the chemistry of amino, nitroso, nitro and related groups, part 1 - supplement f2 - patai

Supplement F2: The Chemistry of Amino, Nitroso, Nitro and Related Groups. Edited by Saul Patai Copyright 1996 John Wiley & Sons, Ltd. ISBN: 0-471-95171-4

Supplement F2 The chemistry of amino, nitroso, nitro and related groups

THE CHEMISTRY OF FUNCTIONAL GROUPSA series of advanced treatises under the general editorship of Professors Saul Patai and Zvi RappoportThe chemistry of alkenes (2 volumes) The chemistry of the carbonyl group (2 volumes) The chemistry of the ether linkage The chemistry of the amino group The chemistry of the nitro and nitroso groups (2 parts) The chemistry of carboxylic acids and esters The chemistry of the carbon nitrogen double bond The chemistry of amides The chemistry of the cyano group The chemistry of the hydroxyl group (2 parts) The chemistry of the azido group The chemistry of acyl halides The chemistry of the carbon halogen bond (2 parts) The chemistry of the quinonoid compounds (2 volumes, 4 parts) The chemistry of the thiol group (2 parts) The chemistry of the hydrazo, azo and azoxy groups (2 parts) The chemistry of amidines and imidates (2 volumes) The chemistry of cyanates and their thio derivatives (2 parts) The chemistry of diazonium and diazo groups (2 parts) The chemistry of the carbon carbon triple bond (2 parts) The chemistry of ketenes, allenes and related compounds (2 parts) The chemistry of the sulphonium group (2 parts) Supplement A: The chemistry of double-bonded functional groups (2 volumes, 4 parts) Supplement B: The chemistry of acid derivatives (2 volumes, 4 parts) Supplement C: The chemistry of triple-bonded functional groups (2 volumes, 3 parts) Supplement D: The chemistry of halides, pseudo-halides and azides (2 volumes, 4 parts) Supplement E: The chemistry of ethers, crown ethers, hydroxyl groups and their sulphur analogues (2 volumes, 3 parts) Supplement F: The chemistry of amino, nitroso and nitro compounds and their derivatives (2 parts) The chemistry of the metal carbon bond (5 volumes) The chemistry of peroxides The chemistry of organic selenium and tellurium compounds (2 volumes) The chemistry of the cyclopropyl group (2 parts) The chemistry of sulphones and sulphoxides The chemistry of organic silicon compounds (2 parts) The chemistry of enones (2 parts) The chemistry of sulphinic acids, esters and their derivatives The chemistry of sulphenic acids and their derivatives The chemistry of enols The chemistry of organophosphorus compounds (4 volumes) The chemistry of sulphonic acids, esters and their derivatives The chemistry of alkanes and cycloalkanes Supplement S: The chemistry of sulphur-containing functional groups The chemistry of organic arsenic, antimony and bismuth compounds The chemistry of enamines (2 parts) The chemistry of organic germanium, tin and lead compounds UPDATES The chemistry of -haloketones, -haloaldehydes and -haloimines Nitrones, nitronates and nitroxides Crown ethers and analogs Cyclopropane derived reactive intermediates Synthesis of carboxylic acids, esters and their derivatives The silicon heteroatom bond Syntheses of lactones and lactams The syntheses of sulphones, sulphoxides and cyclic sulphides Patais 1992 guide to the chemistry of functional groups

Saul Patai

C NH2

C NO

C NO2

Supplement F2

The chemistry of amino, nitroso, nitro and related groupsPart 1

Edited by SAUL PATAI The Hebrew University, Jerusalem

1996JOHN WILEY & SONSCHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE

An Interscience R Publication

Copyright 1996 John Wiley & Sons Ltd, Bafns Lane, Chichester, West Sussex PO19 1UD, England National 01243 779777 International (C44) 1243 779777 e-mail (for orders and customer service enquiries): [email protected] Visit our Home Page on http://www.wiley.co.uk or http://www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1P 9HE, UK, without the permission in writing of the publisher Other Wiley Editorial Ofces John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, USA Jacaranda Wiley Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Canada) Ltd, 22 Worcester Road, Rexdale, Ontario M9W 1L1, Canada John Wiley & Sons (Asia) Pte Ltd, Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809

Library of Congress Cataloging-in-Publication Data

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0 471 95171 4 Typeset in 9/10pt Times by Laser Words, Madras, India Printed and bound in Great Britain by Biddles Ltd, Guildford, Surrey This book is printed on acid-free paper responsibly manufactured from sustainable forestation, for which at least two trees are planted for each one used for paper production.

Contributing authorsPinchas Aped Shmuel Bittner

Richard D. Bowen G. V. Boyd Silvia Bradamante

Mary Stinecipher Campbell

Lars Carlsen

H. K. Chagger Y. L. Chow Helge Egsgaard Peter Eyer

Luciano Forlani Albert J. Fry D. Gallemann

T. I. Ho

Department of Chemistry, Bar-Ilan University, RamatGan 52900, Israel Institutes for Applied Research and Department of Chemistry, Ben-Gurion University of the Negev, BeerSheva 84105, Israel Chemistry and Chemical Technology, University of Bradford, Bradford, West Yorkshire BD7 1DP, UK Department of Organic Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Universit degli Studi di Milano, CNR, Centro di Studio a sulla Sintesi e Stereochimica di Speciali Sistemi Organici, via Golgi 19, 20133 Milano, Italy DX-2 Explosive Science Technology, MS C920, Los Alamos National Laboratory, Los Alamos, New Mexico 87545-0000, USA Department of Environmental Chemistry, National Environmental Research Institute, P.O.Box 358, Frederiksborgvej 399, DK-4000 Roskilde, Denmark Department of Fuel and Energy, University of Leeds, Leeds LS2 9JT, UK Department of Chemistry, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada Environmental Science and Technology Department, Ris National Laboratory, DK-4000 Roskilde, Denmark Walther-Straub-Institut f r Pharmakologie und Toxikolou gie der Ludwig-Maximilians-Universit t M nchen, a u Nussbaumstrasse 26, D-80336 M nchen, Germany u Universit` di Bologna, Dipartimento di Chimica Organica a A. Mangini, viale Risorgimento 4, 40136 Bologna, Italy Department of Chemistry, Wesleyan University, Middletown, Connecticut 06459, USA Walther-Straub-Institut f r Pharmakologie und Toxikolou gie der Ludwig-Maximilians-Universit t M nchen, a u Nussbaumstrasse 26, D-80336 M nchen, Germany u National Taiwan University, Department of Chemistry, Roosevelt Road, Sec. 4, Taipei, Taiwan, Republic of China v

viWilliam M. Horspool Joel F. Liebman

Contributing authors Department of Chemistry, The University of Dundee, Dundee DD1 4HN, Scotland Department of Chemistry and Biochemistry, University of Maryland, Baltimore County Campus, 1000 Hilltop Circle, Baltimore, Maryland 21250, USA 10401 Grosvenor Place, Apt. 404, Rockville, Maryland 20852, USA Department of Chemistry, University of Athens, 15771 Athens, Greece Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina Institut f r organische Chemie der Universit t Essen, u a D-45117 Essen, Germany Department of Chemistry, Queen Mary and Westeld College, Mile End Road, London E1 4NS, UK University of Exeter, Department of Chemistry, Chemistry Building, Stocker Road, Exeter EX4 4QD, UK Department of Chemistry, Columbia University, New York, NY 10027, USA School of Chemistry, University, of Hull, Hull HU6 7RX, UK Department of Chemistry, George Mason University, 4400 University Drive, Fairfax, Virginia 22030-4444, USA Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235, USA Dipartimento di Chimica, Universit` di Perugia, via Elce a di sotto 10, 06100 Perugia, Italy Department of Chemistry and Biochemistry, Laurentian University, Ramsey Lake Road, Sudbury, Ontario, Canada P3E 2C6 Department of Fuel and Energy, University of Leeds, Leeds LS2 9JT, UK University of Durham, Department of Chemistry, Science Laboratories, South Road, Durham DH1 3LE, UK Institutes for Applied Research and Department of Chemistry, Ben-Gurion University of the Negev, BeerSheva 84105, Israel Technisch-Chemisches Laboratorium, ETH-Zentrum, CH-8092 Z rich, Switzerland u

Alan H. Mehler Christiana A. Mitsopoulou Norma S. Nudelman

Paul Rademacher Edward W. Randall J. P. B. Sandall Hanoch Senderowitz John Shorter Suzanne W. Slayden

Howard E. Smith Salvatore Sorriso Kenneth C. Westaway

A. Williams D. Lyn H. Williams Jacob Zabicky

Heinrich Zollinger

ForewordThe material reviewed in the present volume Supplement F2: The chemistry of amino, nitroso, nitro and related groups has been previously covered in the following books in the Chemistry of the Functional Groups series: The chemistry of the amino group (1968); The chemistry of the nitro and nitroso groups, Parts 1 and 2 (1969); Supplement F: The chemistry of amino, nitroso and nitro compounds and their derivatives, Parts 1 and 2 (1982). Nitrones, nitronates and nitroxides (Update volume, 1989). The chapters in this Supplement F2 generally contain references up to the middle of 1995. Of the planned contents of this book, only three chapters failed to materialize. These were on NQR and ESR, on pyrolysis, and on photoinduced electron transfer reactions. I hope that these missing subjects will be dealt with in a later forthcoming supplementary volume of the series. I would be very grateful to any reader who would communicate to me comments or criticisms regarding the contents or the presentation of this volume.

