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TITLE
CERTIFICATE
DECLARATION
PREFACE
ACKNOWLEDGEMENT
CONTENTS
1. BASIC THEORY
1.1 INTRODUCTION
1.2 NORMAL CO-ORDINATE. ANALYSIS
1.3 MATHEMATICAL FORMALISM
1.4 THE UNDER-DETERMINED NATURE OFTHE PROBLEM
1.5 NEW APPROACH
1.6 THE MEAN AMPLITUDES OF VIBRATION
1.7 POTENTIAL ENERGY OF A MOLECULE
2. A NEW CRITERION FOR MOLECULAR GEOMETRY
2.3 MATHEMATICAL FORMALISM
2.4 THE PARAMETRIC APPROACH
2.5 RESULTS AND DISCUSSIONS
2.6 BENDING ENERGY MINIMISATION
2.7 AN APPROXIMATION CRITERION
Table II.1 data on vibrational frequencies of xy2 bent symmetric type molecules
Table II.2 Inter bond angle determined from Bending Energy considerations
Table II.3 Interbond angle from interaction energy consideration
Fig.2 a. shows the variation of the Bending energy with lnter bond angle for Cl02
Fig.2 b shows the variation of interaction energy with inter bond angle for ClO2
Fig.2 c shows the variation of stretch and stretch-stretch interaction energy with inter bond angle for CI02
Fig.2 d shows the variation of the Bending energy with lnter bond angle for NO2
Fig.2 e shows the variation of interaction energy with inter bond angle for NO2
Fig.2 f shows thc variation of stretch and stretch-stretch interaction energy for NO2
Fig.2 g. shows the variation of the Bending energy with lnter bond angle for SO2
Fig.2 h shows the variation of the Interaction energy with Inter bond angle for SO2
Fig.2 i shows the vanation of the Bending energy with Inter bond angle for Cl2S
Fig.2 j shows the variation of interaction energy with inter bond angle for Cl2s2
Fig.2 k shows the variation of the Bending energy with lnter bond angle for Cl2O
Fig.2 l shows the vanation of interaction energy with inter bond angle for Cl2O
Fig.2 m shows the ariation of the Bending energy with Inter bond angle for H2O
Fig.2 n shows the variation of the Interaction energy with Inter bond angle for H20
Fig.2 o shows the variation of the stretch -energy and stretch-stretch interaction energy with Inter bond angle for H20
Fig.2 p shows the variation of the Bending energy with Inter bond angle for HJ
Fig.2 q shows the variation of the Interaction energy with Inter bond angle for H2S
Fig.2 r shows the variation of the stretch energy and stretch-stretch interaction energy with Inter bond angle for H2S
Fig.2 s shows the variation of the Bending energy with Inter bond angle for H2Se
Fig.2 t shohs the variation of interaction energy with inter bond angle for H2Se
Fig.2 u shows the variation of the stretch -energy and stretch-stretch interaction energy with Inter bond angle for H2Se
3. BENDING ENERGY MINIMIZATION CRITERION APPLIED TO XY3 PYRAMIDAL SYSTEMS FOR PREDICTING THEIR GEOMETRY
3.1 INTRODUCTION
3.2 SYMMETRY CONSIDERATION
3.3 MATHEMATICAL FORMALISM
3.4 RESULTS AND DISCUSSIONS
Table III.1Data table for XY3 Pyramidal type molecules
Table III.2 Inter bond angle determined from Energy considertations
Table 3 Inter bond angle determinwd from energy considertations
Fig. 3.a Shows the variation of Bending energy with lnter bond angle for SbH3
Fig.3.b shows the variation of Stretch energy with Inter bond angle for SbH3
Fig.3 c shows the variation of interaction energy with Inter bond angle for SbH3
Fig.3 d shows the variation of Bending energy with Inter bond angle for NH3
