�� E NATURE OF
`
`AND THE STRUCTURE OF
`MOLECULES AND CRYSTALS:
`
`An Introduction to Modern Structural Chemistry···
`
`BY LINUS PAULING
`>..
`
`Professor of Ch°efnist:ry in the
`
`California Institute of Technology
`
`THIRD EDITION
`
`
`
`Ithaca, New York
`
`CORNELL UNIVERSITY PRESS
`1960
`
`I
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`Copyright 1939 and 1940 by
`
`CORNELL UNIVERSITY
`
`Third edition@ 1960 by Cornell University
`
`Third edition first published 1960
`Second printing 1960
`
`<
`
`PRINTED IN THE UNITED STATES OF AMERICA
`
`BY THE GEORGE BANTA COMPANY, INC.
`
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`Contents
`
`Prefaces
`
`.. ��vii
`
`CHAPTER·!
`Resonance and the Chemical Band
`
`I •
`
`.
`
`1-1. The Development of the Theory of Valence
`1-2. Types of Chemical Bonds .
`The Chemical Bond Defined .
`The Ionic Bond and Other Electrostatic Bonds
`The Covalent Bond
`The Metallic Bond; Fractional Bonds
`1-3. The Concept of Resonance .
`1-4. The Hydrogen Molecule-Ion and the One-Electron Bond
`The Normal 'Hydrogen Atom
`The Hydrogen Molecule-Ion.
`The Virial Theorem .
`The Hellmann-Feynman Theorem
`The Conditions for the Formation of a One-Electron Bond
`1-5. The Jlydrogen Molecule and the Electron-Pair Bond
`.
`CondoJi's Treatment of the Hydrogen Molecule
`.
`The Reitler-London Treatment of the Hydrogen Molecule
`Partial Ionic Character and Deformation .
`The Conditions for the Formation of an Electron-Pair Bonu
`
`CHAPTER 2
`The Electronic Structure of Atoms and the;Formal Rules
`f�r the Formation of Covalent Bonds
`
`2-1. The Interpretation of Line Spectra
`2-2. Stationary States; The Bohr Frequency Principle
`2-3. Stationary States· of the Hydrogen Atom .
`Xlll
`
`3
`5
`6
`6
`7
`10
`10
`1 4
`14
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`XlV
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`Contents
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`2-4. The Electronic Structure of Alkali Atoms.
`The Selection Rule for l
`.
`2-5. The Spinning Electron and the.Fine Structure of Spectral Lines
`2-6. The Electronic Structure of Atoms with Two or More Valence
`Electrons .
`2-7. The Pauli Exclusion Principle and the Periodic Syste� of the Ele-
`ments .
`2 -8. The Zeeman Effect and the Magnetic Properties of Atoms and
`Monatomic Ions .
`Hybrid Atomic States.
`2-9. The Formal Rules for the Formation of Covalent Bonds
`
`CHAPTER 3
`The Partial Ionic Character of Covalent Bonds and the
`Relative Electronegativity of Atoms
`
`.
`
`3-1 . The Transition from One Extreme Bond Type to Another .
`Continuous Change in Bond Type .
`Discontinuous Change in Bond Type
`3 -2. Bond Type and Atomic Arrangement .
`3-3. The Nature of the Bonds in Diatomic Ha.logenide Molecules
`3 -4. Bond Energies of Halogenide Molecules; The Energies of N orma.l
`.
`Cova.lent Bonds
`The Postulate of the Geometric Mean .
`3-5. Empirical Values of Single-Bond Energies
`3-6. The Electronega.tivity Scale of the Elements .
`The Formulation of the Electronega.tivity Scale
`3-7. Heats of Formation of Compounds· in Their Standard Sta.tee; The
`Scale .
`Complete Electronegativity
`,
`3-8. Relation to Other Properties
`3-9. The Electronegativity of Atoms and the Partial Ionic Character of
`Bonds .
`3-10. The Enthalpy Change in Organic Rearrangements and the Electro­
`nega.tivity Scale
`.
`3-11. The Correlation of Color and Bo,nd Character
`
`CHAPTER 4
`
`37
`40
`41
`
`44
`
`47
`
`5 8
`59
`61
`
`65
`66
`68
`69
`73
`
`79
`82
`83
`88
`88
`
`91
`95
`
`97 '
`
`103
`105
`
`...
`
`"
`
`The Directed Covalent Bond; Bond Strengths and Bond Angles
`
`4-1. The Nature and Bond-forming Power of Atomic Orbitals
`4-2. Hybrid Bond Orbitals; The Tetrahedral Carbon Atom .
`Derivation of Results about Tetrahedral Orbitals
`Quantum-mechanical Description of the Quadrivalent Carbon
`Atom .
`4-3. The Effect of an Unshared Pair on Hybridization
`
`1 0 8
`11 1
`1 1 6
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`1 1 8
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`Contents
`Contribution of Unshared Electron Pairs to the Electric Dipole
`·
`Moments of Molecules .