Jerusalem June 1996

SAUL PATAI

vii

The Chemistry of Functional Groups Preface to the seriesThe series The Chemistry of Functional Groups was originally planned to cover in each volume all aspects of the chemistry of one of the important functional groups in organic chemistry. The emphasis is laid on the preparation, properties and reactions of the functional group treated and on the effects which it exerts both in the immediate vicinity of the group in question and in the whole molecule. A voluntary restriction on the treatment of the various functional groups in these volumes is that material included in easily and generally available secondary or tertiary sources, such as Chemical Reviews, Quarterly Reviews, Organic Reactions, various Advances and Progress series and in textbooks (i.e. in books which are usually found in the chemical libraries of most universities and research institutes), should not, as a rule, be repeated in detail, unless it is necessary for the balanced treatment of the topic. Therefore each of the authors is asked not to give an encyclopaedic coverage of his subject, but to concentrate on the most important recent developments and mainly on material that has not been adequately covered by reviews or other secondary sources by the time of writing of the chapter, and to address himself to a reader who is assumed to be at a fairly advanced postgraduate level. It is realized that no plan can be devised for a volume that would give a complete coverage of the eld with no overlap between chapters, while at the same time preserving the readability of the text. The Editors set themselves the goal of attaining reasonable coverage with moderate overlap, with a minimum of cross-references between the chapters. In this manner, sufcient freedom is given to the authors to produce readable quasi-monographic chapters. The general plan of each volume includes the following main sections: (a) An introductory chapter deals with the general and theoretical aspects of the group. (b) Chapters discuss the characterization and characteristics of the functional groups, i.e. qualitative and quantitative methods of determination including chemical and physical methods, MS, UV, IR, NMR, ESR and PES as well as activating and directive effects exerted by the group, and its basicity, acidity and complex-forming ability. (c) One or more chapters deal with the formation of the functional group in question, either from other groups already present in the molecule or by introducing the new group directly or indirectly. This is usually followed by a description of the synthetic uses of the group, including its reactions, transformations and rearrangements. (d) Additional chapters deal with special topics such as electrochemistry, photochemistry, radiation chemistry, thermochemistry, syntheses and uses of isotopically labelled compounds, as well as with biochemistry, pharmacology and toxicology. Whenever applicable, unique chapters relevant only to single functional groups are also included (e.g. Polyethers, Tetraaminoethylenes or Siloxanes). ix

x

Preface to the series

This plan entails that the breadth, depth and thought-provoking nature of each chapter will differ with the views and inclinations of the authors and the presentation will necessarily be somewhat uneven. Moreover, a serious problem is caused by authors who deliver their manuscript late or not at all. In order to overcome this problem at least to some extent, some volumes may be published without giving consideration to the originally planned logical order of the chapters. Since the beginning of the Series in 1964, two main developments have occurred. The rst of these is the publication of supplementary volumes which contain material relating to several kindred functional groups (Supplements A, B, C, D, E, F and S). The second ramication is the publication of a series of Updates, which contain in each volume selected and related chapters, reprinted in the original form in which they were published, together with an extensive updating of the subjects, if possible, by the authors of the original chapters. A complete list of all above mentioned volumes published to date will be found on the page opposite the inner title page of this book. Unfortunately, the publication of the Updates has been discontinued for economic reasons. Advice or criticism regarding the plan and execution of this series will be welcomed by the Editors. The publication of this series would never have been started, let alone continued, without the support of many persons in Israel and overseas, including colleagues, friends and family. The efcient and patient co-operation of staff-members of the publisher also rendered us invaluable aid. Our sincere thanks are due to all of them. The Hebrew University Jerusalem, Israel SAUL PATAI ZVI RAPPOPORT

Contents1 2 3 4 5 Molecular mechanics calculations Pinchas Aped and Hanoch Senderowitz Structural chemistry Salvatore Sorriso Chiroptical properties of amino compounds Howard E. Smith Photoelectron spectra of amines, nitroso and nitro compounds Paul Rademacher The chemistry of ionized, protonated and cationated amines in the gas phase Richard D. Bowen Mass spectrometry of nitro and nitroso compounds Helge Egsgaard and Lars Carlsen NMR of compounds containing NH2 , NO2 and NO groups Edward W. Randall and Christiana A. Mitsopoulou Thermochemistry of amines, nitroso compounds, nitro compounds and related species Joel F. Liebman, Mary Stinecipher Campbell and Suzanne W. Slayden Acidity and basicity Silvia Bradamante Hydrogen bonding and complex formation involving compounds with amino, nitroso and nitro groups Luciano Forlani Electronic effects of nitro, nitroso, amino and related groups John Shorter Advances in the chemistry of amino and nitro compounds G. V. Boyd Diazotization of amines and dediazoniation of diazonium ions Heinrich Zollinger 1 85 105 159

205 249 295

6 7 8

337

9 10

379

423 479 533 627

11 12 13

xi

xii14 15 16 17 18 19

ContentsS -Nitroso compounds, formation, reactions and biological activity D. Lyn H. WilliamsPhotochemistry of amines and amino compounds Tong Ing Ho and Yuan L. Chow Photochemistry of nitro and nitroso compounds Tong-Ing Ho and Yuan L. Chow Radiation chemistry of amines, nitro and nitroso compounds William M. Horspool The electrochemistry of nitro, nitroso, and related compounds Albert J. Fry Rearrangement reactions involving the amino, nitro and nitroso groups D. Lyn H. Williams The synthesis and uses of isotopically labelled amino and quaternary ammonium salts Kenneth C. Westaway Displacement and ipso-substitution in nitration J. P. B. Sandall Nitric oxide from arginine: a biological surprise Alan H. Mehler Reactions of nitrosoarenes with SH groups P. Eyer and D. Galleman Analytical aspects of amino, quaternary ammonium, nitro, nitroso and related functional groups Jacob Zabicky and Shmuel Bittner Environmental aspects of compounds containing nitro, nitroso and amino groups H. K. Chagger and A. Williams SN Ar reactions of amines in aprotic solvents Norma S. Nudelman 665 683 747 823 837

857

20

893 949 973 999

21 22 23 24

1041

25

1169 1215 1301 1393

26

Author index Subject index

List of abbreviations usedAc acac Ad AIBN Alk All An Ar Bz Bu CD CI CIDNP CNDO Cp Cp DABCO DBN DBU DIBAH DME DMF DMSO ee EI ESCA ESR Et eV acetyl (MeCO) acetylacetone adamantyl azoisobutyronitrile alkyl allyl anisyl aryl benzoyl (C6 H5 CO) butyl (also t-Bu or But ) circular dichroism chemical ionization chemically induced dynamic nuclear polarization complete neglect of differential overlap 5 -cyclopentadienyl 5 -pentamethylcyclopentadienyl 1,4-diazabicyclo[2.2.2]octane 1,5-diazabicyclo[4.3.0]non-5-ene 1,8-diazabicyclo[5.4.0]undec-7-ene diisobutylaluminium hydride 1,2-dimethoxyethane N,N-dimethylformamide dimethyl sulphoxide enantiomeric excess electron impact electron spectroscopy for chemical analysis electron spin resonance ethyl electron volt

xiii

xiv Fc FD FI FT Fu GLC Hex c-Hex HMPA HOMO HPLC iIp IR ICR LAH LCAO LDA LUMO M M MCPBA Me MNDO MS n Naph NBS NCS NMR Pc Pen Pip Ph ppm Pr PTC Pyr

List of abbreviations used ferrocenyl eld desorption eld ionization Fourier transform furyl(OC4 H3 ) gas liquid chromatography hexyl(C6 H13 ) cyclohexyl(C6 H11 ) hexamethylphosphortriamide highest occupied molecular orbital high performance liquid chromatography iso ionization potential infrared ion cyclotron resonance lithium aluminium hydride linear combination of atomic orbitals lithium diisopropylamide lowest unoccupied molecular orbital metal parent molecule m-chloroperbenzoic acid methyl modied neglect of diatomic overlap mass spectrum normal naphthyl N-bromosuccinimide N-chlorosuccinimide nuclear magnetic resonance phthalocyanine pentyl(C5 H11 ) piperidyl(C5 H10 N) phenyl parts per million propyl (also i-Pr or Pri ) phase transfer catalysis or phase transfer conditions pyridyl (C5 H4 N)

List of abbreviations used R RT sSET SOMO tTCNE TFA THF Thi TLC TMEDA TMS Tol Tos or Ts Trityl Xyl any radical room temperature secondary single electron transfer singly occupied molecular orbital tertiary tetracyanoethylene triuoroacetic acid tetrahydrofuran thienyl(SC4 H3 ) thin layer chromatography tetramethylethylene diamine trimethylsilyl or tetramethylsilane tolyl(MeC6 H4 ) tosyl(p-toluenesulphonyl) triphenylmethyl(Ph3 C) xylyl(Me2 C6 H3 )

xv

In addition, entries in the List of Radical Names in IUPAC Nomenclature of Organic Chemistry, 1979 Edition. Pergamon Press, Oxford, 1979, p. 305 322, will also be used in their unabbreviated forms, both in the text and in formulae instead of explicitly drawn structures.

Supplement F2: The Chemistry of Amino, Nitroso, Nitro and Related Groups. Edited by Saul Patai Copyright 1996 John Wiley & Sons, Ltd. ISBN: 0-471-95171-4

CHAPTER

1

Molecular mechanics calculationsPINCHAS APEDDepartment of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel Fax: (972-3)535-1250 e-mail: [email protected]

HANOCH SENDEROWITZDepartment of Chemistry, Columbia University, New York, NY 10027, USA Fax: (001 212)678 9039; e-mail: [email protected]

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. DEVELOPMENT OF THE COMPUTATIONAL MODEL . . . . . . . . . . . . A. Molecular Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Specic Force Fields MM2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. MM2 potential functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. MM2 parameterization of amines . . . . . . . . . . . . . . . . . . . . . . . . a. Acyclic amines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Cyclic amines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Heats of formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Dipole moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. MM20 parameterization of nitro compounds and MM2 parameterization of nitrosamines, nitramines, nitrates and oximes . . . 4. MM2 parameterization of nitro compounds, enamines and aniline derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. MM2 parameterization of the N C N anomeric moiety . . . . . . . . C. MM3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. MM3 potential functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. MM3 parameterization of amines . . . . . . . . . . . . . . . . . . . . . . . . a. Bond length and bond angle parameters . . . . . . . . . . . . . . . . . b. Torsional angle parameters . . . . . . . . . . . . . . . . . . . . . . . . . . c. Moments of inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Four-membered and ve-membered rings . . . . . . . . . . . . . . . . e. Hydrogen bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f. Heats of formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 3 3 5 5 6 6 8 10 11 11 14 14 20 21 23 23 24 24 24 27 29

1

2

Pinchas Aped and Hanoch Senderowitz 29 30 31 32 32 33 33 34 35 35 35 35 36 37 38 40 42 43 43 55 55 57 59 60 62 66 66 68 69 70 72 76 81 81

