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 α − E . All non-overlap integrals are equal to 0 . The overlap integrals of non-neighbours is 0 . The overlap integrals of neighbours is β .

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Answer 1

Question

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

Explanation of Solution

The structure of azulene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

Explanation of Solution

The structure of acenaphthylene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

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

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Answer 2

Question

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

Explanation of Solution

The structure of azulene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

Explanation of Solution

The structure of acenaphthylene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

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

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Answer 3

Question

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

Explanation of Solution

The structure of azulene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

Explanation of Solution

The structure of acenaphthylene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

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

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Answer 4

Question

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

Explanation of Solution

The structure of azulene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

Explanation of Solution

The structure of acenaphthylene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

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

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Answer 5

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

Explanation of Solution

The structure of azulene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

Explanation of Solution

The structure of acenaphthylene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

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

Answer 6

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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

Explanation of Solution

The structure of azulene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

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

Answer 7

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 α−E.

All non-overlap integrals are equal to 0.

The overlap integrals of non-neighbours is 0.

The overlap integrals of neighbours is β.

Answer 8

(i)

Expert Solution

Answer to Problem 9E.4BE

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

H=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

Answer 9

(i)

Expert Solution

Answer 10

(i)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The structure of azulene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ0000000ββα−Eβ00000000βα−Eβ00000000βα−Eβ0000β000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eβ00000000βα−Eββ00β0000βα−E)

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

Answer 13

(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 α−E.

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

Answer to Problem 9E.4BE

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

H=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

Explanation of Solution

The structure of acenaphthylene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

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

Answer 14

(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 α−E.

All non-overlap integrals are equal to 0.

The overlap integrals of non-neighbours is 0.

The overlap integrals of neighbours is β.

Answer 15

(ii)

Expert Solution

Answer to Problem 9E.4BE

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

H=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)

Answer 16

(ii)

Expert Solution

Answer 17

(ii)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The structure of acenaphthylene is shown below.

Atkins' Physical Chemistry, 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 α−E.

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=(α−Eβ00000000βββα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ00000β0000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0000000000βα−Eβ0β00000000βα−Eβ0β00000000βα−Eββ000β000β0βα−E)