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- •COMPUTATIONAL CHEMISTRY
- •CONTENTS
- •PREFACE
- •1.1 WHAT YOU CAN DO WITH COMPUTATIONAL CHEMISTRY
- •1.2 THE TOOLS OF COMPUTATIONAL CHEMISTRY
- •1.3 PUTTING IT ALL TOGETHER
- •1.4 THE PHILOSOPHY OF COMPUTATIONAL CHEMISTRY
- •1.5 SUMMARY OF CHAPTER 1
- •REFERENCES
- •EASIER QUESTIONS
- •HARDER QUESTIONS
- •2.1 PERSPECTIVE
- •2.2 STATIONARY POINTS
- •2.3 THE BORN–OPPENHEIMER APPROXIMATION
- •2.4 GEOMETRY OPTIMIZATION
- •2.6 SYMMETRY
- •2.7 SUMMARY OF CHAPTER 2
- •REFERENCES
- •EASIER QUESTIONS
- •HARDER QUESTIONS
- •3.1 PERSPECTIVE
- •3.2 THE BASIC PRINCIPLES OF MM
- •3.2.1 Developing a forcefield
- •3.2.2 Parameterizing a forcefield
- •3.2.3 A calculation using our forcefield
- •3.3 EXAMPLES OF THE USE OF MM
- •3.3.2 Geometries and energies of polymers
- •3.3.3 Geometries and energies of transition states
- •3.3.4 MM in organic synthesis
- •3.3.5 Molecular dynamics and Monte Carlo simulations
- •3.4 GEOMETRIES CALCULATED BY MM
- •3.5 FREQUENCIES CALCULATED BY MM
- •3.6 STRENGTHS AND WEAKNESSES OF MM
- •3.6.1 Strengths
- •3.6.2 Weaknesses
- •3.7 SUMMARY OF CHAPTER 3
- •REFERENCES
- •EASIER QUESTIONS
- •HARDER QUESTIONS
- •4.1 PERSPECTIVE
- •4.2.1 The origins of quantum theory: blackbody radiation and the photoelectric effect
- •4.2.2 Radioactivity
- •4.2.3 Relativity
- •4.2.4 The nuclear atom
- •4.2.5 The Bohr atom
- •4.2.6 The wave mechanical atom and the Schrödinger equation
- •4.3.1 Introduction
- •4.3.2 Hybridization
- •4.3.3 Matrices and determinants
- •4.3.4 The simple Hückel method – theory
- •4.3.5 The simple Hückel method – applications
- •4.3.6 Strengths and weaknesses of the SHM
- •4.4.1 Theory
- •4.4.2 An illustration of the EHM: the protonated helium molecule
- •4.4.3 The extended Hückel method – applications
- •4.4.4 Strengths and weaknesses of the EHM
- •4.5 SUMMARY OF CHAPTER 4
- •REFERENCES
- •EASIER QUESTIONS
- •5.1 PERSPECTIVE
- •5.2.1 Preliminaries
- •5.2.2 The Hartree SCF method
- •5.2.3 The HF equations
- •5.2.3.1 Slater determinants
- •5.2.3.2 Calculating the atomic or molecular energy
- •5.2.3.3 The variation theorem (variation principle)
- •5.2.3.4 Minimizing the energy; the HF equations
- •5.2.3.5 The meaning of the HF equations
- •5.2.3.6a Deriving the Roothaan–Hall equations
- •5.3 BASIS SETS
- •5.3.1 Introduction
- •5.3.2 Gaussian functions; basis set preliminaries; direct SCF
- •5.3.3 Types of basis sets and their uses
- •5.4 POST-HF CALCULATIONS: ELECTRON CORRELATION
- •5.4.1 Electron correlation
- •5.4.3 The configuration interaction approach to electron correlation
- •5.5.1 Geometries
- •5.5.2 Energies
- •5.5.2.1 Energies: Preliminaries
- •5.5.2.2 Energies: calculating quantities relevant to thermodynamics and to kinetics
- •5.5.2.2a Thermodynamics; “direct” methods, isodesmic reactions
- •5.5.2.2b Thermodynamics; high-accuracy calculations
- •5.5.2.3 Thermodynamics; calculating heats of formation
- •5.5.2.3a Kinetics; calculating reaction rates
- •5.5.2.3b Energies: concluding remarks
- •5.5.3 Frequencies
- •Dipole moments
- •Charges and bond orders
- •Electrostatic potential
- •Atoms-in-molecules
- •5.5.5 Miscellaneous properties – UV and NMR spectra, ionization energies, and electron affinities
- •5.5.6 Visualization
- •5.6 STRENGTHS AND WEAKNESSES OF AB INITIO CALCULATIONS
- •5.7 SUMMARY OF CHAPTER 5
- •REFERENCES
- •EASIER QUESTIONS
- •HARDER QUESTIONS
- •6.1 PERSPECTIVE
- •6.2 THE BASIC PRINCIPLES OF SCF SE METHODS