3. MM2 and MM3 parameterization of nitro compounds . . . . . . . . . . a. Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Rotational barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Vibrational spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Heats of formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. MM2 and MM3 parameterization of enamines and aniline derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Conformational energies and rotational barriers . . . . . . . . . . . . . c. Heats of formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Vibrational spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Other force elds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. AMBER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Tripos 5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. DREIDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Universal Force Field (UFF) . . . . . . . . . . . . . . . . . . . . . . . . . D. Energetic comparison between MM2, MM3, AMBER, Tripos 5.2, DREIDING and UFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. APPLICATION OF THE COMPUTATIONAL MODEL . . . . . . . . . . . . . A. Conformational Analysis and Structural Investigation . . . . . . . . . . . . . 1. Tertiary amines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Polyamines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Diamines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b. Tri- and tetraamines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Cryptands and azacrown ethers . . . . . . . . . . . . . . . . . . . . . . . 3. Medium-size rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Biologically active compounds . . . . . . . . . . . . . . . . . . . . . . . . . B. Spectroscopic Experiments and the Study of Chemical Effects . . . . . . . 1. Nitrogen proton afnities and amine basicity . . . . . . . . . . . . . . . . 2. Magnetic anisotropy of cyclopropane and cyclobutane . . . . . . . . . . 3. CD spectra of N-nitrosopyrrolidines . . . . . . . . . . . . . . . . . . . . . . 4. 17 O and 15 N NMR spectra of N-nitrosamines . . . . . . . . . . . . . . . . C. Mechanisms of Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . D. Heat of Formation and Density Calculations of Energetic Materials . . . IV. ACKNOWLEDGMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I. INTRODUCTION

Theory plays an invaluable role in our understanding of organic chemistry and is enhanced by the usage of rigorously built computational models. While ab initio calculations are certainly the most physically correct way to treat chemical systems, they are limited, with current computer technology, to molecules with a relatively small number of heavy (nonhydrogen) atoms. Larger systems are best handled by molecular mechanics provided that high-quality force-eld parameters are available. In such cases, the method can provide accurate molecular properties using only a fraction of the computational resources needed by quantum mechanical methods. The rapid increase in affordable computational power and the integration of many force elds into user friendly molecular modeling packages has further contributed to the development and widespread usage of the method. In Section II of this review we develop the molecular mechanics computational model by presenting the potential functions of several commonly used force elds and discussing, in some detail, the parameterization procedures for the type of compounds considered

1. Molecular mechanics calculations

3

in this work. In Section III, we describe the applications of the resulting force elds to a variety of problems in amino, nitro and nitroso chemistry. Typically, molecular mechanics calculations have been used, primarily, to obtain (minimum energy) molecular structures and conformational energies. However, the examples provided in this review span a much broader range of applications, from traditional conformational analysis and structural investigation to spectroscopic experiments, heats of formation calculations of energetic materials and the study of chemical effects and reaction mechanisms. Of the molecular systems considered here, the vast majority of calculations has been performed for amines while fewer examples are found for nitro compounds and, still fewer, for nitroso ones. Calculations of other nitrogen-containing molecules, in particular, organometallic complexes and biological macromolecules, are also found in the literature but these fall beyond the scope of the current work. Finally, we would like to point out that although we made a special effort to cover most of the seminal works, this review is not intended to provide an exhaustive coverage of the available literature, but rather, to serve as a guideline to the usage of molecular mechanics calculations in this eld.II. DEVELOPMENT OF THE COMPUTATIONAL MODEL A. Molecular Mechanics

Molecular mechanics1 is an empirical computational method which can provide accurate molecular properties with minimal computational cost. The method treats the molecule as a collection of atoms held together by forces. The forces are described by classical potential functions and the set of all these functions is the force eld. The force eld denes a multidimensional Born Oppenheimer surface but, in contrast with quantum mechanics, only the motion of the nuclei is considered and the electrons are assumed to nd the optimal distribution among them. Since there are no strict rules regarding the number or type of potential functions to be used, many different molecular mechanics force elds have been developed over the years. These can be classied according to the type of potential functions employed in their construction. In the following we concentrate on extended valence force elds which include both diagonal (stretching, bending, torsion and nonbonded interactions) and off-diagonal terms (cross terms). The latter are employed when two internal coordinates end on the same atom or on nearest-neighbor atoms. The potential energy of the molecule in the force eld arises due to deviations from ideal geometry dened by structural parameters and is given by a sum of energy contributions (equation 1). Etotal D Estretch C Ebend C Etorsion C Enonbonded C Ecrossterms

1

The rst three terms, stretch, bend and torsion, are common to most force elds although their explicit form may vary. The nonbonded terms may be further divided into contributions from Van der Waals (VdW), electrostatic and hydrogen-bond interactions. Most force elds include potential functions for the rst two interaction types (Lennard-Jones type or Buckingham type functions for VdW interactions and charge charge or dipole dipole terms for the electrostatic interactions). Explicit hydrogen-bond functions are less common and such interactions are often modeled by the VdW expression with special parameters for the atoms which participate in the hydrogen bond (see below). The number and type of cross terms vary among different force elds. Thus, AMBER2 contains no cross terms, MM23 uses stretch bend interactions only and MM34 uses stretch bend, bend bend and stretch torsion interactions. Cross terms are essential for an accurate reproduction of vibrational spectra and for a good treatment of strained molecular systems, but have only a small effect on conformational energies. Given a set of potential functions, the results of any molecular mechanics calculation depend critically on the parameters. These may be obtained from two main sources,

4

Pinchas Aped and Hanoch Senderowitz

namely experimental data or high-level quantum mechanics (usually ab initio) calculations. Experimentally based parameters have two main advantages: (1) they describe the real world rather than another computational model of it; (2) they reect molecular free energies rather than enthalpies. However, such parameters are often hard to obtain, not available for all systems of interest, nonuniform (that is, obtained by different experimental techniques and often in diverse media) and usually do not provide a complete description of the molecular potential surface including all minima and transition states. In contrast, parameters from high-level quantum mechanical calculations are available for all molecular systems, up to a certain size, are uniform (that is, always describe an isolated molecule and, if desired, may be obtained at the same level of theory) and can provide a complete description of the molecular potential energy surface. The two main disadvantages of such parameters, namely their possibly high computational cost and dependence on the theoretical model, are gradually resolved with the rapid development of computational power (which by far exceeds similar developments in experimental techniques) and the consequent accumulation of experience in this eld, and today, many parameters for use in molecular mechanics calculations are derived in such a manner. Regardless of the source of the parameters, an essential (although not necessarily correct) assumption for the applicability and usefulness of molecular mechanics is their transferability, i.e. once they are derived, usually from a small set of model compounds, they may be used for other larger (but similar) systems. In order for a force eld to be considered adequate for treatment of a particular molecular system (or a class of molecules) it must provide an accurate description of its properties such as geometry, dipole moment, conformational energies, barriers to rotation, heat of formation and vibrational spectra, while the reference data come either from experiment or from high-level ab initio calculations. Some care must be taken when evaluating the performance of molecular mechanics force elds through comparison with experimental or theoretical data1 : Since different experimental techniques provide different structural and energetic parameters which also differ from those obtained by quantum mechanical calculations, a force eld parameterized according to data from a specic source can reproduce data from other sources only qualitatively (a partial solution to this problem is provided in MM3-94, where it is possible to obtain re bond lengths which are supposed to provide the best t to ab initio results4 ). Several force elds have been used in molecular mechanics calculations of amino, nitro and nitroso compounds but for only two, MM25,15 17,20,21,43,44 and MM36,43,44 , has a specic parameterization been reported in the literature. Several features of these systems are of particular importance and a challenge to molecular mechanics calculations and must be included in any critical evaluation of the force-eld performance. For amino compounds these are the treatments of nitrogen inversion, the reproduction of changes in C H bond lengths when antiperiplanar to a nitrogen lone pair (lp) and the consequent calculation of the Bohlmann bands in the IR spectra, the reproduction of the shortening of C N bonds in tertiary amines, the treatment of inter- and intramolecular hydrogen bonds and the reproduction of structural and energetic manifestations of stereoelectronic effects such as the anomeric effect characterstic of N C X moieties and the gauche effect characteristic of N C C X moieties (X D electronegative atom/group). As for nitro compounds, the two most challenging aspects are the possible conjugation of the nitro group to other systems and the consequent geometry of the molecule and the barriers for rotation around the C N bond in aromatic and aliphatic nitro compounds. In the following we will present the explicit form of the potential functions and the parameterization of most of the force elds used in molecular mechanics calculations of amino, nitro and nitroso compounds and evaluate their performance according to these criteria.

1. Molecular mechanics calculationsB. Specic Force Fields MM2

5

Several force elds have been used in molecular mechanics calculations of amino, nitro and nitroso compounds. The most intensive work has been done with MM2 and, in recent years, also with MM3, probably due to the generally recognized high performance of these force elds and since they are the only ones which have undergone extensive specic parameterization for these systems, however, several other calculations are also found in the literature (see below). We therefore start with the MM2 and MM3 force elds where we briey outline the specic form of the potential functions and discuss, in some detail, the parameterization procedure for the type of compounds discussed in this chapter. We then turn to several other force elds which have not undergone specic parameterization but were nevertheless used in the calculations (AMBER, Tripos, DREIDING, UFF). We conclude with a brief comparison of the energetic performance of all force elds. The MM2 force eld3 is probably the most extensively parameterized and intensively used force eld to date. It reproduces a variety of molecular properties such as geometry, dipole moments, conformational energies, barriers to rotation and heats of formation. Of particular importance for calculations of amines is that MM2 treats lone pairs on sp3 nitrogens (and oxygens) as pseudo atoms with a special atom type and parameters. A closely related force eld, MM207 , was derived from MM2 by Osawa and Jaime. MM20 uses the same potential functions as MM2, but employs a different set of parameters in an attempt to better reproduce barriers to rotation about single C C bonds.1. MM2 potential functions1,3

Within the MM2 force eld, the molecular steric energy is given by Etotal D Estretch C Ebend C Estretchbend

C Etorsion C EVdW C Eelectrostatic

2

The stretching energy is given by a sum of quadratic (harmonic) and cubic terms: Estretch i,j D K rij0 rij 2

C K1 rij

0 rij

3

3

0 where rij and rij are the actual and natural bond lengths between atoms i and j, 0 respectively, and K and K1 are stretching force constants: rij is subjected to primary electronegativity effects8 which allow for a better reproduction of experimental data such as, for example, the shortening of C N bonds along the series CH3 NH2 ! (CH3 )2 NH ! (CH3 )3 N (see Section II.C.2 for more details). The bending energy is given by

Ebend i,j,k D K ijk

0 ijk

2

C K1 ijk

0 ijk

6

4

0 where ijk and ijk are the actual and natural i j k bond angles and K and K1 are bending force constants. The stretch bend energy allows for the i j and j k bonds to stretch when the angle between them (i j k) closes and is given by

Estretch

bend

D K[ rij

0 rij C rjk

0 rjk ] ijk

0 ijk

5

where K is the stretch bend force constant and all other parameters have their usual meaning.

