APPLICATIONS AND EXTENSIONS OF THE THEORY OF ATOMS IN MOLECULES

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1 A THEORETICA~ STUDY OF REACTIVITIES AND SYNTHESIS OF MOLECULES: APPLICATIONS AND EXTENSIONS OF THE THEORY OF ATOMS IN MOLECULES By CHENG CHANG, M.Sc. A Thesis Submitted to the School of Graduate Studies in Partial Fulfilment of the Requirements for the Degree Doctor of Philosophy McMaster University (c) Copyright by Cheng Chang, November 1990

2 A THIDRETICAL STUDY OF THE REACl'IVITY AND SYNTHESIS OF MOLECULES

3 DOCTOR OF PHILOSOPHY (1990) (Chemistry) McMASTER UNIVERSITY Hamilton. Ontorio TITLE: A THEORFl'ICAL STUDY OF THE REACTIVITY AND SYNTHESIS OF MOLECULES: APPLICATIONS AND EXrENSIONS OF THE THFnRY OF ATOMS IN MOLECULES AUTHOR: Cheng Chang. B.Sc. (B~jjing Teacher"s College) M.Sc. (Beijing Teacher's College) SUPERVISOR: Professor R.F.W. Bader NUMBER OF PAGES: xv. 198 ii

4 ABSTRACI' This thesis 8P?lies and extends the theory of atoms in molecules to some general, important and chemically interesting subjects: a means of studying molecules of biochemical size using high-lev~l quantum chemistry. the chemical reactivities of aromatic molecules as well as the nature of ~ type hydrogen bonding. Quantum mechanical principles define an atom in a molecule and its properties as well as the chemical bonds which link the atoms to yield a molecular structure. The resulting theory is called the theory of atoms in molecules. The theory also predicts the chemical reactivity of a molecule through the properties of the Laplacian of its electronic charge distribution. the Laplacian of the charge density also provides the physical basis of the Lewis and VSEPR models. The theory is reviewed in Chapter 1. Molecules of biochemical interest always cause difficulties for computational chemists because of the size. Semiempirical methods have been used in the past. but must alternatively be replaced by ab initio theory. An attempt to use a nonempirical method with reliable trial functions to solve such problems, as made possible through the application of the tools provided in the theory of atoms in molecules, is presented in Chapter 2, and gives ml encouraging result. The study of the chemical reactivities of aromatic I10lecules is of general interest to chemists. An enormous amount of research has been dene in this area. A new way of using the theory to study the reactbities and energetics of monosubstituted benzenes and their para and meta protonatecl intermediates is presented in Chapters 3 and 4. The directing ability of a iii

5 substituent and its ability to activat~ or deactivate the phenyl group in electrophilic substitution reaction are related to atomic, bond and molecular properties of the aromatic molecules. The nature of n-type hydrogen bonding is discussed in Chapter 5. The molecular structures of three CaHaHF complexes are determined for the first time.,. iv

6 AC:IiliOWT.EOOMENTS I wish to take this chance to thank all the members of Dr.Bader's Theoretical Chemistry Laboratory for their help, ~ooperation and friendship during the time I have been studying here, This is the first time for me to leave my country to study in a completely different environment -- different language, different culture, different concepts of value, almost everything is different except for the language and concepts of science. It was the friendship of Dr. Marshall Carroll and Hr. James Cheeseman that encouraged me to overcome many unexpected difficulties with regard to both the study and life aspects of my early time here. I would also like to thank Dr. Preston MacDougall for his help in my understanding of many important concepts of the theory; talking with him about science has always been stimulating. I would like particularly to thank Dr. Keith Laidig and Hr. Danny Legare. The former contributed to developing, maintaining and converting the programs I used and the computers on which they have been run; a part of this thesis could not be done without his work. The latter contributed his precious time in proof-reading and helping me to correct my English gr8dlldbr. I would like to give my special thanks to Dr. Richard Bader, my supervisor. I have really enjoyed the many discussions I have had with him, fran which I have leamed so mch, although at times the discussions were filled with heated arguments and differences of opinion. His enthusibsll in approaching chemistry and his being ultimately responsible for each of the subjects en which we collaborated and for this thesis have v

7 left a deep impression on me. (" ;/ '.. /: ',",".-,... Y1

8 This thesis is dedicated to my wife J Sufang Wang J my parents and my motherland -- China..-=:. vii (

9 TABI.E OF mntents Abstract Acknowledgements Table of Contents EAGE iii v viii List of Figures ~ List of Tables xii Introduction 1 Chapter 1. The Theory of Atoms in Molecules Molecular Electronic Charge Distribution Topological Properties of Charge Distribution Topology of the Laplacian of the Charge Density Properties of Atoms in Molecules 29 Chapter 2. The Theoretical Synthesis of POlypeptides from Amino Acid Fragments Conformation and Structure The Transferability of Amino Acid Fragments The Synthesis of Polypeptides From Amino Acid Fragments Conclusion 87 Chapter 3. Electrophilic Aromatic Substitution The History and Background of the Study of the Electrophilic Aromatic Substitution Calculations Molecular Structure and Bond Properties of Monosubstituted Benzenes Atomic Properties of Monosubstituted Benzenes 104 viii

10 TABLE OF mn'i'ents (con d) 3.5 Susceptibility to F,lectrophilic Attack &S Determined by the Laplacian of ~ 3.6. Conclusion Chapter 4. Energetics of Protonated Monosubstituted Benzenes 4.1. Calculations Molecular Structures and Atomic Properties of Arenium Ion Intermediates Energies of Formation of Protonated Monosubstituted Benzenes 4.4. Conclusions " Chapter 5. Hydrogen-BondP.d Complexes of Unsaturated Hydrocarbons Geometries and Structures Comparisons of the Properties of Tt-Type and a-type Hydrogen Bvnd Complexes 180 References 193 ix

