PAPER No.13 :Applications of molecular symmetry and group theory Module No.35: Symmetry and chemical bonding part-6 MO

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1 1 Subject Chemistry Paper No and Title 13: Applications of molecular symmetry and group theory Module No and Title 35: Symmetry and chemical bonding part-v MO Module Tag CHE_P13_M35

2 2 TABLE O CONTENTS 1. Learning Outcomes 2. Introduction 3. ormation of Molecular orbitals 3.1 Construction of MO for B (C 4v ) molecule 3.2 Construction of MO for B 3 molecule 3.3 Construction of MO for CCl 4 molecule 4. Summary

3 3 1. Learning Outcomes After studying this module, you shall be able to Know more about of MO Construct MO for B molecule Construct MO for B 3 molecule Construct MO for CCl 4 molecule 2. Introduction In this module we will continue with of molecular orbitals by taking few more examples.this will give to the reader more insight in the procedure for MO construction. 3. ormation of Molecular orbitals 3.1 Construction of MO for B (C 4v ) molecule or this molecule we have already discussed σ-bomding hybridization in previous modules. In this module we will discuss of molecular orbital and energy level diagram for the same. Let us follow the various steps Step I Point group the molecule is C 4v Step-II The central atom is bromine. Bromine has valence electronic configuration [Ar] 3d 10 4s 2 4p 5. Thus the valence atomic obitals are; one s orbital and three p orbitals (i.e. four). The symmetries of these atomic orbitals under C 4v symmetries can be obtained from character table of C 4v point group and these are given as follows: s A 1 ie a 1 type orbital p x E ie e type orbital p y E ie e type orbital p z A 1 ie a 1 type orbital

4 4 d xy B 2 ieb 2 type orbital d xz d yz E ie e type orbital d X2-y B 1 d z A 1 ieb 1 type orbital iea 1 type orbital Step-III The structure and various bond vectors in B are shown in figure.1 C 4 Br ig.1 Structure and bond vectors in B The effects of symmetry operations of C 4v point group on Br- vectors,,,, and are shown in fig.2

5 5 Br No vector shifted Br C 2 only one vector is not shifted E along C 4 axis Br C 4 B (C 4v ) σ v Br C 4 only three vectors are not shifted σ d Br only one vector is not shifted Br only one vector is not shifted ig.2 Effects of symmetry operations of C 4v point group on Br- vectors,,,, and The results of symmetry operations of C 4v point group on Br- bond vectors is summarized in table.1 The vector which is unshifted contributes χ =+1. The vector which is shifted contributes χ =0. The vector which is unshifted but only direction is reversed contributes χ = -1 Table.1 Effects of the symmetry operations on five Br- bond vectors C 4v E 2C 4 C 2 2σ v 2 σ d Unshifted vectors Multiplication factor X1 X1 X1 X1 X1 Γ Br Γ Br- can be reduced by standard reduction formula as

6 6 Γ Br- = 2 A 1 +B 1 +E It means ligand group orbitals must of a 1 and b 1 and e type. Step-IV Using projection operators corresponding to 2 A 1,B 1,E ie A1 p, B1 p and E p on,,, and orbital functions one can get SALC of LGO ie five orbitals fragment. SALC will not be worked out here. Using LGO a 1 and b 1 and e type of 5 fragment on the right hand side of the MO diagram and symmetry of the s and p atomic orbitals of bromine atom on left hand side and matching the symmetry and taking into energy consideration, the MO diagram for B molecule may be constructed as shown in figure.3

7 7 ig.3 Qualitative MO diagram of B molecule 3.2 Construction of MO for B 3 molecule Step-I Point group of the B 3 ids D 3h Step-II Symmetries of atomic orbitals of boron in D 3h can be read from the character table of D 3h point group

8 8 D 3h E 2C 3 (z) 3C' 2 h (xy) 2S 3 3 v linear functions, rotations quadratic functions A' x 2 +y 2, z 2 s A' R z - E' (x, y) or (p x,p y ) (x 2 -y 2, xy) A'' A'' z or p z - E'' (R x, R y ) (xz, yz) s A 1 ie a 1 type orbital p x E ie e type orbital p y E ie p z A 2 ie e type orbital a 2 type orbital Step-III Structure and bond vectors in B 3 are shown in figure.4 C 3 B

9 9 ig.4 Structure and bond vectors in B 3 molecule The effect of symmetry operations of D 3h point group on three B- bond vectors are shown in figure.5 B No vector shifted E or σ h C 3 B C 2 or σ v 1 C 3 or 1 S3 C 2 orσ v B B only one vector not shifted All vectors shifted ig.5 Effect of symmetry operation on B- bond vectors The results of symmetry operations of D 3h point group on B- bond vectors is summarized in table.2 The vector which is unshifted contributes χ =+1. The vector which is shifted contributes χ =0. The vector which is unshifted but only direction is reversed contributes χ = -1 Table.2 Effect of symmetry operations on three B- bond vectors D 3h E 2C 3 3C 2 σ h 2S 3 3σ v Unshifted vectors Multiplication X1 X 0 X 1 X 1 X 0 X 1

