CHEM01200604005 A. K. Pathak - Homi Bhabha National Institute

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quantum mechanics based approaches bypass this problem, investigations based on this approach are limited only to clusters of small size 82-83 . More importantly, simulation or quantum mechanics based study does not provide any explicit analytical expression for the dependence on the number of solvent molecules. Work in this direction was earlier initiated by Jortner and coworkers 33 . Theoretical considerations of the ion solvation in clusters of finite size predict that the detachment energies of a solvated anion should scale as 1/R linearly, where R is the radius of the solvated clusters and is proportional to the solvent number, n. In this model, the solvent number dependent detachment energy (both ΔE VDE (n) and ΔE ADE (n) ) of the cluster expressed as 9 , ∆E =∆E ∞ +A ‐1/3 1 Where, refers to ADE or VDE, ∆E ∞ is the bulk detachment energy and A is the proportionality constant. Here δ is an equivalent solvent number corresponding to the solute and accounts for the contribution of the solute to the cluster volume. However, the extrapolation results obtained from this simple model are found to be in poor agreement with the experimental results 9, 35 . Dixon and coworkers raised an important question concerning whether the exponent (1/3) is constant for all anionic clusters of different charges or not and argued that the exponent should be dependent on the nature of the ion. 35 Accordingly, another empirical law was proposed, written as ∆E = ∆E ∞ + A (n+ ‐p 2 The calculated results based on this model were better than the earlier models but the error was still quite significant, particularly for the di-anion hydrated clusters. Most importantly, the variation of p from system to system is not properly defined. The 124
possible breakdown of these laws may be due to the fact that all these empirical laws are proposed by including two or three unknown parameters in an arbitrary way which is based on the continuum theory wherein the microscopic details are not considered. However, if solute-solvent and solvent-solvent motions are strongly correlated, the continuum theory breaks down and one needs to have a microscopic theory in order to understand the solvent number (n) dependence of ∆E VDE (n) and ∆E ADE (n). Hence, in the present chapter, the objective has been to address an important issue in obtaining the proper n-dependence of the expressions for the solvation energy in a generalized manner. 8.2. Theoretical Methodology The system that is considered here consists of a single negative ion of charge –q and n number of polar solvent molecules surrounding it. The solvation energies of the negative ion and its mono ionized form with charge –(q-1) are respectively defined as , , , 3 , , , 4 Where, , and , , respectively, represent the interaction potential energy between the ions with charge –q and –(q-1) with the polar solvent molecules and g i (r, ω, n) (i=1,2) represents the static pair distribution function between the ion and solvent molecules for the system containing a finite number (n) of solvent molecules. Here, ρ represents the bulk density of the solvent molecules. The quantities of interest are the 125
Page 1 and 2:
MICROSOLVATION OF CHARGED AND NEUTR
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STATEMENT BY AUTHOR This dissertati
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Dedicated to my Daughter, Wife and
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CONTENTS Page No. SYNOPSIS LIST OF
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CHAPTER 4 Solubility of Halogen Gas
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7.3.4. IR and Raman Spectra 117-121
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S Macroscopic Microscopic Dual leve
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molecular level interaction during
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Chapter 3: This chapter describes I
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In this system the conformers of a
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LIST OF FIGURES Page No. Fig. 1.1 2
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Fig. 2.6 54 (I) Plot of calculated
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(IIIA) Cl 2 .3H 2 O; (IIIB) Br 2 .3
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Fig. 6.3 104-105 Calculated scaled
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LIST OF TABLES Page No. Table. 2.1
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CHAPTER 1 Introduction 1.1. Microso
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1.2. Motivation 1.2.1. Macrosolvati
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ulk water and pure neutral water cl
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insight about the electronic struct
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Newton -Raphson (NR) method expand
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potential energy surface for these
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terms, the energy can be written in
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Boyd proposed the use of Gaussian t
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eported experimental findings. Theo
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hydrated halide series, X¯.nH 2 O,
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anions (Cl •− 2 , Br •− 2 &
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geometrical parameters close to MP2
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symmetrical DHB, SHB or WHB arrange
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of I-I axis and having the least I-
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Br •− 2 .nH 2 O hydrated cluste
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VI-F VI-G VII-A VII-B VII-C VII-D V
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To see the effect of hydration on t
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Five minimum energy structures disp
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arrangements. In total, it has one
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NO 3 − .nH2 O (n ≥ 6), a few eq
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V-E V-F V-G V-H V-I VI-A VI-B VI-C
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VII-D VII-E VII-F VII-G VII-H VII-I
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VIII-K VIII-L Fig.2.2. Fully optimi
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clusters. Hydrated cluster having c
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However, these calculations do not
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Table 2.1. Weighted average energy
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Where, E[I •− 2 .nH 2 O] is the
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The variation of the weighted avera
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CHAPTER 3 IR Spectra of Water Embed
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ecome more meaningful. At present,
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I-A II-A II-B III-A III-B III-C III
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Cluster experiments are carried out
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3350-3500 cm -1 (scaling factor ~0.
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these systems, X. nH 2 O (X= Br 2
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CHAPTER 4 Solubility of Halogen Gas
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including polarized and diffuse fun
Page 103 and 104: and I 2 systems. The most stable st
Page 105 and 106: Cl Cl Br Br I I VA VB VC Cl Cl Br B
Page 107 and 108: (Br δ+ -Br δ- ) in the studied hy
Page 109 and 110: stabilization energy does not follo
Page 111 and 112: 80 Cl 2 .nH 2 O (n=1-8) 80 Br 2 .nH
Page 113 and 114: separated ion pair in presence of s
Page 115 and 116: adical ( • OH) reacts with HCO 3
Page 117 and 118: most stable conformer for each size
Page 119 and 120: The structures of the hydrated clus
Page 121 and 122: Table 5.1. Calculated absorption ma
Page 123 and 124: molar extinction coefficient value
Page 125 and 126: ammonia. 61-62 Hydrogen bonded wate
Page 127 and 128: stable minimum energy structure is
Page 129 and 130: IV-A IV-B V-A V-B V-C VI-A VI-B VI-
Page 131 and 132: 6.3.3. Vertical Ionization Potentia
Page 133 and 134: 311++G(2d,2p) level, the scaling fa
Page 135 and 136: K(NH 3 ) 4 K(NH 3 ) 5 IR Intensity
Page 137 and 138: CHAPTER 7 Structure, Energetics and
Page 139 and 140: Thus Monte Carlo based simulated an
Page 141 and 142: I I I I I I I I A B C D I I I I I I
Page 143 and 144: interaction as well as solvent-solv
Page 145 and 146: Table 7.1. Various energy parameter
Page 147 and 148: change in VDE is observed. This is
Page 149 and 150: symmetric C-O stretching mode of CO
Page 151 and 152: to the maximum charge transfer of t
Page 153: CHAPTER 8 A Generalized Microscopic
Page 157 and 158: P 7 P , , P , ,, 1 ∂ 2
Page 159 and 160: M DE = (r, ω)C DE , (r,
Page 161 and 162: known. However, for most of the com
Page 163 and 164: The calculated bulk detachment ener
Page 165 and 166: espect to experimentally measured v
Page 167 and 168: References 1. Ohtaki, H.; Radani, T
Page 169 and 170: 29. Turi, L.; Sheu, W.; Rossky,P.J.
Page 171 and 172: 61. (a) Ehrler, O. T.; Neumark, D.
Page 173 and 174: LIST OF PUBLICATIONS *1. “σ/σ
Page 175 and 176: 13. “Vibrational analysis of I
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CHEM01200604005 A. K. Pathak - Homi Bhabha National Institute

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