in the molecule. 2 Two unpaired electrons are present, so the molecule is paramagnetic. 3. Flourine Molecule F2: The atomic number of fluorine is 9 The electronic configuration of fluorine is is 1S2 2S2 2P5 According to molecular orbital approach, the electronic configuration of F2 is- σ1s2, σ *1s2, σ 2s2, σ *2s2, σ 2pz2, [π2px2 = π2py2], [π*2px1= π*2py1], σ *2pz1 Bond order of F2: Bond Order = 1(8 - 6) = 1 2 In F-F there are no unpaired electrons, so the molecule is diamagnetic.  Molecular orbital energy level diagrams of Hetero-nuclear diatomic molecules CO, NO, HF 4. CO Molecule: The atomic number of Carbon is 6 The atomic number of Oxygen is 8 The electronic configuration of carbon is is 1S2 2S2 2P2 The electronic configuration of Oxygen is is 1S2 2S2 2P4 According to molecular orbital approach, the electronic configuration of CO is- σ1s2, σ *1s2, σ 2s2, σ *2s2, σ 2pz2, [π2px2 = π2py2] 5. NO Molecule: The atomic number of Nitrogen is 7 The atomic number of Oxygen is 8 The electronic configuration of Nitrogen is is 1S2 2S2 2P3 The electronic configuration of Oxygen is is 1S2 2S2 2P4 According to molecular orbital approach, the electronic configuration of NO is- σ1s2, σ *1s2, σ 2s2, σ *2s2, σ 2pz2, σ *2pz1, [π2px2 = π2py2] 6. HF Molecule: The atomic number of Hydrogen is 1 The atomic number of Florine is 9 Interaction occurs between the 1s orbital on hydrogen and the 2p orbital in fluorine causing the formation of a sigma-bonding and a sigma-antibonding molecular orbital, as shown below