`.·
`4-4. Orbitals for Incomplete s-p Shells .
`4-5. Concentration of Bond Orbitals
`4-6. Electron Distribution in Completed Shells
`4-7. Restricted Rotation about Single Bonds
`.
`Restricted Rotation about Single Bonds between Atoms with Un-
`shared Electron Pairs .
`4-8. Orbitals and Bond Angles for Multiple Bonds
`4-9. Partial Ionic Character of Multiple Bonds
`4-10 .
`. The Effect of Unshared Pairs on Bond Energies and Bond Lengths
`'
`
`xv
`
`123
`124
`126
`128
`130
`
`134
`136
`142
`142
`
`CHAPTER 5
`Complex Bond Orbitals; The Magnetic Criterion for Bond Type
`
`5-1. Bonds Involving d Orbitals .
`5-2. Octahedral Bond Orbitals
`.
`5-3. Square Bond Orbitals
`5-4. The Magnetic Criterion for Bond Type
`5 -5. The Magnetic Moments of Octahedral Complexes
`5-6. The Magnetic Moments of Tetrahedral and Square Coordinated
`Complexes.
`5-7. The Electroneutrality Principle and the Stability of Octahedral
`. ·
`Complexes.
`5-8. Ligand Field Theory
`5-9. Other Configuration� Involving d Orbitals
`5-10. Configurations for Atoms with Unshared Electron Pairs
`
`145
`147
`153
`161
`1 62
`
`168
`
`172
`174
`1 75
`1 80
`
`CHAPTER 6
`1 The Resonance of Molecule� among Several
`Valence-Bond Structures
`
`6-1. Resonance .in Nitrous Oxide and Benzene.
`6-2. Resonance Energy
`Values of Bond Energies for Multiple Bonds
`Ionic Resonance Energy and Partial Ionic Character of Multiple
`Bonds.
`190
`The Nitrogen-Nitrogen Triple Bond
`191
`Empirical Values of Resonance Energies
`191
`6-3. The Structure of Aromatic Molecules .
`19 8
`The Quantitative Treatment of Resonance in Aromatic Molecules 203
`The Orientation of Substituents in Aromatic Molecules
`205
`.
`The Effect of Resonance on the Electric Dipole Moments of
`Molecules
`• 209
`
`183
`188
`1 89
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`XVI
`
`Contents
`6-4. The Structure and Stability of the Hydrocarbon Free Radicals
`6-5. The Nature of the Theory of Resonance
`
`211
`215
`
`CHAPTER 7
`I nteratomic Distances and Their Relation to the Structure
`of M olecuzes and Crystals
`
`7-1. Interatomic Distances in Normal Covalent Molecules: Covalent
`Radii
`.
`7-2. The Correction for Electronegativity Difference .
`7-3. Double-Bond and Triple-Bond Radii .
`7-4. Interatomic Distances and Force Constants of Bonds
`7-5. Interatomic Distances and··Resonance
`Bond Le_ngt� in _Aromatic Hy�rocarbons .
`7-6. Bond Order.and Bond Length; Change in Bond Length Caused by
`Resonance between Two Equivalent Structures .
`7-7. Single-Bond:Triple-Bond Resonance
`'.
`7-8. The Conditions for Equivalence or Nonequivalence of Bonds
`7-9. Tetrahedral and· Octahedral Covalent Radii
`Tetrahedral Radii .
`Octahedral Radii
`.
`Other Covalent Radii .
`The Anomal9us Manganese Radius .
`7-10. Interatomic Distances for Fractional Bonds
`7-11. Values of Single-Bond Metallic Radii .
`7-12. Van der Waals and Nonbonded Radii of Atoms .
`
`CHAPTER 8
`Types of Resonance in Molecules
`
`S-1. The Structure of Simple Resonating Molecvles
`Carbon Monoxide and Carbon Monosulfide
`Carbon Dioxide and Related Molecµles.
`The Cyanides and Isocyanides
`.
`8-2. The Adjacent-Charge Rule and the Electroneutrality Rule.
`Cyanates and Thiocyanates .
`8-3. The Nitro and Carboxyl Groups; Acid and Base Strengths.
`8-4. The Structure of Amides and Peptides
`8-5. The Carbonate, Nitrate, and Borate Ions and Relii,ted Molecules
`8-6. The Structure and Properties of the Chloroethylenes and Chloro-
`·
`benzeries
`.
`8-7. Resonance in Cop.jugated Systems .
`Overcrowded Molecules
`.
`Conjugated Systems Involving Triple Bonds
`8-8. Re�on�nc� in Heterocyclic Molecules
`8-9. Hyperconjugation
`
`221
`228
`230
`231
`232
`236
`
`239
`240
`241
`244
`244
`248
`252
`254
`255
`256
`257
`
`265
`265
`267
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`273
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`282
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`Contents.
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`xvn
`
`CHAPTER 9
`The Structure of Molecules and Complex Ions Involving
`Bonds with Partial Double-Bond Character
`
`..
