Atkins' Physical chemistry
Atkins' Physical chemistry
11th Edition
ISBN: 9780198814740
Author: ATKINS, P. W. (peter William), 1940- (author.)
Publisher: Oxford University Press,
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Chapter 10, Problem 10C.9BE

(i)

Interpretation Introduction

Interpretation:

The states of anthracene that might be reached by electric dipole transitions from its ground state have to be stated.

Concept introduction:

The selection rules for molecular transitions can be made on the basis of group theory by knowing the symmetry species of the wavefunctions.  The intensity of transition depends on the electric transition dipole moment.

(i)

Expert Solution
Check Mark

Answer to Problem 10C.9BE

The states of anthracene that might be reached by electric dipole transitions from its ground state are B1u, B2u, and B3u.

Explanation of Solution

The structure of anthracene is shown below.

Atkins' Physical chemistry, Chapter 10, Problem 10C.9BE , additional homework tip  1

Figure 1

The anthracene molecule belongs to the D2h point group.

The dipole integral of D2h point group is B1u+B2u+B3u.

The character table for D6h point group is given below.

D2hEC2(x)C2(y)C2(z)iσ(xy)σ(yz)σ(zx)
Ag11111111
B1u111111111
B2u11111111
B3u11111111

The electric transition dipole moment is calculated using the formula given below.

    μq,fi=eψf*qψidτ        (1)

Where,

  • q is the component in x,y or z direction.
  • ψi is the initial wavefunction.
  • ψf* is the conjugate of the final wavefunction.
  • μq,fi is the electric transition dipole moment.
  • e is the charge of an electron.

The ground state is Ag.

The transition ψAgψB1u is considered.

This gives the product in the integral to be Ag×q×B1u.

The product of Ag×A2u=B1u.  Therefore, the product in the integral can be written as B1u×q.

The product in the integral will be equal to Ag and is allowed only when the q component is equal to B1u.

The q component has symmetry species B1u, therefore, the transition ψAgψB1u is allowed and polarized at z-axis.

The transition ψAgψB2u is considered.

This gives the product in the integral to be Ag×q×B2u.

The product of Ag×A2u=B2u.  Therefore, the product in the integral can be written as B2u×q.

The product in the integral will be equal to Ag and is allowed only when the q component is equal to B2u.

The q component has symmetry species B2u, therefore, the transition ψAgψB2u is allowed and polarized at y-axis.

The transition ψAgψB3u is considered.

This gives the product in the integral to be Ag×q×B3u.

The product of Ag×A2u=B3u.  Therefore, the product in the integral can be written as B3u×q.

The product in the integral will be equal to Ag and is allowed only when the q component is equal to B3u.

The q component has symmetry species B3u, therefore, the transition ψAgψB3u is allowed and polarized at x-axis.

(b)

Interpretation Introduction

Interpretation:

The states of coronene that might be reached by electric dipole transitions from its ground state have to be stated.

Concept introduction:

As mentioned in the concept introduction in part (a).

(b)

Expert Solution
Check Mark

Answer to Problem 10C.9BE

The states of coronene that might be reached by electric dipole transitions from its ground state are A2u and E1u.

Explanation of Solution

The structure of coronene is shown below.

Atkins' Physical chemistry, Chapter 10, Problem 10C.9BE , additional homework tip  2

Figure 2

The anthracene molecule belongs to the D6h point group.

The dipole integral of D6h point group is A2u+E1u.

The character table for D6h point group is given below.

D6hE2C62C3C23C2'3C2"i2S32S6σh3σd3σv
A1g111111111111
A2u111111111111
E1u211200211200

The electric transition dipole moment is calculated using the formula given below.

    μq,fi=eψf*qψidτ        (1)

Where,

  • q is the component in x,y or z direction.
  • ψi is the initial wavefunction.
  • ψf* is the conjugate of the final wavefunction.
  • μq,fi is the electric transition dipole moment.
  • e is the charge of an electron.

