(Theoretical and computational chemistry 6) z b maksić and w j orville thomas (eds ) paulings legacy modem modelling of the chemical bond elsevier science (1999)

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THEORETICAL A N D C O M P U T A T I O N A L CHEMISTRY

Pauling’s Legacy
Modem Modelling of the Chemical Bond


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THEORETICAL AND COMPUTATIONAL CHEMISTRY

SERIES EDITORS

Professor P. Politzer

Professor Z.B. Maksi6

Department of Chemistry
University of New Orleans
New Orleans, LA 70418, U.S.A.

Rudjer Bos"kovi~Institute
P.O. Box 1016,
10001 Zagreb, Croatia

VOLUME 1
Quantitative Treatments of Solute/Solvent Interactions

P. Politzer and J.S. Murray (Editors)

VOLUME 2
Modern Density Functional Theory: A Tool for Chemistry
J.M. Seminario and P. Politzer (Editors)

VOLUME 3
Molecular Electrostatic Potentials: Concepts and Applications
J.S. Murray and K. Sen (Editors)

VOLUME 4
Recent Developments and Applications of Modern Density Functional Theory
J.M. Seminario (Editor)

VOLUME 5
Theoretical Organic Chemistry

C. Pdrkdnyi (Editor)
VOLUME 6
Pauling's Legacy: Modern Modelling of the Chemical Bond
Z.B. Maksic"and W.J. Orville-Thomas (Editors)


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O

THEORETICAL AND C O M P U T A T I O N A L CHEMISTRY

Pauling's Legacy
Modem Modelling of the Chemical Bond

Edited by
Z.B. M a k s i ~

Rudjer Bo~kovid. Institute
P.O. Box 1 0 1 6

Bijeni~ka 5 4
10001 Zagreb, Croatia
W.J. Orville-Thomas

Caer
Cae Melyn
Aberystwyth
Dyfed SY23 2HA, Wales,

UK

ELSEVIER
1999
Amsterdam - Lausanne - New York - Oxford - Shannon - S i n g a p o r e - Tokyo


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PREFACE

Theory and experiment in chemistry today provide a wealth of data, but such data
have no meaning unless they are correctly interpreted by sound and transparent physical
models. Linus Pauling was second to none in the modelling of molecular properties, as
we discuss later in the prologue to this book. Indeed, many of his models have served
chemistry for decades, and that has been his lasting legacy for chemists all over the world.
The aim of this book has been to put such simple models into the language of modern
quantum chemistry, thus providing a deeper justification for many of Pauling's ideas
and concepts. However, it should be stressed that many contributions to this book,
written by some of the world's most prominent theoretical chemists, do not merely follow
Pauling's footprints. By taking his example, they made bold leaps forward to overcome
the limitations of the old models thus opening new scientific vistas.
We are grateful for the effort, inspiration, care, and patience the authors have shown in
the preparation of their contributions to this book. We trust that this spirit of "Pauling's
legacy" will apeal to many chemists, both younger and older, in the areas ranging from
chemical physics to physical organic chemistry. We thank Mr.B. Kova~evi5 for some

technical help.

Z.B. Maksi5
W.J. Orville-Thomas

December 1998


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vii

TABLE

OF CONTENTS

Prologue:

The Chemical Bond on the Eve of the 21st Century ....................... X I X
Zvonimir B. Maksid and W. J. Orville - Thomas

Chapter 1. Theoretical Treatise on Molecular Structure and Geometry .............. 1
Jerzy Cioslowski
1.
2.

3.
4.

5.
6.
7.
8.

I n t r o d u c t i o n : T h e H i e r a r c h y of M o d e l s in C h e m i s t r y ......................... 1
M o l e c u l a r W a v e f u n c t i o n s ...................................................................... 3
D e c o u p l i n g of N u c l e a r and E l e c t r o n i c D e g r e e s of F r e e d o m ................. 4
The R e l e v a n c e of S p e c t r o s c o p i c States .................................................. 6
4.1. T i m e D e p e n d e n c e ........................................................................ 6
4.2. I n t e r a c t i o n s w i t h E x t e r n a l F i e l d s ............................................... 7
4.3. I n t e r m o l e c u l a r I n t e r a c t i o n s ....................................................... 8
D e s c r i p t i o n of M o l e c u l a r P h e n o m e n a with S p e c t r o s c o p i c and
L o c a l i z e d States .................................................................................... 11
T h e C o n c e p t of M o l e c u l a r G e o m e t r y .................................................. 13
T h e C o n c e p t of M o l e c u l a r S t r u c t u r e ................................................... 15
C o n c l u d i n g R e m a r k s ............................................................................ 16

Chapter 2. Beyond the Born-Oppenheimer Approximation ................................. 21
D. B. Kinghorn and L. Adamowicz
1. I n t r o d u c t i o n .......................................................................................... 21
2. E q u i v a l e n t T r e a t m e n t of N u c l e i and E l e c t r o n s
2.1. E x p l i c i t S e p a r a t i o n of the C e n t e r - o f - m a s s M o t i o n
( M e t h o d I) ................................................................................... 22
2.2. E f f e c t i v e N o n - a d i a b a t i c M e t h o d ( M e t h o d II) ........................... 25
3. G r o u n d - s t a t e W a v e f u n c t i o n ................................................................. 29
4. V a r i a t i o n a l C a l c u l a t i o n s ....................................................................... 31

5. S a m p l e A p p l i c a t i o n s ............................................................................. 37
5.1. E x p l i c i t S e p a r a t i o n of the C e n t e r - o f - m a s s M o t i o n in
V a r i a t i o n a l C a l c u l a t i o n s of E l e c t r o n Affinities of H-,
D- and T-. ................................................................................... 37
5.2. C a l c u l a t i o n on H D ~ with E f f ect i ve N o n - a d i a b a t i c
M e t h o d ....................................................................................... 39
6. G e n e r a l N - b o d y N o n - a d i a b a t i c W a v e f u n c t i o n .................................. 42
7. S u m m a r y ............................................................................................... 44

Chapter 3. The Mills-Nixon Effect: Fallacies, Facts and Chemical
Relevance .............................................................................................. 47
Zvonimir B. Maksi~, Mirjana Eckert-Maksi~, Otilia M6
and Manuel Yd~ez
1. I n t r o d u c t i o n .......................................................................................... 47