`
`310
`313
`
`9-1. The Structure of Silicon Tetrachloride and Related Molecules
`9-2. Silicon Tetrafluoride and Related Molecules .
`9-3. The Fluorochloromethanes and . Related Molecules; The Effect of
`Bond Type on Chemical Reactivity
`9-4. Partial Double-Bond Character of Bonds between the Heavier Non-
`metal Atoms .
`316
`9-5. The Boron Halogenides .
`317
`9-6. The Oxides and Oxygen Acids of the Heavier Elements.
`320
`The Chlorate Ion and Related Ions
`323
`The Strengths of the Oxygen Acids .
`324
`Sulfuryl Fluoride and Related Molecules
`328
`Oxides of the Heavier Elements .
`329
`,
`9-7. The Structure and Stability of Carbonyls and Other Covalent Com-
`plexes of the Transition Metals.
`331
`The Cyanide and Nitro Complexes of the Transition Elements: 336
`
`314
`
`CHAPTER 10
`The One-Electron Bond and the Three-Electron Bond;
`Electron-deficient Substances
`
`10-1. The One-Electron Bond .
`10-2. The Three-Electron Bond
`'.l'he Conditions for Formation of a Stable Three-Electron Bond
`The Helium Molecule-Ion
`10-3. The Oxides of Nitrogen. and Their Derivatives
`Nitric Oxide
`Dinitrogen Dioxide
`The Nitrosyl Halogenides.
`Nitrosyl-Metal Complexes
`Nitrogen Dioxide
`.
`Dinitrogen Tetroxide .
`10-4. The Superoxide Ion and the Oxygen Molecule
`The Ozonide Ion
`.
`· 10-5. Other Molecules Containing the Three-E�ectron Bond
`The Structure of the Semiquinones and Related Substances
`10-6. Electron-deficient Substances
`.
`10-'7. The Structure of the Boranes
`.
`10-8. Substances Related to the Boranes.
`10-9. Substances Containing Bridging Methyl Groups
`Carbonium Ions as Reaction Intermediates
`Complexes of Olefines and Silver Ion
`
`340
`341
`342
`343
`343
`343
`344
`345
`347
`348
`349
`351
`354
`355
`357
`363
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`XVlll
`
`Contents
`
`10-10. Ferrocene and Related Substances
`A Resonating-Bond Treatment of Ferrocene
`
`:, .
`
`CHAPTER 11
`The Metallic Bond
`
`11-1. The Properties of Metals
`11-2. Metallic Valence .
`11-3. The Metallic Orbital
`11-4. Interatomic Distances and Bond Numbers in Metals
`11-5. The Closest Packing of Spheres
`Cubic and Hexagonal Closest Packing of Equivalent Spheres
`Closest-packed Structures Containing Nonequivalent Spheres
`11-6. The Atomic Arrangements in Crystals of Metallic Elements
`Closest-packed Structures
`Metal Structures Related to Closest-packed Structures
`The Cubic Body-centered Arrangement
`11-7. The Electronic Structure of the Transition Metals
`11-8. Metallic Radii and Hybrid Bond Orbitals
`11-9. Bond Lengths in Intermetallic Compounds
`.
`11-10. Structures of Intermetallic Compounds Based on the Simple Ele-
`.
`mentary Structures
`11-11. Icosahedral Struc.tures
`.
`11-12. The 'Y-Alloys; Brillouin Polyhedra .
`11-13. Electron Transfer in Intermetallic Compounds
`11-14. Compounds-of Metals with Boron, Carbon, and Nitrogen
`11-15. Molecules and Crystals Containing Metal-Metal Bonds
`11-16. The Structures of Sulfide Minerals.
`
`385
`386
`
`393
`394
`398
`400
`404
`404
`407
`409
`409
`412
`414
`414
`417
`421
`
`424
`425
`429
`431
`435
`436
`442
`
`CHAPTER 12
`The Hydrogen Bond
`
`12-1. The Nature of the Hydrogen Bond
`12-2. The Effect of the Hydrogen Bond on the Physical Properties of
`Substances
`12-3. Hydrogen Bonds Involving Fluorine Atoms
`12-4. Ice and Water; Clathrate Compounds.
`Clathrate Compounds.
`.
`Water
`12-5. Alcohols and Related Substances
`12-6. Carboxylic Acids .
`Symmetrical Hydrogen Bonds between Oxygen Atoms
`12-7. The Spectroscopic Study of the Hydrogen Bond
`Compounds Showing Strong Hydrogen-Bond Formation
`The Formation of Weak Intramolecular Hydrogen Bonds
`Factors Affecting Hydrogen-Bond Formation .
`
`449
`
`454
`460
`464
`469
`472
`473
`477
`484
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`Contents
`12-8. Hydrogen Bond.S in Proteins
`12-9. Hydrogen Bonds in Nucleic Acids .
