Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 13, Problem 13.71E

Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H 2 S .

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Interpretation Introduction

Interpretation:

The symmetry-adapted linear combination molecular orbitals for hydrogen sulfide are to be constructed.

Concept introduction:

A symmetry operation is defined as an action on an object to reproduce an arrangement that is identical to its original spatial arrangement. The spatial arrangement of the object remains identical after a symmetry operation. The point of reference through which a symmetry operation takes place is termed as a symmetry element.

Answer to Problem 13.71E

The symmetry-adapted linear combination molecular orbitals for hydrogen sulfide with A1 are shown below.

ΨA1=12(1sH1+1sH2)ΨA1=3sSΨA1=3pz,S

The symmetry-adapted linear combination molecular orbitals for hydrogen sulfide with B1 are shown below.

ΨB1=12(1sH11sH2)ΨB1=12(1sH21sH1)ΨB1=3px,S

The symmetry-adapted linear combination molecular orbitals for hydrogen sulfide with B2 are shown below.

ΨB2=3py,S

Explanation of Solution

The character table for C2v symmetry is shown below.

C2v E C2 σv σv'
A1 1 1 1 1
A2 1 1 1 1
B1 1 1 1 1
B2 1 1 1 1

The structure of H2S is shown below.

Physical Chemistry, Chapter 13, Problem 13.71E

Figure 1

The geometry of hydrogen selenide is bent due to presence of two lone pair of electrons. The 180° out of plane rotation of the molecule produces same structure. Hence, it contains C2 symmetry operation. It contains vertical plane of symmetry, σv and σv' in two different planes. Hence, the point group of the molecule is C2v.

The atomic orbitals of H which participates in bonding are 1sH1 and 1sH2. The atomic orbitals of sulfur atom which are involved in the bond formation are 1sS, 2sS, 2px,S, 2py,S, 2pz,S, 3sS, 3px,S, 3py,S and 3py,S. Only outer orbitals are to be considered. The table for A1 is shown below.

1sH1 1sH2 3sS 3px,S 3py,S 3pz,S
E 11sH1 11sH2 13sS 13px,S 13py,S 13pz,S
C2 11sH2 11sH1 13sS 13px,S 13py,S 13pz,S
σv 11sH1 11sH2 13sS 13px,S 13py,S 13pz,S
σv' 11sH2 11sH1 13sS 13px,S 13py,S 13pz,S

The six linear combinations can be obtained from the above table as shown below.

ΨA1=14(1sH1+1sH2+1sH1+1sH2)ΨA1=14(1sH2+1sH1+1sH2+1sH1)ΨA1=14(3sS+3sS+3sS+3sS)ΨA1=14(3px,S3px,S+3px,S3px,S)

The linear combination for 3py,S and 3pz,S are shown below.

ΨA1=14(3py,S3py,S3py,S+3py,S)ΨA1=14(3pz,S+3pz,S+3pz,S+3pz,S)

The first and second combinations are the same. The fourth and fifth combinations are exactly zero. Therefore, the unique wavefunctions after the simplification for A1 are shown below.

ΨA1=12(1sH1+1sH2)ΨA1=3sSΨA1=3pz,S

The table for A2 is shown below.

1sH1 1sH2 3sS 3px,S 3py,S 3pz,S
E 11sH1 11sH2 13sS 13px,S 13py,S 13pz,S
C2 11sH2 11sH1 13sS 13px,S 13py,S 13pz,S
σv 11sH1 11sH2 13sS 13px,S 13py,S 13pz,S
σv' 11sH2 11sH1 13sS 13px,S 13py,S 13pz,S

The six linear combinations can be obtained from the above table as shown below.

ΨA2=14(1sH1+1sH21sH11sH2)ΨA2=14(1sH2+1sH11sH21sH1)ΨA2=14(3sS+3sS3sS3sS)ΨA2=14(3px,S3px,S3px,S+3px,S)

The linear combination for 3py,S and 3pz,S are shown below.

ΨA2=14(3py,S3py,S+3py,S3py,S)ΨA2=14(3pz,S+3pz,S3pz,S3pz,S)

All combinations are exactly zero.

The table for B1 is shown below.

1sH1 1sH2 3sS 3px,S 3py,S 3pz,S
E 11sH1 11sH2 13sS 13px,S 13py,S 13pz,S
C2 11sH2 11sH1 13sS 13px,S 13py,S 13pz,S
σv 11sH1 11sH2 13sS 13px,S 13py,S 13pz,S
σv' 11sH2 11sH1 13sS 13px,S 13py,S 13pz,S

The six linear combinations can be obtained from the above table as shown below.

ΨB1=14(1sH11sH2+1sH11sH2)ΨB1=14(1sH21sH1+1sH21sH1)ΨB1=14(3sS3sS+3sS3sS)ΨB1=14(3px,S+3px,S+3px,S+3px,S)

The linear combination for 3py,S and 3pz,S are shown below.

ΨB1=14(3py,S+3py,S3py,S3py,S)ΨB1=14(3pz,S3pz,S+3pz,S3pz,S)

The third, fifth and sixth combinations are exactly zero. Therefore, the unique wavefunctions after the simplification for B1 are shown below.

ΨB1=12(1sH11sH2)ΨB1=12(1sH21sH1)ΨB1=3px,S

The table for B2 is shown below.

1sH1 1sH2 3sS 3px,S 3py,S 3pz,S
E 11sH1 11sH2 13sS 13px,S 13py,S 13pz,S
C2 11sH2 11sH1 13sS 13px,S 13py,S 13pz,S
σv 11sH1 11sH2 13sS 13px,S 13py,S 13pz,S
σv' 11sH2 11sH1 13sS 13px,S 13py,S 13pz,S

The six linear combinations can be obtained from the above table as shown below.

ΨB2=14(1sH11sH21sH1+1sH2)=0ΨB2=14(1sH21sH11sH2+1sH1)=0ΨB2=14(3sS3sS3sS+3sS)=0ΨB2=14(3px,S+3px,S3px,S3px,S)=0

The linear combination for 3py,S and 3pz,S are shown below.

ΨB2=14(3py,S+3py,S+3py,S+3py,S)=3py,SΨB2=14(3pz,S3pz,S3pz,S+3pz,S)=0

All combinations except the fifth combination are exactly zero. Therefore, the unique wavefunctions after the simplification for B2 are shown below.

ΨB2=3py,S

Conclusion

The symmetry-adapted linear combination molecular orbitals for hydrogen sulfide with A1 are shown below.

ΨA1=12(1sH1+1sH2)ΨA1=3sSΨA1=3pz,S

The symmetry-adapted linear combination molecular orbitals for hydrogen sulfide with B1 are shown below.

ΨB1=12(1sH11sH2)ΨB1=12(1sH21sH1)ΨB1=3px,S

The symmetry-adapted linear combination molecular orbitals for hydrogen sulfide with B2 are shown below.

ΨB2=3py,S

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Chapter 13 Solutions

Physical Chemistry

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