The ground state is A1g.

The transition ψA1gψA1u is considered.

This gives the product in the integral to be A1g×q×A2u.

The product of A1g×A2u=A2u.  Therefore, the product in the integral can be written as A2u×q.

The product in the integral will be equal to A1g and is allowed only when the q component is equal to A2u.

The q component has symmetry species A2u, therefore, the transition ψA1gψA1u is allowed and polarized at z-axis.

The transition ψA1gψE1u is considered.

This gives the product in the integral to be A1g×q×E1u.

The product of A1g×A2u=E1u.  Therefore, the product in the integral can be written as E1u×q.

The product in the integral will be equal to A1g and is allowed only when the q component is equal to E1u.

The q component has symmetry species E1u, therefore, the transition ψA1gψE1u is allowed and polarized at x-axis and y axis.

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Chapter 10 Solutions

Atkins' Physical chemistry

Ch. 10 - Prob. 10A.2AECh. 10 - Prob. 10A.2BECh. 10 - Prob. 10A.3AECh. 10 - Prob. 10A.3BECh. 10 - Prob. 10A.4AECh. 10 - Prob. 10A.4BECh. 10 - Prob. 10A.5AECh. 10 - Prob. 10A.5BECh. 10 - Prob. 10A.6AECh. 10 - Prob. 10A.6BECh. 10 - Prob. 10A.7AECh. 10 - Prob. 10A.1PCh. 10 - Prob. 10A.2PCh. 10 - Prob. 10A.3PCh. 10 - Prob. 10A.4PCh. 10 - Prob. 10A.5PCh. 10 - Prob. 10B.1DQCh. 10 - Prob. 10B.2DQCh. 10 - Prob. 10B.3DQCh. 10 - Prob. 10B.4DQCh. 10 - Prob. 10B.5DQCh. 10 - Prob. 10B.1AECh. 10 - Prob. 10B.1BECh. 10 - Prob. 10B.2AECh. 10 - Prob. 10B.2BECh. 10 - Prob. 10B.3AECh. 10 - Prob. 10B.3BECh. 10 - Prob. 10B.4AECh. 10 - Prob. 10B.4BECh. 10 - Prob. 10B.5AECh. 10 - Prob. 10B.5BECh. 10 - Prob. 10B.6AECh. 10 - Prob. 10B.6BECh. 10 - Prob. 10B.7AECh. 10 - Prob. 10B.7BECh. 10 - Prob. 10B.1PCh. 10 - Prob. 10B.2PCh. 10 - Prob. 10B.3PCh. 10 - Prob. 10B.4PCh. 10 - Prob. 10B.5PCh. 10 - Prob. 10B.6PCh. 10 - Prob. 10B.7PCh. 10 - Prob. 10B.8PCh. 10 - Prob. 10B.9PCh. 10 - Prob. 10B.10PCh. 10 - Prob. 10C.1DQCh. 10 - Prob. 10C.2DQCh. 10 - Prob. 10C.1AECh. 10 - Prob. 10C.1BECh. 10 - Prob. 10C.2AECh. 10 - Prob. 10C.2BECh. 10 - Prob. 10C.3AECh. 10 - Prob. 10C.3BECh. 10 - Prob. 10C.4AECh. 10 - Prob. 10C.4BECh. 10 - Prob. 10C.5AECh. 10 - Prob. 10C.6AECh. 10 - Prob. 10C.6BECh. 10 - Prob. 10C.7AECh. 10 - Prob. 10C.7BECh. 10 - Prob. 10C.8AECh. 10 - Prob. 10C.8BECh. 10 - Prob. 10C.9AECh. 10 - Prob. 10C.9BECh. 10 - Prob. 10C.1PCh. 10 - Prob. 10C.2PCh. 10 - Prob. 10C.3PCh. 10 - Prob. 10C.4PCh. 10 - Prob. 10C.5PCh. 10 - Prob. 10C.6P
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