The secular determinant for anthracene 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.4AE

(i)

Interpretation Introduction

Interpretation:

The secular determinant for anthracene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

Explanation of Solution

The structure of anthracene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 1

Figure 1

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

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

(ii)

Interpretation Introduction

Interpretation:

The secular determinant for phenanthrene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

Explanation of Solution

The structure of phenanthrene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 2

Figure 2

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

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

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Answer 2

Question

Chapter 9, Problem 9E.4AE

(i)

Interpretation Introduction

Interpretation:

The secular determinant for anthracene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

Explanation of Solution

The structure of anthracene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 1

Figure 1

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

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

(ii)

Interpretation Introduction

Interpretation:

The secular determinant for phenanthrene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

Explanation of Solution

The structure of phenanthrene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 2

Figure 2

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

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

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Answer 3

Question

Chapter 9, Problem 9E.4AE

(i)

Interpretation Introduction

Interpretation:

The secular determinant for anthracene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

Explanation of Solution

The structure of anthracene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 1

Figure 1

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

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

(ii)

Interpretation Introduction

Interpretation:

The secular determinant for phenanthrene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

Explanation of Solution

The structure of phenanthrene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 2

Figure 2

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

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

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Answer 4

Question

Chapter 9, Problem 9E.4AE

(i)

Interpretation Introduction

Interpretation:

The secular determinant for anthracene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

Explanation of Solution

The structure of anthracene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 1

Figure 1

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

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

(ii)

Interpretation Introduction

Interpretation:

The secular determinant for phenanthrene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

Explanation of Solution

The structure of phenanthrene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 2

Figure 2

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

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

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Answer 5

Chapter 9, Problem 9E.4AE

(i)

Interpretation Introduction

Interpretation:

The secular determinant for anthracene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

Explanation of Solution

The structure of anthracene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 1

Figure 1

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

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

(ii)

Interpretation Introduction

Interpretation:

The secular determinant for phenanthrene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

Explanation of Solution

The structure of phenanthrene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 2

Figure 2

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

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

Answer 6

Chapter 9, Problem 9E.4AE

(i)

Interpretation Introduction

Interpretation:

The secular determinant for anthracene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

Explanation of Solution

The structure of anthracene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 1

Figure 1

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

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

Answer 7

Chapter 9, Problem 9E.4AE

(i)

Interpretation Introduction

Interpretation:

The secular determinant for anthracene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

Answer 9

(i)

Expert Solution

Answer 10

(i)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The structure of anthracene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 1

Figure 1

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000000000000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eββ00β00000000βα−E)

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

Answer 13

(ii)

Interpretation Introduction

Interpretation:

The secular determinant for phenanthrene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

Explanation of Solution

The structure of phenanthrene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 2

Figure 2

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

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

Answer 14

(ii)

Interpretation Introduction

Interpretation:

The secular determinant for phenanthrene 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.4AE

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

H=(α−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)

Answer 16

(ii)

Expert Solution

Answer 17

(ii)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The structure of phenanthrene is shown below.

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH), Chapter 9, Problem 9E.4AE , additional homework tip 2

Figure 2

The total number of carbon atoms in anthracene is 14.

Therefore, a 14×14 determinant is obtained.

H=(H11H12H13H14H15H16H17H18H19H110H111H112H113H114 H21H22H23H24H25H26H27H28H29H210H211H212H213H214H31H32H33H34H35H36H37H38H39H310H311H312H313H314H41H42H43H44H45H46H47H48H49H410H411H412H413H414H51H52H53H54H55H56H57H58H59H510H511H512H513H514H61H62H63H64H65H66H67H68H69H610H611H612H613H613H71H72H73H74H75H76H77H78H79H710H711H712H713H714H81H82H83H84H85H86H87H88H89H810H811H812H813H814H91H92H93H94H95H96H97H98H99H910H911H912H913H914H101H102H103H104H105H106H107H108H109H1010H1011H1012H1013H1014H111H112H113H114H115H116H117H118H119H1110H1111H1112H1113H1114H121H122H123H124H125H126H127H128H129H1210H1211H1212H1213H1214H131H132H133H134H135H136H137H138H139H1310H1311H1312H1313H1314H141H142H143H144H145H146H147H148H149H1410H1411H1412H1413H1414)

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−Eβ00000000000ββα−Eβ000000000000βα−Eβ0000000β0000βα−Eβ000β00000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ00000000β000βα−Eβ000000000000βα−Eβ000000000000βα−Eβ0000β0000000βα−Eβ000000000000βα−Eββ00000000000βα−E)