Editors

Prof. Dr. Gaston Berthier Universite de Paris Institut de Biologie Physico-Chimique Fondation Edmond de Rothschild 13, rue Pierre et Marie Curie F-75005 Paris

Prof. Dr. Michael J. S. Dewar Department of Chemistry The University of Texas Austin, Texas 78712/USA

Prof. Dr. Hanns Fischer Physikalisch-Chemisches Institut der Universitat Zurich Ramistr.76 CH-8001 Zurich

Prof. Kenichi Fukui Kyoto University Dept. of Hydrocarbon Chemistry Kyoto/Japan

Prof. Dr. George G. Hall Department of Mathematics The University of Nottingham University Park Nottingham NG7 2RD/Great Britain

Prof. Dr. Jurgen Hinze Fakultat fOr Chemie Universitat Bielefeld Postfach 8640 0-4800 Bielefeld

Prof. Dr. Hans H. Jaffe Department of Chemistry University of Cincinnati Cincinnati, Ohio 452211USA

Prof. Joshua Jortner Institute of Chemistry Tel-Aviv University 61390 Ramat-Aviv Tel-Avivllsrael

Prof. Dr. Werner Kutzelnigg Lehrstuhl fOr Theoretische Chemie der Universitat Bochum Postfach 102148 0-4630 Bochum 1

Prof. Dr. Klaus Ruedenberg Department of Chemistry Iowa State University Ames, Iowa 50010/USA

Eigentum Verband der Chemischen Industrie.e. V.

- Fonds der Chemischen Industrie -KarlstraBe 21, 6000 Frankfurt/Main

Konto-Nr • .................... Q1 .. 7.. ... ? .................. . Der Geschiiftsfiihrer

Dr. B. Ording

Lecture Notes in Chemistry Edited by G. Berthier M. J. S. Dewar H. Fischer K. Fukui G. G. Hall J. Hinze H. H. Jaffe J. Jortner W. Kutzelnigg K. Ruedenberg

37

Kjeld Rasmussen

Potential Energy Functions in Conformational Analysis

Springer-Verlag Berlin Heidelberg New York Tokyo 1985

Author

Kjeld Rasmussen Chemistry Department, Technical University of Denmark DK-2800 Lyngby

ISBN-13: 978-3-540-13906-5 DOl: 10.1007/978-3-642-45591-9

e-ISBN-13: 978-3-642-45591-9

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to 'Verwertungsgesellschaft Wort", Munich.

© by Springer-Verlag Berlin Heidelberg 1985

2152/3140-543210

Foreword

I get by with a little help from my friends

The Beatles: Sgt. Pepper

This book should have been in Danish. Any decent person must be

able to express himself in his mother's tongue, also when expounding

scientific ideas and results.

Had I stuck to this ideal, the book would have been read by very

few people, and, indeed, appreciated by even fewer. Having it publ­

ished in English gives me a chance to fulfill one ambition: to be

read and judged by the international scientific community.

Another reason is that the majority of my professional friends

are regrettably unread in Danish, just as I am in Hebrew, Finnish

and even Italian. I want to deprive them of the most obvious excuse

for not reading my opus.

Like a man I admired, I will first of all thank my wife. In his

autobiography, Meir Weisgal, then President of the Weizmann Insti­

tute of SCience, wrote about his wife: "In addition to her natural

endowments - which are considerable - she was a more than competent

part-tim~ secretary." He wrote on, and so shall I.

The book has been edited by my wife. So if the reader finds the

layout pleasant as, in actual fact, I myself do, Birgit is to be

praised. If there are blemishes, I am to be blamed for not having

caught them.

After having thanked the immediate victim of my decade-long pre­

occupation with CFF methods, who for long periods put aside her own

interests to assist me, I shall make the other acknowledgements more

explicitly.

Three men meant a lot to me in the formative years of my scien­

tific career, and still do: Niels Hofman-Bang, Flemming Woldbye and

Shneior Lifson. Professor Hofman-Bang was Director of Chemistry

Department A for r:J.any years, and responsible for employing me in

IV

1967. He took a chance then, as I was older than most, and I fear

there have been times when he regretted his choice. Returning to

academic life after seven years in industry was not dead easy; Hof­

man-Bang helped and corrected me when necessary.

Professor Flemming Wo1dbye supervised my Ph. D. (lic. techn.)

work 1967 - 1970. During this period he got both his D. Sc. (dr.

phil.) and his chair, and it would happen that we did not meet for

months. This situation made me admire his capacity for absorbing

information, and for making quick and, in the long run, correct

decisions. It was he who established the contact between Lifson and

me, which was to become so fruitful in several respects.

