Presentation on theme: "NORMAL COORDINATE ANALYSIS OF XY2 BENT MOLECULE – PART 3"— Presentation transcript:
1NORMAL COORDINATE ANALYSIS OF XY2 BENT MOLECULE – PART 3 Dr.D.UTHRAHead, Dept.of PhysicsDG Vaishnav College, Chennai-106
2This presentation has been designed to serve as a self-study material for Postgraduate Physics students pursuing their programme under Indian Universities, especially University of Madras and its affiliated colleges. If this aids the teachers too who deal this subject, to make their lectures more interesting, the purpose is achieved.-D.Uthra
3I acknowledge my sincere gratitude to my teacher Dr.S.Gunasekaran, for teaching me group theory withso much dedication and patience & for inspiring meand many of my friends to pursue research.My acknowledgement to all my students whoinspired me to design this presentation.- D.Uthra
4F-G matrix method Developed by Wilson, Decius and Cross adopted by many scientists toElucidate structure of a moleculeDetermine molecular parametersDetermine vibration frequenciesTo learn more check the list of reference
5Master equation |FG–λE| ≡ 0 F - matrix of potential constants and thus brings the potential energies of vibrations into the equationG - matrix that involves masses and certain spatial relationships of the atoms and thus brings the kinetic energies of vibration into the secular equationE - unit matrixλ = 42C2ν2, brings the vibrational frequency ν into the equationBy this F-G matrix method, all the required relations are combined in the master secular equation
6F-matrixFrom the potential constants or force constants of the bonds, you can understand the potential energy required for every vibrationF-matrix gives an idea of P.E and so the bond strengthThe stronger the bond, the more the force constantHence, F-matrix is indicates the bond strength
7G-matrixIt is formed with the knowledge of masses and spatial relationships (bond lengths and bond angles) of the atomsG-matrix gives an idea of K.E of vibrationFrom earlier presentations, you know to form G-matrix
8E-matrixE-matrix is just a unit matrix of dimension as G-matrix
9λ = 42C2ν2 λ brings the vibrational frequency ν into the equation Spectroscopists record vibrational spectrum of the molecule under investigationFrom the vibrational spectrum of the molecule,Spectroscopists assign vibrational frequencies (ν) to various vibrations of the moleculeHence, λ values are calculated for every vibrationThere are cases where, F and G matrices are calculated by researchers and from there, they try to evaluate λ and hence find ν.They compare the calculated frequencies with the frequencies from recorded spectrum.This way, they try to ascertain their work and/or refine their data.
10Purpose of nca… Vibrational frequencies can hence be predicted With the knowledge of masses of atoms ,bond lengths and bond angles of the molecule under study, G-matrix can be formedWith the knowledge of force constants of the bonds, (or by comparing with similar molecules whose data is already known), F-matrix can be formedUsing the secular equation,|FG–λE| ≡ 0Vibrational frequencies can hence be predictedYou can see , with the knowledge of physical parameters, vibrational frequencies can be predicted!! Can you guess how does these predictions help a researcher?
11Hence, by forming F and G matrices, vibrational frequencies can be deduced If the calculated values do not match with the observed values, then the values of the parameters chosen to form F and G matrices need to be refined or changed in steps slowlyThis way, it helps you to deduce the structure of the molecule under studyAlso, the correctness of the assumed structure of the molecule can be checkedIt may also give an idea about the change in environment of the molecule under study, because of which there is change in observed frequencies
12record vibrational spectrum of the molecule On the other hand, if you construct G-matrix by knowing masses of atoms, bond lengths and bond angles andrecord vibrational spectrum of the moleculeassign vibrational frequencies (ν) to various vibrations of the moleculehence, calculate λ values for every vibrationUsing the secular equation,|FG–λE| ≡ 0Force constants can be deduced, which gives you an idea of bond nature and bond strengthThis require tedious computation by iteration technique in olden days. These days, with help of computers, you can achieve it faster, but with hard work.To learn more check the list of reference.