Atkins' Physical chemistry
Atkins' Physical chemistry
11th Edition
ISBN: 9780198814740
Author: ATKINS, P. W. (peter William), 1940- (author.)
Publisher: Oxford University Press,
bartleby

Videos

Question
Book Icon
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.

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 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.

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 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.

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!

Chapter 9 Solutions

Atkins' Physical chemistry

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
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.
Recommended textbooks for you
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Text book image
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Text book image
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Text book image
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY
Linear Combination of Atomic Orbitals LCAO; Author: Edmerls;https://www.youtube.com/watch?v=nq1zwrAIr4c;License: Standard YouTube License, CC-BY
Quantum Molecular Orbital Theory (PChem Lecture: LCAO and gerade ungerade orbitals); Author: Prof Melko;https://www.youtube.com/watch?v=l59CGEstSGU;License: Standard YouTube License, CC-BY