6

Pinchas Aped and Hanoch Senderowitz Torsional energy is given by

cos 2ijkl C 0.5V3 1 C cos 3ijkl 6 where V1, V2 and V3 are adjustable parameters and ijkl is the torsional angle. The VdW energy is given by a Buckingham type potential function9 : EVdW i,j D [2.9 105 exp 12.5rij /rij /r 2 336.176 rij ij 2.25 rij /rij 6 ] r /r 3.311 r /r > 3.311

Etorsion i,j,k,l D 0.5V1 1 C cos ijkl C 0.5V2 1

(7)

where rij D ri C rj D sum of VdW radii of atoms i and j and D i j 0.5 is the well depth of the i j VdW potential curve. The electrostatic energy is given by charge charge or dipole dipole interactions:

Echarge Edipole

charge dipole

i,j D qi qj /rij ij D3 i j /rij

(8) cos 3 cos i cos j (9)

where, in equation 8, qi and qj are partial atomic charges on atoms i and j, is the dielectric constant and rij is the distance between atoms i and j. All the terms in equation 9 are dened in structure 1.i i j rij j

(1)

2. MM2 parameterization of amines5

The parameterization of the MM2 force eld for amines5 was originally based on experimental data with occasional references to quantum mechanical calculations mainly to evaluate conformational energies. Missing parameters (bond lengths and angles) for several unique amino functionalities were later evaluated from ab initio calculations and incorporated into the force eld10 . As in the case of alcohols it was found necessary to include explicit lp on sp3 nitrogens. The main disadvantage of this treatment is that ammonia, for example, does not invert through a symmetrical transition state. However, apart from this shortcoming, the lp formalism seems to reproduce well the structural and energetic characteristics of amines. A complete list of amine parameters is provided in Reference 5. a. Acyclic amines. An initial set of amine parameters was based on the microwave (MW) structures of ammonia and methylamines. A comparison of MM2, ab initio, MW and infrared (IR) structures for these model compounds is provided in Table 1. Four discrepancies between calculations and experiment are apparent: (1) MM2 calculations do not reproduce the decrease in C N bond lengths on going from primary to secondary


7

TABLE 1. Calculated (MM2, MM3 and ab initio) and observed structural parameters for ammonia and methylamines (bond lengths in A, bond angles and tilt angles in degrees, dipole moments in Debye)5,6 . Reprinted with permission from Refs. 5 and 6. Copyright (1985, 1990) American Chemical Society Parameter Ammonia N H H N H dipole moment Methylamine C H C N N H H C H C N H H N H N C H CH3 tilt dipole moment Dimethylamine (2) N H C N C H C H0 C H00 C N H C N C N C H N C H0 N C H00 H C H0 H C H00 H0 C H00 CH3 tilt dipole moment Trimethylamine C N C N C N C H dipole moment MM2 1.013 107.6 1.43 1.114 1.454 1.015 109.0 (a)c 109.1 (s)c 111.3 105.4 MM3a 1.015 107.1 1.49 1.110 1.463 1.014 108.71 107.79 112.29 106.42 111.01 110.27 1.29 1.018 1.462 1.110 1.110 1.110 109.83 112.42 110.28 110.47 110.22 107.65 108.48 109.64 1.07 1.460 111.20 111.37 110.54 110.30 0.62 1.445 111.9 113.0 109.8 0.75 0.999 1.461 1.080 1.081 1.090 112.3 115.1 109.4 109.2 114.0 108.0 108.5 107.6 Ab initiob 1.003 107.2 1.92 1.095 1.086 1.484 1.010 108.4 107.5 110.0 105.9 (a) (s) (a) (s) MW 1.0144 0.002 107.1 0.9 1.47 1.093 0.006 1.474 0.005 1.014 109.47 0.8 112.1 0.8 105.85 0.6 110.3d 3.5 1.336 1.019 0.007 1.463 0.005 1.084 0.005 1.098 0.004 1.098 0.004 108.9 0.3 112.2 0.2 109.7 0.3 108.2 0.3 113.8 0.3 109.0 0.2 109.2 0.2 107.2 0.3 3.4 1.03 1.454 0.003 110.9 0.6 1.00 0.2 1.455 0.002 1.106 0.002 1.106 0.002 1.106 0.002 107 2.0 111.8 0.6 112.0 0.8 106.8 0.8 106.8 0.8 106.8 0.8 1.467 0.002 ED

0.19 1.33 1.017 1.460 1.115 1.115 1.115 109.5 112.1 109.4 110.7 110.7 108.2 108.3 109.4 0.9 1.10 1.465 110.9

3.9

1.454 0.002 110.2e 110.2 110.2

0.64

0.63

a MM3 data for ammonia were calculated for this work with MM3-94. b ab initio data for ammonia (HF/6-31G ) were taken from P. C. Hariharan and J. A. Pople, Mol. Phys., 27, 209 (1974). Ab initio data for trimethylamine (HF/6-31G ) were calculated for this work. c (a) D one hydrogen is anti to the nitrogens lp and the other is gauche to the nitrogens lp; (s) D both hydrogens

are gauche to the nitrogens lp. d Taken from Reference 11. e Taken from Reference 12.

8


to tertiary amines. This problem has been dealt with in later versions of MM2 through the electronegativity effect (see Section II.B.1 and Section II.C.1). (2) Both IR spectra and ab initio calculations5 have demonstrated the increase in C H bond lengths when antiperiplanar to a nitrogen lp. This effect is not reproduced by MM2 (but is reproduced by later versions of MM3, see Section II.C.1). (3) The MM2 C N H and C N C angles are much closer to the MW values than the ab initio ones. (4) The H0 C H00 angle (see structure 2) is approximately tetrahedral in contrast with both MW and ab initio results, which show ca 2 shrinkage.H H

CH3 (2)

H

The torsional parameters for the methylamine fragment were chosen to reproduce the barriers to rotation in methylamine, dimethylamine and trimethylamine. The calculated values, 1.90, 3.04 and 4.22 kcal mol 1 for the three methylamines, respectively, are in good agreement with the experimental ones (1.98, 3.22 and 4.35 kcal mol 1 ). The torsional parameters for the C C N H and C C N lp fragments were chosen to reproduce the axial/equatorial energy difference in piperidine (0.30 and 0.25 0.74 kcal mol 1 in favour of the equatorial hydrogen conformation from MM2 calculations and NMR experiments, respectively) at the expense of ethylamine (0.13 and 0.6 kcal mol 1 in favor of the C C N lp gauche conformation from MM2 calculations and experiment, respectively), since it was not possible to t both molecules with the same set of torsional parameters. Finally, the C N C C fragment was chosen to reproduce the experimental free-energy difference between the trans and gauche conformations of methylethylamine (>1.3 and 1.14 kcal mol 1 from MW and MM2, respectively). b. Cyclic amines. The smallest cyclic amine considered during MM2 parameterization is the four-membered ring azetidine (3). As customary with MM2 treatments of 4-membered rings, unique bending and torsional parameters were applied to this molecule. A far-IR study has shown azetidine to be puckered with a planar barrier height of 1.26 kcal mol 1 13 and an equatorial hydrogen preference of 0.27 kcal mol 1 . An electron diffraction (ED) study conrmed the nonplanarity of the system with an observed puckering angle (see 14 structure 3) of 33 . The MM2 numbers are 1.09 and 0.05 kcal mol 1 for the barrier height and equatorial hydrogen preference, respectively, and 36.2 for the puckering angle. While the calculated barrier and puckering angle are in good agreement with the experimental values, MM2 overestimates the stability of the H-axial conformer, probably due toN q H

(3)

1. Molecular mechanics calculationsTABLE 2. Calculated (MM2 and MM3) and observed (ED and MW/ED) structure of azetidine (bond lengths in A, bond angles, , q and , in degrees; see structure 3 for the denition of , q and )5,6 . Reprinted with permission from Refs. 5 and 6. Copyright (1985, 1990) American Chemical Society Structural feature C C C N C C C H q N C H H N C C C MM2a 1.471 1.549 1.116 1.014 92.5 86.6 86.4 114.3 36.2 0.311 10.7 MM3b 1.475 1.563 91.26 84.85 88.24 29.0 ED 1.482 0.006 1.553 0.009 1.107 0.003 1.002 0.014 92.2 0.4 86.9 0.4 85.8 0.4 110.0 0.7 33.1 2.4 MW/ED 1.473 1.563 91.2 84.6 88.2 29.7

9

C C N H

a The MM2 force eld was parameterized to reproduce the ED values. b The MM3 force eld was parameterized to reproduce the MW/ED values.

a lp effect which prevents a realistic inversion of the nitrogen and thus stabilizes this form (in the real world this minima may vanish due to repulsion between the axial hydrogen and the C3 methylene which leads to nitrogen inversion). A comparison of MW and MM2 structures for azetidine is provided in Table 2 and shows good agreement between theory and experiment. Not much information is available for the ve-membered ring pyrrolidine (4). MM2 calculations predicted that the 2-half-chair form is preferred over a host of other conformers by an average of 0.3 kcal mol 1 with a 4.37 kcal mol 1 barrier to planarity. The equatorial hydrogen is calculated to be favored by E D 0.20 kcal mol 1 over the axial one. Much controversy is found in the literature regarding the conformational preference of the six-membered ring piperidine (5)5 . However, most experimental evidence is consistent with a predominance of the H-equatorial conformer by 0.25 0.74 kcal mol 1 . As noted above, the C C N H and C C N lp torsional parameters were adjusted to reproduce an intermediate value of 0.30 kcal mol 1 . MM2 calculations of this system have revealed, perhaps contrary to chemical intuition, that most of the energy difference between the Haxial and H-equatorial conformers results from torsional energy while the 1,3-diaxial interactions have only a negligible contribution5 .H N

NH

(4)

(5)

The conformational behavior of N-methyl-piperidine (6) had been extensively studied. Most researchers now agree that the Me-equatorial conformer is favored by about 5 2.7 kcal mol 1 . The C N C C torsional parameter was adjusted to produce an energy difference, E, of 2.50 kcal mol 1 , most of which comes from torsional and bending contributions. A comparison of calculated and observed conformational energies in simple mono-cyclic amines is given in Table 3. In most cases the agreement between MM2 and experimental values is very good. One notable exception is cis-2,6-di-t-butylpiperidine,

