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322 15 Basic Mathematics for <strong>Computational</strong> <strong>Chemis</strong>tryFig. 15.1 Independent equationsthe second equation is just two times the first equation, so they are actually equivalentand would both be equations of the same line. Because the two equationsdescribe the same line, they have all their points in common; hence, there are an infinitenumber of solutions to the system (Fig. 15.2). If you try to solve a dependentsystem by algebraic methods, you will eventually run into an equation that is anidentity. An identity is an equation that is always true, independent of the value(s)of any variable(s). For example, you might get an equation that looks like x = x, or3 = 3. This would tell you that the system is a dependent system, and you could stopright there because you will never find a unique solution.Fig. 15.2 Dependent equations
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Computational Chemistry and Molecul
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Dr. K. I. RamachandranDr. G. DeepaK
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PrefaceComputational chemistry and
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PrefaceixSome typical projects/rese
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Contents1 Introduction ............
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Contentsxiii3.4.14 Answer7.........
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Contentsxv6.18 Exercises ..........
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Contentsxvii11.9 EnergyDuetoBending
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Contentsxix13.13 Clustering Through
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ContentsxxiD Simultaneous Spectroph
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2 1 IntroductionMeeting these chall
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4 1 Introductionare more accurate t
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6 1 IntroductionAn alternative ab i
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8 1 Introduction1.5.6 Statistical M
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10 1 Introductionis time-consuming,
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12 1 Introduction1. Peter Lykos and
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14 1 Introduction1.10 Some Topics o
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Chapter 2Symmetry and Point Groups2
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2.3 Symmetry Operations and Element
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2.5 Point Groups 27Fig. 2.15 S 4 -a
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2.6 The Procedure for Determining t
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2.7 Typical Molecular Models 31Fig.
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2.9 Irreducible Representations 332
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References 353. NH 2 Cl − E,σ :
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38 3 Quantum Mechanics: A Brief Int
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54 4 Hückel Molecular Orbital Theo
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Chapter 5Hartree-Fock Theory5.1 Int
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5.2 The Hartree Method 95The second
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5.5 The Slater Determinant 97+1/2 s
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5.7 The Hartree-Fock Equation 99whe
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5.7 The Hartree-Fock Equation 101
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5.7 The Hartree-Fock Equation 103Th
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5.9 Restricted and Unrestricted HF
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5.12 Elements of the Fock Matrix 10
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5.12 Elements of the Fock Matrix 10
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5.15 Electron Correlation 111Fig. 5
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References 113Table 5.1 Energy valu
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116 6 Basis SetsTable 6.1 Radial an
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118 6 Basis SetsBased on the variat
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120 6 Basis SetsSubstituting the fo
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122 6 Basis Setswherethethreevalues
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124 6 Basis Sets6.6 Classification
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126 6 Basis Sets0.1688554040, β 1
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128 6 Basis SetsTable 6.3 The 3-21G
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130 6 Basis SetsFig. 6.8 Output of
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132 6 Basis Setsscribed using more
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134 6 Basis SetsTable 6.5 Interacti
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136 6 Basis Sets6.15 The Intermolec
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138 6 Basis Sets6.18 Exercises1. De
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140 7 Semiempirical MethodsIt means
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142 7 Semiempirical Methods7.7 The
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144 7 Semiempirical MethodsThe mole
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146 7 Semiempirical MethodsC B is t
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148 7 Semiempirical MethodsIn the A
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150 7 Semiempirical MethodsTable 7.
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152 7 Semiempirical Methodstion. Th
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154 7 Semiempirical Methods(Hint: F
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156 8 The Ab Initio MethodFig. 8.1
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158 8 The Ab Initio Method8.4 Confi
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160 8 The Ab Initio Methodcan, ther
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162 8 The Ab Initio MethodThe groun
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164 8 The Ab Initio MethodSubstitut
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166 8 The Ab Initio MethodThus:ψ C
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168 8 The Ab Initio Method3. Triple
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170 8 The Ab Initio Method7. Using
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172 9 Density Functional Theorydist
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174 9 Density Functional Theory9.6
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176 9 Density Functional TheoryAddi
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180 9 Density Functional Theoryand
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182 9 Density Functional Theoryand:
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188 9 Density Functional TheoryH =
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190 9 Density Functional TheoryTabl
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192 9 Density Functional TheoryHowe
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Chapter 10Reduced Density Matrix10.
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10.3 N-Representability Conditions
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10.5 The SDP Formulation of the RDM
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10.7 Research in RDM 20110.6 Compar
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References 2036. Garrod C, Fusco MA
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206 11 Molecular MechanicsTable 11.
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208 11 Molecular Mechanicsthe zero
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210 11 Molecular MechanicsFig. 11.3
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212 11 Molecular Mechanics11.8 Ener
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214 11 Molecular MechanicsD is the
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216 11 Molecular Mechanics11.18 The
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218 11 Molecular Mechanicsleads to
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220 11 Molecular Mechanics11.21.4.1
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222 11 Molecular Mechanics11.21.5 T
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Chapter 12The Modeling of Molecules
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12.2 Optimization 231Fig. 12.2 Cont
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12.2 Optimization 233matrix or all
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12.2 Optimization 235(AB) T = B T A
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12.2 Optimization 237In the differe
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12.2 Optimization 239Fig. 12.6 A-or
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12.2 Optimization 241This is for th
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12.3 Potential Energy Surfaces 2431
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12.4 The Search for Transition Stat
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12.4 The Search for Transition Stat
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12.5 The Single Point Energy Calcul
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12.6 The Computation of Solvation 2
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12.7 The Population Analysis Method
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12.7 The Population Analysis Method
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12.9 Electric Multipoles and Multip
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12.9 Electric Multipoles and Multip
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12.10 Vibrational Frequencies 261Ta
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12.12 Molecular Orbital Methods 263
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12.13 Input Formats for Computation
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12.13 Input Formats for Computation
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12.14 A Comparison of Methods 269Ta
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12.14 A Comparison of Methods 271Ta
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12.15 Exercises 2736. Find the sing
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Chapter 13High Performance Computin
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13.5 Clustering Tools and Libraries
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13.7 Clustermatic 279Fig. 13.2 For
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13.12 The Steps to Configure a Clus
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13.14 Installing the Windows Cluste
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13.16 Types of Resources Required t
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13.16 Types of Resources Required t
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13.19 Bundles and Grid Packaging Te
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13.20 The HPC for Computational Che
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13.21 The Pseudopotential Method 29
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Page 668: 15.6 Systems of Linear Equations 32
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Page 676: 15.7 The Least-Squares Method 327Ex
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Appendix CUsing Microsoft Excel to
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C.3 Undermined Systems 351Thus, the
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C.4 Balancing as an Optimization Pr
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C.4 Balancing as an Optimization Pr
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Appendix DSimultaneous Spectrophoto
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D.2 The Absorption Spectrum 359was
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Appendix EBond Enthalpy of Hydrocar
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Appendix FGraphing Chemical Analysi
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F.2 Example: Beer’s Law Absorptio
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F.2 Example: Beer’s Law Absorptio
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F.4 Using the Regression Equation t
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376 G Titration Data PlottingFig. G
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384 H Curve Fitting in Chemistryhyd
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Appendix IThe Solvation of Potassiu
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Appendix JPartial Molal Volume of Z
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IndexAA2 enzyme 151Ab-initio potent
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Index 393Eigenfunctions 345Eigensta
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Index 395Molecular geometry 268Mole
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Index 397Symmetry operations 17TT-c
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