Patai S., Rappoport Z. 1996 The chemistry of functional groups. The chemistry of amino, nitroso, nitro and related groups / 0001 84

Supplement F2: The Chemistry of Amino, Nitroso, Nitro and Related Groups.

Edited by Saul Patai Copyright 1996 John Wiley & Sons, Ltd.

ISBN: 0-471-95171-4

CHAPTER 1

Molecular mechanics calculations

PINCHAS APED

Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel Fax: [phone] e-mail: [e-mail]

and

HANOCH SENDEROWITZ

Department of Chemistry, Columbia University, New York, NY 10027, USA
Fax: (001		212)678		9039;		e-mail: [e-mail]
I. INTRODUCTION . . . .						.	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	2
II. DEVELOPMENT OF THE COMPUTATIONAL MODEL . . . . . . . . . . . .								3
A. Molecular Mechanics						.	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	3
B. Specific Force Fields							MM2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .	5
1.	MM2 potential functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .							5
2.	MM2 parameterization of amines . . . . . . . . . . . . . . . . . . . . . . . .							6
	a. Acyclic amines					.	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	6
	b. Cyclic amines					.	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	8
	c. Heats of formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .							10
	d. Dipole moments						. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	11
3.	MM20 parameterization of nitro compounds and MM2
	parameterization of nitrosamines, nitramines, nitrates and oximes . . .							11
4.	MM2 parameterization of nitro compounds, enamines
	and aniline derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .							14
5.	MM2 parameterization of the N C N anomeric moiety . . . . . . . .							14
C. MM3 . . . . . . . . . .						.	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	20
1.	MM3 potential functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .							21
2.	MM3 parameterization of amines . . . . . . . . . . . . . . . . . . . . . . . .							23
	a. Bond length and bond angle parameters . . . . . . . . . . . . . . . . .							23
	b. Torsional angle parameters . . . . . . . . . . . . . . . . . . . . . . . . . .							24
	c. Moments of inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .							24
	d. Four-membered and five-membered rings . . . . . . . . . . . . . . . .							24
	e. Hydrogen bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .							27
	f. Heats of formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .							29

1

2	Pinchas Aped and Hanoch Senderowitz
3.	MM2 and MM3 parameterization of nitro compounds . . . . . . . . . .	29
	a. Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	30
	b. Rotational barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	31
	c. Vibrational spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	32
	d. Heats of formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	32
4.	MM2 and MM3 parameterization of enamines and
	aniline derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	33
	a. Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	33
	b. Conformational energies and rotational barriers . . . . . . . . . . . . .	34
	c. Heats of formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	35
	d. Vibrational spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	35
5.	Other force fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	35
	a. AMBER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	35
	b. Tripos 5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	36
	c. DREIDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	37
	d. Universal Force Field (UFF) . . . . . . . . . . . . . . . . . . . . . . . . .	38
D. Energetic comparison between MM2, MM3, AMBER, Tripos 5.2,
DREIDING and UFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		40
III. APPLICATION OF THE COMPUTATIONAL MODEL . . . . . . . . . . . . .		42
A. Conformational Analysis and Structural Investigation . . . . . . . . . . . . .		43
1.	Tertiary amines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	43
2.	Polyamines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	55
	a. Diamines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	55
	b. Triand tetraamines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	57
	c. Cryptands and azacrown ethers . . . . . . . . . . . . . . . . . . . . . . .	59
3.	Medium-size rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	60
4.	Biologically active compounds . . . . . . . . . . . . . . . . . . . . . . . . .	62
B. Spectroscopic Experiments and the Study of Chemical Effects . . . . . . .		66
1.	Nitrogen proton affinities and amine basicity . . . . . . . . . . . . . . . .	66
2.	Magnetic anisotropy of cyclopropane and cyclobutane . . . . . . . . . .	68
3.	CD spectra of N-nitrosopyrrolidines . . . . . . . . . . . . . . . . . . . . . .	69
4.	17O and 15N NMR spectra of N-nitrosamines . . . . . . . . . . . . . . . .	70
C. Mechanisms of Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . .		72
D. Heat of Formation and Density Calculations of Energetic Materials . . .		76
IV. ACKNOWLEDGMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		81
V. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		81

I. INTRODUCTION

Theory plays an invaluable role in our understanding of organic chemistry and is enhanced by the usage of rigorously built computational models. While ab initio calculations are certainly the most physically ‘correct’ way to treat chemical systems, they are limited, with current computer technology, to molecules with a relatively small number of heavy (nonhydrogen) atoms. Larger systems are best handled by molecular mechanics provided that high-quality force-field parameters are available. In such cases, the method can provide accurate molecular properties using only a fraction of the computational resources needed by quantum mechanical methods. The rapid increase in affordable computational power and the integration of many force fields into ‘user friendly’ molecular modeling packages has further contributed to the development and widespread usage of the method.