10


TABLE 3. Calculated (MM2) and observed conformational energies (kcal mol 1 ) in monocyclic amines5 . Reprinted with permission from Ref. 5. Copyright (1985) American Chemical Society Compound Azetidine Pyrrolidine Cyclobutylamine Cyclohexylamine 1-Amino-1-methylcyclohexane eq-1-Amino-2-methylcyclohexane 1-Amino-eq-2-methylcyclohexane 1-Amino-2,2-dimethylcyclohexane Piperidine eq-2-Methylpiperidine ax-2-Methylpiperidine 3-Methylpiperidine eq-3-Methylpiperidine ax-3-Methylpiperidine 4-Methylpiperidine 2,2,6,6-Tetramethylpiperdine cis-2,6-Di-t-butylpiperidine N-Methylpiperidine 2-Methylpiperidine (N H eq) eq-2-Methyl-N-methylpiperidine eq-3-Methyl-N-methylpiperidine eq-4-Methyl-N-methylpiperidine eq-4-t-Butyl-N-methylpiperidine 1,2,2,6-Tetramethylpiperidine 1-eq,2-Dimethylpiperidine 1-eq,3-Dimethylpiperidine 1-eq,4-Dimethylpiperidine 2,3,3-Trimethylpiperidine 2,2,3-Trimethylpiperidine 1-eq,2,3,3-Tetramethylpiperidine Stable conformer puckered, N H eq 2-env. or half-chair NH2 eq (gg)a NH2 eq (gg)a Methyl eq Methyl eq NH2 eq NH2 eq N H eq N H eq N H eq CH3 eq N H eq N H eq CH3 eq N H eq N H ax CH3 eq CH3 eq N CH3 eq N CH3 eq N CH3 eq N CH3 eq N CH3 eq 2-CH3 eq 3-CH3 eq 4-CH3 eq 2-CH3 eq 3-CH3 eq 2-CH3 eq Ecalculated 0.05 0.24 0.15 1.37 0.64 1.45 1.28 1.12 0.30 0.29 0.23 1.62 0.30 0.49 1.75 0.40 0.65 2.50 2.11 1.68 2.57 2.47 2.52 1.70 1.68 1.62 1.72 1.24 1.13 0.60 Eexperimental 0.27 0.20 0.04 0.16 1.1 1.8

0.3 0.8 1.6, 1.65 1.9, 1.93 0.65 0.4 3.15 2.5b 2.5b 2.5b 2.5b 2.5b 1.95 0.2 1.5, 1.9, 1.7 1.5, 1.77, 1.6 1.98, 1.8

a Each C C N lp torsion is qauche. b This approximate value was taken as an average from analogous systems.

where MM2 calculations favor the H-axial conformation (axial:equatorial ratio of 3:1) in contrast with experiment (axial:equatorial ratio of 1:3). One possible explanation to this discrepancy is an inverted assignment of the IR bands to the two conformers. The last molecule considered in this parameterization study was 1,5,9,13tetraazacyclohexadecane (7). A comparison between MM2 and X-ray results (see structure 7)5 reveals good t between theory and experiment (the X-ray C C bond lengths are shorter than the MM2 corresponding ones, partly since the data were collected at room temperature with no corrections for thermal motion). c. Heats of formation. The parameters used in the calculation of heats of formation for aliphatic amines are C N, N H, N Me, N CHR2 , R2 NH, R3 N and N CR3 . These were obtained according to the following method: Using bond enthalpies from the hydrocarbon part of the force eld, the sum of the hydrocarbon fragment contributions, torsional increments (necessary to account for the thermal excitation of the rotation about bonds with low rotational barriers), conformational population increments (necessary to account for any additional conformations), translation-rotation increments (4kT) and steric energy was

1. Molecular mechanics calculationsNMe

11

(6) 1.515 112.5 1.450 112.9 1.451 114.8 114.4 N 2.92 N 112.6 112.7 1.501 1.460 1.510 2.92 116.6 115.8 4.16 1.517 112.0 1.451 1.508 N N 114.0 112.2 1.468 1.461 1.452 116.1 112.8 111.6 1.503 1.519 1.515 115.7 X-ray (7)

115.5 N

N

112.5 1.461 1.462 113.2 2.96 N 112.0 1.540 4.18 2.96 115.5 112.6 1.540 N 113.1 1.461 1.462 115.5 112.1 1.540 MM2

calculated and matched against the experimental heats of formation of 20 aliphatic amines in a least-squares manner to derive appropriate values for the aforementioned parameters. These were incorporated in the force eld and used in all subsequent heat of formation calculations. A comparison between calculated and experimental results is provided in Table 4. As expected from a least-squares procedure, the agreement between experiment and calculation is generally very good with a standard deviation over 18 comparisons of 0.46 kcal mol 1 (two molecules, cyclobutylamine and 3-azabicyclo[3.2.2]nonane, were excluded from the above comparison since their experimental heats of formation are suspected to be erroneous5 ). However, the true test of these parameters, and indeed of all force eld parameters developed in this and similar studies, should involve systems which were not included in the data set for the parameterization. d. Dipole moments. Calculation of dipole moments for amines required the assignment of bond moments to the N lp, N H and N C bonds. This was done by tting the calculated dipole moments of several aliphatic amines to the calculated ones via a leastsquares procedure. The results are presented in Table 5 and show good agreement between MM2 and experimental values. The only notable exception is quinuclidine, where the approximations inherent to the dipole moment calculation scheme employed in MM2 (neglect of induced dipole moments) have the largest effect.3. MM2 0 parameterization of nitro compounds and MM2 parameterization of nitrosamines, nitramines, nitrates and oximes

Molecular mechanics calculations of the title compounds are much less common than those of amines, probably due to the lack of high quality parameters. In particular, none of these systems (save the nitro group, see Section II.C.3) has been parameterized during the original development of, and later additions to, the MM2 force elds by the Allinger group. Consequently, any serious attempt at modeling such systems must begin with the development of suitable parameters for their unique functionalities. In the following we list several examples where MM2 was parameterized for, and subsequently used in, the structural and energetic study of nitro compounds, nitrosamines, nitramines, nitrates and oximes.

12

Pinchas Aped and Hanoch SenderowitzTABLE 4. Heats of formation and standard deviations (SD) (kcal mol 1 ) for amino com5,6 pounds as calculated by the MM2 and MM3 force elds and observed by experimenta . Reprinted with permission from Refs. 5 and 6. Copyright (1985, 1990) American Chemical Society Compound Methylamine Dimethylamine Trimethylamine Ethylamine Diethylamine Triethylamine n-propylamine Isopropylamine n-Butylamine sec-Butylamine Isobutylamine t-Butylamine Piperidine 2-Methylpiperidine Cyclobutylamine Cyclopentylamine Quinuclidine Diisopropylamine Cyclohexylamine Pyrrolidine Azetidine 3-Azabicyclo[3.2.2]nonane 2,2,6,6-Tetramethyl-4-piperidone SDbvalue was used.

MM2 5.10 4.06 6.15 11.82 17.60 21.66 16.89 20.38 21.95 24.79 23.77 28.90 11.73 20.39 11.10 13.68 0.98 0.43 7.21 65.64 0.46 (18)

MM3 5.04 4.04 6.09 11.92 17.41 21.49 16.95 20.31 21.85 24.31 23.51 28.90 11.83 20.30 9.90 13.70 1.29 31.67 24.86 0.94 24.62

Experiment 5.50 4.43 5.76 11.35 17.33 22.17 16.77 20.02 21.98 25.06 23.57 28.90 11.76 20.19 9.90 13.13 1.03 34.41 2.06 0.80 24.62 10.44 65.43

0.35 (20)

a When a discrepancy occurred between the experimental data reported in References 5 and 6, the later b Number of comparisons are given in parentheses.

TABLE 5. Calculated (MM2) and observed dipole moments of amines (Debye)5 . Reprinted with permission from Ref. 5. Copyright (1985) American Chemical Society Compound Ammonia Methylamine Dimethylamine Trimethylamine n-Propylamine Isopropylamine Ethylamine Diethylamine Triethylamine n-Butylamine Pyrrolidine N-Methylpiperidine Piperidine N-Methylpiperidine 2-Methylpiperidine Quinuclidinea 6-31G ab initio calculations.

MM2 1.43 1.33 1.10 0.64 1.33 1.33 1.33 1.10 0.64 1.33 1.11 0.64 1.10 0.64 1.10 0.64

Experiment 1.47 1.30 1.03 0.63, 0.79 0.91 1.17, 1.25 1.20, 1.45 1.23 1.04 1.27 0.67 1.02 1.33 1.45 1.34, 1.44 0.80 1.34 1.05 1.35 0.65 0.95 1.171a 1.17, 1.22, 1.57


13

Parameters for the nitro group have been developed within the framework of the MM20 force eld15 . The nitro group was considered to be composed of a ve-valent nitrogen connected to two oxygen atoms by two double bonds. Structural and energetic parameterization was based on the experimental structures of nitromethane, nitroethylene and nitrobenzene and on experimental heats of formation of nitromethane, nitroethane, nitropropane, nitrobutane, dinitromethane, trinitromethane and nitrobenzene, respectively. Parameters were determined by a least-squares t procedure. The resulting force eld faithfully reproduced the experimental data for all the molecules used in the parameterization data set with an average absolute error between experiment and calculation of 0.009 A (8 comparisons) for bond lengths, 0.7 (8 comparisons) for bond angles, 0.015 D (2 comparisons) for dipole moments and 1.0 kcal mol 1 (7 comparisons) for heats of formation. A complete list of parameters and force eld results is given in Reference 15. Delpeyroux and coworkers16 have developed a set of molecular mechanics parameters for nitramines (R N NO2 ) for the EMO program and used it in conjunction with MM2-85 parameters to calculate the structures of 1,4-dinitro-glycoluryl (8), 1,3-dinitro4,6-diacetylglycoluryl (9) and 2,5,7,9-tetranitro-tetraazabicyclo(4.3.0)nonanone (10). The complete parameter list for the nitramine functionality is provided in Reference 16 but the parameterization procedure is not discussed.H N O N NO2 (8) NO2 N NO2 N O N NO2 (10) N NO2 (11) NO N N H NO2 N O O N Ac (9) N NO2 Ac N NO2 N O

A set of MM2 (QCPE 395, 1980) parameters for nitrosamines (R N NO) was developed by Polonski and coworkers17 in the course of their study on the conformational dependence of Circular Dichroism of N-nitrosopyrolidines (11). Parameters for the N N torsion were obtained by tting the barrier to rotation of the nitroso group as determined from NMR measurements for similar systems (ca 23 kcal mol 1 ). Other parameters involving the Nsp2 were taken from a set used for azoalkanes18 . N-Nitrosodimethylamine ((CH3 )2 N NO) was chosen as a model compound and its gas-phase electron diffraction structure was used to determine natural bond lengths and angles. The remaining stretching and bending parameters were determined according to Pearlstein and Hopnger19 where the corresponding potential functions for N-nitrosodimethylamine were calculated