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2. The M i l l s - N i x o n Effect: The first E x p e r i m e n t a l R e s u l t and
T h e o r e t i c a l I n t e r p r e t a t i o n by S u t t o n and P a u l i n g .............................. 48
2.1. Definition of the M N - e f f e c t and some C o m m o n
Fallacies ..................................................................................... 49
3. Structural C o n s e q u e n c e s of the M N - E f f e c t ......................................... 53
3.1. The R o l e of R e h y b r i d i z a t i o n ..................................................... 53
3.2. The Role of 7t-Delocalization .................................................... 57
3.3. P a r a d i g m a t i c I n d a n and T e t r a l i n Cases ................................... 59
3.4. The Ring Size Effect .................................................................. 61
3.5. The Effect of the D o u b l e Bond and L o n e Pair(s) ..................... 67
3.6. Amplification of the M i l l s - N i x o n Effect .................................... 72

3.7. E x t e n d e d ~ - S y s t e m s : [ N ] p h e n y l e n e s .......................................... 75
4. R e v e r s e d M i l l s - N i x o n Effect ................................................................. 79
5. C h e m i c a l C o n s e q u e n c e s of the M i l l s - N i x o n Effect .............................. 85
5.1. E l e c t r o p h i l i c S u b s t i t u t i o n R e a c t i v i t y ........................................ 85
5.2. M i s c e l l a n e o u s P h y s i c a l and C h e m i c a l Properties .................... 94
6. C o n c l u d i n g R e m a r k s ............................................................................ 96

Chapter 4. Predicting Structures of Compounds in the Solid State by
the G l o b a l O p t i m i z a t i o n A p p r o a c h ................................................... 103
J.C. SchOn and M. Jansen
1.
2.
3.
4.

I n t r o d u c t i o n ........................................................................................ 103
T h e E n e r g y L a n d s c a p e ....................................................................... 105
T h e L i d - and the T r e s h o l d - a l g o r i t h m ............................................. 108
S t r u c t u r e P r e d i c t i o n at L o w T e m p e r a t u r e s ....................................... 110
4.1. G e n e r a l Aspects ....................................................................... 110
4.2. Specific O p t i m i z a t i o n A l g o r i t h m s ........................................... 111
4.3. Specific Empirical Potentials .................................................. 112
5. E x a m p l e s ............................................................................................. 114
6. C o n n e c t i o n s to Earlier Studies of the E n e r g y Surface of
C o m p l e x S y s t e m s ................................................................................ 123

Chapter 5. P o l a r i z a b i l i t y a n d H y p e r p o l a r i z a b i f i t y of Atoms and Ions ............... 129
David M. Bishop
1. Historic T i m e s ..................................................................................... 129
2. T h e P a p e r ............................................................................................ 131

3. S u r v e y of P o l a r i z a b i l i t y and H y p e r p o l a r i z a b i l i t y C a l c u l a t i o n s ........ 134
3.1. Static Dipole Polarizabilities (~) ............................................. 135
3.1.1. The He Isoelectronic Series ....................................... 136
3.1.2. The Ne Isoelectronic Series ....................................... 138
3.1.3. The Ar Isoelectronic Series ....................................... 138
3.2. Static D i p o l e H y p e r p o l a r i z a b i l i t i e s ......................................... 138
3.2.1. The H A t o m ............................................................... 139
3.2.2. The He Isoelectronic Series ....................................... 139
3.2.3. The Ne Isoelectronic Series ....................................... 139
3.2.4. The Ar Isoelectronic Series ....................................... 140


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3.3. D y n a m i c Dipole Polarizabilities and H y p e r p o l a r i z a b i l i t i e s . . . 141
3.3.1. T h e H A t o m ............................................................... 142
3.3.2. The He Isoelectronic Series ....................................... 142
3.3.3. The Ne and Ar I s o e l e c t r o n i c Series .......................... 143
4. C o n c l u s i o n s and O t h e r Aspects ........................................................... 143

Chapter 6. Molecular Polarizabilities and Magnetizabilities .............................. 147

P~I Dahle, Keneth Ruud, Trygve Helgaker and Peter R. Taylor
1. I n t r o d u c t i o n ........................................................................................ 147
2. M o l e c u l a r Properties as E n e r g y D e r i v a t i v e s ..................................... 149
3. M o l e c u l a r Properties in the D i a g o n a l R e p r e s e n t a t i o n of the
H a m i l t o n i a n ........................................................................................ 156
4. E x p l i c i t E x p r e s s i o n s for Electric and M a g n e t i c P r o p e r t i e s .............. 159

5. L o n d o n O r b i t a l s .................................................................................. 162
6. T h e C a l c u l a t i o n of M o l e c u l a r M a g n e t i z a b i l i t i e s :
C o m p a r i s i o n with E x p e r i m e n t ........................................................... 170
7. P a s c a l ' s Rule and G-Ring C u r r e n t s ................................................... 172
8. A r o m a t i c M o l e c u l e s and ~ - B o n d C u r r e n t s ....................................... 178
9. T h e P o l a r i z a b i l i t y of N o r m a l - and C y c l o - alkanes .......................... 179
10. The P o l a r i z a b i l i t y of P o l y a r o m a t i c H y d r o c a r b o n s ........................... 183
11. C o n c l u s i o n s ......................................................................................... 184

Chapter 7. The Concept of Electronegativity of Atoms in Molecules ................. 189

Juergen Hinze
1.
2.
3.
4.
5.
6.
7.

I n t r o d u c t i o n ........................................................................................ 189
P a u l i n g ' s Definition of E l e c t r o n e g a t i v i t y ........................................... 190
M u l l i k e n ' s Definition of E l e c t r o n e g a t i v i t y ......................................... 193
Orbital E l e c t r o n e g a t i v i t y and Electrical P o t e n t i a l ............................ 195
Orbital E l e c t r o n e g a t i v i t y V a l u e s ........................................................ 199
E l e c t r o n e g a t i v i t y E q u a l i z a t i o n and C h a r g e D i s t r i b u t i o n .................. 202
M o l e c u l a r P r o p e r t i e s .......................................................................... 204
7.1. B o n d L e n g t h s ........................................................................... 205
7.2. B o n d E n e r g i e s .......................................................................... 208
8. C o n c l u s i o n ........................................................................................... 210

Chapter 8. On Hybrid Orbitals in M o m e n t u m Space ......................................... 213