- •6.2.1 Preliminaries
- •6.2.2 The Pariser-Parr-Pople (PPP) method
- •6.2.3 The complete neglect of differential overlap (CNDO) method
- •6.2.4 The intermediate neglect of differential overlap (INDO) method
- •6.2.5 The neglect of diatomic differential overlap (NDDO) method
- •6.2.5.2 Heats of formation from SE electronic energies
- •6.2.5.3 MNDO
- •6.2.5.7 Inclusion of d orbitals: MNDO/d and PM3t; explicit electron correlation: MNDOC
- •6.3 APPLICATIONS OF SE METHODS
- •6.3.1 Geometries
- •6.3.2 Energies
- •6.3.2.1 Energies: preliminaries
- •6.3.2.2 Energies: calculating quantities relevant to thermodynamics and kinetics
- •6.3.3 Frequencies
- •6.3.4 Properties arising from electron distribution: dipole moments, charges, bond orders
- •6.3.5 Miscellaneous properties – UV spectra, ionization energies, and electron affinities
- •6.3.6 Visualization
- •6.3.7 Some general remarks
- •6.4 STRENGTHS AND WEAKNESSES OF SE METHODS
- •6.5 SUMMARY OF CHAPTER 6
- •REFERENCES
- •EASIER QUESTIONS
- •HARDER QUESTIONS
- •7.1 PERSPECTIVE
- •7.2 THE BASIC PRINCIPLES OF DENSITY FUNCTIONAL THEORY
- •7.2.1 Preliminaries
- •7.2.2 Forerunners to current DFT methods
- •7.2.3.1 Functionals: The Hohenberg–Kohn theorems
- •7.2.3.2 The Kohn–Sham energy and the KS equations
- •7.2.3.3 Solving the KS equations
- •7.2.3.4a The local density approximation (LDA)
- •7.2.3.4b The local spin density approximation (LSDA)
- •7.2.3.4c Gradient-corrected functionals and hybrid functionals
- •7.3 APPLICATIONS OF DENSITY FUNCTIONAL THEORY
- •7.3.1 Geometries
- •7.3.2 Energies
- •7.3.2.1 Energies: preliminaries
- •7.3.2.2 Energies: calculating quantities relevant to thermodynamics and kinetics
- •7.3.2.2a Thermodynamics
- •7.3.2.2b Kinetics
- •7.3.3 Frequencies
- •7.3.6 Visualization
- •7.4 STRENGTHS AND WEAKNESSES OF DFT
- •7.5 SUMMARY OF CHAPTER 7
- •REFERENCES
- •EASIER QUESTIONS
- •HARDER QUESTIONS
- •8.1 FROM THE LITERATURE
- •8.1.1.1 Oxirene
- •8.1.1.2 Nitrogen pentafluoride
- •8.1.1.3 Pyramidane
- •8.1.1.4 Beyond dinitrogen
- •8.1.2 Mechanisms
- •8.1.2.1 The Diels–Alder reaction
- •8.1.2.2 Abstraction of H from amino acids by the OH radical
- •8.1.3 Concepts
- •8.1.3.1 Resonance vs. inductive effects
- •8.1.3.2 Homoaromaticity
- •8.2 TO THE LITERATURE
- •8.2.1 Books
- •8.2.2 The Worldwide Web
- •8.3 SOFTWARE AND HARDWARE
- •8.3.1 Software
- •8.3.2 Hardware
- •8.3.3 Postscript
- •REFERENCES
- •INDEX
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An Outline of Computational Chemistry 5
DFT methods – based on approximate solutions of the Schrödinger equation, bypassing the wavefunction that is a central feature of ab initio and semiempirical methods;
Molecular dynamics methods study molecules in motion.
Ab initio and the faster DFT enable novel molecules of theoretical interest to be studied, provided they are not too big. Semiempirical methods, which are much faster than ab initio or even DFT, can be applied to fairly large molecules (e.g. cholesterol, while MM will calculate geometries and energies of very large molecules such as proteins and nucleic acids; however, MM does not give information on electronic properties. Computational chemistry is widely used in the pharmaceutical industry to explore the interactions of potential drugs with biomolecules, for example by docking a candidate drug into the active site of an enzyme. It is also used to investigate the properties of solids (e.g. plastics) in materials science.