14


with MNDO. Bond dipole moments were estimated from partial atomic charges obtained by a Mulliken population analysis of an ab initio wavefunction. The complete nitrosamines parameters set is provided in Reference 17. MM2-85 and MM2-87 parameters for a ve-membered heterocyclic aromatic ring incorporating the N O unit and for conjugated oximes (R D N O H) were developed by Kooijman and colleagues as part of their work on muscarinic agonists20 . Parameters were derived based on Cambridge Structural Database statistics and semiempirical calculations, but the derivation procedure is not discussed by these authors. The new parameters are claimed to reproduce bond lengths and angles in a set of appropriate test structures retrieved from the Cambridge Structural Database to within 0.02 A and 3 of the experimental data and to reproduce the observed dipole moments for a set of ve-membered heterocyclic rings to within 0.4 D, but no detailed comparison is provided in the paper. A complete list of the new parameter is available in Reference 20. Parameters for nitrates (R O NO2 ) have been developed for the MM2-85 force eld by Wang and coworkers21 . Force constants and natural values for bond lengths and angles involving the nitrate group were obtained from the microwave structure of methyl nitrate and ethyl nitrate. The force constant, natural bond length and dipole moment for the C O bond were modied from the MM2 original ones to account for the electron-withdrawing properties of the NO2 group. Torsional parameters for rotation around the HC- - -ONO2 and CC- - -ONO2 bonds were obtained by tting the experimental barrier to rotation of methyl nitrate and ethyl nitrate, respectively. Those for rotation around the HCO- - -NO2 and CDC- - -CONO2 bonds were obtained by tting the corresponding torsional proles of methyl nitrate and propenyl nitrate as calculated by MINDO/3. Finally, heat of formation parameters for N O and NDO were obtained by tting the experimental values for methyl nitrate, ethyl nitrate and 1,2,3-propanetriol trinitrate. A comparison between force eld results and experimental data reveals moderately reasonable reproduction of the latter for all systems used in the data set for the parameterization. In particular, bond lengths and angles (heavy atoms only) for methyl nitrate and ethyl nitrate are reproduced to within 0.01 A and 7 from their respective microwave values, those for 1,2,3-propanetriol trinitrate to within 0.02 A and 5 from their X-ray values and dipole moments and heats of formation for methyl nitrate, ethyl nitrate and 1,2,3-propanetriol trinitrate are reproduced to within 0.3 D and 0.4 kcal mol 1 . The trans gauche energy difference of ethyl nitrate is also in very good agreement with the experimental value (0.5 kcal mol 1 from both experiment and calculations). However, the performance of these parameters for other nitrates could not be evaluated since the only other compounds calculated in this work, isopropyl nitrate, propenyl nitrate and benzyl nitrate, have not been experimentally reported at the time of its publication. A complete list of the new force eld parameters is provided in Reference 21.4. MM2 parameterization of nitro compounds, enamines and aniline derivatives

Parameterization of MM2 for nitro compounds, enamines and aniline derivatives has been performed in conjunction with the parameterization of MM3 and will be discussed in Sections II.C.3 and II.C.4.5. MM2 parameterization of the N C N anomeric moiety

Although the treatment of stereoelectronic effects is somewhat beyond the traditional capabilities of molecular mechanics, force elds can be suitably parameterized to reproduce their energetic and structural manifestations. In the following, we discuss the parameterization of MM2-80 and MM2-87 for the anomeric effect characteristic of the N C N moiety22 .


15

The anomeric effects23 was rst observed in carbohydrates and dened as the preference of an electronegative substituent at the anomeric center of a pyranose ring for the axial (12) rather than the equatorial (13) position, in contrast to what is expected from steric considerations. Extensive theoretical and experimental work23,24 has subsequently revealed the generality of the phenomenon and the effect was redened as the tendency of an R X C Y moiety (X D O, N, S; Y D OR, NR2 , halogen) to adopt gauche rather than anti conformation around the X C and when present, C Y bonds (the latter referred to as the exo-anomeric effect). The currently most accepted explanation of the anomeric effect is given in Molecular Orbitals terms25 and invokes delocalization of a lone pair situated on X into the adjacent C Y orbital (14). This is a two-electron two-orbital stabilizing interaction whose magnitude depends on the relative orientation of the participating orbitals and on the energy gap between them. Thus, attention is shifted from an R X C Y gauche orientation to an X C Y lp anti one. The manifestations of the anomeric effect, relevant to molecular mechanics calculations, are twofold: (1) energetic preference of conformers having a lp antiperiplanar to a orbital; (2) changes in bond lengths and angles as a results of such lp interaction.O O X X R X C Y R (12) (13) (14) R Y R + X C

Several studies have been devoted to the parameterization of molecular mechanics force elds for the anomeric effect22,26 . Here we concentrate on the works of the Tel Aviv group relevant to amines, namely the modication and parameterization of MM280 and, later, MM2-87 to allow the treatment of stereoelectronic effects characteristic of the R N C N R (R D H, alkyl) moiety22 . These include: (1) energetic preference of conformers with a nitrogen lp antiperiplanar to an adjacent C N bond; (2) energetic preference of conformers with an intramolecular hydrogen bond; (3) structural changes in the R N C N R moiety where an N2 C3 N4 lp antiperiplanar arrangement results in shortening of the C3 N4 bond, elongation of the N2 C3 bond and opening of the C1 N2 C3 and N2 C3 N4 bond angles; (4) changes in C N bond lengths to tertiary amines incorporated in anomeric moieties. It has long been recognized22 25 that the anomeric effect in the N C N moiety is weaker than that in O C O due to the poorer acceptor characteristics of the C N bond and the consequent weaker lpN C N overlap. As a result its energetic and structural manifestations are expected to be less pronounced than in the case of the oxygen analog. Most of the data for these parameterization studies came from ab initio calculations although other sources were also used, in particular, to validate the resulting force eld. Thus a set of small model molecules with different conformations of the R N C N R moiety was calculated at various levels of theory and the results used to derive torsional parameters, hydrogen bond parameters and conformationally dependent correction terms for natural bond lengths and angles, as described below: Torsional parameters. These (in conjunction with hydrogen bonding parameters, see below) were chosen to reproduce the ab initio conformational energies of the model compounds. Hydrogen bonds. When an N C N moiety has hydrogen atoms on either nitrogens, several of its conformations may be stabilized by intramolecular hydrogen bonds. Since MM2 does not have a special potential function for hydrogen bonding, such interactions

16


were originally treated, in a nondirectional manner, by assigning special VdW parameters to the H. . .N atom pair. This treatment has been replaced by directional hydrogen bonding where the VdW parameter (equation 7) is correlated with the geometry of the hydrogen bond according to: 10 D 0 G exp DR where is a new VdW energy parameter, DR D abs r term given by: For the N lp. . .H N interaction: G D cos 46.26240356 exp where is the lp N. . .N H torsion. For the N lp. . .H(C N) interaction: G D 1 cos 1 cos (12) 4 0 < < 80 80 < < 180 (11) r 0 and G is a geometrical t

In equation 12, is the N lp . . . H angle and is the lp . . . H C angle. Structural parameters. Variations of bond lengths and bond angles in the C1 N2 C3 N4 C5 moiety as a result of the aforementioned lpN C N overlap were introduced into MM2 by deriving conformationally dependent correction terms for r 0 and 0 . This treatment circumvented the electronegativity correction to bond lengths implemented in MM2-87 (Sections II.B.1 and II.C.1). Inner C N bonds. r 0 was made a function of the geometry of the anomeric moiety according to: 0 13 r 0 D r 0 r where, for the N2 C3 bond, for example, r is given by: r D 0.5K1[1 C cos 223 ] 0.5K2[1 C cos 234 ] C d 14

where 23 and 34 are the lp N2 C3 N4 and N2 C3 N4 lp torsions. The rst term in equation 14 causes r 0 shortening while the second causes its elongation; d is used to correct for conformationally independent bond length variations such as bond shortening, known to appear when several heteroatoms are connected to the same carbon8 . The values of K1, K2 and d were determined by tting MM2 results to the ab initio values. Outer C N bonds. Outer C N bonds in the R N C N R moiety are known22,26 to inversely depend on the adjacent inner bond lengths probably due to a hybridization effect. Natural bond lengths for those bonds were determined according to: r0 D r0 C D D D ar C b0

(15) (16)

where r is the change in the adjacent inner bond while a and b were determined as before, by tting ab initio results. C N bond lengths in tertiary amines. Experimental and ab initio calculations have demonstrated the gradual decrease in C N bond lengths when going from primary (CH3 NH2 ) to secondary ((CH3 )2 NH) to tertiary ((CH3 )3 N) amines5 . However, when a tertiary amine is incorporated in an anomeric unit, the cumulative effect of anomeric interactions, steric interactions and conformationally independent C X bond shortening8 add up to level off this trend. Moreover, a statistical analysis of C N bond lengths in


17

primary, secondary and tertiary amines retrieved from the Cambridge Structural Database revealed only negligible differences22b . Correction terms for tertiary C N natural bond lengths were derived for the N C N moiety based on a comparison with the results of ab initio calculations of suitable model systems. N C N bond angles. The natural value ( 0 ) for the N C N bond angle was determined from ab initio calculations of suitable model compounds. Since this angle depends on the conformation of the anomeric moiety, conformationally dependent correction terms for 0 were derived according to: 0 D 0 C D 0.5K1[cos 223 1] C 0.5K2[cos 234 1]0

(17) (18)

where 23 and 34 are dened as in equation 14 and K1 and K2 determined by tting ab initio results. C N C bond angles. Theory predicts22 25 an opening of these angles as a result of an anomeric interaction. Thus conformationally dependent correction terms for 0 were derived according to: 0 D 0 C D 0.5K1[1 C cos 223 ] C 0.5K2[1 C cos 234 ]0

(19) (20)

where 23 and 34 are dened as in equation 14 and K1 and K2 determined by tting ab initio results. Torsional parameters and VdW parameters for internal hydrogen bonds in the N C N moiety were obtained by tting the ab initio rotational proles of methylenediamine (MDA, 15) and N-methylmethylenediamine (NMMDA, 16). A comparison of relative conformational energies between ab initio and MM2 results for 15 and 16 is provided in Table 6. Bond length correction terms for inner and outer C N bonds (K1, K2 andTABLE 6. Relative energies (kcal mol 1 ) of all possible conformers of methylenediamine (MDA, 15) and Nmethylmethylenediamine (NMMDA, 16) as calculated ab initio (HF/3-21G//HF/3-21G) and with the reparameterized force eld (MM2-87 version)a . Reproduced from Ref. 22b by permission of Elsevier Science Ltd ab initio MDA (15) aa ag gC gC gC g NMMDA (16) aa ag agC gC a g g gC gC 0.00 1.62 2.70 8.23 0.00 1.23 1.69 1.50 2.27 2.48 MM2 0.00 1.21 3.39 5.56 0.00 1.46 1.95 1.36 4.10 3.55D

a Conformers of the lp N2 C3 N4 lp moiety are dened

via two torsional angles: D1 D lp N2 C3 N4; D2 N2 C3 N4 lp, a D anti, g D gauche22b .

