PHYSICAL CHEMISTRY-WEBASSIGN
PHYSICAL CHEMISTRY-WEBASSIGN
11th Edition
ISBN: 9780357087411
Author: ATKINS
Publisher: CENGAGE L
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Chapter 9, Problem 9E.4BE

(i)

Interpretation Introduction

Interpretation:

The secular determinant for azulene has to be set within Huckel approximation and using the out-of-plane C2p orbitals as the basis set.

Concept introduction:

Huckel approximations are used to construct the π molecular orbital energy level diagrams of conjugated molecules.

The approximations for in Huckel method are given below.

  • All overlap integrals are equal to αE.
  • All non-overlap integrals are equal to 0.
  • The overlap integrals of non-neighbours is 0.
  • The overlap integrals of neighbours is β.

(i)

Expert Solution
Check Mark

Answer to Problem 9E.4BE

The secular determinant for azulene is set within Huckel approximation as shown below.

H=(αEβ0000000ββαEβ00000000βαEβ00000000βαEβ0000β000βαEβ00000000βαEβ00000000βαEβ00000000βαEβ00000000βαEββ00β0000βαE)

Explanation of Solution

The structure of azulene is shown below.

PHYSICAL CHEMISTRY-WEBASSIGN, Chapter 9, Problem 9E.4BE , additional homework tip  1

Figure 1

The total number of carbon atoms in anthracene is 10.

Therefore, a 10×10 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H21H22H23H24H25H26H27H28H29H210H31H32H33H34H35H36H37H38H39H310H41H42H43H44H45H46H47H48H49H410H51H52H53H54H55H56H57H58H59H510H61H62H63H64H65H66H67H68H69H610H71H72H73H74H75H76H77H78H79H710H81H82H83H84H85H86H87H88H89H810H91H92H93H94H95H96H97H98H99H910H101H102H103H104H105H106H107H108H109H1010)

According to Huckel approximation, all overlap integrals are equal to αE.

All non-overlap integrals are equal to 0.

The overlap integrals of non-neighbours is 0.

The overlap integrals of neighbours is β.

Apply this approximation to the above determinant as shown below.

H=(αEβ0000000ββαEβ00000000βαEβ00000000βαEβ0000β000βαEβ00000000βαEβ00000000βαEβ00000000βαEβ00000000βαEββ00β0000βαE)

Therefore, the secular determinant for azulene has been obtained above.

(ii)

Interpretation Introduction

Interpretation:

The secular determinant for acenaphthylene has to be set within Huckel approximation and using the out-of-plane C2p orbitals as the basis set.

Concept introduction:

Huckel approximations are used to construct the π molecular orbital energy level diagrams of conjugated molecules.

The approximations for in Huckel method are given below.

  • All overlap integrals are equal to αE.
  • All non-overlap integrals are equal to 0.
  • The overlap integrals of non-neighbours is 0.
  • The overlap integrals of neighbours is β.

(ii)

Expert Solution
Check Mark

Answer to Problem 9E.4BE

The secular determinant for acenaphthylene has been set within Huckel approximation as shown below.

H=(αEβ00000000βββαEβ0000000000βαEβ0000000000βαEβ0000000000βαEβ00000β0000βαEβ0000000000βαEβ0000000000βαEβ0000000000βαEβ0β00000000βαEβ0β00000000βαEββ000β000β0βαE)

Explanation of Solution

The structure of acenaphthylene is shown below.

PHYSICAL CHEMISTRY-WEBASSIGN, Chapter 9, Problem 9E.4BE , additional homework tip  2

Figure 1

The total number of carbon atoms in anthracene is 12.

Therefore, a 12×12 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H21H22H23H24H25H26H27H28H29H210H211H212H31H32H33H34H35H36H37H38H39H310H311H312H41H42H43H44H45H46H47H48H49H410H411H412H51H52H53H54H55H56H57H58H59H510H511H512H61H62H63H64H65H66H67H68H69H610H611H612H71H72H73H74H75H76H77H78H79H710H711H712H81H82H83H84H85H86H87H88H89H810H811H812H91H92H93H94H95H96H97H98H99H910H911H912H101H102H103H104H105H106H107H108H109H1010H1011H1012H111H112H113H114H115H116H117H118H119H1110H1111H1112H121H122H123H124H125H126H127H128H129H1210H1211H1212)

According to Huckel approximation, all overlap integrals are equal to αE.

