Computational chemistry and molecular modeling: principles and applications
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Format: | Buch |
Sprache: | English |
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Berlin [u.a.]
Springer
2008
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Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XXI, 397 S. Ill., graph. Darst. |
ISBN: | 9783540773023 9783540773047 |
Internformat
MARC
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100 | 1 | |a Ramachandran, K. I. |e Verfasser |4 aut | |
245 | 1 | 0 | |a Computational chemistry and molecular modeling |b principles and applications |c K. I. Ramachandran ; G. Deepa ; K. Namboori |
264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
300 | |a XXI, 397 S. |b Ill., graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
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689 | 0 | |5 DE-604 | |
700 | 1 | |a Deepa, Gopakumar |e Verfasser |4 aut | |
700 | 1 | |a Namboori, Krishnan |e Verfasser |4 aut | |
856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016669390&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
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adam_text | Contents
1 Introduction 1
1.1 A Definition of Computational Chemistry 1
1.2 Models 2
1.3 Approximations 3
1.4 Reality 4
1.5 Computational Chemistry Methods 4
1.5.1 Ab Initio Calculations 5
1.5.2 Semiempirical Calculations 6
1.5.3 Modeling the Solid State 6
1.5.4 Molecular Mechanics 7
1.5.5 Molecular Simulation 7
1.5.6 Statistical Mechanics 8
1.5.7 Thermodynamics 8
1.5.8 Structure-Property Relationships 8
1.5.9 Symbolic Calculations 9
1.5.10 Artificial Intelligence 9
1.5.11 The Design of a Computational Research Program 9
1.5.12 Visualization 10
1.6 Journals and Book Series Focusing
on Computational Chemistry 10
1.7 Journals and Book Series
Often Including Computational Chemistry 11
1.8 Common Reference Books Available
on Computational Chemistry 11
1.9 Computational Chemistry on the Internet 13
1.10 Some Topics of Research Interest Related
to Computational Chemistry 14
References 15
xi
xii Contents
2 Symmetry and Point Groups 17
2.1 Introduction 17
2.2 Symmetry Operations and Symmetry Elements 17
2.3 Symmetry Operations and Elements of Symmetry 18
2.3.1 The Identity Operation 18
2.3.2 Rotation Operations 19
2.3.3 Reflection Planes (or Mirror Planes) 22
2.3.4 Inversion Operation 25
2.3.5 Improper Rotations 26
2.4 Consequences for Chirality 26
2.5 Point Groups 27
2.6 The Procedure for Determining the Point Group of Molecules .... 28
2.7 Typical Molecular Models 30
2.8 Group Representation of Symmetry Operations 32
2.9 Irreducible Representations 33
2.10 Labeling of Electronic Terms 34
2.11 Exercises 34
2.11.1 Questions 34
2.11.2 Answers to Selected Questions 34
References 35
3 Quantum Mechanics: A Brief Introduction 37
3.1 Introduction 37
3.1.1 The Ultraviolet Catastrophe 37
3.1.2 The Photoelectric Effect 38
3.1.3 The Quantization of the Electronic Angular Momentum .. 39
3.1.4 Wave-Particle Duality 39
3.2 The Schrödinger Equation 41
3.2.1 The Time-Independent Schrödinger Equation 41
3.2.2 The Time-Dependent Schrödinger Equation 43
3.3 The Solution to the Schrödinger Equation 45
3.4 Exercises 45
3.4.1 Question 1 45
3.4.2 Answer 1 45
3.4.3 Question 2 46
3.4.4 Answer 2 46
3.4.5 Question 3 46
3.4.6 Answer 3 46
3.4.7 Question 4 47
3.4.8 Answer 4 47
3.4.9 Question 5 48
3.4.10 Answer 5 48
3.4.11 Question 6 48
3.4.12 Answer 6 48
3.4.13 Question 7 49
Contents xiii
3.4.14 Answer 7 49
3.4.15 Question8 50
3.4.16 Answer 8 50
3.4.17 Question9 50
3.4.18 Answer 9 50
3.4.19 QuestionlO 51
3.4.20 Answer 10 51
3.5 Exercises 51
References 52
4 Hückel Molecular Orbital Theory 53
4.1 Introduction 53
4.2 The Born-Oppenheimer Approximation 53
4.3 Independent Particle Approximation 56
4.4 ^-Electron Approximation 58
4.5 Hückel s Calculation 58
4.6 The Variational Method and the Expectation Value 59
4.7 The Expectation Energy and the Hückel MO 60
4.8 The Overlap Integral (S,7) 62
4.9 The Coulomb Integral (a) 63
4.10 The Resonance (Exchange) Integral (ß) 63
4.11 The Solution to the Secular Matrix 63
4.12 Generalization 64
4.13 The Eigenvector Calculation of the Secular Matrix 66
4.14 The Chemical Applications of Hückel s MOT 66
4.15 Charge Density 67
4.16 The Hückel (4n + 2) Rule and Aromaticity 69
4.17 The Delocalization Energy 71
