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Molecular Energy Levels
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sanaja...@gmail.com
May 26, 2013, 7:51:32 AM5/26/13
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Molecular Energy Levels
sanaja...@gmail.com
May 26, 2013, 7:53:25 AM5/26/13
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On Sunday, May 26, 2013 4:51:32 PM UTC+5, sanaja...@gmail.com wrote:
> Molecular Energy Levels
The combination of two 1s atomic orbitals of atoms form two new molecular orbitals designated as σ 1s and σ* 1s. In the same manner , the 2s and 2p atomic orbitals ie., eight atomic orbitals of two atoms give rise to eight new molecular orbitals viz.,
σ 2s , σ * 2s; π 2Px , π* 2Px ; π 2Py , π* 2Py ; σ 2Pz ; σ * 2Pz.
The increasing order of energies of various molecular orbitals are given below.
σ1s , σ* 1s ; σ 2s , σ * 2s; σ 2Pz ; π 2Px = π 2Py ; π * 2Px = π* 2Py ; σ * 2Pz.
The molecular orbital energy diagram for homonuclear diatomic molecules likeMolecular Energy Level Diagram for diatomic molecules such as O2 , F2 etc.
However, the given sequence of energy levels of molecular orbitals is not correct for all molecules. For instance , it has been observed experimentally that in some diatomic molecules such as B2 , C2 , N2 etc. the molecular orbital energy level diagram shown in Fig is followed.
Molecular Orbital Energy Level Diagram for Diatomic Homonuclear molecules such as B2 , C2 , N2 etc .
Note
The order for writing molecular orbital configurations of B2 , C2 and N2 molecules can be understood in terms of
electron-electron or orbital-orbital interactions which come into play during overlap of orbitals. Thus, owing to these interactions the energy level diagram is modified. Due to the close proximity of 2s and 2Pz orbitals , σ 2s , σ * 2s and
σ* 2Pz . orbitals undergo mixing interactions in view of which the energy of σ 2Pz orbitals is raised and it becomes greater than π 2Px and π 2Py which do not experience these intermixing interactions.
It may be noted that following N2 , the next molecules O2 and F2 do not exhibit these interactions. It is presumably because of large difference of energy between their 2s and 2Pz orbitals ,such intermixing is insignificant. The fact is also supported by spectroscopic measurements.
RULES FOR ADDING ELECTRONS TO MOs
The molecules are built up by adding electrons to molecular orbitals in the same way as the atoms are built up by adding electrons to atomic orbitals. The principle involved are the same in both cases. These may be summed up as follows :
The molecular orbital with lowest energy is filled first.
The maximum number of electrons in a MO cannot exceed two and the two electrons must have opposite spins.
If there are two or more orbitals at the same energy level, pairing of electrons will occur only after each orbital of same energy has one electron.
ELECTRONIC CONFIGURATION OF A MOLECULE
The distribution of electrons among various molecular orbitals is called electronic configuration of the molecule. It can give us very important information about the molecule. From electronic configuration, it is possible to find out the number of electrons in bonding molecular orbitals (Nb) and number of electrons in anti-bonding molecular orbitals (Na).
The molecule is stable if Nb > Na
The molecule is unstable if Nb < Na
The molecule is unstable if Nb = Na
It may be noted that even if number of electrons in bonding MO and number of electrons in anti-bonding MO are equal , the atoms do not combine to form molecule. This is because of the fact that effect of anti-bonding electrons is slightly more than that of bonding electrons.
BOND ORDER
The stability of the molecule can be determined from the parameter called 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.
Bond order = ½ [Nb − Na]
INFORMATIONS CONVEYED BY BOND ORDER
The Bond Order conveys the important informations :
If the value of bond order is positive , it indicates a stable molecule and if the value of bond order is negative or zero, it means that the molecule is unstable and is not formed.
Dissociation energy of the molecule is directly proportional to the bond order of the molecule. In other words, greater the bond order, the greater is the bond dissociation energy.
Bond length of the molecule is inversely proportional to the bond order of the molecule. In other words , greater the bond order shorter will be the bond length.
Knowing the bond order, the number of covalent bonds between the atoms in the molecule can be predicted. Bond order of a molecule is equal to the number of covalent bonds between the atoms in the molecule.
The magnetic behaviour of molecules can also be predicted, i.e., if all the electrons in a molecule are paired, the substance is diamagnetic and in case there are unpaired electrons in a molecule, the substance is paramagnetic .