18

TABLE 7. Selected structural parameters (bond lengths in A, bond angles and torsional angles in degrees) of methylenediamine (MDA, 15), N-methylmethylenediamine (NMMDA, 16), N,N-dimethylmethylenediamine (NNDMMDA, 17) and tetramethylmethylenediamine (TMMDA, 18) as calculated ab initio (ai, HF/321G//HF/3-21G) and with the reparameterized force eld (MM2-87 version)a . Reproduced from Ref. 22b by permission of Elsevier Science Ltd ag MM2 1.458 1.470 113.6 aa MM2 1.458 1.469 1.468 114.3 112.6 66.9 ag gC gC ai 1.455 1.471 1.467 113.3 114.9 172.3 MM2 1.458 1.469 1.468 113.1 112.4 175.8 ai 1.468 1.457 1.470 114.4 114.4 57.8 MM2 1.472 1.456 1.469 114.4 114.0 66.1 ai 1.461 1.458 1.467 108.5 115.0 66.2 MM2 1.464 1.459 1.469 109.8 114.2 67.1 agC g g ai 1.460 1.458 1.464 107.5 115.6 179.0 gC a gC gC MM2 1.461 1.459 1.468 108.7 112.1 179.9 ai 1.461 1.461 106.9 MM2 1.460 1.460 107.9 ai 1.464 1.464 110.4 MM2 1.461 1.461 108.7 gC gC gC g

MDA (15)

aa

N1 C2 C2 N3 N1 C2 N3 NMMDA (16)

ai 1.466 1.466 118.3

MM2 1.468 1.468 117.8

ai 1.459 1.470 113.4

aa

N1 C2 C2 N3 N3 C4 N1 C2 N3 C2 N3 C4 N1 C2 N3 C4 NNDMMDA (17)

ai 1.464 1.464 1.467 118.2 115.9 61.9

MM2 1.469 1.466 1.467 118.4 112.3 61.2

ai 1.457 1.467 1.465 113.8 115.7 70.9

aa

N1 C2 N3 N3 N1 C2 C2 N1 N1

C2 N3 C4 C5 C2 N3 N3 C2 C2

N3 C4 C5 N3 C4 N3 C5

ai 1.461 1.465 1.464 1.464 118.0 114.4 114.4 66.8 66.0

MM2 1.470 1.462 1.461 1.461 119.2 111.0 111.0 61.9 62.1

ai 1.452 1.472 1.465 1.464 114.5 112.9 113.8 166.3 63.4

MM2 1.460 1.466 1.463 1.462 114.3 110.7 111.2 172.5 64.4

ai 1.459 1.460 1.463 1.465 109.2 113.6 113.5 167.1 61.7

MM2 1.466 1.457 1.465 1.465 110.1 109.5 112.8 171.7 65.8

TMMDA (18)

b

N1 N1 N1 N1 C4 C5 C4 C5

C2 C4 C5 C2 N1 N1 N1 N1

N3 C2 C2 C2 N3 C2 N3

gC gC ai MM2 1.458 1.466 1.463 1.466 1.465 1.466 110.4 114.0 113.9 109.2 113.1 113.6 165.9 177.2 63.5 60.4

a Conformers of the lp N2 C3 N4 lp moiety are dened via two torsional angles: D1 D lp N2 C3 N4; D2 D N2 C3 N4 lp, a D anti, g D gauche22b . b The only conformer of this molecule observed experimentally.


19

d of equation 14 and a and b of equation 16) were derived through tting MM2 results to ab initio geometries of 15, 16, N,N-dimethylmethylenediamine (NNDMMDA, 17) and tertramethylmethylenediamine (TMMDA, 18). The latter two molecules were also used to derive correction terms for tting tertiary C N bonds. A natural value for the N C N angle and correction terms for the N C N and C N C angles were derived in a similar manner. A comparison of selected structural parameters between ab initio and MM2 results for 15 18 is provided in Table 7 and a complete list of the parameters is given in References 22a and 22b.NH2 (15) NH2 NH2 (16) NHMe NH2 (17) N(Me)2 (Me)2 N (18) N(Me)2

The performance of the modied force eld was evaluated by comparing calculated and experimental relative stability of a series of 1,3-diaza cyclic compounds (19 24).R N NR

a R = H R = H

b

c

d

e

f

g

(19)

Me t-Bu H H

Me Et i-Pr t-Bu Me Et i-Pr Me

Me N N R = Me Me N N N R Me (20) N

Me R N Me Me (21) Me N

Me N Me

R a b N R c d R = H Me H Me R = H H Me Me 16 N 1 3 9 N4 10 12 (25) 11 (26) N N 2 N N

(22)

(23) 15 Me N 6 N Me (24) 13 7 N 5 14 8 N

20


TABLE 8. Conformational energies (kcal mol 1 ) of 1,3-diazacyclic compounds (19 24) as calculated by the modied MM2 force eld (MM2-80 version) and observed experimentally (eq. equatorial; ax. axial)22a . Reproduced by permission of John Wiley & Sons, Inc. System 19a-Calc. 19b-Calc. 19b-Exp. 19c-Calc. 19c-Exp. 19d-Calc. 19d-Exp. 19e-Calc. 19e-Exp. 19f-Calc. 19f-Exp. 19g-Calc. 19g-Exp. 20(R0 D eq)-Calc. 20(R0 D eq)-Exp. 20(R0 D ax)-Calc. 21-Calc. 21-Exp. 22-Calc. 22-Exp. 23a-Calc. 23a-Exp. 23b-Calc. 23b-Exp. 23c-Calc. 23c-Exp. 23d-Calc. 23d-Exp. 24-Calc. 24-Exp. eq.eq. 4.9 3.4 3.5 1.76 favored 1.9 favored 2.5 favored 1.9 favored 3.7 4.2 0.0 100% 0.0 100% 4.9 3.6 60% 3.4 25% 2.11 40% 4.3 eq.ax. 1.1 0.0 N-Hax predominant 0.0 N-Hax 66% 0.0 0.0 0.0 0.0 0.0 favored 1.0 1.8 3.8 4.0 14.3 1.1 0.1 1.5 0.41 0.0 100% 1.2 1.2 0.0 0.0 0.0 favored 0.0 0.2 3.92 1.4 ax.eq. 1.4 5.5 ax.ax. 0.0 0.1 4.7 4.03 4.0 5.8

The results, presented in Table 8, show that in most cases the conformer with the lowest steric energy indeed corresponds to the experimentally most favored one. In addition, several molecules containing the N C N moiety were retrieved from the Cambridge Structural Database and calculated with the new parameter set. A comparison between MM2 and X-ray geometries (selected structural parameters only) for two conformers of 1,4,5,8-tetraazadecalin (25, 26) is provided in Table 9 and shows good t between the experimental and calculated data. Other nitrogen-containing anomeric moieties, similarly treated within the MM2 framework, are N C O27,28 and N C F29 . These works, however, exceed the scope of this chapter and will not be discussed here.C. MM3

The MM3 force eld4 was developed in order to correct for some of the basic limitations and ows in MM2 by providing a better description of the molecular potential surface in terms of the potential functions and the parameters. One major outcome of the improved force eld is the omission of lone pairs on nitrogen and oxygen since the reason for their inclusion in MM2 was no longer pertinent. This allows for a realistic


21

TABLE 9. Selected structural parameters (bond lengths in A, bond angles and torsional angles in degrees) of 25 and 26 as calculated by the modied MM2 force eld (MM2-80 version) and observed experimentally (X-ray diffraction)22a . Reproduced by permission of John Wiley & Sons, Inc. 25 X-ray Anomeric center C2 N1 C8 N8 C7 N1 C2 1.467(1) N1 C9 (endo) 1.474(1) C9 N8 (endo) 1.456(1) N8 C7 1.468(1) N1 C16 1.482(1) N8 C14 1.494(1) C2 N1 C9 109.0(1) N1 C9 N8 112.6(1) C7 C8 C9 109.6(1) C2 N1 C9 N8 177.9(1) C16 N1 C9 N8 61.5(1) N1 C9 N8 C7 66.8(1) N1 C9 N8 C14 60.8(1) Anomeric center C3 N4 C10 N5 C6 N5 C6 1.463(1) N5 C10 (endo) 1.470(1) C10 N4 (endo) 1.457(1) N4 C3 1.468(1) N4 C11 1.496(1) N5 C13 1.479(1) C6 N5 C10 108.9(1) N5 C10 N4 112.5(1) C3 N4 C10 109.0(1) C6 N5 C10 N4 178.3(1) C13 N5 C10 N4 60.8(1) N5 C10 N4 C3 66.2(1) N5 C10 N4 C11 61.2(1) MM2 1.65 1.462 1.452 1.466 1.76 1.480 109.6 113.5 110.8 178.7 56.1 71.6 57.3 1.465 1.462 1.452 1.466 1.480 1.476 109.6 113.5 110.8 178.7 56.2 71.6 57.3 X-ray 1.463(4) 1.451(4) 1.471(2) 1.467(4) 1.476(3) 1.496(3) 109.9(2) 113.5(2) 110.4(2) 66.8(2) 58.0(3) 175.6(2) 57.6(3) 1.457(2) 1.449(3) 1.489(3) 1.471(3) 1.490(3) 1.471(3) 110.9(2) 112.0(2) 109.6(2) 68.3(2) 60.3(2) 175.8(2) 58.0(2) 26 MM2 1.465 1.448 1.465 1.467 1.466 1.486 111.8 113.7 109.7 70.5 56.8 179.4 54.9 1.464 1.449 1.466 1.466 1.487 1.468 111.8 113.4 109.9 71.8 56.7 179.5 54.9

treatment of nitrogen inversion, a process which was not handled by MM26 . Of particular interest for amino compounds is the inclusion of a directional hydrogen bond potential function30b and an improved treatment of the electronegativity and Bohlmann effects for C H bonds31 . A new feature in MM3 is the full Newton Raphson minimization algorithm. This allows for the location and verication of transition states and for the calculation of vibrational spectra. Indeed, many of the new potential functions in MM3 were included to provide a better description of the potential energy surface which is required for an accurate calculation of vibrational spectra.1. MM3 potential functions4

