Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics

COMPUTATIONAL CHEMISTRY......Page 2
CONTENTS......Page 8
PREFACE......Page 10
1.1 WHAT YOU CAN DO WITH COMPUTATIONAL CHEMISTRY......Page 12
1.2 THE TOOLS OF COMPUTATIONAL CHEMISTRY......Page 13
1.3 PUTTING IT ALL TOGETHER......Page 14
1.5 SUMMARY OF CHAPTER 1......Page 15
REFERENCES......Page 16
HARDER QUESTIONS......Page 17
2.1 PERSPECTIVE......Page 20
2.2 STATIONARY POINTS......Page 24
2.3 THE BORN–OPPENHEIMER APPROXIMATION......Page 31
2.4 GEOMETRY OPTIMIZATION......Page 33
2.5 STATIONARY POINTS AND NORMAL-MODE VIBRATIONS: ZPE......Page 40
2.6 SYMMETRY......Page 44
2.7 SUMMARY OF CHAPTER 2......Page 49
REFERENCES......Page 50
HARDER QUESTIONS......Page 51
3.1 PERSPECTIVE......Page 54
3.2.1 Developing a forcefield......Page 56
3.2.2 Parameterizing a forcefield......Page 61
3.2.3 A calculation using our forcefield......Page 65
3.3.1 Geometries and energies of small- to medium-sized molecules......Page 68
3.3.2 Geometries and energies of polymers......Page 69
3.3.3 Geometries and energies of transition states......Page 70
3.3.4 MM in organic synthesis......Page 72
3.3.5 Molecular dynamics and Monte Carlo simulations......Page 74
3.4 GEOMETRIES CALCULATED BY MM......Page 75
3.5 FREQUENCIES CALCULATED BY MM......Page 79
3.6.1 Strengths......Page 83
3.6.2 Weaknesses......Page 84
REFERENCES......Page 86
HARDER QUESTIONS......Page 89
4.1 PERSPECTIVE......Page 92
4.2.1 The origins of quantum theory: blackbody radiation and the photoelectric effect......Page 93
4.2.2 Radioactivity......Page 97
4.2.4 The nuclear atom......Page 98
4.2.5 The Bohr atom......Page 100
4.2.6 The wave mechanical atom and the Schrödinger equation......Page 102
4.3.1 Introduction......Page 106
4.3.2 Hybridization......Page 107
4.3.3 Matrices and determinants......Page 112
4.3.4 The simple Hückel method – theory......Page 120
4.3.5 The simple Hückel method – applications......Page 133
4.3.6 Strengths and weaknesses of the SHM......Page 144
4.3.7 The determinant method of calculating the Hückel c’s and energy levels......Page 146
4.4.1 Theory......Page 151
4.4.2 An illustration of the EHM: the protonated helium molecule......Page 157
4.4.4 Strengths and weaknesses of the EHM......Page 160
4.5 SUMMARY OF CHAPTER 4......Page 162
REFERENCES......Page 164
HARDER QUESTIONS......Page 168
5.1 PERSPECTIVE......Page 170
5.2.2 The Hartree SCF method......Page 171
5.2.3.1 Slater determinants......Page 175
5.2.3.2 Calculating the atomic or molecular energy......Page 178
5.2.3.4 Minimizing the energy; the HF equations......Page 182
5.2.3.5 The meaning of the HF equations......Page 187
5.2.3.6a Deriving the Roothaan–Hall equations......Page 188
5.2.3.6b Using the Roothaan–Hall equations to do ab initio calculations - the SCF procedure......Page 194
5.2.3.6c Using the Roothaan–Hall equations to do ab initio calculations – the equations in terms of the c’s and ofthe LCAO expansion......Page 196
5.2.3.6d Using the Roothaan–Hall equations to do ab initio calculations - some details......Page 199
5.2.3.6e Using the Roothaan–Hall equations to do ab initio calculations - an example......Page 203
5.3.1 Introduction......Page 221
5.3.2 Gaussian functions; basis set preliminaries; direct SCF......Page 222
5.3.3 Types of basis sets and their uses......Page 227
5.4.1 Electron correlation......Page 242
5.4.2 The Møller-Plesset approach to electron correlation......Page 248
5.4.3 The configuration interaction approach to electron correlation......Page 253