`
`. XIX
`
`498
`503
`
`CHAPTER 13
`The Sizes of Ions and the Structure of Ionic Crystals
`
`.
`
`505
`510
`511
`519
`520
`·522
`
`523
`530
`533
`533
`
`13-1. Interionic Forces and Crystal Energy .
`The Born-Haber Thermochemical Cycle
`13-2. The Sizes of Ions: Univalent Radii and Crystal Radii
`13-3. The Alkali Halogenide Crystals
`Anion Contact and Double Repulsion
`The Cesium Chloride Arrangement .
`A Detailed Discussion of the Effect of Relative Ionic Sizes on the
`Properties of the Alkali Halogenides .
`Alkali Halogenide Gas Molecules
`13-4. The Structure of Other Simple Ionic Crystals
`The Alkaline-Earth Oxides, Sulfides, Selenides, and Tellurides
`Crystals with the Rutile and the Fluorite_ Structures; Interionic
`Distances for Substances of Unsymmetrical Valence Type
`.
`The Effect of Ligancy on Interionic Distance .
`The Effect of Radius Ratio in Determining the Relative Stability
`of Different Structures .
`540
`13-5. The Closest Packing of Large Ions in Ionic Crystals
`541
`13-6. The Principles Determining the Structure of Complex Ionic Crystals 543
`The Nature of the Coordinated Polyhedra
`544
`The Number of Polyhedra with a Common Corner: The Electro-
`static Valen.Ce Rule .
`The Sharing of Polyhedron Corners, Edges, and Faces
`
`· 533
`537
`
`547
`559
`
`CHAPTER 14
`A Summarizing Discussion of Resonance and
`Its Significance for Chemistry
`
`.
`14-1. The Nature of Resonance
`14-2. The Relation between Resonance and Tautomerism..
`14-3. The Reality of the Constituent Structures of a Resonating System
`14-4. The Future Development and Application of the Concept of
`Resonance
`
`563
`564
`567
`
`569
`
`..J
`
`Appendices and Indices
`
`I. Values of Physical Constants
`II. The Bohr Atom
`.
`III. Hydrogenlike Orbitals
`IV. Russell-Saunders States of Atom.S Allowed by the Pauli Exclusion
`·
`Principle
`
`573
`574
`576
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`580
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`xx
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`Contents
`
`The Zeeman Effect
`The Paschen-Back Effect .
`The Extreme Pa.schen-Back Effect
`Two Equivalent p Electrons
`The Lande g-Fa.ctor
`V. Resonance Energy
`VI. Wave Functions for Valence-Bond Structures.
`VII. Molecular Spectroscopy .
`Electronic Energy Curves; The Morse Function
`The Vibration and Rotation of Molecules
`Microwave Spectroscopy
`.
`Electronic Molecular Spectra .
`Ra.man Spectra .
`VIII. The Boltzmann Distribution Law
`The Boltzmann Distribution Law in Clallsical Mechanics.
`IX. Electric Polarizabilities and Electric Dipole Moments of Atoms,
`Ions, and Molecules .
`Electric Polarization and Dielectric Constant
`Electronic Polarizability
`.
`The Debye Equation for Dielectric Constant
`X. The Magnetic Properties of Substances
`Diamagnetism
`.
`Paramagnetism .
`Ferromagnetism
`Antiferromagnctism
`Ferrima.gnetism
`XI. The Strengths of the Hydrohalogeuic Acids
`XII. Bond Energy and Bond-Dissociation Energy
`Author Index .
`Subject Index .
`
`581
`583
`584
`584
`586
`589
`592
`594
`595
`596
`599
`600
`601
`602
`603
`
`605
`605
`608
`608
`611
`. 611
`612
`614
`615
`617
`618
`622
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`/
`
`THE NATURE OF
`
`THE CHEMICAL BOND
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`CHAPTER 7
`
`lnteratomic Distances and Their Relation
`
`to the Structure of Molecules
`
`and Crystals
`
`7-1. INTERATOMIC DISTANCES IN NORMAL COVALENT
`MOLECULES: COVALENT RADII
`
`As a result. of the development of the x-ray method of studying the
`structure of crystals and the band-spectroscopic method and especially
`the electron-diffraction method of studying gas molecules, a large
`amount of information about interatomic distances in molecules and
`crystals has been collected. It ha$ been found that the values of inter­
`atomic distances corresp.onding to covalent bonds can be correlated
`in a simple way in terms of a set of values of covalent bond radii of
`atoms, as described below.1
`
`1 Interatomic-distance values obtained in various ways are reliable to an ex­
`tent determined by the nature of the method. Sp ectroscopic values for diatomic
`molecules are us ually acc urate to within 0.001 A; those for polyatomic molecules
`are somewhat less reliable. M an y accurate interatomic distances (to within
`0.001 A) for moderately complex molecules, such as methyl cyanide, h ave in
`recent years b een determined b y the methods of microwave spectroscopy.