Within the latest published MM3 force eld (MM3-94), the molecular energy is given by: Etotal D Estretch C Ebend C Estretch C Etorsionstretch bend

C Ebend

bend

C Etorsionbond

C EVdW C Eelectrostatic C Ehydrogen

(21)

22


The stretch bend, torsional, electrostatic and VdW terms in MM3 are identical in form to the corresponding ones in MM2 (although the electrostatic treatment in MM3 also includes charge-dipole interactions and the VdW terms have slightly different numerical coefcients) and will not be further discussed here. The stretching energy is an extension of the expression used in MM2: Estretch i,j D K rij0 rij 2

C K1 rij

0 rij

3

C K2 rij

0 rij

4

22

0 where K, K1 and K2, rij and rij have their usual meanings. All natural bond lengths 0 ) are subjected to a primary electronegativity correction of the form8,31 : (r

r 0 (new) D r 0 (old) C ra C 0.62 rb C 0.62 2 rc C 0.62 3 rd C

23

Thus, r 0 for an X Y bond is shortened or elongated when electronegative or electropositive atoms (a, b, c, d,. . .) are connected to either X or Y, respectively. The amount of change in r 0 decreases with the substituent number (i.e. the rst substituent has the largest effect, the second a smaller one and so on; substituents are ordered according to their r values). A secondary electronegativity effect which changes r 0 of X Y in X Y Z based on the substituent on Z, and which amounts to 0.4 times the primary effect, is also used in MM3. It has been known for a long time that amines which have a hydrogen on a carbon attached to the nitrogen so that the C H bond is antiperiplanar to the lone pair, show abnormally low stretching frequencies for those C H bonds. In order to reproduce this (Bohlmann) effect MM3 corrects the natural bond lengths and force constants of such C H bonds by31 : r 0 D V0 C 0.5V1 1 C cos C 0.5V2 1 K D [2 2 c 2/ 0.0001023 2 ] r 0 cos 2 (24) (25)

1.3982 r 0

where, in equation 24, V0, V1 and V2 are parameters and is a torsional angle which describes the relationship between the hydrogen and the nitrogens lone pair and, in equation 25, is the reduced mass, r 0 is the natural bond length and r 0 is the cumulative correction to r 0 (i.e. from the electronegativity and Bohlmann effects). The bending energy in MM3 is given by: Ebend i,j,k D K ijk0 ijk 2

C K1 ijk5

0 ijk

3

C K2 ijk6

0 ijk

4

C K3 ijk

0 ijk

C K4 ijk

0 ijk

(26)

where all the variables have their usual meaning. The bend bend energy in MM3 is given by: Ebendbend

D K 1

0 1 2

0 2

27

where 1 and 2 are bond angles centered on the same atom. The torsion stretch energy is given by: Etorsionstretch

i,j,k,l D K rjk

0 rjk 1 C 3 cos ijkl

28

0 where rjk and rjk are the actual and natural bond lengths of the central bond and ijkl is the torsional angle. This type of interaction allows for the j k bond to elongate upon eclipsing of atoms i and l.


23

In the original MM3 force eld, hydrogen bonding energy was described as a sum of electrostatic (dipole dipole) interactions and an explicit hydrogen bonding energy function of the VdW form. This type of approach lacked the directionality associated with hydrogen bonding and consequently did not perform satisfactorily in all cases. A directional term was therefore added on top of the hydrogen bonding function to MM3-92 and its parameters optimized in MM3-94. The explicit form of the function is30b : Ehydrogenbond

D HB f184000 exp[ 12.0rYH /r]

F ,rXH 2.25 r/rYH 6 g/

(29) (30)

0 F ,rXH D cos rXH /rXH

Here, HB is the hydrogen bonding energy parameter, r is the natural hydrogen bond distance, rYH is the actual hydrogen bond distance Y . . . H, is the H X . . . Y angle, 0 rXH and rXH are the actual and natural H X bond lengths, respectively, and is the dielectric constant.2. MM3 parameterization of amines6

As in the case of the MM2 force eld, parameterization of MM3 for amines was based mainly on experimental data with occasional references to ab initio calculations, mainly to evaluate relative conformational energies and derive appropriate torsional parameters. As mentioned above, one notable difference between the two force elds is the removal of lp on sp3 nitrogens from MM3. This simplies the treatment of vibrational spectra and allows for a realistic treatment of nitrogen inversion which could not be handled by MM2. As usual with MM3, parameterization was aimed at reproducing a variety of molecular properties such as structure, steric energy, dipole moments, moments of inertia, heat of formation and vibrational spectra. A complete list of MM3 parameters for amines is provided in Reference 6. a. Bond length and bond angle parameters. A comparison of selected structural parameters between MM3, ED and MW results for methylamine, dimethylamine and trimethylamine is provided in Table 1. Natural bond lengths and force constants for C N and N H bonds were derived by tting the experimentally observed structures and vibrational spectra of the three methylamines. By using an appropriate electronegativity correction for the natural C N bond length when a hydrogen is connected to the nitrogen, MM3 reproduces the decrease in C N bond lengths along the primary ! secondary ! tertiary amine series5,6 . The overall agreement between calculated and experimental bond lengths is very good. However, since the MM3 version used in this parameterization study did not include corrections for the Bohlmann effect, vibrational frequencies of C H bonds anti to a nitrogen lp were consistently calculated to be too high. Appropriate corrections were introduced in subsequent versions of MM3 and the overall RMS error between calculation and experiment in C H frequencies in a more extended set of amines (33 C H comparisons) was reduced from 47 to 17 cm 1 , close to the hydrocarbon limit of the force eld31 . N H and C N bond moments were chosen to reproduce the dipole moments of ammonia and trimethylamine, respectively, and were later slightly modied to evenly distribute the error among all methylamines. The results (Table 1) show good agreement between theory and experiment. Parameters for bond angles were derived in a similar manner, rst by considering the methylamines only, and later by modifying the resulting parameters to reproduce the observed structures of the bulkier amines, diisopropylamine and di-t-butylamine. The N C C angle was chosen to t ethylamine. However, since in its current form the force eld cannot reproduce the experimentally observed dependence of this angle on the

24


lp N C C torsion32 , compromise values where chosen that yield 113.1 (experiment: 115.0 ) and 112.1 (experiment: 109.7 ) for trans and gauche ethylamine, respectively. Fitting the bending force constants was complicated by the coupling of vibrational modes, in particular for the H C N and H N C angles. In principle, improvements in these frequencies require the usage of additional cross-terms, but these are not included in MM3. The inversion barrier of ammonia is calculated by MM3 to be 5.5 kcal mol 1 , in very 33 good agreement with the experimental value of 5.8 kcal mol 1 . b. Torsional angle parameters. Deriving torsional parameters for the amino compounds presented several problems, the most notable of which are: (1) the lack of experimental data for some important torsions; (2) the different quantitative and qualitative conformational preferences around the lp N C C torsion in different molecules (for example, ethylamine and piperidine, see Section II.B.2.a); (3) the need to simultaneously t multiple conformational energies of different systems. The rst difculty was dealt with by utilizing ab initio data for a number of key rotational barriers (e.g. in propylamine34 and methylethylamine35 ) and the two latter ones, by employing a procedure for a simultaneous minimization of the RMS error between the results of MM3 calculations and a set of reference data for up to 10 torsional parameters of as many as 10 compounds with up to 10 conformers per compound. Thus, based on the conformational preference of methylamine, ethylamine, isopropylamine, methylethylamine, piperidine and 2-methylpiperidine, the H N C H, H N C C and C N C C torsional parameters were determined together to describe the rotation around the N C bond. Similarly, ethylamine, propylamine and N-3-dimethylpiperidine were employed to describe the rotation around the C C bond by simultaneously tting the C C C N and H C C N torsions. A comparison between MM3 and experimental results for selected systems is provided in Table 10 and generally shows good agreement between theory and experiment. The N C C N rotational prole was not determined in conjunction with the other parameters for rotation around the C C bond, but rather was t to a series of ethylenediamine conformers calculated ab initio36 . The results (Table 11) are less satisfying than what is usual with MM3. Although the relative energies of the two most stable conformers are reasonably well reproduced, all conformers with a gauche N C C N orientation are calculated to be too low in energy. It was suggested that the lack of a directional component in the hydrogen bonding function employed in this study is the route of this problem, causing MM3 to report similar H-bonding energies regardless of the orientation of the nitrogen lp with respect to the other amino hydrogens6 . However, subsequent calculations of this system with a later version of the force eld which included a directional hydrogen bond function30b did not lead to a signicant improvement (Table 11). c. Moments of inertia. The overall quality of structures obtained from MM3 calculations can be deduced by comparing the calculated and experimental (MW) moments of inertia. Such a comparison for several amino compounds is provided in Table 12 and shows good agreement between theory and experiment (MM3 moments of inertia are expected to be slightly larger than those obtained by MW, since the former method is parameterized to give rg structures while the latter gives ro structures). d. Four-membered and ve-membered rings. As customary with MM3, four- and vemembered rings were assigned unique parameters based on appropriate model compounds. Parameterization for four-membered rings was based on the structure of azetidine (3) which is available from electron diffraction14 , combined MO/ED studies37 and a combined

1. Molecular mechanics calculations1)

25

TABLE 10. Calculated (MM3) and observed conformational energies (kcal mol in simple amines6 . Reprinted with permission from Ref. 6. Copyright (1990) American Chemical Society Compound Methylamine Ethylamine Ethylamine gauche Ethylamine anti Methylethylamineb Conformer staggered Methyl eclipsed trans gauche Methyl staggered Methyl eclipsed Methyl staggered Methyl eclipsed C N C C D 180 C N C C D 120 C N C C D 60 C N C C D 0 C N C C D 300 C N C C D 240 Tt Gt Tg0 Gg GG0 GG GT equatorial axial H-eq; Me-eq H-eq, Me-ax diequatorial 3-ax, N-eq Ecalculated 0 1.4493 0 0.1035 0 2.9967 0 2.9976 0 3.2453 1.1788 5.9479 1.1989 3.0686 0 0.8259 0 0.8831 0.4840

the chemistry of amino, nitroso, nitro and related groups, part 1 - supplement f2 - patai

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