CHEM01200604005 A. K. Pathak - Homi Bhabha National Institute

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chemical species may be different from those in the gas phase as well as the bulk. Bulk properties of a molecular system may emerge from the extrapolation of its clusters having sufficiently large size. Bulk properties of a solute in solution result from the combined effect of solute-solvent and solvent-solvent interactions. It cannot be obtained from the properties of the isolated solute species alone. To connect molecular properties of a chemical species to its bulk properties, one has to study clusters of sufficiently large size. Hence, studies on clusters help to understand how the properties of these solvated clusters evolve with the size and geometry. Size selected cluster study has been used to extract the bulk properties, like detachment energies of an excess electron using the empirical extrapolation model based on the continuum model. 9,33-34 But this model fails to reproduce bulk detachment energy in many cases. 9,35 The present thesis also covers an attempt to develop a formalism to extract bulk detachment energies of the solvated anion from the knowledge of the finite size hydrated cluster of that anion. 1.3. Theoretical Methodology 1.3.1. Geometry Search The heart of the microsolvation study is the geometry of the microsolvated species (cluster). Many procedures are available to locate good minimum energy structure like conjugate gradient, steepest decent, Newton-Raphson, etc. At present pseudo Newton-Raphson (NR) method for geometry search along with Monte Carlo method based simulated annealing procedure for global minimum energy structure search procedure is discussed. The energy of a particular structure is calculated by self consistent field (SCF) method. 8
Newton –Raphson (NR) method expand the true function (energy) to second order around the current point x 0 . 1 f ( x) f( x ) g( x x ) H( x x ) 2 2 = 0 + − 0 + − 0 (1) where, g is the gradient (force) and H is the Hessian. Requiring the force to be zero (in eq. 1) produces the following step, ( − ) = − (2) −1 x x0 H g In the co-ordinate system (x) where the Hessian is diagonal, the NR step may be written as f Δ x = ∑ Δx Δ x =− (3) ' ' ' i i, i i εi where f i is the projection of the gradient (force) along the Hessian eigenvector with eigen value ε i . As the real function contains terms beyond the second order, the NR formula may be used iteratively for approaching towards the stationary point. Near minimum, all the Hessian eigenvalues are positive and the step direction is opposite to the gradient direction. If, one Hessian eigenvalue is negative, the step in this direction will be along the gradient and thus increase the function value. In this circumstances, the optimization may end up at a stationary point, which, having one negative Hessian eigenvalue, first order saddle point. If the stationary point has n negative Hessian eigenvalues, it is called n th order saddle point in the potential energy surface. So, in general the NR method will attempt to converge on the nearest stationary point (either minimum or saddle point). Other problem is the use of inverse Hessian for control of the step size. If one of the 9
Page 1 and 2: MICROSOLVATION OF CHARGED AND NEUTR
Page 3 and 4: STATEMENT BY AUTHOR This dissertati
Page 5 and 6: Dedicated to my Daughter, Wife and
Page 7 and 8: CONTENTS Page No. SYNOPSIS LIST OF
Page 9 and 10: CHAPTER 4 Solubility of Halogen Gas
Page 11 and 12: 7.3.4. IR and Raman Spectra 117-121
Page 13 and 14: S Macroscopic Microscopic Dual leve
Page 15 and 16: molecular level interaction during
Page 17 and 18: Chapter 3: This chapter describes I
Page 19 and 20: In this system the conformers of a
Page 21 and 22: LIST OF FIGURES Page No. Fig. 1.1 2
Page 23 and 24: Fig. 2.6 54 (I) Plot of calculated
Page 25 and 26: (IIIA) Cl 2 .3H 2 O; (IIIB) Br 2 .3
Page 27 and 28: Fig. 6.3 104-105 Calculated scaled
Page 29 and 30: LIST OF TABLES Page No. Table. 2.1
Page 31 and 32: CHAPTER 1 Introduction 1.1. Microso
Page 33 and 34: 1.2. Motivation 1.2.1. Macrosolvati
Page 35 and 36: ulk water and pure neutral water cl
Page 37: insight about the electronic struct
Page 41 and 42: potential energy surface for these
Page 43 and 44: terms, the energy can be written in
Page 45 and 46: Boyd proposed the use of Gaussian t
Page 47 and 48: eported experimental findings. Theo
Page 49 and 50: hydrated halide series, X¯.nH 2 O,
Page 51 and 52: anions (Cl •− 2 , Br •− 2 &
Page 53 and 54: geometrical parameters close to MP2
Page 55 and 56: symmetrical DHB, SHB or WHB arrange
Page 57 and 58: of I-I axis and having the least I-
Page 59 and 60: Br •− 2 .nH 2 O hydrated cluste
Page 61 and 62: VI-F VI-G VII-A VII-B VII-C VII-D V
Page 63 and 64: To see the effect of hydration on t
Page 65 and 66: Five minimum energy structures disp
Page 67 and 68: arrangements. In total, it has one
Page 69 and 70: NO 3 − .nH2 O (n ≥ 6), a few eq
Page 71 and 72: V-E V-F V-G V-H V-I VI-A VI-B VI-C
Page 73 and 74: VII-D VII-E VII-F VII-G VII-H VII-I
Page 75 and 76: VIII-K VIII-L Fig.2.2. Fully optimi
Page 77 and 78: clusters. Hydrated cluster having c
Page 79 and 80: However, these calculations do not
Page 81 and 82: Table 2.1. Weighted average energy
Page 83 and 84: Where, E[I •− 2 .nH 2 O] is the
Page 85 and 86: The variation of the weighted avera
Page 87 and 88: CHAPTER 3 IR Spectra of Water Embed
Page 89 and 90:
ecome more meaningful. At present,
Page 91 and 92:
I-A II-A II-B III-A III-B III-C III
Page 93 and 94:
Cluster experiments are carried out
Page 95 and 96:
3350-3500 cm -1 (scaling factor ~0.
Page 97 and 98:
these systems, X. nH 2 O (X= Br 2
Page 99 and 100:
CHAPTER 4 Solubility of Halogen Gas
Page 101 and 102:
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 and 154:
CHAPTER 8 A Generalized Microscopic
Page 155 and 156:
possible breakdown of these laws ma
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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