`Electron-diffraction values for gas molecules may be assigned probable errors of
`from 0.005 to 0.05 A or more, depending on the care with which the investiga­
`tion has been carried o ut and the complexity of the molecule. X-ray values for
`crystals may b e reliabl e to ,0.001 A, if the interatomic distance is determined
`directly b y the size of the unit cell (as in diamond). In general, however, they
`depend also on some additional parameters evaluated with use of intensity data;
`they �re then reliable to 0.005 A only in exceptional cases. The probable errors
`for x-ray crystal structure values involving several parameters are around 0.005
`A for investigations carried out carefully in recent years, and 0.05 A or more for
`others. X-ray diffraction values for gas molecules are reliable only to ·0.1 or
`0.2 A. Tables of values of interatomic distances are given by P. W. Allen
`and L. E. Sutton, Acta Cryst. 3, 46 (1950), G. W. Wheland, Resonance in
`221
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`222
`
`I nteratomic Distances
`The values found for the equilibrium distance between two atoms
`A and B connected by a covalent bond of fixed type (single, double,
`etc.) in different molecules and crystals are in most cases very nearly
`the same, so that it becomes possible to assign a constant value to the
`A-B bond distance for use in any molecule involving this bond. For
`example, the carbon-carbon distance in diamond (representing a
`0
`single covalent bond) is 1.542 A, and the values found in the seven
`molecules given in Table 7-1, as well as in many others, lie between 1.53
`
`TA�LE 7-1.-EXPERIMENTAL VALUES OF CARBON;CARBON
`SINGLE-BOND DIST.A.NCES4
`
`Substance
`
`C-C distance
`
`Diamond
`Ethane
`Propane
`rv-Butane
`Neopentane
`n-Heptane
`Cyclohexane
`Adamantane, C10Hu
`
`1. 5 42 A
`1 . 533
`1. 5 4
`1.534
`1.54
`1.532
`1 .53
`1 . 5 4
`
`a These values a.re good to about ±0 .01 A. The value for ethane is that ob­
`tained by K. Hedberg and V. Schomaker, J.A.C.S. 73, 1482 ( 1951) , by combining
`the results of electron-diffraction and microwave studies. The next five hydro­
`carbon values are from th� electron-diffraction study by L. Pauling and L. 0.
`Brockway, ibid. 59, 1223 ( 19 37), and R. A. Bonham and L. S. Bartell, J.A.C.S.
`81, 3 49 1 ( 1959). The value for adamantane is due to W. Nowacki and K. Hed­
`berg, J.A.C.S. 70 , 1497 ( 1948) , and W. Nowacki, Helv. Chim. Acta 28, 1233
`(1945).
`
`and 1.54 A, being equal to the diamond value to within their probable
`errors. This constancy is of interest in view of the varied nature of
`the molecules.
`It will be pointed out later (Chap. 8) that the interaction of a methyl
`group and a double bond or an aromatic group (hyperconjugation)
`0
`causes some shortening of the single bond, about 0.03 A. There is a
`0
`larger shortening, about 0.08 A, for a single bond adjacent to a triple
`bond. A large shortening is also observed for a single bond between
`two double bonds or aromatic nuclei, forming a conjugated system.
`Some shortening is also observed in small rings (1.524 A in cyclo-
`
`Organic Chemistry, John Wiley and Sons, New York, 1955, and Sutton, Inter­
`atomic Distances. Most of the values for crystals are from Strukturbericht, vols.
`I to VII (1913 to 1939), and Structure Reports, vol. 8 and later volumes. A useful
`compilation is R. W. G. Wyckoff, Crystal Structures, Interscience Publishers,
`New York, 1948 on.
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`7-1
`
`Distances in Normal Covalent M olec-ules
`
`223
`
`propane) ; this effect, which may be attributed to the bending of the
`bonds,. has already been discussed (Sec. 4-8).
`In cyclobutane the carbon-carbon distance2 is found to be 1.568 .
`+ 0.020 A, somewhat larger than the normal value. The presumably
`correct explanation that has been proposed2 is that the bonds are
`stretched because of the repulsion of the atoms separated by the
`diagonal of the square. Similar distances (1.555 ± 0.010 A and
`,
`0
`1.563 ± 0.010 A) have been reported3 in two other molecules con-
`taining four-membered rings, bicycloheptane and the polycyclo­
`hydrocarbon C12Hu.
`Similar constancy is shown by other covalent bond distances (with
`certain exceptions that will be discussed later). For the carbon-
`o
`oxygen single bond, for example, the value 1.43 A has been reported
`for methanol,4 ethanol, ethylene glycol, dimethyl ether, paraldehyde,
`metaldehyde, and many other molecules; this value is accepted as
`standard for the C-0 bond.