5.5.1 Geometries......Page 264
5.5.2.1 Energies: Preliminaries......Page 273
5.5.2.2a Thermodynamics; “direct” methods, isodesmic reactions......Page 279
5.5.2.2b Thermodynamics; high-accuracy calculations......Page 283
5.5.2.3 Thermodynamics; calculating heats of formation......Page 286
5.5.2.3a Kinetics; calculating reaction rates......Page 292
5.5.2.3b Energies: concluding remarks......Page 298
5.5.3 Frequencies......Page 300
5.5.4 Properties arising from electron distribution......Page 307
Dipole moments......Page 308
Charges and bond orders......Page 311
Electrostatic potential......Page 318
Atoms-in-molecules......Page 319
5.5.5 Miscellaneous properties – UV and NMR spectra, ionization energies, and electron affinities......Page 323
5.5.6 Visualization......Page 327
5.6 STRENGTHS AND WEAKNESSES OF AB INITIO CALCULATIONS......Page 333
5.7 SUMMARY OF CHAPTER 5......Page 334
REFERENCES......Page 335
HARDER QUESTIONS......Page 347
6.1 PERSPECTIVE......Page 350
6.2.1 Preliminaries......Page 351
6.2.2 The Pariser-Parr-Pople (PPP) method......Page 354
6.2.3 The complete neglect of differential overlap (CNDO) method......Page 355
6.2.5.1 NDDO-based methods from the Dewar group: MNDO, AM1, PM3 and SAM1 - preliminaries......Page 357
6.2.5.2 Heats of formation from SE electronic energies......Page 359
6.2.5.3 MNDO......Page 360
6.2.5.4 AM1......Page 363
6.2.5.5 PM3......Page 364
6.2.5.7 Inclusion of d orbitals: MNDO/d and PM3t; explicit electron correlation: MNDOC......Page 365
6.3.1 Geometries......Page 366
6.3.2.1 Energies: preliminaries......Page 372
6.3.2.2 Energies: calculating quantities relevant to thermodynamics and kinetics......Page 373
6.3.3 Frequencies......Page 375
6.3.4 Properties arising from electron distribution: dipole moments, charges, bond orders......Page 379
6.3.5 Miscellaneous properties – UV spectra, ionization energies, and electron affinities......Page 384
6.3.6 Visualization......Page 386
6.3.7 Some general remarks......Page 387
6.4 STRENGTHS AND WEAKNESSES OF SE METHODS......Page 388
REFERENCES......Page 389
HARDER QUESTIONS......Page 393
7.1 PERSPECTIVE......Page 396
7.2.2 Forerunners to current DFT methods......Page 398
7.2.3.1 Functionals: The Hohenberg–Kohn theorems......Page 399
7.2.3.2 The Kohn–Sham energy and the KS equations......Page 400
7.2.3.3 Solving the KS equations......Page 405
7.2.3.4a The local density approximation (LDA)......Page 407
7.2.3.4c Gradient-corrected functionals and hybrid functionals......Page 408
7.3 APPLICATIONS OF DENSITY FUNCTIONAL THEORY......Page 410
7.3.1 Geometries......Page 411
7.3.2.1 Energies: preliminaries......Page 417
7.3.2.2a Thermodynamics......Page 418
7.3.2.2b Kinetics......Page 422
7.3.3 Frequencies......Page 424
7.3.4 Properties arising from electron distribution – dipole moments, charges, bond orders, atoms-in-molecules......Page 425
7.3.5 Miscellaneous properties......Page 430
7.4 STRENGTHS AND WEAKNESSES OF DFT......Page 447
7.5 SUMMARY OF CHAPTER 7......Page 448
REFERENCES......Page 449
EASIER QUESTIONS......Page 455
HARDER QUESTIONS......Page 456
8.1.1.1 Oxirene......Page 458
8.1.1.3 Pyramidane......Page 460
8.1.2 Mechanisms......Page 461
8.1.2.2 Abstraction of H from amino acids by the OH radical......Page 462
8.1.3.1 Resonance vs. inductive effects......Page 463
8.1.3.2 Homoaromaticity......Page 464
8.2.1 Books......Page 466
8.3 SOFTWARE AND HARDWARE......Page 468
8.3.1 Software......Page 469
8.3.2 Hardware......Page 470
REFERENCES......Page 471
INDEX......Page 474