Physical Chemistry 2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Ball, David W. (david Warren), BAER, Tomas
1 Gases And The Zeroth Law Of Thermodynamics 2 The First Law Of Thermodynamics 3 The Second And Third Laws Of Thermodynamics 4 Gibbs Energy And Chemical Potential 5 Introduction To Chemical Equilibrium 6 Equilibria In Single-component Systems 7 Equilibria In Multiple-component Systems 8 Electrochemistry And Ionic Solutions 9 Pre-quantum Mechanics 10 Introduction To Quantum Mechanics 11 Quantum Mechanics: Model Systems And The Hydrogen Atom 12 Atoms And Molecules 13 Introduction To Symmetry In Quantum Mechanics 14 Rotational And Vibrational Spectroscopy 15 Introduction To Electronic Spectroscopy And Structure 16 Introduction To Magnetic Spectroscopy 17 Statistical Thermodynamics: Introduction 18 More Statistical Thermodynamics 19 The Kinetic Theory Of Gases 20 Kinetics 21 The Solid State: Crystals 22 Surfaces Chapter13: Introduction To Symmetry In Quantum Mechanics
Chapter Questions Section: Chapter Questions
Problem 13.1E: In your own words, explain why an object that has more symmetry elements is said to have higher... Problem 13.2E: Identify the symmetry elements present in the following objects. a A ream of blank paper, no holes.... Problem 13.3E: Identify the symmetry elements present in the following objects. a The Eiffel Tower. You may have to... Problem 13.4E Problem 13.5E Problem 13.6E Problem 13.7E Problem 13.8E Problem 13.9E: Any axis of symmetry Cn that rotates an object by =360/n about the z-axis can be generalized by the... Problem 13.10E Problem 13.11E Problem 13.12E Problem 13.13E Problem 13.14E: What are the number of classes and the order of the following point groups? a C2v b D2h c D6h d S4 e... Problem 13.15E Problem 13.16E: a Show that the C3v point group satisfies the closure property of a mathematical group. b Show that... Problem 13.17E: a In the Td point group, an S41 improper rotation is equivalent to what other improper rotation? b... Problem 13.18E: Determine which single symmetry operation of the following point groups is equivalent to the given... Problem 13.19E Problem 13.20E Problem 13.21E Problem 13.22E: Figure 13.27 shows the structure of the molecule porphine. Figure 13.27 The structure of porphine.... Problem 13.23E Problem 13.24E: Identify all the symmetry elements present in the tetrahedron, the cube, and the octahedron. Problem 13.25E: Point groups are called such because all of the symmetry elements in the group intersect at one... Problem 13.26E: Determine the point groups of the following molecules. a Hydrogen peroxide, H2O2 it is not planar. b... Problem 13.27E: Determine the point group of the following molecules. a cis1,2 Dichloroethylene b trans1,2... Problem 13.28E: Determine the point groups of the following molecules. a Hydrogen selenide, H2Se b Partially... Problem 13.29E: Determine the point groups of the following molecules. a Fe(CO)5, which has a trigonal bipyramidal... Problem 13.30E: Structural isomers can have very different point groups. Determine the point groups of... Problem 13.31E: Structural isomers can have very different point groups. There are three isomers of dichlorobenzene.... Problem 13.32E Problem 13.33E: Identify the point group of the wave functions of the following molecules. a Deuterium oxide, D2O... Problem 13.34E: Identify the point group of the wave functions of the following molecules. a Hydrogen chloride, HCl... Problem 13.35E Problem 13.36E: Determine if the following species have permanent dipole moments. a Dichloromethane, CH2Cl2 b... Problem 13.37E: Determine if the following species have permanent dipole moments. a The carbonate ion, CO32 b The... Problem 13.38E: Which of the following species will not have permanent dipole moments? a Hydrogen cyanide, HCN b... Problem 13.39E Problem 13.40E: Explain why a molecule with a center of inversion cannot have a dipole moment. Problem 13.41E: a Unlike methane, bromochlorofluoromethane (CHBrClF) is chiral. Determine all symmetry elements that... Problem 13.42E Problem 13.43E Problem 13.44E Problem 13.45E: Show that the irreducible representations of the D2d point group satisfy the closure requirement.... Problem 13.46E: Show that any two of the irreducible representations of the following point groups are orthogonal to... Problem 13.47E: Show that any irreducible representation of these point groups is normalized. a C2 b D2d c Oh d C4h... Problem 13.48E: Explain why this proposed irreducible representation for C2v is impossible. EC2A?1100 Problem 13.49E Problem 13.50E Problem 13.51E: Why is it unnecessary to consider whether an irreducible representation from C4h is orthogonal to an... Problem 13.52E Problem 13.53E Problem 13.54E Problem 13.55E Problem 13.56E Problem 13.57E Problem 13.58E Problem 13.59E: Reduce the following reducible representations using the great orthogonality theorem. a In the C2... Problem 13.60E: Determine the resulting representations for the following products of irreducible representations. a... Problem 13.61E Problem 13.62E: Without using the great orthogonality theorem, reduce the given irreducible representation in C2v... Problem 13.63E: Assume that you are evaluating the integral of products of functions having symmetry labels in... Problem 13.64E Problem 13.65E: Assume that x- polarized light can be assigned an E symmetry species in a system that has C4v... Problem 13.66E Problem 13.67E Problem 13.68E Problem 13.69E Problem 13.70E Problem 13.71E: Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S. Problem 13.72E Problem 13.73E Problem 13.74E Problem 13.75E Problem 13.76E Problem 13.77E Problem 13.78E: Suppose you use p0,p1 and p+1 along with s orbitals to construct hybrid orbitals. Will they be the... Problem 13.79E: Show that the individual sp orbitals, as written in equation 13.16, are orthogonal. Problem 13.80E Problem 13.81E: What is the rough hybridization of the carbon orbitals in the methyl carbonium ion, CH3+, which is... Problem 13.82E: Determine the symmetry species of the D3h point group for the sp2 hybrid orbitals, assuming that the... Problem 13.83E: Determine the D3h symmetry species of the sp3d hybrid orbitals, assuming that the C3 axis is... Problem 13.84E Problem 13.85E: In propene CH3CH=CH2, the first carbon has sp3 hybrid orbitals and the second carbon has sp2 hybrid... Problem 13.87E Problem 13.88E Problem 13.89E Problem 13.56E
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Transcribed Image Text: When using a computer to perform numerical integration, the spin coordinates must be integrated
out so that only integrals involving spatial functions remain. Using the fact that the spin functions
are orthonormal, show that
1
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Branch of chemistry that studies how atoms, molecules, and materials interact with each other. Physical chemistry focuses on the behavior of matter, such as solids, liquids, and gases, as they interact with other matter. The study of physical chemistry is crucial to thermodynamics, quantum mechanics, and photochemistry.
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