Molecular Properties Symmetry

Molecular orbitals and molecular motions belong to certain symmetry species of the point group of the molecule.

Examples of the special ways in which vectors or functions can be affected by symmetry operations are illustrated here. All wave functions solutions, or eigenfunctions, for an atom or a molecule transform according to one or another of the special symmetry species of a point group. We thus have a very powerful guide to the form of any vector or function that describes the properties or behaviour of a symmetric molecule. Each vector or function must transform according to one of the symmetry species of the point group to which the molecule belongs.

Typically, in dealing with ,molecular properties, we proceed from simple and easily pictured or easily described functions or vectors associated with the atoms of a molecule. We use these to build up functions or vectors appropriate to the whole molecule. Thus to describe the translational, rotational and vibrational motion of a molecule, we might start with the three Cartesian displacement coordinates of each atom of the molecule. To describe the translational, rotational and vibrational motion of a molecule, we often adopt a linear combination of atomic orbitals(LCAO) approach.

Now we begin the steps that let us use easy to deal with vectors or functions to deduce the symmetry of molecular vectors or functions.

Characters of transformation matrices: suppose you were to construct transformation matrices, n the basis of a set of vectors or functions. Suppose also that there existed other vectors or functions which were linear combinations of the first set of vectors or functions. You would find that the sum of the diagonal elements of the transformation matrix that represents any symmetry operation would be the same fr any basis vectors or functions. (The transformation matrices themselves would be different for different basis vectors or functions.)

The sum of the diagonal elements of a transformation matrix of a representation is known as the character of the matrix. Thus, the characters of the transformation matrices that represent a group are the same for all basis vectors or functions that are or could be formed each other by linear combinations.

We generally would need large matrices to show the effect of each symmetry operation on the molecule. For example, if we use the three Cartesian displacement coordinates on each atom of an n-atom molecule as our basis, we generally need matrices of order 3n to describe the effects of the operations. If we use bond orbitals as a basis, we generally need transformation matrices with an order equal to the number of bonds. These large matrices can be converted, or reduced, to sets of smaller matrices by forming linear combinations of the original basis vectors. The original sets of large matrices constitute a reducible representation. The smallest matrix representations obtained by appropriate linear combinations of the basis vectors are called irreducible representations. The characters of the reducible representation are the same as the sum of the characters of the irreducible representations that are obtained from the original representation.

The use of characters rather than the transformation matrices themselves brings a great simplicity and elegance to the use of symmetry. First we introduced the tables used to display these characters, and we investigate some of the special properties of the characters of the irreducible representation matrices. 

   Related Questions in Chemistry

  • Q : Problem based on molarity Select the

    Select the right answer of the question. If 18 gm of glucose (C6H12O6) is present in 1000 gm of an aqueous solution of glucose, it is said to be: (a)1 molal (b)1.1 molal (c)0.5 molal (d)0.1 molal

  • Q : Concentration of Calcium carbonate Help

    Help me to go through this problem. 1000 gms aqueous solution of CaCO3 contains 10 gms of carbonate. Concentration of the solution is : (a)10 ppm (b)100 ppm (c)1000 ppm (d)10000 ppm

  • Q : Theory of three dimensional motion

    Partition function; that the translational energy of 1 mol of molecules is 3/2 RT will come as no surprise. But the calculation of this result further illustrates the use of quantized states and the partition function to obtain macroscopic properties. The partition fu

  • Q : Calculating number of moles from

    Choose the right answer from following. If 0.50 mol of CaCl2 is mixed with 0.20 mol of Na3PO4, the maximum number of moles of Ca3 (PO2)2 which can be formed: (a) 0.70 (b) 0.50 (c) 0.20 (d) 0.10

  • Q : Organic structure of cetearyl alcohol

    Can we demonstration the organic structure of cetearyl alcohol and state me what organic family it is?

  • Q : Relative reactivity Which is more

    Which is more reactive towards nucleophilic substitution aryl halide or vinyl halides

  • Q : Molality of Sulfuric acid Choose the

    Choose the right answer from following. The molality of 90% H2SO4 solution is: [density=1.8 gm/ml]  (a)1.8 (b) 48.4 (c) 9.18 (d) 94.6

  • Q : Determining highest normality What is

    What is the correct answer. Which of the given solutions contains highest normality: (i) 8 gm of KOH/litre (ii) N phosphoric acid (iii) 6 gm of NaOH /100 ml (iv) 0.5M H2SO4

  • Q : Symmetry Elements The symmetry of the

    The symmetry of the molecules can be described in terms of electrons of symmetry and the corresponding symmetry operations.Clearly some molecules, like H2O and CH4, are symmetric. Now w

  • Q : Simulate the column in HYSYS The

    The objective of this work is to separate a binary mixture and to cool down the bottom product for storage. (Check table below to see which mixture you are asked to study). 100 kmol of feed containing 10 mol percent of the lighter component enters a continuous distillation column at the m

©TutorsGlobe All rights reserved 2022-2023.