4.18 Energy Levels and Spectrum 73
4.19 Wave Functions 74
4.19.1 Step 1: Writing the Secular Matrix 74
4.19.2 Step 2: Solving the Secular Matrix 74
4.20 Bond Order 77
4.21 The Free Valence Index 78
4.22 Molecules with Nonbonding Molecular Orbitals 80
4.23 The Prediction of Chemical Reactivity 81
4.24 The HMO and Symmetry 82
4.25 Molecules Containing Heteroatoms 85
4.26 The Extended Hückel Method 86
4.27 Exercises 88
References 91
xiv Contents
5 Hartree-Fock Theory 93
5.1 Introduction 93
5.2 The Hartree Method 93
5.3 Bosons and Fermions 96
5.4 Spin Multiplicity 96
5.5 The Slater Determinant 97
5.6 Properties of the Slater Determinant 99
5.7 The Hartree-Fock Equation 99
5.8 The Secular Determinant 104
5.9 Restricted and Unrestricted HF Models 104
5.10 The Fock Matrix 106
5.11 Roothaan-Hall Equations 106
5.12 Elements of the Fock Matrix 107
5.13 Steps for the HF Calculation 110
5.14 Koopman s Theorem 110
5.15 Electron Correlation 110
5.16 Exercises 112
References 113
6 Basis Sets 115
6.1 Introduction 115
6.2 The Energy Calculation from the STO Function 117
6.3 The Energy Calculation of Multielectron Systems 120
6.4 Gaussian Type Orbitals 121
6.5 Differences Between STOs and GTOs 122
6.6 Classification of Basis Sets 124
6.7 Minimal Basis Sets 124
6.8 A Comparison of Energy Calculations of the Hydrogen Atom
Based on STO-nG Basis Sets 125
6.8.1 STO-2G 125
6.8.2 STO-3G 125
6.8.3 STO-6G 126
6.9 Contracted Gaussian Type Orbitals 126
6.10 Double- and Triple-Zeta Basis Sets
and the Split-Valence Basis Sets 128
6.11 Polarized Basis Sets 130
6.12 Basis Set Truncation Errors 133
6.13 Basis Set Superposition Error 133
6.14 Methods to Overcome BSSEs 135
6.14.1 The Chemical Hamiltonian Approach 135
6.14.2 The Counterpoise Method 135
6.15 The Intermolecular Interaction Energy
of Ion Water Clusters 136
6.16 A List of Commonly Available Basis Sets 137
6.17 Internet Resources for Generating Basis Sets 137
Contents xv
6.18 Exercises 138
References 138
7 Semiempirical Methods 139
7.1 Introduction 139
7.2 The Neglect of Differential Overlap Method 140
7.3 The Complete Neglect of Differential Overlap Method 140
7.4 The Modified Neglect of the Diatomic Overlap Method 140
7.5 The Austin Model 1 Method 141
7.6 The Parametric Method 3 Model 141
7.7 The Pairwize Distance Directed Gaussian Method 142
7.8 The Zero Differential Overlap Approximation Method 142
7.9 The Hamiltonian in the Semiempirical Method 143
7.9.1 The Computation of H^ 145
7.9.2 The Computation of H=°£ 145
7.10 Comparisons of Semiempirical Methods 148
7.11 Software Used for Semiempirical Calculations 153
7.12 Exercises 153
References 154
8 The Ab Initio Method 155
8.1 Introduction 155
8.2 The Computation of the Correlation Energy 156
8.3 The Computation of the SD of the Excited States 157
8.4 Configuration Interaction 158
8.5 Secular Equations 159
8.6 Many-Body Perturbation Theory 159
8.7 The Möller-Plesset Perturbation 161
8.8 The Coupled Cluster Method 165
8.9 Research Topics 168
8.10 Exercises 168
References 170
9 Density Functional Theory 171
9.1 Introduction 171
9.2 Electron Density 171
9.3 Pair Density 172
9.4 The Development of DFT 172
9.5 The Functional 173
9.6 The Hohenberg and Kohn Theorem 174
9.7 The Kohn and Sham Method 178
9.8 Implementations of the KS Method 180
9.9 Density Functionals 181
9.10 The Dirac-Slater Exchange Energy Functional and the Potential... 182
xvi Contents
9.11 The von Barth-Hedin Exchange Energy Functional
and the Potential 183
9.12 The Becke Exchange Energy Functional and the Potential 183
9.13 The Perdew-Wang 91 Exchange Energy Functional
and the Potential 184
9.14 The Perdew-Zunger LSD Correlation Energy Functional
and the Potential 185
9.15 The Vosko-Wilk-Nusair Correlation Energy Functional 186
9.16 The von Barth-Hedin Correlation Energy Functional
and the Potential 186
9.17 The Perdew 86 Correlation Energy Functional and the Potential... 187
9.18 The Perdew 91 Correlation Energy Functional and the Potential... 187
9.19 The Lee, Yang, and Parr Correlation Energy Functional
and the Potential 188
9.20 DFTMethods 189
9.21 Applications of DFT 190
9.22 The Performance of DFT 191
9.23 Advantages of DFT in Biological Chemistry 192
9.24 Exercises 192
References 193
10 Reduced Density Matrix 195
10.1 Introduction 195
10.2 Reduced Density Matrices 195
10.3 7V-Representability Conditions 197
10.3.1 G-Condition (Garrod) and Percus 198