B. James Clark, Hartmut L. Schmider and Vedene H. Smith, Jr.
1. I n t r o d u c t i o n ....................................................................................... 1213
2. F o u r i e r T r a n s f o r m s of P o s i t i o n - s p a c e H y b r i d s ................................. 214
3. H y b r i d s in M o m e n t u m Space ............................................................. 215
3.1. H y b r i d s of the spa-Type ........................................................... 215
3.2. H y b r i d s I n v o l v i n g d-Orbitals .................................................. 217
4. M o m e n t s of the H y b r i d Orbitals ........................................................ 226
5. C o n c l u s i o n ........................................................................................... 228


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Chapter 9. Theory as a Viable Partner for Experiment- The Quest
for Trivalent Silylium Ions in Solution .............................................. 231
Carl-Henrik Ottosson, Elfi Kraka and Dieter Cremer
1. I n t r o d u c t i o n ........................................................................................ 231
1.1. W h y to Investigate S i l y l i u m Ions in Solution ? ...................... 232
1.2. C o n n e c t i o n to P a u l i n g ' s W o r k and Scope of the Article ....... 234
2. The N M R / a b i n i t i o / I G L O M e t h o d ................................................... 235
3. The S i l y l i u m Ion P r o b l e m ................................................................... 242
3.t. Properties of S i l y l i u m Ions in the Gas Phase .......................... 243
4. S i l y l i u m and C a r b e n i u m Ions in Solution. I n t e r a c t i o n
of S o l v e n t s and C o u n t e r i o n s ............................................................... 246
4.1. Definition of a Nearly Free Silylium Ion R3Si ~
in S o l u t i o n ................................................................................ 246
4.2. C a r b e n i u m Ions R 3 C + in Solution ........................................... 254
5. S o l v a t i o n of Neutral Silyl C o m p o u n d s R3SiX and

S i l y l i u m Ions R3Si +.............................................................................. 256
5.1. N e u t r a l S i - c o m p o u n d s in S o l u t i o n ......................................... 257
5.2. Specific C o m p l e x a t i o n of R3Si + by
Nucleophilic Solvent Molecules .............................................. 258
5.3. C o u n t e r i o n s used in R e s e a r c h on R3Si ~ a n d
R 3 C ~- Ions in S o l u t i o n .............................................................. 260
6. Structure D e t e r m i n a t i o n of Silyl Cations in S o l u t i o n ....................... 262
6.1. S t r u c t u r e D e t e r m i n a t i o n by the
N M R / a b i n i t i o / I G L O M e t h o d ................................................. 263
7. I n t r a m o l e c u l a r Solvation of S i l y l i u m Ions ......................................... 266
7.1. Strong I n t r a m o l e c u l a r S o l v a t i o n of Silyl Cations .................. 267
7.2. W e a k I n t r a m o l e c u l a r Solvation of S i l y l i u m Ions ................... 272
8. A p p r o a c h i n g a nearly Free S i l y l i u m Ion in S o l u t i o n ......................... 277
8.1. T r i a l k y l s i l y l i u m Ions in A r o m a t i c Solvents ............................ 277
8.2. Silyl Substituted S i l y l i u m Ions in Solution ............................. 281
8.3. D i a l k y l b o r y l Substituted S i l y l i u m Ions in S o l u t i o n ................ 284
9. The S o l u t i o n of the P r o b l e m : First G e n e r a t i o n of a
Free S i l y l i u m Cation in C o n d e n s e d Phases ....................................... 287

Chapter 10. Bond Energies, Enthalpies of Formation, and Homologies:
The Energetics of Aliphatic and Alicyclic Hydrocarbons and
some of their Derivatives ................................................................... 303
Suzanne W. Slayden and Joel F. Liebman
1. T e t r a c o o r d i n a t i o n , T e t r a h e d r a l G e o m e t r y and
H y b r i d i z a t i o n ..................................................................................... 303
2. The N u m b e r of C o m p o u n d s and the N e c e s s i t y for
I n t e r c o n n e c t i o n s , H o m o l o g i e s and H o m o l o g o u s Series ................... 304
3. H o m o l o g o u s Series: The 1-Substituted Alkanes ............................... 304
4. H o m o l o g o u s Series: C y c l o a l k a n e s ..................................................... 310
5. H o m o l o g o u s Series: Saturated P o l y c y c l i c H y d r o c a r b o n s ................ 310

6. T e t r a h e d r a n e and [ 1.1. l ] P r o p e l a n e .................................................. 312


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6.1. T e t r a h e d r a n e ........................................................................... 313
6.2. [ 1 . 1 . 1 ] P r o p e l l a n e ...................................................................... 315

Chapter 11. Stabilization and Destabilization Energies of Distorted Amides ..... 321
Arthur Greenberg and David T. Moore
1. I n t r o d u c t i o n ....................................................................................... 321
1.1.
1.2.
1.3.
1.4.
1.5.

C h e m i c a l I m p l i c a t i o n s of S t r a i n e d A m i d e s and L a c t a m s ..... 321
B i o l o g i c a l I m p l i c a t i o n s ............................................................ 322
Effects of D i s t o r t i o n on A c i d / B a s e P r o p e r t i e s ........................ 323
D e f i n i n g D i s t o r t i o n of the A m i d e L i n k a g e ............................. 323
L a r g e r B r i d g e h e a d B i c y c l i c L a c t a m s : Are T h e y
H y p e r s t a b l e ? ............................................................................ 324
2. B a c k g r o u n d ........................................................................................ 325
2.1. E n e r g e t i c s of D i s t o r t e d L a c t a m s ............................................. 325
2.2. B o n d i n g in L a c t a m s : Is there Still a R o l e for
R e s o n a n c e ? .............................................................................. 326
2.3. P r o t o n Affinities of B r i d g e h e a d B i c y c l i c L a c t a m s :

N vs. O ..................................................................................... 327
2.4. State of C a l c u l a t i o n a l Studies of D i s t o r t e d A m i d e
L i n k a g e s ................................................................................... 328
3. C o m p u t a t i o n a l S t u d i e s ...................................................................... 328
3.1. M o l e c u l a r M e c h a n i c s .............................................................. 328
3.2. Ab initio C a l c u l a t i o n s ............................................................. 334
3.3. S e m i - e m p i r i c a l R e s u l t s ............................................................ 337
4. S u m m a r y ............................................................................................ 343