10 10 factor Γ B Γ B- can be reduced to Γ B- = A 1 + E. It means that the fragment 3 of three pendent fluorines have the symmetry of A 1 +E. Thus these LGO are of the type a 1 and e type of orbitals. 1s orbital in boron is completely filled up and it will not be considered for qualitative MO of B 3 molecule. The 2s orbitals in boron and 2p orbitals are used in MO. Using LGO of a 1 and e type on the right hand side of the diagram and symmetry of the atomic orbitals of boron atom on left hand side and matching the symmetry and taking into energy consideration, the MO diagram for boron tri fluoride molecule may be constructed as shown in figure.6 2a' 1 e' 2p x 2p y 2p z 2s e' a" 2 a' 1 a" 2 e' a' 1 a' 1 + e' e 1s 1a' 1 a 1 a 1 non bonding Boron atomic orbitals MO of B 3 LGO of 3 luorines ig.6 Qualitative MO diagram of B 3 molecule 3.3 Construction of MO for CCl 4 molecule Step-I The point group of the molecule is T d Step II Symmetries of atomic orbitas of carbon atom is given as(see character table of T d point group): T d E 8C 3 3C 2 6S 4 6 d linear functions, rotations quadratic functions A x 2 +y 2 +z 2

11 11 A E (2z 2 -x 2 -y 2, x 2 - y 2 ) T (R x, R y, R z ) - T (x, y, z) (xy, xz, yz) s A 1 ie a 1 type orbital p x T 2 ie t 2 type orbital p y T 2 ie t 2 type orbital p z T 2 ie t 2 type orbital d xy T 2 ie t 2 type orbital d yz T 2 ie t 2 type orbital d xz T 2 ie t 2 type orbital Step-III The structure and four C-Cl bond vectors in CCl 4 are shown in figure.7 z C 2z Cl 2 C 2x x C Cl 1 Cl 4 C 2y y Cl 3 ig.7 Symmetry elements and C-Cl bond vectors in CCl 4 molecule The effects of symmetry operations on these four C-Cl bond vectors are summarized in table-3

12 12 Table.3 Effects of symmetry operations on four C-Cl bond vectors T d E 8C 3 3C 2 6S 4 6σ d Unshifted vectors Multiplication factor X1 X1 X0 X0 X0 Γ Γ r can be reduced to irreducible representations by the standard formula and the results are Γ r =A 1 +T 2 It means the LGO of Cl 4 fragment invoving C-Cl bonds only are of a 1 and t 2 type 1s orbital in carbon is completely filled up and it will not be considered for qualitative MO of CCL 4 molecule. The 2s orbitals in carbon and 2p orbitals are used in MO. Using LGO of a 1 and t 2 type on the right hand side of the diagram and symmetry of the atomic orbitals of carbon atom on left hand side and matching the symmetry and taking into energy consideration, the MO diagram forcarbon tetra chloride molecule may be constructed as shown in figure.8 2t 2 (σ ) p t 2 a 1 (σ ) s a 1 1t 2 (σ ) d t 2 +e e(nb) E a 1 +t 2 t 2 (σ) a 1 (σ) Carbon atomic orbitals MO of CCl 4 molecule Chlorine group orbitals ig.8 Qualitative MO diagram of CCl 4 involving σ-bonding

13 13 The d-orbitals which are also of right symmetry for bond have also been included in MO scheme for CCl 4 molecule. ollowing table-4 gives at a glance the type of atomic orbitals at central atom involved σ- and π- bonding MO.. Table-4 Type of atomic orbital involved in σ- and π- bonding MO Type of Octahedral Tetrahedral Square planar Trigonal planar bonding (O h ) (T d ) (D 4h ) (D 3h ) In (d z 2,d x2-y2, s, p z ) (s,p x,p y,p z ) or s, d x2-y2, p x,p y or d z 2, s,p x,p y,p z σ- ( s,d xy,d yz,d zx ) d z 2,d x2-y2, p x,p y bonding In (p x,p y, d xy, d yz, d zx ) (p x,p y,p z ),(d xy,d yz,d zx ) p z, d yz,d zx d x2-y2, d xy p x,p y,p z π- d z 2, d x2-y2 d yz,d zx bonding 4. Summary More about of MO mentioned Construct MO for B molecule has been discussed in detailed manner Construct MO for B 3 molecule has been discussed in detailed manner Construct MO for CCl 4 molecule has been discussed in detailed manner

13 Applications of molecular symmetry and group theory

Subject Chemistry Paper No and Title Module No and Title Module Tag 13 Applications of molecular symmetry and 26 and and vibrational spectroscopy part-iii CHE_P13_M26 TABLE OF CONTENTS 1. Learning Outcomes