Professor Shneior Lifson was founder and for many years director

of Chemical Physics Department at the Weizmann Institute of Science

in Israel. He introduced me unreservedly to the methods for which

he, with Blxon, Warshel and LeVitt, laid the foundations, and during

my stays in Rehovot I always had the benefit of his help and advice.

Even more than that our family always felt a warm welcome with

Shneior Lifson, his wife Hanna, and the whole department.

Two former graduate students and present friends were indispensa­

ble in earlier phases of the work: Svetozar R. Niketic and Steen G.

Melberg; one is so in the current phase: Lars-Olof Pietila.

Niketic came to us for his Ph. D. (lic. techn.) work at a crucial

time and was instrumental in the development of chemical formula

treatment and of minimisation. He also developed our first potential

energy function for coordination complexes and performed a large

part of the calculations.

Melberg, during his M. Sc. (cand. polyt.) and Ph. D. (lic.

techn.) work, laid the foundations for our present and future work

on saccharides. He prepared very conscientiously a survey of the

literature on Lipid A and began the calculations with the develop­

ment of a potential energy function for glucose. He then performed

all calculations on disaccharides prior to 1979.

Pietila is doing a large part of his work for his Ph. D. (dr.

philos) at the University of Helsinki with me. He has done most of

the extension to the crystal version.

v

Other students have given valuable assistance since 1973: Poul

Bach, Lars Christensen, Niels Hald, Jens Hansen, Oliver Jacobsen,

Klavs Kildeby, Jan Larsen. The methods and techniques they intro­

duced are all in use today. This also applies to Dr. Cornelis J. M.

Huige in Utrecht who found and corrected a crucial error in the

treatment of planar molecules.

Many colleagues and friends at foreign universities and other

learned institutions have on many occasions given me the benefit of

their advice and criticism when they and their students endured a

seminar or a series of lectures. For this assistance I feel very

grateful to my friends in Freiburg, Fribourg, HelSinki, Jerusalem,

Novara, Oslo, Rehovot, Tel Aviv, Troms¢, as well as Copenhagen and

Aarhus.

Among those colleagues I would like to mention three who have

contributed substantially to this work.

Professor Camillo Tosi of Istituto Guido Donegani in Novara has

installed and further developed the UNIVAC version of the CFF pro­

gram. He is responsible for the ab initio calculations behind some

of the potential energy function developments. Together we work on

conformations of amines and of nucleotides.

Dr. Tom Sundius of the Accelerator Laboratory at University of

Helsinki made, with Mr. Ernst Kruckow of RECKU in Copenhagen, the

UNIVAC version of the CFF. He then modified his program MOLVIB, one

of the best programs available for more traditional normal coordi­

nate analYSis, so that it can work in unison with the CFF program.

I have always had good assistance at the computer centres of the

Technical University of Denmark, the Weizmann Institute of Science,

Istituto Donegani, and the Universities of Copenhagen and Fribourg.

It remains to mention who paid for all of this.

The Danish Natural Science Research Council paid the salary of

Niketic for a total of 36 months and the computational costs during

the years 1970 to 1980.

Two funds have been particularly helpful.

Otto M¢nsteds Fond paid for one of my screen terminals and for my

colour raster plotter.

VI

The Technical University Fund for Technical Chemistry supported

Birgit Rasmussen for about half of the time she worked on these pro­jects.

Three other private funds supported her: Frants Allings Legat, G. A. Hagemanns Mindefond and Holger Rabitz' Legat.

In addition, substantial support was received from the following

institutions: European Molecular Biology Organization, Kulturfonden

for Danmark og Finland, Nordic Council, Tribute to the Danes through

Scholarship in Israel, Weizmann Institute of Science.

On several occasions, such help, even with small allocations, has

saved an ongoing project, when University money was not available.