Chapter 12. Some Chemical and Structural Factors Related to
the Metastabilities of Energetic Compounds ................................... 347
Peter Politzer and Jane S. Murray
1. I n t r o d u c t i o n ....................................................................................... 347
2. I m p a c t / S h o c k S e n s i t i v i t y and M o l e c u l a r St ruct ure:
S o m e B a c k g r o u n d ............................................................................ 348
2.1. S t r u c t u r e - sensitivity R e l a t i o n s h i p ........................................ 348
2.2. S o m e Specific D e c o m p o s i t i o n P a t h w a y s ................................. 349
3. R e l a t i o n s h i p s B e t w e e n I m p a c t Sensitivities and
M o l e c u l a r S u r f a c e E l e c t r o s t a t i c P o t e n t i a l s ...................................... 351
3.1. A n a l y s i s and C h a r a c t e r i z a t i o n of S u r f a c e P o t e n t i a l s ............ 351
3.2. U n s a t u r e t e d C - N i t r o D e r i v a t i v e s : N i t r o a r o m a t i c s and
N i t r o h e t e r o c y c l e s ..................................................................... 352
3.3. I m p a c t S e n s i t i v i t y and S u r f a c e P o t e n t i a l I m b a l a n c e ............. 354
4. S u m m a r y ............................................................................................ 358

Chapter 13. Valence Bond Theory: A Re-examination of Concepts and
Methodology ...................................................................................... 365
Roy Mc Weeny
1. I n t r o d u c t i o n ....................................................................................... 365

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2. T h e E l e c t r o n - p a i r B o n d : S o m e P r e l i m i n a r i e s ..................................
3. C l a s s i c a l VB T h e o r y : P e r f e c t - p a i r i n g and R e s o n a n c e .....................
3.1. S y m m e t r y C o n s i d e r a t i o n s .......................................................
3.2. C a l c u l a t i o n of the E n e r g y ........................................................
4. T h e Rise and Fall of C l a s s i c a l VB T h e o r y ........................................
5. M o d e r n VB T h e o r y ...........................................................................
5.1. VB T h e o r y w i t h O r t h o g o n a l O r b i t a l s .....................................
5.2. T h e " N i g h t m a r e of the I n n e r S h e l l s " . .....................................
5.3. VB T h e o r y with N o n - o r t h o g o n a l O r b i t a l s ..............................
5.4. C o n n e c t i o n w i t h O t h e r M e t h o d s .............................................
6. S o m e I l l u s t r a t i v e A p p l i c a t i o n s ..........................................................
6.1. T h e W a t e r M o l e c u l e ................................................................
6.2. M e t h y l l i t h i u m ..........................................................................
6.3. L i t h i u m F l u o r i d e .....................................................................
6.4. B e n z e n e and Its Ions ................................................................
7. C o n c l u s i o n ..........................................................................................

365
371
372
376
380
383
383
384

387
389
392
392
394
394
396
397

Chapter 14. Advances in Many-body Valence-bond Theory ............................... 403
Douglas J. Klein
1.
2.
3.
4.

I n t r o d u c t o r y S u r v e y ..........................................................................
VB T h e o r y : Bases, M o d e l s , & R e s o n a n c e .........................................
M a n y - b o d y T h e o r y ............................................................................
M a n y - b o d y T e c h n i q u e s for VB M o d e l s ............................................
4.1. C o n f i g u r a t i o n I n t e r a c t i o n .......................................................
4.2. M a n y - b o d y P e r t u r b a t i o n T h e o r y ............................................
4.3. C l u s t e r and M o m e n t M e t h o d s ................................................
4.4. S p i n - w a v e s and G r e e n ' s F u n c t i o n s .........................................
4.5. W a v e - f u n c t i o n C l u s t e r E x p a n s i o n ..........................................
4.6. M o n t e C a r l o C o m p u t a t i o n s .....................................................
4.7. R e n o r m a l i z a t i o n - g r o u p T e c h n i q u e s ........................................
4.8. M i s c e l l a n y ................................................................................
5. O v e r v i e w and P r o s p e c t s ....................................................................

403
405
407
409
409
410
411
411
412
413
413
413
414

Chapter 15. Ab Initio Valence Bond Description of Diatomic Dications ............ 423
Harold Basch, Pinchas Aped, Shmaryahu Haz and Moshe
Goldberg
1. I n t r o d u c t i o n ....................................................................................... 424
2. He2 + .................................................................................................. 426
3. 022+ .....................................................................................................
428
4. N F 2+.................................................................................................... 433
5. S u m m a r y ........................................................................................... 438

Chapter 16. One-electron and Three-electron Chemical Bonding, and
Increased-Valence Structures ........................................................... 449
Richard D. Harcourt
1. I n t r o d u c t i o n ....................................................................................... 449

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2. The O n e - e l e c t r o n B o n d ..................................................................... 450
3. The O n e - e l e c t r o n B o n d and N o n - p a i r e d Spatial
O r b i t a l S t r u c t u r e s ............................................................................. 452
4. A T h e o r e m ......................................................................................... 454
5. The T h r e e - e l e c t r o n Bond, or T h r e e - e l e c t r o n H a l f - b o n d ................. 454
5.1. P a r a m a g n e t i c Electron Rich M o l e c u l e s and M o l e c u l a r
Ions that I n v o l v e A t o m s of M a i n - g r o u p E l e m e n t s ................. 456
5.2. H y p o l i g a t e d Transition Metal C o m p l e x e s , such as
High-spin (S=2) [Fe(H20)6] a+ .................................................. 456
5.3. F+-type C o l o u r Centers ............................................................ 457
5.4. n - T y p e S e m i c o n d u c t o r s ........................................................... 458
5.5. C o n d u c t i o n in Alkali Metals in the Solid State ...................... 458
6. Instability of T h r e e - e l e c t r o n Bonds .................................................. 458
7. The T h r e e - e l e c t r o n B o n d with F o u r or M o r e A O s .......................... 460
8. T h r e e - e l e c t r o n B o n d s and I n c r e a s e d - v a l e n c e Structures for
F o u r - e l e c t r o n T h r e e - c e n t r e B o n d i n g ................................................ 462
9. I n c r e a s e d - v a l e n c e Structures and M u l l i k e n - D o n o r acceptor C o m p l e x e s ........................................................................... 464
10. I n c r e a s e d - v a l e n c e Structures and SN2 Reactions ............................. 465
11. T h r e e - E l e c t r o n B o n d s and F i v e - e l e c t r o n T h r e e - c e n t r e
B o n d i n g .............................................................................................. 466
12. T h r e e - E l e c t r o n B o n d s and I n c r e a s e d - v a l e n c e Structures
for E x t e n d e d S i x - e l e c t r o n F o u r - c e n t r e B o n d i n g .............................. 469
13. T h r e e - e l e c t r o n B o n d s and I n c r e a s e d - v a l e n c e Structures
for Cyclic Six-electron Four-centre B o n d i n g .................................. 473
14. T h r e e - e l e c t r o n B o n d s and C o v a l e n t - i o n i c R e s o n a n c e ..................... 475
15. Conclusions ........................................................................................ 477

Chapter 17. Valence Bond Description of ~-Electron Systems ............................ 481
Joseph Paldus and X. Li
1.
2.
3.
4.

