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 O 1,2 1, 1, 1, 1, 1 02, 2 1, 2, 2

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 O 1,2 1, 1, 1, 1, 1 02, 2 1, 2, 2

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter13: Introduction To Symmetry In Quantum Mechanics

Section: Chapter Questions

Problem 13.46E: Show that any two of the irreducible representations of the following point groups are orthogonal to...

See similar textbooks

Related questions

Q: Consider the D2d point group. a. What is the order (h)? b. How many classes are there? c. How many…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: The chlorophylls that participate in photosynthesis and the haem (heme) groups of cytochromes are…

A: Chlorophyll is a macromolecule. It consists of a porphyrin ring containing magnesium metal in the…

Q: H CI H A

A: By applying a particular symmetry operation, if we get identical molecule, then that symmetry…

Q: Chemistry Identify and draw the symmetry elements for NH3

A: The symmetry elements of NH3 are E, 2C3, and 3 sigma-v.

Q: Identify the point groups to which the following objects belong: (i) a sphere, (ii) an isosceles…

A: a. The circle has its origin fixed so that it belongs to the r3 point group which has its origin…

Q: of Identify all symmetry elements and point group CHF3

A: The symmetry elements and point group of CHF3 are given below

Q: Using its x, y, and z coordinates, construct the 15 x 15 matrix that describes the application of…

A: The explanation is given below-

Q: Determine the symmetry labels of the hydrogen-like p orbitals in Td symmetry.

A: The symmetry label of the hydrogen-like p orbitals in Td symmetry has to be determined.

Q: The above drawing represents a SALC made up of H1s orbitals for the molecule ethene. This molecule…

A: To identify the irreducible representation for the Given SALC of ethene which belongs to the D2h…

Q: (a) SCIFs List symmetry operations: Point group:

A: To find the symmetry elements and point group of a main group molecule SClF5.Use the concept of…

Q: The tetrahedral borohydride anion (BH4) has Ta symmetry and is commonly used as a reductant in…

A: To identify the labels for the 2s and 2p orbital of the B atom for tetrahedral borohydride ion…

Q: Identify all symmetry elements and point group of So Fy

A: Symmetry element: The point, line or a plane about which symmetry operations like center of…

Q: Allene, C3H4, has point group symmetry D2d, with character table provided below. It can be embedded…

A: The allene molecule is given to have a D2d point group whose point group table is given as follows:…

Q: (a) Identify the principal (z) rotational axis for all molecules provided below. (b) Provide a…

A: Symmetry operation is an action perfomed on a molecule , yields an new orientation of it that is…

Q: Which one of the following molecule do not belong to the high symmetry group? O Cla O SF. O XeF2 O…

A: Group theory explains the symmetry of the molecules based upon the symmetry elements. These elements…

Q: B) Identify all the elements of symmetry of IrCl(CO) [P(C6H5)3]2 and the point group assignment.…

A: The elements of symmetry are the referential points about which any symmetry operation can take…

Q: (b) Decompose the representation below into the irreducible representations of C3v. 2C3 1 C3v T E…

A: An irreducible representation of a group is a group representation that has no nontrivial invariant…

Q: Make a list of all symmetry operations present in Bh3 and H2O?

Q: identify the symmetry elements for each isomer of Ma3b2.

Q: Determine all the symmetry elements of the following molecules Ethene Tetraphenylmethane ,…

A: 1. Ethene belongs to D2h point group. and it contains 3 C2 axes and 3 sigma planes symmetry…

Q: (ii) List and depict all the symmetry elements and deduce the point group. NH2 N' NH2 B

A: There are several rules applied to determine the point group of a compound depending on the symmetry…

Q: Find the point groups of the following shapes, interpreting (a) as a square and (b)-(p) as…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: C=C H H H B. HH CO エーm

A: As you not specified so I am giving answer of first three question as per guidlines Point group…

Q: The point group for a square pyramidal geometry is C4v. Assign the nine s, p, and d orbitals to…

A: In molecular geometry, square pyramidal geometry describes the shape of certain compounds with the…