11 LIST OF FIGURES FIGURE 1.1 Contour plots and corresponding relief maps of the electron density of benzene EAGE Plots of a function. f(x), its first and second derivatives Gradient vector field map of the electron density of benzene 1.4 Contour plot of the electron density on the cross section of C~ bond of benzene Plot of a monotonically decreasing function f(x) and its first 1.6 and second derivatives Laplacian distribution of the isolated Argon atoill Contour plot of v~ for molecules with valence-shell and close-shell interactions Contour plot and corresponding relef map of -v2.p of formaldel13'de 27,.., Display of quadrupole moment in different cases au ch&rge density envelopes for hydrocarbon molecules 36 Molecular graphs of neutral glycine and alanine molecules 44 Three different forms of glycine fragment in polypeptides 46 Display of the common fragments of glycine and alanine in different molecules Geometrical parameters of the optimized molecules Contour plot of v2.p for Gly-Gly dipeptide Contour plots of p for the mcx:lel molecules containing GI, IG"I and IG' fragments respectively Contour plots of P for the synthesized and calculated Gly-Gly 81 x

12 LIST OE EIGURES (con'd) 2.8 Contour plots of P for the synthesized and calculated Gly-Gly-Gly Structures of monosubstituted benzenes and the atomic net charges Relationship between bond. atomic properties and Taft's aa D resonance parameter for monosubstituted benzenes Relationship between the relative R population of carbons and quadrupole moment for monosubstituted benzenes Atomic graphs of the VS:X of a carbon atom in methane and benzene Relief maps of the negative of the Laplacian of t=' for benzene and phenoxide Displays of the Laplacian distribution for substituted benzenes Molecular graphs of protonated monosusbtituted benzenes and the benzenium ion Molecular structures of hydrogen-bond complexes of unsaturated hydrocarbons and hydrogen fluoride Molecular graph of slightly distorted C2H4-HF complex Displays of the hydrogen-bond path of CaHeHF(D) and CeHaHF(E) Contour plot of P for CiH4HF overlaid with a contour plot of P for C2H4 186,': xi

13 LIST OF TABLES T.AB.LE EAGE Optimized geometries of glycine and alanine molecules for 4-31G basis set 45 Geometrical comparison of glycine fragments in different molecules 53 Geometrical comparison of alanine fragments in different molecules Comparison of properties of P at bond critical points for glycine fragments in different molecules Comparison of properties of P at bond critical points for alanine frasma~ts in different molecules Comparison of atomic populations for glycine fragments in different molecules Comparison of atomic populations for alanine fraglnents in different molecules Comparison of atomic energies for glycine fragments in different molecules Comparison of atomic energies for alanine fragments in different molecules Comparison of atomic volumes for glycine fragments in different molecules Comparison of atomic volumes for alanine fragments in different molecules Comparison of properties at critical points in v~ for glycine fragments in different molecules xii

14 LIST OF TABLES (can'd) TABLE 2.13 Comparison of properties at critical points in q~ for alanine fragments jn different molecules A Comparison of total properties of synthesised molecules with the calculated ones 83 Crystal structure data of zwitterions: glycine. alanine. gly-g!y. gly-ala. ala-gly and gly-gly-gly 90 Values of Pb in monosubstituted benzenes 99 Values of 'V2fb in monosubstituted benzenes 100 Ellipticities at bond critical points of monosubstituted benzenes 102 Atomic populations of monosubstituted benzenes 106 Atomic It populations of monosubstituted benzenes 107 Relative atomic populations of monosubstituted benzenes 109 Relative atomic It populations of monosubstituted benzenes 110 Relative atomic 0 populations of monosubstituted benzenes 111 Relative quadruple moments of monosubstituted benzenes 119 Relative values of 'V2P in monosubstituted benzenes 125 Off-axis angle of reactive centers in the Laplacian of monosubstituted benzenes Comparison of Complementary Anglesa of Secondary Concentrations With Their Relative 'V2p values Optimized geometry of planar aniline at 6-31G level Atomic populations of pyramidal aniline 128 Charge xiii

15 LIST OF TABLES (COD d) TABLE Energies and Virial ratios for substituted benzenes, arenium intermediates. and pentadienyl Cation 138 Bond and ring critical point data for arenium ion intermediates 143 Comparison of bond and atomic properties of benzenium and Pentadienyl cations Atomic charges q(q) in arenium ion intermediates Quadrupole moments ~(Q) of arenium ion intermediates 151 Atomic populations of arenium ion intermediates relative to their values in Ph-X Energies of formation and group contributions for arenium ions Charges and atomic first moments of C1 and bonded substituent atom Xl in Ph-X and [Ph-X]H Atomic Energies of arenium ion intermedialts [Ph-X]H+ relative to their values in Ph-X 159 A4.1 Optimized Geometries of protonated benzene for various basis sets 165 A4.2 Optimized geometries of protonated fluorobenzene for various basis sets 166 A4.3 Optimized geometries ofprotonated phenol fur various basis sets 167 A4.4 Optimized geometries of protonated cyanobenzene for various basis sets 168 xiv

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APPLICATION OF THE THEORY OF ATOMS IN MOLECULES

APPLICATION OF THE THEORY OF ATOMS IN MOLECULES By Clement D.H. Lau, B.Sc. A Thesis Submitted to the School of Graduate Studies in Partial Fulfilment of the Requirements for the Degree Doctor of Philosophy