I n t r o d u c t i o n ....................................................................................... 481
P P P - t y p e H a m i l t o n i a n s ..................................................................... 483
PPP-VB M o d e l .................................................................................. 486
A p p l i c a t i o n s ....................................................................................... 488
4.1. C o r r e l a t e d G r o u n d States, Basic T r a n s f e r a b i l i t y
and The R o l e of Ionic Structures ............................................ 488
4.2. Spin P r o p e r t i e s ........................................................................ 490
4.3. Electron Delocalization, R e s o n a n c e and B o n d L e n g t h
A l t e r n a t i o n .............................................................................. 492
4.4. Excited States ........................................................................... 493
4.5. VB C o r r e c t e d C o u p l e d C l u s t e r M e t h o d ................................. 493
4.6. Ionization Potentials and Electron Affinities .......................... 494
5. Conclusions ........................................................................................ 495


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Chapter 18. The Spin-coupled Description of Aromatic, Antiaromatic and
Nonaromatic Systems ........................................................................ 503
David L. Cooper, Joseph Gerratt and Mario Raimondi

1.
2.
3.
4.
5.
6.

I n t r o d u c t i o n .......................................................................................
S p i n - c o u p l e d W a v e f u n c t i o n s ............................................................
B e n z e n e ..............................................................................................
C y c l o b u t a d i e n e ..................................................................................
C y c l o o c t a t e t r a e n e ...............................................................................
C o n c l u s i o n s ........................................................................................

503
505
507
511
514
514

Chapter 19. Aromaticity and Its Chemical Manifestations ................................. 519
Keneth B. Wiberg
1. H i s t o r i c a l P r e l u d e .............................................................................. 519
2.
3.
4.
5.

V a l e n c e B o n d vs. M o l e c u l a r O r b i t a l T h e o r y ....................................

M a n i f e s t a t i o n s o f " A r o m a t i c " S t a b i l i z a t i o n .....................................
S i g m a C o n t r i b u t i o n to the G e o m e t r y o f B e n z e n e ............................
M a g n e t i c P r o p e r t i e s ..........................................................................
6. O r i g i n of the S t a b i l i z a t i o n o f B e n z e n e ..............................................
7. H e t e r o c y c l i c A r o m a t i c S y s t e m s ........................................................
8. S u m m a r y ...........................................................................................

521
523
527
529
532
532
533

Chapter 20. Hypercoordinate Bonding to Main Group Elements: The
Spin-coupled Point of V i e w ............................................................... 537
David L. Cooper, Joseph Gerratt and Mario Raimondi
1. I n t r o d u c t i o n ....................................................................................... 537
2. d - O r b i t a l P a r t i c i p a t i o n V e r s u s D e m o c r a c y ..................................... 538
3. H y p e r c o o r d i n a t e B o n d i n g to F i r s t - r o w A t o m s ................................ 543
3.1. 1.3-Dipoles ................................................................................ 543
3.2. O x o h a l i d e s of H y p e r c o o r d i n a t e N i t r o g e n and P h o s p h o r o u s 547
4. F u r t h e r E x a m p l e s .............................................................................. 548
4.1. O x o f l u o r i d e s of H y p e r c o o r d i n a t e S u l f u r ................................ 548
4.2. C h l o r i n e F l u o r i d e s and C h l o r i n e O x i d e F l u o r i d e s ................. 550
4.3. F l u o r o p h o s p h o r a n e s ................................................................ 550
4.4. Y X X Y D i h a l i d e s and D i h y d r i d e s of D i o x y g e n and Disulfur..551
5. C o n c l u s i o n s ........................................................................................ 551

Chapter 21. The Electronic Structure of Transition Metal Compounds ............. 555
Gernot Frenking, C. Boehme and U. Pidun
1. I n t r o d u c t i o n ....................................................................................... 555
2. C o m p u t a t i o n a l D e t a i l s ...................................................................... 556
3. R e s u l t s and D i s c u s s i o n ...................................................................... 558
3.1. C h e m i c a l B o n d i n g in [(CO)sW-A1CI(NH3)2] a n d
[(CO)sW-A1C1] ........................................................................ 558
3.2. T h e Series [(CO)sW-XCI(NH3)2] (X = B,A1,Ga,In,T1) ........... 562
3.3. T h e series [ ( C O ) s W - Y ] (Y = [SiC12(NH3)], [A1CI(NH3)2],
[Mg(NH3)3], [Na(NH3)3]) ......................................................... 565


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4. S u m m a r y and C o n c l u s i o n s ............................................................... 568

Chapter 22. Fundamental Features of Hydrogen Bonds ..................................... 571
Steve Scheiner
1. I n t r o d u c t i o n ....................................................................................... 571
2.
3.
4.
5.

H y d r o g e n B o n d i n g S t r e n g t h .............................................................
C o n t r i b u t i o n of E l e c t r o s t a t i c s ...........................................................
R e l a t i o n s B e t w e e n V a r i o u s P r o p e r t i e s .............................................
C o o p e r a t i v i t y .....................................................................................

5.1. G e o m e t r i e s ...............................................................................
5.2. E n e r g e t i c s .................................................................................
5.3. V i b r a t i o n a l S p e c t r a .................................................................
5.4. E n e r g y C o m p o n e n t s ................................................................
6. S u m m a r y ...........................................................................................

572
574
578
581
582
584
585
586
589

Chapter 23. Molecular Similarity and Host-guest Interactions ........................... 593
Paul G. Mezey
1.
2.
3.
4.