All non-overlap integrals are equal to 0.

The overlap integrals of non-neighbours is 0.

The overlap integrals of neighbours is β.

Apply this approximation to the above determinant as shown below.

H=(αEβ00000000βββαEβ0000000000βαEβ0000000000βαEβ0000000000βαEβ00000β0000βαEβ0000000000βαEβ0000000000βαEβ0000000000βαEβ0β00000000βαEβ0β00000000βαEββ000β000β0βαE)

Therefore, the secular determinant for acenaphthylene has been obtained above.

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Chapter 9 Solutions

PHYSICAL CHEMISTRY-WEBASSIGN

Ch. 9 - Prob. 9A.3AECh. 9 - Prob. 9A.3BECh. 9 - Prob. 9A.4AECh. 9 - Prob. 9A.4BECh. 9 - Prob. 9A.5AECh. 9 - Prob. 9A.5BECh. 9 - Prob. 9A.6AECh. 9 - Prob. 9A.6BECh. 9 - Prob. 9A.7AECh. 9 - Prob. 9A.7BECh. 9 - Prob. 9A.8AECh. 9 - Prob. 9A.8BECh. 9 - Prob. 9A.1PCh. 9 - Prob. 9A.2PCh. 9 - Prob. 9A.3PCh. 9 - Prob. 9B.2DQCh. 9 - Prob. 9B.3DQCh. 9 - Prob. 9B.1AECh. 9 - Prob. 9B.1BECh. 9 - Prob. 9B.2AECh. 9 - Prob. 9B.2BECh. 9 - Prob. 9B.3AECh. 9 - Prob. 9B.3BECh. 9 - Prob. 9B.4AECh. 9 - Prob. 9B.4BECh. 9 - Prob. 9B.1PCh. 9 - Prob. 9B.2PCh. 9 - Prob. 9B.3PCh. 9 - Prob. 9C.1DQCh. 9 - Prob. 9C.2DQCh. 9 - Prob. 9C.3DQCh. 9 - Prob. 9C.4DQCh. 9 - Prob. 9C.1AECh. 9 - Prob. 9C.1BECh. 9 - Prob. 9C.2AECh. 9 - Prob. 9C.2BECh. 9 - Prob. 9C.3AECh. 9 - Prob. 9C.3BECh. 9 - Prob. 9C.4AECh. 9 - Prob. 9C.4BECh. 9 - Prob. 9C.5AECh. 9 - Prob. 9C.5BECh. 9 - Prob. 9C.6AECh. 9 - Prob. 9C.6BECh. 9 - Prob. 9C.2PCh. 9 - Prob. 9C.4PCh. 9 - Prob. 9D.1DQCh. 9 - Prob. 9D.2DQCh. 9 - Prob. 9D.3DQCh. 9 - Prob. 9D.4DQCh. 9 - Prob. 9D.1AECh. 9 - Prob. 9D.1BECh. 9 - Prob. 9D.2AECh. 9 - Prob. 9D.2BECh. 9 - Prob. 9D.3AECh. 9 - Prob. 9D.3BECh. 9 - Prob. 9D.4AECh. 9 - Prob. 9D.4BECh. 9 - Prob. 9D.5AECh. 9 - Prob. 9D.5BECh. 9 - Prob. 9D.6AECh. 9 - Prob. 9D.6BECh. 9 - Prob. 9D.7AECh. 9 - Prob. 9D.7BECh. 9 - Prob. 9D.1PCh. 9 - Prob. 9E.1DQCh. 9 - Prob. 9E.2DQCh. 9 - Prob. 9E.3DQCh. 9 - Prob. 9E.4DQCh. 9 - Prob. 9E.5DQCh. 9 - Prob. 9E.1AECh. 9 - Prob. 9E.1BECh. 9 - Prob. 9E.2AECh. 9 - Prob. 9E.2BECh. 9 - Prob. 9E.3AECh. 9 - Prob. 9E.3BECh. 9 - Prob. 9E.4AECh. 9 - Prob. 9E.4BECh. 9 - Prob. 9E.6AECh. 9 - Prob. 9E.6BECh. 9 - Prob. 9E.1PCh. 9 - Prob. 9E.2PCh. 9 - Prob. 9E.3PCh. 9 - Prob. 9E.6PCh. 9 - Prob. 9.1IACh. 9 - Prob. 9.2IACh. 9 - Prob. 9.4IA
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