10.3.2 T-Conditions (Erdahl) 198
10.3.3 T2 Condition 198
10.4 Computations Using the RDM Method 199
10.5 The SDP Formulation of the RDM Method 199
10.6 Comparison of Results 201
10.7 Research in RDM 201
10.8 Exercises 202
References 202
11 Molecular Mechanics 205
11.1 Introduction 205
11.2 Triad Tools 206
11.3 The Morse Potential Model 207
11.4 The Harmonie Oscillator Model for Molecules 208
11.5 The Comparison of the Morse Potential
with the Harmonie Potential 209
11.6 Two Atoms Connected by a Bond 210
11.7 Polyatomic Molecules 211
11.8 Energy Due to Stretching 212
Contents xvii
11.9 Energy Due to Bending 212
11.10 Energy Due to Stretch-Bend Interactions 212
11.11 Energy Due to Torsional Strain 213
11.12 Energy Due to van der Waals Interactions 213
11.13 Energy Due to Dipole-Dipole Interactions 213
11.14 The Lennard-Jones Type Potential 214
11.15 The Truncated Lennard-Jones Potential 214
11.16 The Kihara Potential 215
11.17 The Exponential -6 Potential 215
11.18 The BFW Two-Body Potential 216
11.19 The Ab Initio Potential 216
11.20 The Ionic and Polar Potential 216
11.21 Commonly Available Force Fields 217
11.21.1 MM2, MM3, and MM4 217
11.21.2 AMBER 218
11.21.3 CHARMM 219
11.21.4 Merck Molecular Force Field 219
11.21.5 The Consistent Force Field 222
11.22 Some Other Useful Potential Fields 222
11.23 The Merits and Demerits of the Force Field Approach 223
11.24 Parameterization 224
11.25 Some MM Software Packages 225
11.26 Exercises 225
References 227
12 The Modeling of Molecules Through Computational Methods 229
12.1 Introduction 229
12.2 Optimization 229
12.2.1 Multivariable Optimization Algorithms 229
12.2.2 Level Sets, Level Curves, and Gradients 230
12.2.3 Optimality Criteria 232
12.2.4 The Unidirectional Search 233
12.2.5 Finding the Minimum Point Along 5 233
12.2.6 Gradient-Based Methods 234
12.2.7 The Method of Steepest Descent 235
12.2.8 The Method of Conjugate Directions 238
12.2.9 The Gram-Schmidt Conjugation Method 240
12.2.10 The Conjugate Gradient Method 241
12.3 Potential Energy Surfaces 243
12.3.1 Convergence Criteria 244
12.3.2 Characterizing Stationary Points 245
12.4 The Search for Transition States 245
12.4.1 Computing the Activated Complex Formation 246
12.5 The Single Point Energy Calculation 249
12.6 The Computation of Solvation 250
xviii Contents
12.6.1 The Theory of Solvation 250
12.6.2 The Solvent Accessible Surface Area 251
12.6.3 The Onsager Model 251
12.6.4 The Poisson Equation 251
12.6.5 The Self-Consistent Reaction Field Calculation 251
12.6.6 The Self-Consistent Isodensity
Polarized Continuum Model 252
12.7 The Population Analysis Method 253
12.7.1 The Mulliken Population Analysis Method 253
12.7.2 The Merz-Singh-Kollman Scheme 254
12.7.3 Charges from Electrostatic Potentials
Using a Grid-Based Method (CHELPG) 255
12.7.4 The Natural Population Analysis Method 255
12.8 Shielding 256
12.9 Electric Multipoles and Multipole Moments 257
12.9.1 The Quantum Mechanical Dipole Operator 258
12.9.2 The Dielectric Polarization 259
12.10 Vibrational Frequencies 260
12.11 Thermodynamic Properties 262
12.12 Molecular Orbital Methods 263
12.13 Input Formats for Computations 264
12.13.1 The Z-Matrix Input as the Common Standard Format 264
12.13.2 Multipurpose Internet Mail Extensions 265
12.13.3 Converting Between Formats 266
12.14 A Comparison of Methods 268
12.14.1 Molecular Geometry 268
12.14.2 Energy Changes 270
12.14.3 Dipole Moments 271
12.14.4 Generalizations 272
12.15 Exercises 272
References 274
13 High Performance Computing 275
13.1 Introduction - Supercomputers vs. Clusters 275
13.2 Clustering 275
13.3 How Clusters Work 276
13.4 Computational Clusters 277
13.5 Clustering Tools and Libraries 277
13.6 The Cluster Architecture 278
13.7 Clustermatic 279
13.8 LinuxBIOS 280
13.9 BProc 280
13.10 Configuration 280
13.11 Setup 281
13.12 The Steps to Configure a Cluster 281
Contents xix
13.13 Clustering Through Windows 282
13.13.1 Network Load Balancing Clusters 282
13.13.2 Server Clusters 283
13.13.3 Component Load Balancing 283
13.14 Installing the Windows Cluster 283
13.15 Grid Computing 284
13.15.1 Exploiting Underutilized Resources 284
13.15.2 Parallel CPU Capacity 285
13.16 Types of Resources Required to Create a Grid 285
13.16.1 Computational Resources 285
13.16.2 Storage Resources 286
13.16.3 Communications Mechanisms 287
13.16.4 The Software and Licenses Required
to Create the Grid 287