I n t r o d u c t i o n ....................................................................................... 594
F r o m F u n c t i o n a l G r o u p s to E x t e n d e d M o l e c u l a r R e g i o n s .............. 596
E l e m e n t s of E l e c t r o n D e n s i t y S h a p e A n a l y s i s .................................. 600
E l e c t r o n D e n s i t y A n a l y s i s o f I s o l a t e d and I n t e r a c t i n g
R e a c t i v e R e g i o n s of M o l e c u l e s .......................................................... 602
5. S h a p e S i m i l a r i t y M e a s u r e s in the S t u d y of H o s t - g u e s t
I n t e r a c t i o n s ........................................................................................ 607

6. S u m m a r y ........................................................................................... 609

Chapter 24. Chemical Bonding in Proteins and Other Macromolecules ............ 613
Paul G. Mezey
1. I n t r o d u c t i o n ....................................................................................... 614
2. M a c r o m o l e c u l a r Q u a n t u m C h e m i s t r y B a s e d on
A d d i t i v e F u z z y D e n s i t y F r a g m e n t a t i o n ( A F D F ) .............................. 616
3. " L o w D e n s i t y G l u e " ( L D G ) B o n d i n g in P r o t e i n s ............................. 624

Chapter 25. Models for Understanding and Predicting Protein Structure ......... 637
Dale F. Mierke
1. I n t r o d u c t i o n .......................................................................................
2. M e t h o d s .............................................................................................
2.1. H o m o l o g y M o d e l l i n g ...............................................................
2.2. S e c o n d a r y S t r u c t u r e P r e d i c t i o n ..............................................
2.3. P r i m a r y to T e r t i a r y P r e d i c t i o n ...............................................
2.4. E n e r g e t i c F o r c e F i e l d s .............................................................
2.5. R e d u c e d A t o m R e p r e s e n t a t i o n ................................................
2.6. R e d u c e d C o n f o r m a t i o n a l S p a c e / L a t t i c e M o d e l s ....................
3. C o n c l u s i o n s ........................................................................................

637
640
641
643
644
645
646
649
650

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Chapter 26. Possible Sources of Error in the Computer Simulation
of Protein Structures and Interactions ............................................. 655
J.M. Garcia de la Vega, J.M.R. Parker and Serafin Fraga
1.
2.
3.
4.

I n t r o d u c t i o n ....................................................................................... 655
Deficiencies of Potential E n e r g y Functions ...................................... 656
C o n f o r m a t i o n a l C h a r a c t e r i z a t i o n .................................................... 658
C o n c l u s i o n s ........................................................................................ 661

Chapter 27. The Nature of Van der Waals Bond ................................................. 665
Grzegorz Chalasinski, Malgorzata M. Szczesniak and Slawomir M.
Cybulski
1.
2.
3.
4.

I n t r o d u c t i o n ......................................................................................... 66
5
F u n d a m e n t a l I n t e r a c t i o n E n e r g y C o m p o n e n t s ............................... 666

Ab Initio A p p r o a c h to I n t e r m o l e c u l a r F o r c e s ................................. 667
4.1. E x c h a n g e R e p u l s i o n versus M o l e c u l a r Shape ........................ 670
4.2. D i s p e r s i o n as the I n t e r m o n o m e r C o r r e l a t i o n Effect .............. 673
4.3. I n d u c t i o n , C h a r g e - t r a n s f e r and S C F D e f o r m a t i o n ............... 675
4.4. E x a m p l e 1. Ar-CO2: Dispersion B o u n d C o m p l e x .................. 676
4.5. E x a m p l e 2. W a t e r D i m e r : I n t r o d u c i n g E l e c t r o s t a t i c s ........... 679
4.6. G e n e r a l C o n s i d e r a t i o n s ........................................................... 682
5. M o d e l l i n g of PES and its C o m p o n e n t s ............................................. 682
5.1. A r - C O 2 ..................................................................................... 683
5.2. W a t e r D i m e r ............................................................................ 684
6. T r i m e r s and N o n a d d i t i v e Effects ...................................................... 687
6.1. A r 2 - C h r o m o p h o r e Clusters: E x c h a n g e and D i s p e r s i o n
N o n a d d i t i v i t y ........................................................................... 688
6.2. W a t e r T r i m e r : I n d u c t i o n N o n a d d i t i v i t y ................................ 695
7. S u m m a r y ........................................................................................... 696

Chapter 28. The Nature of the Chemical Bond in Metals, Alloys, and
Intermetallic Compounds According to Linus Pauling ................... 701
Zelek S. Herman
1.
2.
3.
4.

I n t r o d u c t i o n ....................................................................................... 701
Q u a n t u m M e c h a n i c s and the N a t u r e of M e t a l s ............................... 703
T h e M e t a l l i c Orbital .......................................................................... 705
The D e t a i l e d A n a l y s i s of the Statistical T h e o r y of
U n s y n c h r o n i z e d R e s o n a n c e of C o v a l e n t Bonds ............................... 710
5. C a l c u l a t i o n of the N u m b e r of M e t a l l i c Orbitals per A t o m

from the Statistical T h e o r y of the U n s y n c h r o n i z e d
R e s o n a n c e of C o v a l e n t Bonds ........................................................... 715
6. T h e C r y s t a l S t r u c t u r e s of the M e t a l s and the M a x i m u m
Values of the metallic V a l e n c e .......................................................... 718
7. The C o m p i l a t i o n of M e t a l l i c S i n g l e - b o n d Radii and Radii
for L i g a n c y 12 .................................................................................... 722


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8. The Structure and P r o p e r t i e s of E l e m e n t a l Boron. Is it
a M e t a l ? ............................................................................................. 724
9. The Nature of the M e t a l - M e t a l B o n d in Alloys, I n t e r m e t a l l i c
C o m p o u n d s , and on the Surfaces of Alloys ...................................... 726
10. S u p e r c o n d u c t i v i t y I n t e r p r e t e d in T e r m s of the
U n s y n c h r o n i z e d - r e s o n a t i n g - c o v a l e n t - b o n d T h e o r y of Metals ........ 732
11. Conclusions ........................................................................................ 738

Epilogue:

Linus Pauling, Quintessential Chemist ............................................ 749
Dudley Herschbach

Index

............................................................................................................