`Moreover, covalent bond distances are often related to one another
`in an additive manner; the bond distance A-Bis equal to the arith­
`metic mean of the distances A-A and B-B. For example, the C-C
`0
`distance in diamond is 1.542 A and the Cl-Cl distance in Cl2 is 1. 988
`A. The arithmetic mean of these, 1.765 A, is identical with the Cl-Cl
`distance 1.766 + 0.003 A found in carbon tetrachloride to within the
`the probable error of the experimental value.5 In consequence, it
`becomes possible to assign to the elements covalent radii such that
`the sum of two radii is approximately equal to the equilibrium inter­
`nuclear distance for the two corresponding atoms connected by a
`single covalent bond.
`These covalent radii are for use in molecules in which the atoms form
`covalent bonds to a number determined by their positions in the
`periodic table-carbon four, nitrogen three, and so on. It is found
`empirically that the radii are applicable to covalent bonds with con­
`siderable ionic character; for extreme ionic bonds, however, ionic radii
`are to be used (Chap. 13), and in some molecules, discussed in later
`sections, the partial ,ionic character plays an important part in determ­
`ining the interatomic distances.
`
`2 J. D. Dunitz and V. Schomaker, J. Chem. Phys. 20, 1703 (1952).
`3 C. Wong, A. Berndt, and V. Schomaker, unpublished research, Cal. Inst.
`Tech.
`'The value C--0 = 1 .427 ± 0.007 A. from a microwave study has been re­
`ported by P. Venkateswarlu and W. Gordy, J. Chem. Phys. 23, 1200 (1955).
`The other values, which are in general reliable to ± 0.02 A, are from older electron­
`diffraction and x-ray investfgations.
`a L. S. Bartell, L. 0. Brockway, and R. H. Schwendeman, J. Chem. Phys. 23,
`1854 (1955).
`
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`224
`
`I nteratomic_ Distances
`
`The radii are so chosen that their sums represent average internuclear
`distances for bonded atoms in molecules and crystals at room tempera­
`·
`ture. The atoms carry out thermal oscil_lations,
`which cause the
`internuclear distances to vary about their average values. At room
`temperature these are only slightly different from the values correspond­
`ing to the minima in the potential energy functions.
`Values of the single-bond covalent radii of the nonmetallic elements
`are given in Table 7-2: These values, which were originally obtained
`
`TABLE 7-2. -CO VALE NT RADII FOR ATOMS
`Qa
`0 . 66
`
`Single-bond radius
`Double-bond radius
`Triple-bond radius
`
`Single-bond radius
`Double-bond radius
`Triple-bond radius
`
`Single-bond radius
`Double-bond radius
`
`Single-bond radius
`Double-bond radius
`
`4 See also Table 7-5.
`
`c
`0 .772
`.667
`.603
`Si
`1 . 17
`1 . 0 7
`1 .00
`Ge
`1 .22
`1 .12
`Sn
`1.40
`1 .30
`
`Na
`0 . 70
`
`p
`I.IO
`1 .00
`0 _93
`As
`1 .21
`1 . 1 1
`Sb
`1.41
`1 .31
`
`s
`1 .04
`0 . 94
`. 8 7
`Se
`1 . 1 7
`1 .0 7
`Te
`1.3 7
`1 . 2 7
`
`F"
`o.64 A
`
`Cl
`0 .99
`.89
`
`Br
`1 . 14
`1 .04
`I
`1. 33
`1 .23
`
`largely from x-ray diffraction studies of crystals, may be tested by
`comparison with the results of the many recent investigations of gas
`molecules as well as of crystals.6
`
`6 Shortly after the formulation of a rough set of atomic radii for use in Cl'.ystals
`of all types (W. L: Bragg, Phil. Mag. 40, 169 [1920 1) it was recognized that the
`effective radius of an atom depends on its structure and environment, and es­
`pecially on the nature of the bonds that it forms with adjacent atoms. Between
`1920 and 1927 a complete set of values of ionic radii, for use in ionic molecules
`and crystals, was developed by Lande, Wasastjerna, Goldschmidt, and Pauling;
`this work is discussed in Chap. 13. _ In 1926 M. L_ Huggins (Phys. Rev. 28,
`1086 [1926 )) published a set of atomic radii for use in crystals containing co­
`valent bonds. V. M. Goldschmidt in the same year published values of atomic
`·
`radii obtained from metals as w�ll as from covalent nonmetallic crystals ("Geo-
`chemische Verteilungsgesetze der Elemente," Skrifter Norske Videnskaps-Akad.
`Oslo, I, Mat_.:.Naturv. Kl., 1926); he later collected these and additional values
`into a table of radii. for use in metals and intermetallic compounds (Trans.