It may be noted that if the bond order is fractional, the molecule will be definitely paramagnetic. H2 , H2+ , He2 ,
> Molecular Energy Levels
The combination of two 1s atomic orbitals of atoms form two new molecular orbitals designated as σ 1s and σ* 1s. In the same manner , the 2s and 2p atomic orbitals ie., eight atomic orbitals of two atoms give rise to eight new molecular orbitals viz.,
σ 2s , σ * 2s; π 2Px , π* 2Px ; π 2Py , π* 2Py ; σ 2Pz ; σ * 2Pz.
The increasing order of energies of various molecular orbitals are given below.
σ1s , σ* 1s ; σ 2s , σ * 2s; σ 2Pz ; π 2Px = π 2Py ; π * 2Px = π* 2Py ; σ * 2Pz.
The molecular orbital energy diagram for homonuclear diatomic molecules likeMolecular Energy Level Diagram for diatomic molecules such as O2 , F2 etc.
However, the given sequence of energy levels of molecular orbitals is not correct for all molecules. For instance , it has been observed experimentally that in some diatomic molecules such as B2 , C2 , N2 etc. the molecular orbital energy level diagram shown in Fig is followed.
Molecular Orbital Energy Level Diagram for Diatomic Homonuclear molecules such as B2 , C2 , N2 etc .
Note
The order for writing molecular orbital configurations of B2 , C2 and N2 molecules can be understood in terms of
electron-electron or orbital-orbital interactions which come into play during overlap of orbitals. Thus, owing to these interactions the energy level diagram is modified. Due to the close proximity of 2s and 2Pz orbitals , σ 2s , σ * 2s and
σ* 2Pz . orbitals undergo mixing interactions in view of which the energy of σ 2Pz orbitals is raised and it becomes greater than π 2Px and π 2Py which do not experience these intermixing interactions.
It may be noted that following N2 , the next molecules O2 and F2 do not exhibit these interactions. It is presumably because of large difference of energy between their 2s and 2Pz orbitals ,such intermixing is insignificant. The fact is also supported by spectroscopic measurements.
RULES FOR ADDING ELECTRONS TO MOs
The molecules are built up by adding electrons to molecular orbitals in the same way as the atoms are built up by adding electrons to atomic orbitals. The principle involved are the same in both cases. These may be summed up as follows :
The molecular orbital with lowest energy is filled first.
The maximum number of electrons in a MO cannot exceed two and the two electrons must have opposite spins.
If there are two or more orbitals at the same energy level, pairing of electrons will occur only after each orbital of same energy has one electron.
ELECTRONIC CONFIGURATION OF A MOLECULE
The distribution of electrons among various molecular orbitals is called electronic configuration of the molecule. It can give us very important information about the molecule. From electronic configuration, it is possible to find out the number of electrons in bonding molecular orbitals (Nb) and number of electrons in anti-bonding molecular orbitals (Na).
The molecule is stable if Nb > Na
The molecule is unstable if Nb < Na
The molecule is unstable if Nb = Na
It may be noted that even if number of electrons in bonding MO and number of electrons in anti-bonding MO are equal , the atoms do not combine to form molecule. This is because of the fact that effect of anti-bonding electrons is slightly more than that of bonding electrons.
BOND ORDER
The stability of the molecule can be determined from the parameter called 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.
Bond order = ½ [Nb − Na]
INFORMATIONS CONVEYED BY BOND ORDER
The Bond Order conveys the important informations :
If the value of bond order is positive , it indicates a stable molecule and if the value of bond order is negative or zero, it means that the molecule is unstable and is not formed.
Dissociation energy of the molecule is directly proportional to the bond order of the molecule. In other words, greater the bond order, the greater is the bond dissociation energy.
Bond length of the molecule is inversely proportional to the bond order of the molecule. In other words , greater the bond order shorter will be the bond length.
Knowing the bond order, the number of covalent bonds between the atoms in the molecule can be predicted. Bond order of a molecule is equal to the number of covalent bonds between the atoms in the molecule.
The magnetic behaviour of molecules can also be predicted, i.e., if all the electrons in a molecule are paired, the substance is diamagnetic and in case there are unpaired electrons in a molecule, the substance is paramagnetic .
It may be noted that if the bond order is fractional, the molecule will be definitely paramagnetic. H2 , H2+ , He2 ,
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