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ChemistryPhysical ChemistryGroup theory requires that symmetry operations satisfy the associative law. (a) Do they satisfy the commutative law? That is, does a different order of the same symmetry operations always yield the same answer? Provide a specific example to support your answer. (b) In matrix algebra, matrix multiplication is not commutative. For any two given matrices A and B , it is not a certainty that A B = B A . Does this support or refute your conclusion in part a, and why?BuyFind*launch*

2nd Edition

Ball + 3 others

Publisher: Wadsworth Cengage Learning,

ISBN: 9781133958437

Chapter 13, Problem 13.21E

Textbook Problem

Group theory requires that symmetry operations satisfy the associative law. **(a)** Do they satisfy the commutative law? That is, does a different order of the same symmetry operations always yield the same answer? Provide a specific example to support your answer. **(b)** In matrix algebra, matrix multiplication is not commutative. For any two given matrices

Physical Chemistry

Ch. 13 - In your own words, explain why an object that has...Ch. 13 - Identify the symmetry elements present in the...Ch. 13 - Identify the symmetry elements present in the...Ch. 13 - What would your answer to exercise 13.3d be if all...Ch. 13 - Identify the point groups of the objects in the...Ch. 13 - Show that S1= and S2=i.Ch. 13 - Without referring to Appendix 3, determine whether...Ch. 13 - A molecule that has a C6 axis automatically has...Ch. 13 - Any axis of symmetry Cn that rotates an object by...Ch. 13 - Use equation 13.18 in the above exercise to deduce...

Ch. 13 - In the answer to exercise 13.10, part a, what does...Ch. 13 - List the mathematical properties of a group.Ch. 13 - Use equation 13.18 to construct the matrix...Ch. 13 - What are the number of classes and the order of...Ch. 13 - What are the number of classes and the order of...Ch. 13 - a Show that the C3v point group satisfies the...Ch. 13 - a In the Td point group, an S41 improper rotation...Ch. 13 - Determine which single symmetry operation of the...Ch. 13 - What symmetry operations are the inverse of the...Ch. 13 - What symmetry operations are the inverse of the...Ch. 13 - Group theory requires that symmetry operations...Ch. 13 - Figure 13.27 shows the structure of the molecule...Ch. 13 - In Example 13.3e, we are assuming that resonance...Ch. 13 - Identify all the symmetry elements present in the...Ch. 13 - Point groups are called such because all of the...Ch. 13 - Determine the point groups of the following...Ch. 13 - Determine the point group of the following...Ch. 13 - Determine the point groups of the following...Ch. 13 - Determine the point groups of the following...Ch. 13 - Structural isomers can have very different point...Ch. 13 - Structural isomers can have very different point...Ch. 13 - Chlorination of methane yields CH3Cl,CH2Cl2,CHCl3...Ch. 13 - Identify the point group of the wave functions of...Ch. 13 - Identify the point group of the wave functions of...Ch. 13 - a What would be the formulas of possible molecules...Ch. 13 - Determine if the following species have permanent...Ch. 13 - Determine if the following species have permanent...Ch. 13 - Which of the following species will not have...Ch. 13 - Determine if the following species have permanent...Ch. 13 - Explain why a molecule with a center of inversion...Ch. 13 - a Unlike methane, bromochlorofluoromethane...Ch. 13 - Write out explicitly the 1212 matrices that...Ch. 13 - For NH3, write out explicitly the three 1212...Ch. 13 - Show that the irreducible representations of the...Ch. 13 - Show that the irreducible representations of the...Ch. 13 - Show that any two of the irreducible...Ch. 13 - Show that any irreducible representation of these...Ch. 13 - Explain why this proposed irreducible...Ch. 13 - Using the character tables in Appendix 3, can you...Ch. 13 - Show by using an example that the sum of the...Ch. 13 - Why is it unnecessary to consider whether an...Ch. 13 - Explain why the characters for the proper and...Ch. 13 - Use the expressions in Rh(3) to determine the...Ch. 13 - a What are the symmetry elements present in a plot...Ch. 13 - What are the symmetry elements present in a plot...Ch. 13 - What point groups must the wavefunctions of all...Ch. 13 - The bonds in the ethylene molecule can be...Ch. 13 - Consider the bonds in ethylene shown in the...Ch. 13 - Reduce the following reducible representations...Ch. 13 - Determine the resulting representations for the...Ch. 13 - Determine the resulting representations for the...Ch. 13 - Without using the great orthogonality theorem,...Ch. 13 - Assume that you are evaluating the integral of...Ch. 13 - Assume that you are evaluating the integral of...Ch. 13 - Assume that x- polarized light can be assigned an...Ch. 13 - Show that ss transitions are not allowed in the...Ch. 13 - The ground electronic state of ozone, O3, a C2v...Ch. 13 - The five d orbitals in transition metals can be...Ch. 13 - Determine the symmetry labels of the H-like p...Ch. 13 - Determine the symmetry labels of the H-like f...Ch. 13 - Construct the symmetry-adapted linear combination...Ch. 13 - Referring to exercise 13.71: How would the...Ch. 13 - In Example 13.13, several of the molecular...Ch. 13 - Should the molecular orbitals for H2O found in...Ch. 13 - How many SALCs can be constructed for CH4 using...Ch. 13 - Construct a list comparing and contrasting VB...Ch. 13 - Why might one not be surprised to find that the...Ch. 13 - Suppose you use p0,p1 and p+1 along with s...Ch. 13 - Show that the individual sp orbitals, as written...Ch. 13 - Show that the individual sp3 orbitals, as written...Ch. 13 - What is the rough hybridization of the carbon...Ch. 13 - Determine the symmetry species of the D3h point...Ch. 13 - Determine the D3h symmetry species of the sp3d...Ch. 13 - Determine the Oh symmetry species of the sp3d2...Ch. 13 - In propene CH3CH=CH2, the first carbon has sp3...Ch. 13 - Justify the fact that the nitrogen atom in ammonia...Ch. 13 - What symmetry species is assigned to the lone p...Ch. 13 - Construct 90 probability surface diagrams for sp,...

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