13.17 Grid Types - Intragrid to Intergrid 288
13.18 The Globus Toolkit 289
13.19 Bundles and Grid Packaging Technology 289
13.20 The HPC for Computational Chemistry 291
13.20.1 The Valence-Electron Approximation 291
13.20.2 The Effective Core Potential 291
13.20.3 The Direct SCF Method 292
13.20.4 The Partially Direct SCF Method 292
13.21 The Pseudopotential Method 293
13.21.1 The Block-Localized Wavefunction Method 293
13.22 Exercises 294
References 294
14 Research in Computational Chemistry and Molecular Modeling 297
14.1 Introduction 297
14.2 Molecular Interaction 297
14.3 Shape Selective Catalysts 298
14.4 Optimized Basis Sets for Lanthanide and Actinide Systems 299
14.5 Designing Biomolecular Motors 300
14.6 Protein Folding and Distributed Computing 301
14.7 Computational Drug Designing and Biocomputing 302
14.8 Artificial Photo Synthesis 304
14.9 Quantum Dynamics of Enzyme Reactions 304
14.10 Other Important Topics 305
References 309
15 Basic Mathematics for Computational Chemistry 311
15.1 Introduction and Basic Definitions 311
15.1.1 Example 1 312
15.1.2 Example 2 Using MATLAB 313
15.2 Matrix Addition and Subtraction 313
15.2.1 Example 3: Matrix Addition Using MATLAB 314
xx Contents
15.3 Matrix Multiplication 314
15.3.1 Example 4: Matrix Multiplication Using MATLAB 316
15.4 The Matrix Transpose 316
15.4.1 Example 5: The Transpose of a Matrix Using MATLAB.. 317
15.5 The Matrix Inverse 317
15.5.1 Example 6 318
15.5.2 MATLAB Implementation 319
15.6 Systems of Linear Equations 320
15.6.1 Example 7 320
15.6.2 Example 8 321
15.6.3 Example 9 321
15.6.4 Example 10: A MATLAB Solution
of the Linear System of Equations 323
15.7 The Least-Squares Method 326
15.7.1 Example 11 328
15.8 Eigenvalues and Eigenvectors 333
15.8.1 Example 12 334
15.8.2 Example 13 335
15.8.3 The Computation of Eigenvalues 335
15.8.4 Example 14 336
15.8.5 The Computation of Eigenvectors 336
15.8.6 Example 15 337
15.9 Exercises 340
15.10 Summary 340
References 341
A Operators 343
A. 1 Introduction 343
A.2 Operators and Quantum Mechanics 343
A.3 Basic Properties of Operators 344
A.4 Linear Operators 345
A.5 Eigenfunctions and Eigenvalues 345
B Hückel MO Heteroatom Parameters 347
C Using Microsoft Excel to Balance Chemical Equations 349
C.l Introduction 349
C.2 The Matrix Method 349
C.2.1 Methodology 349
C.2.2 Example 1 350
C.3 Undermined Systems 351
C.4 Balancing as an Optimization Problem 352
C.4.1 Example 3 352
C.4.2 Example 4 355
C.4.3 Example 5 355
Contents xxi
D Simultaneous Spectrophotometric Analysis 357
D.l Introduction 357
D.2 The Absorption Spectram 358
E Bond Enthalpy of Hydrocarbons 361
F Graphing Chemical Analysis Data 363
F. 1 Guidelines 363
F.2 Example: Beer s Law Absorption Spectra Tools 363
F.2.1 Basic Information 363
F.2.2 Beer s Law Scatter Plot and Linear Regression 364
F.3 Creating a Linear Regression Line (Trendline) 369
F.4 Using the Regression Equation to Calculate Concentrations 369
F.4.1 Adjusting the Chart Display 371
G Titration Data Plotting 375
G.l Creating a Scatter Plot of Titration Data 375
G.2 Curve Fitting to Titration Data 376
G.3 Changing the Scatter Plot to a Line Graph 378
G.4 Adding a Reference Line 378
G.5 Modifying the Chart Axis Scale 380
G.6 Extensions 382
H Curve Fitting in Chemistry 383
H.l Membrane Potential 383
H.2 The Determination of the E° of the Silver-Silver Chloride
Reference Cell 384
I The Solvation of Potassium Fluoride 387
J Partial Molal Volume of ZnCl2 389
Index 391
|
adam_txt |
Contents
1 Introduction 1
1.1 A Definition of Computational Chemistry 1
1.2 Models 2
1.3 Approximations 3
1.4 Reality 4
1.5 Computational Chemistry Methods 4
1.5.1 Ab Initio Calculations 5
1.5.2 Semiempirical Calculations 6
1.5.3 Modeling the Solid State 6
1.5.4 Molecular Mechanics 7
1.5.5 Molecular Simulation 7
1.5.6 Statistical Mechanics 8
1.5.7 Thermodynamics 8
1.5.8 Structure-Property Relationships 8
1.5.9 Symbolic Calculations 9
1.5.10 Artificial Intelligence 9
1.5.11 The Design of a Computational Research Program 9
1.5.12 Visualization 10
1.6 Journals and Book Series Focusing
on Computational Chemistry 10
1.7 Journals and Book Series
Often Including Computational Chemistry 11
1.8 Common Reference Books Available
on Computational Chemistry 11
1.9 Computational Chemistry on the Internet 13
1.10 Some Topics of Research Interest Related
to Computational Chemistry 14
References 15
xi
xii Contents