Fig.3 e shows the variation of Stretch energy with Inter bond angle for NH3
Fig.3 f shows the variation of Interaction energy with lnter bond angle for NH3
Fig.3.g shows the variation of Bending energy with Inter bond angle for AsH3
Fig.3 h shows the variation of Stretch energy with lnter bond angle for AsH3
Fig.3.i shows the variation of Interaction enera with lnter bond angle for AsH3
Fig.3.J shows the variation Bending energy with Inter bond angle for PH3
Fig.3 k shows the vanation of stretch energy with Inter bond angle for PH3
Fig.3. l shows the variation of Interaction energy with lnter bond angle for PH3
4. STRUCTURAL ANALYSIS OF X Y2 TYPE MOLECULES [LINEAR VERSUS BENT SYMMETRIC) BASED ON BENDING ENERGY MINIMIZATION CRITERION
4.1 INTRODUCTION
4.2 MATHEMATICAL FORMALISM
4.3 RESULTS AND DISCUSSIONS
Table IV.1 Data Table for CO2 and S2 molecules
Table IV.2 Inter bond angle determined from Bending Energy considertations
Fig 4 Shows the variation of bending energy with inter bond angle for CO2 CS2 and SO2
5. AN APPROXIMATION METHODFOR FORCE FIELD CALCULATION
5.1 INTRODUCTION
5.2 AN INTERESTING OBSERVATION VRX
5.3 MATHEMATICAL FORMULATION
5.4 RESULTS AND DISCUSSION
Table V.1 F matrix elements for some XY2 Bent symmetric molecules based on interaction energy minimum extremum criterion
Table V I Comparison of the valence force constants obtained by the present method and Redington - Aljibury approximation (in 10-2 N/m)
6. MEAN AMPLITUDES OF VIBRATION AS A TOOL FOR STRUCTURAL ANALYSIS OF SIMPLE MOLECULES
6.1 INTRODUCTION
6.2 MEAN AMPLITUDES OF VIBRATION
6.3 MATHEMATICAL FORMALISM
6.4 APPLICATION TO BENT SYMMETRIC XY2 SYSTEM.
6.5 APPLICATION TO XY2 LINEAR SYMMETRIC SYSTEM
6.6 APPLICATION TO XY3 PYRAMIDAL SYSTEMS.
6.7 RESULTS AND DISCUSSIONS
TABLE V1. I Mean amplitudes for XY2 bent - symmetric molecules
TABLE VI.2 Mean amplitudes for XY2 linear - symmetric molecules
TABLE VI.3 Mean ampl ix-y (in 10-2 nm) for XY3 pyramidal moleculesitudes
TABLE VI.4. Inter bond angle form Ixy minimum XY2 bent symmetric molecules
Fig 6 a shows the variation of bonded mean amplitude withinter bond angle for Cl02.
Fig 6 b shows the variation of bonded mean amplitude with inter bond angle for NO2.
Fig.6c Shows the variation of bonded amplitude with inter bond angle for SO2 and CIO2
Fig.6d Shows the variation of bonded mean amplitude with inter bond angle for H2O (---) and Ci2s (-X-X)
Ftg 6.e shows the variation of bonded mean amplitude withinter bond angle for Ha.
Fig 6 f shows the variation of bonded mean amplitude withinter bond angle for CS2 and C02.
Fig 6.g shows the variation of bonded mean amplitude withinter bond an; gle for SbHl (...) ASH, (+ + +)
7. AN INTERESTING CASE STUDY ON THE STRUCTURE OF WATER MOLECULE
7.1 INTRODUCTION
7.2 USE OFBENDING ENERGY MINIMISATION CRITERION
7.3 THE MEAN AMPLITUDES
7.4 SOLUTION TO THE STRUCTURAL AMBIGUITY
Table VII.1 DAta vibrational frequencies of H2O (Hamada)
Fig.7a, shows thc variation of Bending enerby with inter bond angle all) r /& (I (C, structure)
Fig.7b, shows the variation of Bending energy with inter bond angle afor H20 (Dm) s, t ructure)
Fig.7c, shows tlic variation ofMean Amplitude with inter bond angle aSor H2 (? C3, (...) & /Id, (- - -)
8. GENERAL CONCLUSIONS
APPENDIX - PROGRAMME 1
APPENDIX - PROGRAMME 2
REFERENCE