755

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PROLOGUE
T h e C h e m i c a l B o n d o n t h e E v e of t h e 21st C e n t u r y

Zvonimir B. Maksi5 and W.J. Orville-Thomas
Linus Pauling is rated as the most prominent American scientist and the greatest
chemist of this century. To some people he was Moses who has led chemists to the
promised land, whereas others imagined him as the mythical Prometheus who brought
quantum mechanical fire to classical chemistry. One thing is beyond doubt - nobody
made so many important discoveries in so many different branches of chemistry and related disciplines as Linus Pauling. As Dudley Herschbach put it at the end of this book, he
was the quintessential chemist. The younger generation considered him, like his grandson
Alexander Kamb, as a force of nature. The latter is also the title of an excellent biography
skilfully written by Thomas Hager [1].
This book is dedicated to Pauling and his work focusing on the chemical bond. It is,
therefore, appropriate to begin with Pauling's own words: "The concept of the chemical
bond is the most valuable concept in chemistry. Its development over the past 150 years
has been one of the greatest triumphs of the human intellect. I doubt that there is
a chemist in the world who does not use it in his or her thinking. Much of modern
science and technology has developed because of the existance of this concept" [2]. This
is perfectly true: the chemical bond is one of the three most important cornerstones of
classical chemistry, together with the notion of atoms in chemical environments and the

idea of molecular structure and geometry. The latter reflects a multitude of properties
of molecules stored in their structural parameters, size, shape and symmetry. These
classical pillars received a proper interpretation and physical meaning from quantum
mechanics with one notable exception - molecular structure - which still poses a problem
not rigorously solved as yet from first principles. Many researchers have contributed to this
remarkable progress over many decades, and one could characterize the development of
quantum chemistry as a permanent crawling revolution in molecular sciences particularly
taking into account recent advances in computational chemistry. Linus Pauling was,
however, the pioneer and champion of quantum chemistry in the pre-computer era. It
took a genius and a vivid imagination to tackle intricate and perplexing chemical problems
by using a slide rule and to make tremendous leaps in understanding chemical bonding,
which has substantionally contributed to dramatic growth in the life sciences that we have
witnessed in recent years.
By using his astonishing ability to reduce the complex to the simple, Pauling shed light
on the architecture of molecules and crystals. He explained the directional properties of
covalent bonds in an elegant way by introducing polarized local hybrid (chemical) orbitals
and inaugurated the concept of resonance within the classical valence bond (VB) theory,
which in turn is undergoing a remarkable renaissance. Pauling was the first to establish
a quantitative electronegativity scale thus enabling a simple description of charge distributions in molecules and providing a rationalization of the ionic component of chemical
bonding. Combining resonance with the electrostatic interactions, Pauling discovered the
important role of hydrogen bonding in determining weak intra- and intermolecular interactions. These interactions proved crucial in understanding essential features of molecules


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of life to mention only proteins. His work on the nature of the peptide bond and on the
structural patterns of proteins in terms of alpha helices and beta-pleated sheets are milestones in the development of biochemistry and molecular biology. Instead of listing all
discoveries and work which stimulated others to unravel the secrets of Nature - to single

out only the Crick-Watson model of DNA as an enlightening example - we shall succintly
say that he erected a more lasting scientific monument than those made of brass or stone.
Pauling was a grand master of modelling in science. His models were very simple,
reflecting the quintessence of a phenomenon or property under scrutiny and satisfying
the Occam razor principle at the same time. They provide a qualitative understanding
of the fundamental principles of chemical structure, bonding and reactivity, thus serving
as a guide in the research process. These models are close to chemical intuition by
building bridges between a rich chemical experience on one side and rigorous quantum
mechanics on the other [3]. It should be stressed that Pauling's models did not only have
a heuristic value, but also provided important semiquantitative information on a variety
of molecular properties in the pre-computer age. They involve elementary, back of the
envelope, calculations, illustrating in the highest sense of the word van't Hoff's statement
that imagination and shrewed guess work are powerful instruments in acquiring scientific
knowledge. The success of the Pauling's approach is best described by the Figure below,
where the accuracy of theoretical models in reproducing a particular property of a very
large compound or system of chemical interest is schematically plotted against the rigour
of the applied theoretical procedures:

ca.
true
value

~

~

/

f

Pauling Ph.D.
point
point

Figure

~

rigour approaching
full theory
postdoctoral
result


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xxi
This curve possesses several characteristic maxima and minima asymptotically approaching the exact value for the full theory. The first maximum corresponds to the
Pauling point, where a simple and transparent physical model gives insight and reasonable
agreement with experiment by focusing on the dominant effect(s) only. The quantitative
description requires a much more sophisticated theoretical approach and meticulous calculations. It should be emphasized, however, that simple conceptual models have led
to great discoveries in the molecular sciences, which cracked some very important codes
of nature, more frequently than the exact theories and detailed calculations. The latter
usually came in the a posteriori stage to confirm that a bold hypothesis was correct.
Not all of Pauling's models and concepts were new and original. For instance, the
electronegativity idea dates back to Avogadro and Berzelius in the beginning of the 19th
century [4]. However, he gave to many of them a deeper meaning and showed their chemical relevance by utilizing his encyclopedic knowledge. His views on chemical bonding were
summarized in a superb landmark book "The Nature of the Chemical Bond" [5], which
inspired generations of chemists. It is frequently cited as one of the most influential scientific books of our century. This is not surprising because well established models provide
in general a scientific vocabulary and lend themselves to classification purposes. They

give a pervasive physical insight and extract the key features of very complex phenomena,
thus revealing their essence and simplicity. It should be stressed that reliable models
possess a grain of truth, which is not always realised. They are true within the limits of
the approximations involved and within a carefully determined range of applicability - no
more but, at the same time, no less. Metaphorically speaking, models extend the range
of our senses and make it possible to "see" mentally what cannot be seen [6].
In the meantime, breakthroughs in tackling molecular many-body problems by computational quantum chemistry based on new theoretical schemes, novel numerical methods
and the dramatically fast development of computer technology made possible quantitative description of versatile chemical bonding phenomena comparable to that offered by
experiments. It is timely to give a modern, present-day, theoretical description to many
of the apparently successful Pauling models and seminal ideas and to present a refined
interpretation of many subtle effects, which were not amenable to theoretical analysis
earlier. Coverage of the recent advances in modelling of chemical bonding is therefore
the main task of this book written by some of the most prominent experts in the field.
Chapters on the molecular structure, geometries of fused aromatics and their electrophilic
reactivity, bond energy, electronegativity, hybridization, aromaticity, contemporary VB
methods, hydrogen bonding and the structure of the proteins and other large biological
compounds reflect much of the leading current thinking. They are prepared by carefully
avoiding dangers of the Scylla of intricacy and the Charybdis of oversimplification and by
putting a considerable emphasis on the interpretation of theoretical results.
It can be stated safely that most of Pauling's models have stood the test of time and
found rigorous justification. However, it should be pointed out strongly that many authors, by building on Pauling's ideas and by standing on his shoulders, overcame the
limitations of the old, crude and sometimes fully empirical models by making bold steps
forward thus expanding the frontiers of molecular sciences. Although such a book is
never complete, it is our belief and hope that it will contribute to better understanding of the ubiquitous chemical bond and become an indispensable textbook for post-


