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

Videos

Textbook Question
Book Icon
Chapter 13, Problem 13.71E

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

Expert Solution & Answer
Check Mark
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

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
4. (a) Use the simple one-electron molecular orbital method, including overlap, to calculate the energies of the molecular orbitals of the hydrogen molecule (H2) in terms of α, β and S?
Evaluate the bond order of each Period 2 homonuclear diatomic cation, X2+, and anion, X2−.
Why does the energy ordering of the molecular orbitals of the period 2 diatomic molecules change in going from N2 to 0,?

Chapter 13 Solutions

Physical Chemistry

Ch. 13 - Prob. 13.11ECh. 13 - Prob. 13.12ECh. 13 - Prob. 13.13ECh. 13 - What are the number of classes and the order of...Ch. 13 - Prob. 13.15ECh. 13 - a Show that the C3v point group satisfies the...Ch. 13 - a In the Td point group, an S41 improper rotation...Ch. 13 - Determine which single symmetry operation of the...Ch. 13 - Prob. 13.19ECh. 13 - Prob. 13.20ECh. 13 - Prob. 13.21ECh. 13 - Figure 13.27 shows the structure of the molecule...Ch. 13 - Prob. 13.23ECh. 13 - Identify all the symmetry elements present in the...Ch. 13 - Point groups are called such because all of the...Ch. 13 - Determine the point groups of the following...Ch. 13 - Determine the point group of the following...Ch. 13 - Determine the point groups of the following...Ch. 13 - Determine the point groups of the following...Ch. 13 - Structural isomers can have very different point...Ch. 13 - Structural isomers can have very different point...Ch. 13 - Prob. 13.32ECh. 13 - Identify the point group of the wave functions of...Ch. 13 - Identify the point group of the wave functions of...Ch. 13 - Prob. 13.35ECh. 13 - Determine if the following species have permanent...Ch. 13 - Determine if the following species have permanent...Ch. 13 - Which of the following species will not have...Ch. 13 - Prob. 13.39ECh. 13 - Explain why a molecule with a center of inversion...Ch. 13 - a Unlike methane, bromochlorofluoromethane...Ch. 13 - Prob. 13.42ECh. 13 - Prob. 13.43ECh. 13 - Prob. 13.44ECh. 13 - Show that the irreducible representations of the...Ch. 13 - Show that any two of the irreducible...Ch. 13 - Show that any irreducible representation of these...Ch. 13 - Explain why this proposed irreducible...Ch. 13 - Prob. 13.49ECh. 13 - Prob. 13.50ECh. 13 - Why is it unnecessary to consider whether an...Ch. 13 - Prob. 13.52ECh. 13 - Prob. 13.53ECh. 13 - Prob. 13.54ECh. 13 - Prob. 13.55ECh. 13 - Prob. 13.56ECh. 13 - Prob. 13.57ECh. 13 - Prob. 13.58ECh. 13 - Reduce the following reducible representations...Ch. 13 - Determine the resulting representations for the...Ch. 13 - Prob. 13.61ECh. 13 - Without using the great orthogonality theorem,...Ch. 13 - Assume that you are evaluating the integral of...Ch. 13 - Prob. 13.64ECh. 13 - Assume that x- polarized light can be assigned an...Ch. 13 - Prob. 13.66ECh. 13 - Prob. 13.67ECh. 13 - Prob. 13.68ECh. 13 - Prob. 13.69ECh. 13 - Prob. 13.70ECh. 13 - Construct the symmetry-adapted linear combination...Ch. 13 - Prob. 13.72ECh. 13 - Prob. 13.73ECh. 13 - Prob. 13.74ECh. 13 - Prob. 13.75ECh. 13 - Prob. 13.76ECh. 13 - Prob. 13.77ECh. 13 - Suppose you use p0,p1 and p+1 along with s...Ch. 13 - Show that the individual sp orbitals, as written...Ch. 13 - Prob. 13.80ECh. 13 - What is the rough hybridization of the carbon...Ch. 13 - Determine the symmetry species of the D3h point...Ch. 13 - Determine the D3h symmetry species of the sp3d...Ch. 13 - Prob. 13.84ECh. 13 - In propene CH3CH=CH2, the first carbon has sp3...Ch. 13 - Prob. 13.87ECh. 13 - Prob. 13.88ECh. 13 - Prob. 13.89E
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
  • Text book image
    Chemistry & Chemical Reactivity
    Chemistry
    ISBN:9781337399074
    Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
    Publisher:Cengage Learning
    Text book image
    Chemistry & Chemical Reactivity
    Chemistry
    ISBN:9781133949640
    Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
    Publisher:Cengage Learning
    Text book image
    Principles of Modern Chemistry
    Chemistry
    ISBN:9781305079113
    Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
    Publisher:Cengage Learning
  • Text book image
    Chemistry: An Atoms First Approach
    Chemistry
    ISBN:9781305079243
    Author:Steven S. Zumdahl, Susan A. Zumdahl
    Publisher:Cengage Learning
    Text book image
    Chemistry
    Chemistry
    ISBN:9781133611097
    Author:Steven S. Zumdahl
    Publisher:Cengage Learning
    Text book image
    Chemistry
    Chemistry
    ISBN:9781305957404
    Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
    Publisher:Cengage Learning
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781133949640
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Principles of Modern Chemistry
Chemistry
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:Cengage Learning
Text book image
Chemistry: An Atoms First Approach
Chemistry
ISBN:9781305079243
Author:Steven S. Zumdahl, Susan A. Zumdahl
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781133611097
Author:Steven S. Zumdahl
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Group Theory - Learn like Expert with 3D animation | Introduction for Beginners | ONE Chemistry; Author: One Chemistry;https://www.youtube.com/watch?v=Lz2ih8fkgDs;License: Standard YouTube License, CC-BY