REFERENCES
[1]The physical chemist Wilhelm Ostwald (Nobel Prize 1909) was a disciple of the philosopher Ernst Mach. Like Mach, Ostwald attacked the notion of the reality of atoms and molecules (“Nobel Laureates in Chemistry, 1901–1992,” L. K. James, Ed., American Chemical Society
and the Chemical Heritage Foundation, Washington, DC, 1993) and it was only the work of Jean Perrin, published in 1913, that finally convinced him, perhaps the last eminent holdout against the atomic theory, that these entities really existed (Perrin showed that the number of tiny particles suspended in water dropped off with height exactly as predicted in 1905 by Einstein, who had derived an equation assuming the existence of atoms). Ostwald’s philosophical outlook stands in contrast to that of another outstanding physical chemist, Johannes van der Waals, who staunchly defended the atomic/molecular theory and was outraged by the Machian positivism of people like Ostwald. See “Van der Waals and Molecular Science,” A. Ya. Kipnis, B. F. Yavelov and J. S. Powlinson, Oxford University Press, New York, 1996.
For the opposition to and acceptance of atoms in physics see: D. Lindley, “Boltzmann’s Atom. The Great Debate that Launched a Revolution in Physics,” Free Press, New York, 2001; C. Cercignani, “Ludwig Boltzmann: The Man who Trusted Atoms,” Oxford University Press, New York, 1998.
Of course, to anyone who knew anything about organic chemistry, the existence of atoms was in little doubt by 1910, since that science had by that time achieved significant success in the field of synthesis, and a rational synthesis is predicated on assembling atoms in a definite way.
[2]For accounts of the history of the development of structural formulas see M. J. Nye, “From Chemical Philosophy to Theoretical Chemistry,” University of California Press, 1993;
C.A. Russell, “Edward Frankland: Chemistry, Controversy and Conspiracy in Victorian England,” Cambridge University Press, Cambridge, 1996.
[3](a) An assertion of the some adherents of the “postmodernist” school of social studies; see
P.Gross and N. Levitt, “The Academic Left and its Quarrels with Science,” John Hopkins
University Press, 1994. (b) For an account of the exposure of the intellectual vacuity of some members of this school by physicist Alan Sokal’s hoax see M. Gardner, “Skeptical Inquirer,” 1996, 20(6), 14.
6Computational Chemistry
[4](a) A trendy word popularized by the late Thomas Kuhn in his book “ The Structure of Scientific Revolutions,” University of Chicago Press, 1970. For a trenchant comment on Kuhn, see Ref. [3b]. (b) For a kinder perspective on Kuhn, see S. Weinberg, “Facing Up,” Harvard University Press, 2001, chapter 17.
EASIER QUESTIONS
1.What does the term computational chemistry mean?
2.What kinds of questions can computational chemistry answer?
3.Name the main tools available to the computational chemist. Outline (a few sentences for each) the characteristics of each.
4.Generally speaking, which is the fastest computational chemistry method (tool), and which is the slowest?
5.Why is computational chemistry useful in industry?
6.Basically, what does the Schrödinger equation describe, from the chemist’s viewpoint?
7.What is the limit to the kind of molecule for which we can get an exact solution to the Schrtidinger equation?
8.What is parameterization?
9.What advantages does computational chemistry have over “wet chemistry”?
10.Why cannot computational chemistry replace “wet chemistry”?
HARDER QUESTIONS
Discuss the following and justify your conclusions.
1.Was there computational chemistry before electronic computers were available?
2.Can “conventional” physical chemistry, such as the study of kinetics, thermodynamics, spectroscopy and electrochemistry, be regarded as a kind of computational chemistry?
3.The properties of a molecule that are most frequently calculated are geometry, energy (compared to that of other isomers), and spectra. Why is it more of a challenge to calculate “simple” properties like melting point and density?
Hint: Is there a difference between a molecule X and the substance X?
4.Is it surprising that the geometry and energy (compared to that of other isomers) of a molecule can often be accurately calculated by a ball-and-springs model (MM)?
5.What kinds of properties might you expect MM to be unable to calculate?
6.Should calculations from first principles (ab initio) necessarily be preferred to those which make some use of experimental data (semiempirical)?
7.Both experiments and calculations can give wrong answers. Why then should experiment have the last word?
8.Consider the docking of a potential drug molecule X into the active site of an enzyme: a factor influencing how well X will “hold” is clearly the shape of X; can you think of another factor?
Hint: Molecules consist of nuclei and electrons.
An Outline of Computational Chemistry 7
9.In recent years the technique of combinatorial chemistry has been used to quickly synthesize a variety of related compounds which are then tested for pharmacological activity (S. Borman, Chemical & Engineering News: 2001, 27 August, p. 49; 2000, 15 May, p. 53; 1999, 8 March, p. 33). What are the advantages and disadvantages of this method of finding drug candidates, compared with the “rational design” method of studying, with the aid of computational chemistry, how a molecule interacts with an enzyme?
10.Think up some unusual molecule which might be investigated computationally. What is it that makes your molecule unusual?
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