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xxii
graduate/doctoral students in physical and advanced physical organic chemistry. It is

important to point out in this connection that quantum chemistry - the Holy Grail of
molecular sciences - will have an ever-increasing role in the 21st century particularly in
establishing strong links between chemistry and molecular biology and thus featuring as
a unifying methodology.
Finally, we would like to use this opportunity to thank all authors for their scholarly
written and intellectually stimulating chapters, which made this book possible.
REFERENCES
1.
2.
3.

4.
5.
6.

T. Hager, Force of Nature - The Life of Linus Pauling, Simon & Schuster, New York,
NY, 1995.
L. Pauling, The Nature of the Chemical Bond - 1992, J. Chem. Ed., 69 (1992) 519.
Z.B. Maksi(~, On the Significance of Theoretical Models of Chemical Bonding- Prologue to the Special Subject Issue on Conceptual Quantum Chemistry: Models and
Applications, Part 1, Croat. Chem. Acta 57 (1984) No. 5.
W.B. Jensen, Electronegativity from Avogadro to Pauling, J. Chem. Ed., 73 (1996)
11.
L. Pauling, The Nature of the Chemical Bond and the Structure of Molecules and
Crystals, Third Ed., Cornell University Press, 1960.
Z.B. MaksiS, Modelling - A Search for Simplicity, in Theoretical Models of Chemical
Bonding, Vol. 1, Z.B. MaksiS, Ed., Springer Verlag, Berlin- Heidelberg, 1990, p. 13.


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Z.B. Maksid and W.J. Orville-Thomas (Editors)
Pauling's Legacy: Modern Modelling of the Chemical Bond
Theoretical and Computational Chemistry, Vol. 6
9 1999 Elsevier Science B.V. All rights reserved.

THEORETICAL TREATISE ON MOLECULARSTRUCTURE AND GEOMETRY
Jerzy Cios lowski
Department of Chemistry and Supercomputer Computations Research I n s t i t u t e ,
,

Florida St a t e University, Yallahassee, F l o r i d a 32306-3006, USA

1. INTRODUCTION: THE HIERARCHY OF MODELS IN CHEMISTRY
The primary o b j e c t i v e of modern science
f a i t h f u l l y describe the r e a l i t y .
subject

to perpetual

tency.

When a p a r t i c u l a r

reasons.

is

to construct

theories

that

Theories are nothing but models that are

experimental

s c r u t i n y and checks of i n t e r n a l

theory is abandoned,

it

consis-

is for one of several

Some t h e o r i e s , such as those of f l o g i s t o n and c a l o r i c , are simply

proven wrong.

Others,

such as the g e o c e n t r i c theory of the unive rs e ,

superseded by simpler d e s c r i p t i o n s

of r e a l i t y .

Finally,

are

some formalisms

(such as the Newtonian mechanics) are found to possess only a limited val i d i t y or to c o n s t i t u t e special cases of more general ( u n i f i e d ) t h e o r i e s .
In this r e s p e c t , chemistry does not d i f f e r from other sciences.

Contem-

porary chemical research is organized around a hierarchy of models that aid
its practitioners
phenomena.

in t h e i r everyday quest for the understanding of n a t u r a l

The building blocks of the language of chemistry, including the

representations

of molecules

in terms of s t r u c t u r a l

the very bottom of this h i e r a r c h y .
as

reaction

etc.

[2],

types and mechanisms,

come next.

formulae

[1],

occupy

Various phenomenological models, such
thermodynamics and chemical

Quantum chemistry, which at present

kinetics,

is the supreme

theory of e l e c t r o n i c s t r u c t u r e s of atoms and molecules, and thus of the ent i r e realm of chemical phenomena, resides at the very top.

This research was supported by the National Science Foundation under the
grant CHE-9632706.

E-mail address: , web page:

ht tp: //www. scr i. fsu. edu/~j erzy.

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2

Being first formulated in the second half of the nineteenth century, the
concept of molecular structure has evolved from a working hypothesis to the
major tenet of chemistry by the time of the advent of modern quantum mechanics. At last, the new theory provided the means for predicting and explaining properties of atoms and molecules. However, with its description
of matter that was (and still is) alien to many chemists conditioned by the
experiences in the macroscopic world, the new theory stood little chance of
displacing the existing models of chemical species and their transformations. Consequently, peculiar hybrid formalisms that invoke conventional
chemical notions dressed up in the language of quantum mechanics have soon
emerged. These formalisms, which are collectively known as the electronic
structure theory, are in use t o this day.
Modern electronic structure theory employs two levels of simplification.
The use of various mathematical approximations is dictated by the limitations of computer hardware and the need for keeping the cost of quantumchemical calculations within reasonable limits. In contrast, the avoidance
of quantum-mechanical treatment of nuclei i s deeply rooted in the aforementioned conceptual prejudices. While the severity of mathematical approximations is on a constant decrease thanks to the ever-increasing speed and
availability of computers (note the gradual disappearance of semiempirical
calculations from the chemical literature!), the validity of views that
regard molecules as quasi-rigid assemblies of nuclei held together by
electron clouds is rarely questioned by the majority of researchers.
Twenty years have passed since the publication of the original paper by
Woolley [3] in which the incompatibility of the molecular structure concept
with the rigorous quantum-mechanical description of isolated molecules has
been eloquently brought to the attention of chemists. The ensuing flurry
of research publications clarified several misconceptions but did little to
familiarize the broader scientific audience with this important issue.
Regretfully, few quantum or computational chemists are aware of these
papers, which are nowadays seldom discussed or quoted.

This short treatise is intended to provide the reader with a concise
summary of the current theoretical status of the molecular structure and
geometry concepts. A fully quantum-mechanical treatment of molecules is
employed where necessary. The relevance of stationary states of isolated
molecules is discussed and the notion of molecular geometry is contrasted
with that of molecular structure.