Q: 2. Spin-State Transition: LaCoO3 is a perovskite oxide in which the transition metal ion Co is…

Q: List all the symmetry elements of a Cr(CO)6 molecule and identify the symmetry point group to which…

A: Symmetry Elements : Symmetry elements are mathematical tools which are used to analyze the geometry…

Q: Reduce the following representations for C2h. C2v and Cav point groups into corresponding…

Q: Prove

A: He2 have total number of electrons is equal to 2 • 2 = 4 electron ( each He atom have 2 electrons )…

Q: How many symmetry planes does p-dibromobenzene have? O 1 2 3 4

A: A plane of symmetry is a symmetry element. The plane of symmetry is defined as a flat surface that…

Q: Since we use wavefunctions to describe the motion of the electron around the nucleus, the reference…

A: If the wavefunction is symmetric with respect to origin, that means wavefunction has mirror image…

Q: Give all the symmetry elements in the following molecules, and assign the point group of each. a )…

A: a) Xe(O)F4:Symmetry elements seem correct:Identity (E)C4 rotation axisTwo perpendicular σv planesC2…

Q: 5. Use the character table of the Cav point group to assign the nine "s", "p", and d" orbitals to…

A: C3v point group is very common, its character table should be known specially Area IV, containing…

Q: cis [Fe(NH3)2(CO)2Br2] symmetry elements and point group?

A: Structure of cis Fe(NH3)2(CO)2Br2 is

Q: Determine all the symmetry elements of the following molecules Ethene Tetraphenylmethane , C(C6H5)4

Question

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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: Explanation

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

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.

Similar questions

Identify the symmetry elements present in the following objects. a The Eiffel Tower. You may have to look up a picture of it if you dont remember its shape b Any book ignore the printing. c An octagonal wood block. d A jack from the set of jacks pictured here: Note that some of the points end differently.
Show that any two of the irreducible representations of the following point groups are orthogonal to each other. a C2 b C2v c D2h d Oh e Td
In your own words, explain why an object that has more symmetry elements is said to have higher symmetry than an object with fewer symmetry elements.
Using the relationships imposed by the orthogonality theorem, predict the characters, XK(R), that have been omitted from this table, and match each with its correct value. All symmetry elements and irreducible representations (labelled with subscripts k = 1, 2, 3, 4, and 5) are included in this table. + X2(C3) ◆ X3(C₂) + X4(0d) X5(E) - ₁₁ [₂ [3 T4 [5 E 1 3 1 3 _?___ 6 S4 8 C3 1 1 1 -1 T -1 0 ? 1 0 -1 A. 1 B.-2 C. 2 D.-1 E. 3 F. 0 3 C₂ 1 -1 ? 어 -1 2 60d 1 -1 -1 ? O
3
B) Identify all the elements of symmetry of IrCl(CO) [P(C6H5)3]2 and the point group assignment. PPH3 B CI- C=O Ph3P
Using its x, y, and z coordinates, construct the 15 x 15 matrix that describes the application of the S4 symmetry operation to square planar [PtCl 4]2- What is the character of this matrix?
Consider the plane group p31m, explain: What is the detailed full meaning for p in this case? What is the detailed full meaning for 3 in this case? What is the detailed full meaning for 1 in this case? What is the detailed full meaning for m in this case? What symmetry elements are not explicitly listed in the plane group symbol but exist in the actual plane group unit cell? What is the orientation of each of all the symmetry elements identified in the previous question?
For 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″.
H H Of the 5, E, C, o, i, and what are the symmetry operations are possible for square planar [PtCl4]²? 2- CI CI
Å L. Y → X 5 3 Consider the trimethylenecyclopropane molecule (point group D3h). Each carbon atom has a pz orbital to contribute to the pi- MOs of the molecule. Take these 6 pz orbitais as a basis set and answer the following questions: A) How do they divide into subsets of symmetry - equivalent orbitals? B) What representations are spanned by each subset? C) What are the 6 normalized
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 -5