Lyngby, in July, 1984

Kjeld Rasmussen

Contents

Foreword III

Tables . XI

Figures XIII

1 Introduction 1

2 Nomenclature · 5

2.1 Crucial expressions 5 2.1.1 Constitution 5 2.1. 2 Configuration 6 2.1. 3 Conformation · 6 2.1. 4 Conformer 8 2.1. 5 Conformational analysis 10

2.2 Structure · · · · · · · · · · · 10 2.3 Potential energy function · · · . · 12

2.3.1 Parameters · · · · · · · · 13 2.3.2 Potential energy surface 14 2.3,3 Force field · · · · 15 2.3.4 Consistent force field 15

2.4 Molecular mechanics · 16

3 Potential energy functions: A review 17

3.1 Scope · · · · · 17 3.2 Plan . · · · · · · · 19 3.3 Historical background 19 3.4 CFF and variants · 20

3.4.1 Lifson and Warshel · 20 3.4.2 Warshel · · · · 21 3.4.3 Amides · · · · · 22 3.4.4 Hagler and crystals 22 3.4.5 QCFFjPI 23 3.4.6 Ermer 24 3.4.7 Super-CFF 24

3.5 Karplus 25 3.6 Kollman 26 3.7 Schleyer . 27 3.8 Mislow · 28 3.9 Bartell 28 3.10 Boyd and variants 29 3.11 Altona and Faber 29 3.12 The Delft group 30 3.13 White · . · · 30 3.14 Kitaigorodsky 31

4

3.15 3.16 3.17

3.18

Allinger • • • Osawa • • • • Scheraga • • • 3.17.1 ECEPP 3.17 • 2 EPEN.

VIII

Ab initio modelling of non-bonded interactions 3.18.1 Function fitting to calculated energies 3.18.2 Clementi's Bond Energy Analysis 3.18.3 EPEN going quantum ••

Applications: Coordination complexes.

4.1 4.2

4.3

4.4

An early consistent force field Australian and American groups 4.2.1 Gollogly and Hawkins. 4.2.2 Sargeson and coworkers 4.2.3 Brubaker and coworkers. 4.2.4 DeHayes and Busch The Lyngby group • • • • • • • 4.3.1 Niketic and Woldbye 4.3.2 Rasmussen and coworkers Other groups • • • . ~ • • . • • 4.4.1 Pavelcik and Majer ••• 4.4.2 McDougall and coworkers 4.4.3 Australians ••.•• 4.4.4 Laier and Larsen ••• 4.4.5 Bugnon and Schlaepfer 4.4.6 Tapscott and coworkers

5 Applications: Saccharides

5.1 5.2 5.3 5.4 5.5 5.6

The glucoses Maltose Cellobiose " Gentiobiose Galactobiose Misunderstandings

6 Applications: Other compounds

6.1 6.2 6.3 6.4

Amines . . • . . Polynucleotides Spiro compounds Chloroalkanes

7 Optimisation: Algorithms and implementation

7.1 7.2 7.3

The optimisation algorithm .• Termination criteria •••• The partial derivatives 7.3.1 Internal coordinates 7.3.2 Rotational constants 7.3.3 Atomic charges 7.3.4 Dipole moments •..

31 32 32 33

• 34 35 35 36 37

39

40 42 42 42 43 43 43 44 44 46 46 46 47 47 47 48

49

49 51 53 54 58 59

63

63 64 64 65

67

67 70 71 72 74 75 76

7.4 7.5

IX

7.3.5 Internal frequencies ••• Correlation and uncertainty Organisation of the optimisation

8 A data bank for optimisation

8.1

8.2 8.3 8.4 8.5 8.6 8.7

8.8

Structure • • • • • 8.1.1 Alkanes 8.1.2 Cycloalkanes 8.1.3 Ethers ••• 8.1.4 Cyclic ethers 8.1.5 Alcohols. 8.1.6 Esters and lactones 8.1.7 Amines •••• 8.1.8 Chloroalkanes Vibrational frequency Fractional atomic charge Dipole moment Rotational constants Unit cell dimensions • Statistical test • • 8.7.1 Alkanes and cycloalkanes 8.7.2 Ethers and cyclic ethers. Use of the data . • • • • • • • •

9 Potential energy functions: Optimisations

9.2 9.3

PEF300 series . • • • . • • 9.1.1 Experimental data 9.1.2 Initial experiences 9.1.3 Initial results 9.1.4 Further results PEF400 series Comparisons . • • • • •

10 Applications: Alkanes and cycloalkanes

10.1 Non-optimised potential energy functions. 10.2 Optimised potential energy functions

10.2.1 Cyclopentane ••.• 10.2.2 Rotational barriers 10.2.3 Rotational constants 10.2.4 Hexamethylethane •• 10.2.5 Cyclohexane inversion 10.2.6 Cyclodecane