`Faraday Soc. 25, 253 [1929 ]); see Chap. 11). A survey of the interatomic-dis­
`tance values for covalent crystals was then ma.de by L. Pauling and M. L. Hug­
`gins (Z. Krist. 87, 205 (1934]), leading to the formulation of the tables o� tetra­
`hedral radii, octahedral radii, and. square radii given and described in Sec. 7-9 ,
`and b y making small changes in the values of some of the tetrahedral radii in
`
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`7-1
`
`Distances in Normal Covalent Molecules
`
`225
`
`TABLE 7-3. -SINGLE-BOND DISTANCES AND RADII FOR ELEMENTS
`
`.Bond
`
`Substance
`
`Method"
`
`C-C
`Si-Si
`Ge-Ge
`Sn-Sn
`P-P
`
`As-As
`
`Sb-Sb
`s-s
`
`Se-Se
`
`Te-Te
`F-F
`
`Cl-Cl
`Br-Br
`I-I
`
`Diamond
`Si(c)
`Ge(c)
`S�(c)
`P4(g)
`P(c, black)
`Ast(g)
`As(c)
`Sb(c)
`Ss(g)
`Ss(c)
`Ses(c, a)
`Ses(c, fJ)
`Se(c, gray)
`Te(c)
`F2(g)
`F2(g)
`Cl2(g)
`Br2(g)
`I2(g)
`
`X-ray
`X-ray
`X-ray
`X-ray
`EDb
`X-rayc
`EDb
`X-ray
`X-ray
`EDa
`X-ray•
`X-ray/
`X-rayu
`X-ray
`X-ray
`ED"
`Ramani
`Sp
`Sp
`Sp
`
`One-half of
`observed
`distance
`
`0 . 112 A
`1 .17
`1 .22
`1 . 40
`1 . 10
`1 .09, 1 . 10
`1 .22
`1 .25
`1 . 43
`1 .0 4
`1 . 05, 1 .02
`1 . 17
`1 . 17
`1 . 16
`1 . 38
`0.718
`.709
`.99�
`1 . 1 40
`1 .333
`
`Assigned
`radius
`
`0.112 A
`1 .17
`1 .22
`1 .40
`1 . 10
`
`1 .21
`
`1 . 41
`1 .04
`
`1 . 17
`
`1 .37
`0 . 6 4
`
`.99
`1.14
`1 .33
`
`" X-ray signifies the x-ray study of crystals, ED the electron-diffraction study
`of gas molecules, and Sp the spectroscopic study of gas molecules. References are
`not given for the older x-ray and spectroscopic values; they may be obtained from
`standard compilations.
`· b L. R. Maxwell, S. B. Hendricks, and V. M. Mosley, J. Chem. Phys. 3, 698
`.
`( i935).
`" R. Hultgren and .B. E. Warren, Phys. Rev. 47, 808 (1935); approxi�ately
`the same value is found also in amorphous red phosphorus, amorphous black
`phosphorus, and liquid phosphorus: C. D. Thomas and N. S. Gingrich, J. Chem.
`Phys. 6, 659 (1938).
`4 C.-S. Lu and J. Donohue, J.A.C.S. 66, 81 8 (19 44).
`• B. E. Warren and J. T. Burwell, J. Chem. Phys. 3, 6 (1935); S. C. Abrahams,
`Acta Cryst. 8� 661 (19�5).
`I R. D. Burbank, Acta Cryst. 4, 1 40 (1951).
`o R. E. Marsh; L. Pauling, and J. D. McCullough, Acta Cryst. 6, 71 (1953).
`" M. T. Rogers, V. Schomaker, and D. P. Stevenson, J.A.C.S. 63, 2610 (1941).
`·
`• D. Andrychuk, Can. J. Phys. 29, 151 (1951).
`
`the way indicated by the data available at that time for a few normal-valence
`molecules, values of single-bond normal covalent radii differing only slightly
`from those given in Table 7-2 were obtained (see also L. Pauling, Proc. Nat. Acad.
`Sci. U. S. 18, 293 [1932 ]) . Since then the electron-diffraction and microwave
`st\l.dy of gas molecules and further x-ray work on molecular crystals have pro­
`vided many interatomic-distance values for testing and refining the table of
`radii.
`
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`226
`
`I nteratomic Distances
`
`TABLE 7-4.-THE COVALE NT RADIUS OF HYDROGEN
`
`Molecule
`
`Method0
`
`Distance M-H
`
`Radius of
`hydrogen
`
`H2
`HF
`HCl
`HBr
`HI
`H20
`H2S
`H2Se
`NHa
`PH a
`As Ha
`Sb Ha
`CH,
`C2Ha
`C2H,
`CzH2
`CaHa
`HON
`SiH,
`GeH,
`Sn&
`
`Sp
`Sp
`Sp, M
`Sp, M
`Sp
`Sp
`Sp
`Sp
`Sp
`M
`M
`M
`Sp
`ED
`ED, Sp
`Sp
`Sp
`Sp
`Sp
`Sp
`Sp
`
`0 . 74.A
`.918
`1 . 2 7
`1 .42
`1 .61
`0 .96
`1 .34
`1 . 4 7
`1 .01
`1 .42
`1 . 52
`1 . 71
`1 . 095
`1.095
`1 .087
`1 .065
`1 .084
`1 .066
`1 .48
`1 .53
`1 . 70
`
`o.3 7 A
`.28
`.28
`.28
`.28
`.30
`.30
`.30
`.31
`.32
`.31
`.30
`.32
`.32
`.31
`.29
`.31
`.29
`.31
`.31
`.30
`
`0 Here Sp means by infrared or ultraviolet spectroscopy and M by microwave
`spectroscopy. Similar values, in general somewhat less reliable, have also been
`obtained for many molecules by x-ray diffraction of crystals, neutron diffraction
`of crystals, electron diffraction of gas molecules (ED), or analysis of vibrational
`·
`frequencies.