2 Symmetry and Point Groups 17
2.1 Introduction 17
2.2 Symmetry Operations and Symmetry Elements 17
2.3 Symmetry Operations and Elements of Symmetry 18
2.3.1 The Identity Operation 18
2.3.2 Rotation Operations 19
2.3.3 Reflection Planes (or Mirror Planes) 22
2.3.4 Inversion Operation 25
2.3.5 Improper Rotations 26
2.4 Consequences for Chirality 26
2.5 Point Groups 27
2.6 The Procedure for Determining the Point Group of Molecules . 28
2.7 Typical Molecular Models 30
2.8 Group Representation of Symmetry Operations 32
2.9 Irreducible Representations 33
2.10 Labeling of Electronic Terms 34
2.11 Exercises 34
2.11.1 Questions 34
2.11.2 Answers to Selected Questions 34
References 35
3 Quantum Mechanics: A Brief Introduction 37
3.1 Introduction 37
3.1.1 The Ultraviolet Catastrophe 37
3.1.2 The Photoelectric Effect 38
3.1.3 The Quantization of the Electronic Angular Momentum . 39
3.1.4 Wave-Particle Duality 39
3.2 The Schrödinger Equation 41
3.2.1 The Time-Independent Schrödinger Equation 41
3.2.2 The Time-Dependent Schrödinger Equation 43
3.3 The Solution to the Schrödinger Equation 45
3.4 Exercises 45
3.4.1 Question 1 45
3.4.2 Answer 1 45
3.4.3 Question 2 46
3.4.4 Answer 2 46
3.4.5 Question 3 46
3.4.6 Answer 3 46
3.4.7 Question 4 47
3.4.8 Answer 4 47
3.4.9 Question 5 48
3.4.10 Answer 5 48
3.4.11 Question 6 48
3.4.12 Answer 6 48
3.4.13 Question 7 49
Contents xiii
3.4.14 Answer 7 49
3.4.15 Question8 50
3.4.16 Answer 8 50
3.4.17 Question9 50
3.4.18 Answer 9 50
3.4.19 QuestionlO 51
3.4.20 Answer 10 51
3.5 Exercises 51
References 52
4 Hückel Molecular Orbital Theory 53
4.1 Introduction 53
4.2 The Born-Oppenheimer Approximation 53
4.3 Independent Particle Approximation 56
4.4 ^-Electron Approximation 58
4.5 Hückel's Calculation 58
4.6 The Variational Method and the Expectation Value 59
4.7 The Expectation Energy and the Hückel MO 60
4.8 The Overlap Integral (S,7) 62
4.9 The Coulomb Integral (a) 63
4.10 The Resonance (Exchange) Integral (ß) 63
4.11 The Solution to the Secular Matrix 63
4.12 Generalization 64
4.13 The Eigenvector Calculation of the Secular Matrix 66
4.14 The Chemical Applications of Hückel's MOT 66
4.15 Charge Density 67
4.16 The Hückel (4n + 2) Rule and Aromaticity 69
4.17 The Delocalization Energy 71
4.18 Energy Levels and Spectrum 73
4.19 Wave Functions 74
4.19.1 Step 1: Writing the Secular Matrix 74
4.19.2 Step 2: Solving the Secular Matrix 74
4.20 Bond Order 77
4.21 The Free Valence Index 78
4.22 Molecules with Nonbonding Molecular Orbitals 80
4.23 The Prediction of Chemical Reactivity 81
4.24 The HMO and Symmetry 82
4.25 Molecules Containing Heteroatoms 85
4.26 The Extended Hückel Method 86
4.27 Exercises 88
References 91
xiv Contents
5 Hartree-Fock Theory 93
5.1 Introduction 93
5.2 The Hartree Method 93
5.3 Bosons and Fermions 96
5.4 Spin Multiplicity 96
5.5 The Slater Determinant 97
5.6 Properties of the Slater Determinant 99
5.7 The Hartree-Fock Equation 99
5.8 The Secular Determinant 104
5.9 Restricted and Unrestricted HF Models 104
5.10 The Fock Matrix 106
5.11 Roothaan-Hall Equations 106
5.12 Elements of the Fock Matrix 107
5.13 Steps for the HF Calculation 110
5.14 Koopman's Theorem 110
5.15 Electron Correlation 110
5.16 Exercises 112
References 113
6 Basis Sets 115
6.1 Introduction 115
6.2 The Energy Calculation from the STO Function 117
6.3 The Energy Calculation of Multielectron Systems 120
6.4 Gaussian Type Orbitals 121
6.5 Differences Between STOs and GTOs 122
6.6 Classification of Basis Sets 124
6.7 Minimal Basis Sets 124
6.8 A Comparison of Energy Calculations of the Hydrogen Atom
Based on STO-nG Basis Sets 125
6.8.1 STO-2G 125
6.8.2 STO-3G 125
6.8.3 STO-6G 126
6.9 Contracted Gaussian Type Orbitals 126
6.10 Double- and Triple-Zeta Basis Sets
and the Split-Valence Basis Sets 128
6.11 Polarized Basis Sets 130
6.12 Basis Set Truncation Errors 133
6.13 Basis Set Superposition Error 133
6.14 Methods to Overcome BSSEs 135
6.14.1 The Chemical Hamiltonian Approach 135
6.14.2 The Counterpoise Method 135
6.15 The Intermolecular Interaction Energy
of Ion Water Clusters 136
6.16 A List of Commonly Available Basis Sets 137
6.17 Internet Resources for Generating Basis Sets 137
Contents xv
6.18 Exercises 138
References 138
7 Semiempirical Methods 139
7.1 Introduction 139
7.2 The Neglect of Differential Overlap Method 140
7.3 The Complete Neglect of Differential Overlap Method 140