10.3 Reliability

11 Extension to crystals

11.1 Methods •.•• 11.1.1 Coordinate systems 11.1.2 Derivatives 11.1.3 Lattice summation

11.2 Implementation •••••.

• 76 • 79

79

81

• 82 • • • • 83

• 83 84

• • • 84 85 85

• 86 86 87 87 87 88 88 88 89 92 93

95

95 95

101 103 104 105 116

119

119 120 121 121 125 125 126 127 130

131

132 132 134 136 139

11.3

11. 4

11.5 11.6

Test calculations •••• 11.3.1 Argon •••• 11.3.2 Ethane ••••••

x

11.3.3 Potassium chloride and sodium chloride Optimisation on crystals • 11.4.1 Choice of algorithm •••• 11.4.2 Derivatives in parameters Implementa tion • • • • • • • • • • • • Test calculations • • • • • • • • • 11.6.1 Argon and potassium chloride 11.6.2 Alkanes •••••••••••

12 Potential energy functions: Recommendations

12.1 12.2 12.3

General guidelines Packages • • • • • • Parameter sets • • • •

Al Availability of the Lyngby CFF program •

A2 User Manual

A2.1

A2.2

A2.3 A2.4

Summary of the JCL for CFF under IBM r~s • A2.1.1 Routine operation A2.1.2 Program changes •••• A2.1.3 Subprogram statistics Input to the conformational program A2.2.1 Cautioning •••••••••• An example: cyclohexane •••••• A second example: the ethane crystal.

A3 The system of programs •

A3.1 A3.2 A3.3

The CFF system • Interfaces • • • Utilities

A4 JCL procedure CFF

A5 TSO command list CFF •

A6 The future of CFF

Literature references

Index of names •

Subject index

141 141 141 146 147 148 149 150 150 152 152

155

155 156 158

161

163

163 164 164 169 169 184 187 190

193

193 194 195

197

201

207

209

225

229

Table 2-1:

Table 2-2:

Table 4-1:

Table 5-1:

Table 5-2:

Table 5-3:

Table 8-1:

Table 9-1:

Table 9-2:

Table 9-3:

Table 9-4:

Table 9-5:

Table 9-6:

Table 9-7:

Table 9-8:

Tables

Molecular structures •

Structures of propane

Abbreviations of amines

Maltose conformers •••

Conformers of p-gentiobiose in PEF300

Absolute free enthalpies in kJmol-1

Ethane, n-butane and cyclohexane

Parameters of the PEF300 series

Conformations in the PEF300 series •

Vibrational frequencies in the PEF300 series •

Thermodynamics in the PEF300 series •

Parameters of the PEF400 series

Conformations in the PEF400 series

Vibrational frequencies in PEF401 and PEF304 •

From PEF4000pt to PEF401 •

• • 11

12

. 40

• 52

55

• • 60

83

97

99

101

103

106

109

110

111

Table 9-9: Thermodynamics in the PEF400 series 113

Table 10-1: Barriers to internal rotation 124

Table 10-2: Cyclohexane twist-boat - chair energy difference 126

Table 10-3: Relative energy of cyclodecane conformers

Table 10-4: The BCB conformer of cyclodecane •

Table 10-5: The TCCC conformer of cyclodecane

Table 11-1: Energy function parameters for ethane.

Table 11-2: Minimised structures of ethane

Table 11-3: Optimisation on Ar and KCl •

Table 11-4: Alkane crystals in PEF3030pt and PEF3040pt •

128

129

129

143

144

151

154

XII

Table A2-1: Organisation of background memory · · · . . 168

Table A2-2: Usage of parameters KJELD and NIKI · 171

Table A2-3: Coding of energy parameters · · . · . . · · · 173

Table A2-4: Atomic symbols . . . . . · · 173

Table A2-5: Checklist of READ statements · · . · . . · · · . . 186

2-1

2-2

2-3

2-4

2-5

Figures

Molecular constitution

Molecular configuration

Molecular conformation

Gauche conformers of 2,3-butanediamines

One conformer of ~-D-glucose

6

7

8

9

10

2-6 Structures of methane • • • • • 13

2-7 Molecular potential energy functions • 14

4-1 Early optimisation on single chelate rings 41

5-1 ~-gentiobiose in PEF300 (above) and PEF400 (below) and in

7-1

8-1

9-1

9-2

9-3

A3-1

the crystal (thin lines) •••.• 57

Subprograms used in optimisation

c-c and O-C bond lengths with +3<J intervals

Non-bonded part of PEF3020pt

Non-bonded part of PEF4010pt . . Non-bonded part of PEF3040pt . . . . . Structure of the CFF JCL procedure

.

. .

80

. . . . 91

113

114

115

194