`Some of the values are from the papers mentioned in the footnotes to Table
`4-1. Other recent papers are the following:
`CH,: D. R. J. Boyd and H. W. Thompson, Trans. Faraday Soc. 49, 1281
`(1953); H. M. Kaylor and A. H. Nielsen, J. Chem. Phys. 231 2 139 (1955).
`C2H,: L. S. Bartell and R. A. Bonham, J. Chem. Phys. 27, 1414 (195 7) ; W. S.
`Gallaway and E. F. Barker, ibid. 10, 88 (1942) ; H. C. Allen, Jr., and E. K.
`Plyler, J.A.C.S. 80, 2673 (1958).
`C2H2: B. D. Saksena, J. Chem. Phys. 20, 95 (1952); M. T. Christensen, D. R.
`Ea.ton, B. A. Green, and H. W. Thompson, Proc. Roy. Soc. London A238, 15
`( 1956).
`CeHa: B. P. Stoicheff, Can. J. Phys. 32, 339 , 635 (1954); G. Herzberg and
`B. P. Stoicheff, Nature 175, 79 (1955 ) .
`HCN: A . E . Douglas and D. Sharma, J. Chem. Phys. 21, 448 (1953 ) ; I. R . Dagg
`and H. W. Thompson, Trans. Faraday Soc. 52, 455 (1956).
`SiH,: S. R. Polo and M. K. Wilson, J. Chem. Phys. 22, 155 9 (1954).
`GeH,: L. P. Lindeman and M. K. Wilson, J. Chem. Phys. 22, 1 723 (1954).
`SnH,: G. R. Wilkinson and M. K. Wilson, J. Chem. Phys. 25, 784 (1956).
`
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`Distances in Normal Covalent Molecules
`227
`7-1
`Comparison of the radii with half the interatomic distances in ele­
`mentary molecules or crystals involving single bonds may be made as a
`first check on the radii (Table 7-3). For the fourth-row elements,
`crystallizing with the diamond structure, and the halogens (other
`than fluorine) the agreement is perfect, since these were the sources of
`the values in the table. The crystals P, As, $b, Se, and Te also show
`reasonably good agreement. The electron-diffraction results for P,,
`As4, and 88, obtained since the table was formulated, provide a good
`check of the corresponding radii. 7
`
`1.5A
`
`....
`
`a: :I
`·� 1.0 -
`M � · Q Q)
`-; > 0
`0
`
`0.5 ,.....
`H 0
`
`0.0
`
`Fm. 7-1.-Values of covalent radii for the elements.
`
`.
`is more variable than that of other
`The radius of the hydrogen atom
`atoms, as can be seen from the experimental values for M-H dis­
`tances in compounds of hydrogen collected in Table 7-4. The values
`are reliable to about 0.01 A. The average value is about 0.30 A.
`The dependence of the covalent radii of the elements on atomic
`number is shown in Figure 7-1. The relation is a simple one; for
`
`7 One important assumption made in the original formulation of the table of
`.covalent radii was that the s-s single-bond distance ia 2.08 A, as in the crystals
`pyrite, Fe&, and hauerite, MnS2. This has been verified subsequently by meas­
`urements not only on Ss(c) and Ss(g) (Table 7-3) bu�· also on Ss(l) and Ss (plastic)
`(S-S .... 2.07 A, 2.08 A: N. S. Gingrich, Phys. Rev. SS, 236 [1939); J. Chem.
`Phys. 8, 29 [1940)), on H2Sa (S-S = 2.05 ± 0.02 A) and (CilahSa (S-S - 2.04
`± 0.03 A: D. P. Stevenson and J. Y. Beach, J.A.C.S. 60, 2872 [1938)), on
`(CHa)aSs (2.04 ± 0.02 A: J. Donohue and V. Schomaker, J. Chem. Phys. 16,
`92 [1948)), and on (CFshSa and (CFshSa (2.06 ± 0.02 A: H. J. M. Bowen,
`Trans. Faraday Soc. SO, 444, 452, 463 (1954]).
`
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`228
`
`I nteratomic Distances
`the first and second rows of the periodic table smooth curveEi can be
`drawn through the points, whereas for the other rows there is only a
`slight discontinuity between the quadrivalent atoms and their neigh­
`bors, which may be attributed to the change in the nature of the bond
`orbitals.8
`
`7-2. THE CORRECTION FOR ELECTRONEGATIVITY DIFFERENCE
`The first values of covalent radii, as given in Table 7-2