7.4 The Modified Neglect of the Diatomic Overlap Method 140
7.5 The Austin Model 1 Method 141
7.6 The Parametric Method 3 Model 141
7.7 The Pairwize Distance Directed Gaussian Method 142
7.8 The Zero Differential Overlap Approximation Method 142
7.9 The Hamiltonian in the Semiempirical Method 143
7.9.1 The Computation of H^ 145
7.9.2 The Computation of H=°£ 145
7.10 Comparisons of Semiempirical Methods 148
7.11 Software Used for Semiempirical Calculations 153
7.12 Exercises 153
References 154
8 The Ab Initio Method 155
8.1 Introduction 155
8.2 The Computation of the Correlation Energy 156
8.3 The Computation of the SD of the Excited States 157
8.4 Configuration Interaction 158
8.5 Secular Equations 159
8.6 Many-Body Perturbation Theory 159
8.7 The Möller-Plesset Perturbation 161
8.8 The Coupled Cluster Method 165
8.9 Research Topics 168
8.10 Exercises 168
References 170
9 Density Functional Theory 171
9.1 Introduction 171
9.2 Electron Density 171
9.3 Pair Density 172
9.4 The Development of DFT 172
9.5 The Functional 173
9.6 The Hohenberg and Kohn Theorem 174
9.7 The Kohn and Sham Method 178
9.8 Implementations of the KS Method 180
9.9 Density Functionals 181
9.10 The Dirac-Slater Exchange Energy Functional and the Potential. 182
xvi Contents
9.11 The von Barth-Hedin Exchange Energy Functional
and the Potential 183
9.12 The Becke Exchange Energy Functional and the Potential 183
9.13 The Perdew-Wang 91 Exchange Energy Functional
and the Potential 184
9.14 The Perdew-Zunger LSD Correlation Energy Functional
and the Potential 185
9.15 The Vosko-Wilk-Nusair Correlation Energy Functional 186
9.16 The von Barth-Hedin Correlation Energy Functional
and the Potential 186
9.17 The Perdew 86 Correlation Energy Functional and the Potential. 187
9.18 The Perdew 91 Correlation Energy Functional and the Potential. 187
9.19 The Lee, Yang, and Parr Correlation Energy Functional
and the Potential 188
9.20 DFTMethods 189
9.21 Applications of DFT 190
9.22 The Performance of DFT 191
9.23 Advantages of DFT in Biological Chemistry 192
9.24 Exercises 192
References 193
10 Reduced Density Matrix 195
10.1 Introduction 195
10.2 Reduced Density Matrices 195
10.3 7V-Representability Conditions 197
10.3.1 G-Condition (Garrod) and Percus 198
10.3.2 T-Conditions (Erdahl) 198
10.3.3 T2 Condition 198
10.4 Computations Using the RDM Method 199
10.5 The SDP Formulation of the RDM Method 199
10.6 Comparison of Results 201
10.7 Research in RDM 201
10.8 Exercises 202
References 202
11 Molecular Mechanics 205
11.1 Introduction 205
11.2 Triad Tools 206
11.3 The Morse Potential Model 207
11.4 The Harmonie Oscillator Model for Molecules 208
11.5 The Comparison of the Morse Potential
with the Harmonie Potential 209
11.6 Two Atoms Connected by a Bond 210
11.7 Polyatomic Molecules 211
11.8 Energy Due to Stretching 212
Contents xvii
11.9 Energy Due to Bending 212
11.10 Energy Due to Stretch-Bend Interactions 212
11.11 Energy Due to Torsional Strain 213
11.12 Energy Due to van der Waals Interactions 213
11.13 Energy Due to Dipole-Dipole Interactions 213
11.14 The Lennard-Jones Type Potential 214
11.15 The Truncated Lennard-Jones Potential 214
11.16 The Kihara Potential 215
11.17 The Exponential -6 Potential 215
11.18 The BFW Two-Body Potential 216
11.19 The Ab Initio Potential 216
11.20 The Ionic and Polar Potential 216
11.21 Commonly Available Force Fields 217
11.21.1 MM2, MM3, and MM4 217
11.21.2 AMBER 218
11.21.3 CHARMM 219
11.21.4 Merck Molecular Force Field 219
11.21.5 The Consistent Force Field 222
11.22 Some Other Useful Potential Fields 222
11.23 The Merits and Demerits of the Force Field Approach 223
11.24 Parameterization 224
11.25 Some MM Software Packages 225
11.26 Exercises 225
References 227
12 The Modeling of Molecules Through Computational Methods 229
12.1 Introduction 229
12.2 Optimization 229
12.2.1 Multivariable Optimization Algorithms 229
12.2.2 Level Sets, Level Curves, and Gradients 230
12.2.3 Optimality Criteria 232
12.2.4 The Unidirectional Search 233
12.2.5 Finding the Minimum Point Along 5' 233
12.2.6 Gradient-Based Methods 234
12.2.7 The Method of Steepest Descent 235
12.2.8 The Method of Conjugate Directions 238
12.2.9 The Gram-Schmidt Conjugation Method 240
12.2.10 The Conjugate Gradient Method 241
12.3 Potential Energy Surfaces 243
12.3.1 Convergence Criteria 244
12.3.2 Characterizing Stationary Points 245
12.4 The Search for Transition States 245
