EBK PHYSICAL CHEMISTRY
2nd Edition
ISBN: 8220100477560
Author: Ball
Publisher: Cengage Learning US
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Textbook Question
Chapter 13, Problem 13.51E
Why is it unnecessary to consider whether an irreducible representation from
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A symmetry group of order h = 8 is known to have five (5) classes. Three of its irreducible representations have a dimensionality of 1.
Based on this, what are the dimensions of its remaining irreducible representation(s)?
1, 1, 1
1, 2
1, 1, 1, 1, 1
2,2
1, 2, 2
OOO
Im confused with this
C3
C
P
C32
Point Group:
σh
S3
- Determine the irreducible representations with reasons in the following character table.
C
I R R, R xy.
Chapter 13 Solutions
EBK 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 - Prob. 13.4ECh. 13 - Prob. 13.5ECh. 13 - Prob. 13.6ECh. 13 - Prob. 13.7ECh. 13 - Prob. 13.8ECh. 13 - Any axis of symmetry Cn that rotates an object by...Ch. 13 - Prob. 13.10E
Ch. 13 - Prob. 13.11ECh. 13 - Prob. 13.12ECh. 13 - Prob. 13.13ECh. 13 - What are the number of classes and the order of...Ch. 13 - Prob. 13.15ECh. 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 - Prob. 13.19ECh. 13 - Prob. 13.20ECh. 13 - Prob. 13.21ECh. 13 - Figure 13.27 shows the structure of the molecule...Ch. 13 - Prob. 13.23ECh. 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 - Prob. 13.32ECh. 13 - Identify the point group of the wave functions of...Ch. 13 - Identify the point group of the wave functions of...Ch. 13 - Prob. 13.35ECh. 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 - Prob. 13.39ECh. 13 - Explain why a molecule with a center of inversion...Ch. 13 - a Unlike methane, bromochlorofluoromethane...Ch. 13 - Prob. 13.42ECh. 13 - Prob. 13.43ECh. 13 - Prob. 13.44ECh. 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 - Prob. 13.49ECh. 13 - Prob. 13.50ECh. 13 - Why is it unnecessary to consider whether an...Ch. 13 - Prob. 13.52ECh. 13 - Prob. 13.53ECh. 13 - Prob. 13.54ECh. 13 - Prob. 13.55ECh. 13 - Prob. 13.56ECh. 13 - Prob. 13.57ECh. 13 - Prob. 13.58ECh. 13 - Reduce the following reducible representations...Ch. 13 - Determine the resulting representations for the...Ch. 13 - Prob. 13.61ECh. 13 - Without using the great orthogonality theorem,...Ch. 13 - Assume that you are evaluating the integral of...Ch. 13 - Prob. 13.64ECh. 13 - Assume that x- polarized light can be assigned an...Ch. 13 - Prob. 13.66ECh. 13 - Prob. 13.67ECh. 13 - Prob. 13.68ECh. 13 - Prob. 13.69ECh. 13 - Prob. 13.70ECh. 13 - Construct the symmetry-adapted linear combination...Ch. 13 - Prob. 13.72ECh. 13 - Prob. 13.73ECh. 13 - Prob. 13.74ECh. 13 - Prob. 13.75ECh. 13 - Prob. 13.76ECh. 13 - Prob. 13.77ECh. 13 - Suppose you use p0,p1 and p+1 along with s...Ch. 13 - Show that the individual sp orbitals, as written...Ch. 13 - Prob. 13.80ECh. 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 - Prob. 13.84ECh. 13 - In propene CH3CH=CH2, the first carbon has sp3...Ch. 13 - Prob. 13.87ECh. 13 - Prob. 13.88ECh. 13 - Prob. 13.89E
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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.Similar questions
- Give an example, with justification, of a non-trivial irreducible representation of D4.arrow_forwardMolecule: [W(CN)8] 2- . Point Groupd D4h. Use the CN bond vectors as your basis to determine a irreducible representations and total representation.arrow_forwardhow to determine irreducible representations of pyrazine? point group d2harrow_forward
- The molecule PtCl 2 - is an important square planar starting material in synthetic inorganic chemistry. Using the p orbitals of Cl as the basis find the irreducible representations of the p orbitals and indicate which orbitals could possibly overlap with any of the orbitals on Pt . Assume that the pz orbitals on Cl are orientated in the same direction as the principle rotation axis, px orbitals are pointed at the Pt , and the py orbitals are orthogonal to the px orbitals. Show the characters of each orbital and identify which orbitals on Pt would match from a pure symmetry standpoint.arrow_forwardReduce the following reducible representation, r, to obtain the number of constituent reducible representations and then put your answers in the boxes below. Find the character table at this link 2. Ta 8C; 3C, 6S, 60, Г, -1 4 -2 Σ Σ/24 A1 A2 т, T2 Г, - A1+ A2+ E+ T1+ T2arrow_forwardWhat is the point group of a cube? D4h Ohn Tdarrow_forward
- The point group for a square pyramidal geometry is C4v. Assign the nine s, p, and d orbitals to their correct irreducible representations (i.e., Mulliken Symbols) in C4v point group.arrow_forwardExplain what is meant by irreducible representations, non-degenerate representations and degenerate representations. Which point groups will have degenerate directional properties?arrow_forwardWhat is the point group resulting from adding the inversion operation to C2v ?arrow_forward
- Neopentane, C(CH3)4, has Tď symmetry, with character table provided below. Suppose the characters of a reducible representation of this point group are x(E) = 17, x(C3) = 2, x(C₂) = 5, x(S4) = -3, and x(od) = -5 (this is shown explicitly in the last row of the character table). (a) Use the T₁ irreducible representation to determine the order of the point group using the Little Orthogonality Theorem (Vallance Eq. 1.15.13, see Problem 3). (b) Determine how many times each irreducible representation in Ta is contained in this reducible representation. Td A₁ A₂ E Τ1 T₂ r E 1 1 2 3 3 17 8C3 1 1 -1 1 0 0 2 3C₂ 1 1 2 -1 6S4 1 -1 1 101 1.5 7 0 1 713 7. 1.5 -1 -1 60d -3 -1 -1 -5arrow_forwardGive the reducible representation of the trigonal planar with D3h point grouparrow_forwardFor the point group D3h, confirm that the irreducible representation E′ is orthogonal (in the sense defined by eqn 10B.7) to the irreducible representations A′1, A′2 , and E″.arrow_forward
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