12.4.1 Computing the Activated Complex Formation 246
12.5 The Single Point Energy Calculation 249
12.6 The Computation of Solvation 250
xviii Contents
12.6.1 The Theory of Solvation 250
12.6.2 The Solvent Accessible Surface Area 251
12.6.3 The Onsager Model 251
12.6.4 The Poisson Equation 251
12.6.5 The Self-Consistent Reaction Field Calculation 251
12.6.6 The Self-Consistent Isodensity
Polarized Continuum Model 252
12.7 The Population Analysis Method 253
12.7.1 The Mulliken Population Analysis Method 253
12.7.2 The Merz-Singh-Kollman Scheme 254
12.7.3 Charges from Electrostatic Potentials
Using a Grid-Based Method (CHELPG) 255
12.7.4 The Natural Population Analysis Method 255
12.8 Shielding 256
12.9 Electric Multipoles and Multipole Moments 257
12.9.1 The Quantum Mechanical Dipole Operator 258
12.9.2 The Dielectric Polarization 259
12.10 Vibrational Frequencies 260
12.11 Thermodynamic Properties 262
12.12 Molecular Orbital Methods 263
12.13 Input Formats for Computations 264
12.13.1 The Z-Matrix Input as the Common Standard Format 264
12.13.2 Multipurpose Internet Mail Extensions 265
12.13.3 Converting Between Formats 266
12.14 A Comparison of Methods 268
12.14.1 Molecular Geometry 268
12.14.2 Energy Changes 270
12.14.3 Dipole Moments 271
12.14.4 Generalizations 272
12.15 Exercises 272
References 274
13 High Performance Computing 275
13.1 Introduction - Supercomputers vs. Clusters 275
13.2 Clustering 275
13.3 How Clusters Work 276
13.4 Computational Clusters 277
13.5 Clustering Tools and Libraries 277
13.6 The Cluster Architecture 278
13.7 Clustermatic 279
13.8 LinuxBIOS 280
13.9 BProc 280
13.10 Configuration 280
13.11 Setup 281
13.12 The Steps to Configure a Cluster 281
Contents xix
13.13 Clustering Through Windows 282
13.13.1 Network Load Balancing Clusters 282
13.13.2 Server Clusters 283
13.13.3 Component Load Balancing 283
13.14 Installing the Windows Cluster 283
13.15 Grid Computing 284
13.15.1 Exploiting Underutilized Resources 284
13.15.2 Parallel CPU Capacity 285
13.16 Types of Resources Required to Create a Grid 285
13.16.1 Computational Resources 285
13.16.2 Storage Resources 286
13.16.3 Communications Mechanisms 287
13.16.4 The Software and Licenses Required
to Create the Grid 287
13.17 Grid Types - Intragrid to Intergrid 288
13.18 The Globus Toolkit 289
13.19 Bundles and Grid Packaging Technology 289
13.20 The HPC for Computational Chemistry 291
13.20.1 The Valence-Electron Approximation 291
13.20.2 The Effective Core Potential 291
13.20.3 The Direct SCF Method 292
13.20.4 The Partially Direct SCF Method 292
13.21 The Pseudopotential Method 293
13.21.1 The Block-Localized Wavefunction Method 293
13.22 Exercises 294
References 294
14 Research in Computational Chemistry and Molecular Modeling 297
14.1 Introduction 297
14.2 Molecular Interaction 297
14.3 Shape Selective Catalysts 298
14.4 Optimized Basis Sets for Lanthanide and Actinide Systems 299
14.5 Designing Biomolecular Motors 300
14.6 Protein Folding and Distributed Computing 301
14.7 Computational Drug Designing and Biocomputing 302
14.8 Artificial Photo Synthesis 304
14.9 Quantum Dynamics of Enzyme Reactions 304
14.10 Other Important Topics 305
References 309
15 Basic Mathematics for Computational Chemistry 311
15.1 Introduction and Basic Definitions 311
15.1.1 Example 1 312
15.1.2 Example 2 Using MATLAB 313
15.2 Matrix Addition and Subtraction 313
15.2.1 Example 3: Matrix Addition Using MATLAB 314
xx Contents
15.3 Matrix Multiplication 314
15.3.1 Example 4: Matrix Multiplication Using MATLAB 316
15.4 The Matrix Transpose 316
15.4.1 Example 5: The Transpose of a Matrix Using MATLAB. 317
15.5 The Matrix Inverse 317
15.5.1 Example 6 318
15.5.2 MATLAB Implementation 319
15.6 Systems of Linear Equations 320
15.6.1 Example 7 320
15.6.2 Example 8 321
15.6.3 Example 9 321
15.6.4 Example 10: A MATLAB Solution
of the Linear System of Equations 323
15.7 The Least-Squares Method 326
15.7.1 Example 11 328
15.8 Eigenvalues and Eigenvectors 333
15.8.1 Example 12 334
15.8.2 Example 13 335
15.8.3 The Computation of Eigenvalues 335
15.8.4 Example 14 336
15.8.5 The Computation of Eigenvectors 336
15.8.6 Example 15 337
15.9 Exercises 340
15.10 Summary 340
References 341
A Operators 343
A. 1 Introduction 343
A.2 Operators and Quantum Mechanics 343
A.3 Basic Properties of Operators 344
A.4 Linear Operators 345
A.5 Eigenfunctions and Eigenvalues 345
B Hückel MO Heteroatom Parameters 347
C Using Microsoft Excel to Balance Chemical Equations 349
C.l Introduction 349
C.2 The Matrix Method 349
C.2.1 Methodology 349
C.2.2 Example 1 350
C.3 Undermined Systems 351
C.4 Balancing as an Optimization Problem 352
C.4.1 Example 3 352
C.4.2 Example 4 355
C.4.3 Example 5 355
Contents xxi
D Simultaneous Spectrophotometric Analysis 357
D.l Introduction 357
D.2 The Absorption Spectram 358
E Bond Enthalpy of Hydrocarbons 361
F Graphing Chemical Analysis Data 363
F. 1 Guidelines 363
F.2 Example: Beer's Law Absorption Spectra Tools 363
F.2.1 Basic Information 363
F.2.2 Beer's Law Scatter Plot and Linear Regression 364
F.3 Creating a Linear Regression Line (Trendline) 369
F.4 Using the Regression Equation to Calculate Concentrations 369
F.4.1 Adjusting the Chart Display 371
G Titration Data Plotting 375
G.l Creating a Scatter Plot of Titration Data 375
G.2 Curve Fitting to Titration Data 376
G.3 Changing the Scatter Plot to a Line Graph 378
G.4 Adding a Reference Line 378
G.5 Modifying the Chart Axis Scale 380
G.6 Extensions 382
H Curve Fitting in Chemistry 383
H.l Membrane Potential 383
H.2 The Determination of the E° of the Silver-Silver Chloride
Reference Cell 384
I The Solvation of Potassium Fluoride 387
J Partial Molal Volume of ZnCl2 389
Index 391 |
any_adam_object | 1 |
any_adam_object_boolean | 1 |
author | Ramachandran, K. I. Deepa, Gopakumar Namboori, Krishnan |
author_facet | Ramachandran, K. I. Deepa, Gopakumar Namboori, Krishnan |
author_role | aut aut aut |
author_sort | Ramachandran, K. I. |
author_variant | k i r ki kir g d gd k n kn |
building | Verbundindex |
bvnumber | BV023487363 |
classification_rvk | VC 6100 VC 6250 |
ctrlnum | (OCoLC)244036359 (DE-599)DNB986535079 |
dewey-full | 541.220113 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 541 - Physical chemistry |
dewey-raw | 541.220113 |
dewey-search | 541.220113 |
dewey-sort | 3541.220113 |
dewey-tens | 540 - Chemistry and allied sciences |
discipline | Chemie / Pharmazie |
discipline_str_mv | Chemie / Pharmazie |
format | Book |
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spelling | Ramachandran, K. I. Verfasser aut Computational chemistry and molecular modeling principles and applications K. I. Ramachandran ; G. Deepa ; K. Namboori Berlin [u.a.] Springer 2008 XXI, 397 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational chemistry (DE-588)4290091-8 gnd rswk-swf Molekulardesign (DE-588)4265444-0 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Molekulardesign (DE-588)4265444-0 s Computational chemistry (DE-588)4290091-8 s DE-604 Deepa, Gopakumar Verfasser aut Namboori, Krishnan Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016669390&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Ramachandran, K. I. Deepa, Gopakumar Namboori, Krishnan Computational chemistry and molecular modeling principles and applications Computational chemistry (DE-588)4290091-8 gnd Molekulardesign (DE-588)4265444-0 gnd |
subject_GND | (DE-588)4290091-8 (DE-588)4265444-0 (DE-588)4143413-4 |
title | Computational chemistry and molecular modeling principles and applications |
title_auth | Computational chemistry and molecular modeling principles and applications |
title_exact_search | Computational chemistry and molecular modeling principles and applications |
title_exact_search_txtP | Computational chemistry and molecular modeling principles and applications |
title_full | Computational chemistry and molecular modeling principles and applications K. I. Ramachandran ; G. Deepa ; K. Namboori |
title_fullStr | Computational chemistry and molecular modeling principles and applications K. I. Ramachandran ; G. Deepa ; K. Namboori |
title_full_unstemmed | Computational chemistry and molecular modeling principles and applications K. I. Ramachandran ; G. Deepa ; K. Namboori |
title_short | Computational chemistry and molecular modeling |
title_sort | computational chemistry and molecular modeling principles and applications |
title_sub | principles and applications |
topic | Computational chemistry (DE-588)4290091-8 gnd Molekulardesign (DE-588)4265444-0 gnd |
topic_facet | Computational chemistry Molekulardesign Aufsatzsammlung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016669390&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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