In Section II of this review we develop the molecular mechanics computational model by presenting the potential functions of several commonly used force fields and discussing, in some detail, the parameterization procedures for the type of compounds considered

1. Molecular mechanics calculations	3
in this work. In Section III, we describe the applications of the resulting force	fields

to a variety of problems in amino, nitro and nitroso chemistry. Typically, molecular mechanics calculations have been used, primarily, to obtain (minimum energy) molecular structures and conformational energies. However, the examples provided in this review span a much broader range of applications, from ‘traditional’ conformational analysis and structural investigation to spectroscopic experiments, heats of formation calculations of energetic materials and the study of chemical effects and reaction mechanisms. Of the molecular systems considered here, the vast majority of calculations has been performed for amines while fewer examples are found for nitro compounds and, still fewer, for nitroso ones. Calculations of other nitrogen-containing molecules, in particular, organometallic complexes and biological macromolecules, are also found in the literature but these fall beyond the scope of the current work.

Finally, we would like to point out that although we made a special effort to cover most of the seminal works, this review is not intended to provide an exhaustive coverage of the available literature, but rather, to serve as a guideline to the usage of molecular mechanics calculations in this field.

II.DEVELOPMENT OF THE COMPUTATIONAL MODEL

A.Molecular Mechanics

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

Etotal D Estretch C Ebend C Etorsion C Enonbonded C Ecross terms

1

The first three terms, stretch, bend and torsion, are common to most force fields although their explicit form may vary. The nonbonded terms may be further divided into contributions from Van der Waals (VdW), electrostatic and hydrogen-bond interactions. Most force fields include potential functions for the first two interaction types (Lennard-Jones type or Buckingham type functions for VdW interactions and charge charge or dipole dipole terms for the electrostatic interactions). Explicit hydrogen-bond functions are less common and such interactions are often modeled by the VdW expression with special parameters for the atoms which participate in the hydrogen bond (see below).

The number and type of cross terms vary among different force fields. Thus, AMBER2 contains no cross terms, MM23 uses stretch bend interactions only and MM34 uses stretch bend, bend bend and stretch torsion interactions. Cross terms are essential for an accurate reproduction of vibrational spectra and for a good treatment of strained molecular systems, but have only a small effect on conformational energies.

Given a set of potential functions, the results of any molecular mechanics calculation depend critically on the parameters. These may be obtained from two main sources,

4 Pinchas Aped and Hanoch Senderowitz

namely experimental data or high-level quantum mechanics (usually ab initio) calculations. Experimentally based parameters have two main advantages: (1) they describe the ‘real world’ rather than another computational model of it; (2) they reflect molecular free energies rather than enthalpies. However, such parameters are often hard to obtain, not available for all systems of interest, nonuniform (that is, obtained by different experimental techniques and often in diverse media) and usually do not provide a complete description of the molecular potential surface including all minima and transition states. In contrast, parameters from high-level quantum mechanical calculations are available for all molecular systems, up to a certain size, are uniform (that is, always describe an isolated molecule and, if desired, may be obtained at the same level of theory) and can provide a complete description of the molecular potential energy surface. The two main disadvantages of such parameters, namely their possibly high computational cost and dependence on the theoretical model, are gradually resolved with the rapid development of computational power (which by far exceeds similar developments in experimental techniques) and the consequent accumulation of experience in this field, and today, many parameters for use in molecular mechanics calculations are derived in such a manner. Regardless of the source of the parameters, an essential (although not necessarily correct) assumption for the applicability and usefulness of molecular mechanics is their transferability, i.e. once they are derived, usually from a small set of model compounds, they may be used for other larger (but similar) systems.

In order for a force field to be considered adequate for treatment of a particular molecular system (or a class of molecules) it must provide an accurate description of its properties such as geometry, dipole moment, conformational energies, barriers to rotation, heat of formation and vibrational spectra, while the reference data come either from experiment or from high-level ab initio calculations. Some care must be taken when evaluating the performance of molecular mechanics force fields through comparison with experimental or theoretical data1: Since different experimental techniques provide different structural and energetic parameters which also differ from those obtained by quantum mechanical calculations, a force field parameterized according to data from a specific source can reproduce data from other sources only qualitatively (a partial solution to this problem is provided in MM3-94, where it is possible to obtain re bond lengths which are supposed to provide the best fit to ab initio results4).

Several force fields have been used in molecular mechanics calculations of amino, nitro and nitroso compounds but for only two, MM25,15 17,20,21,43,44 and MM36,43,44, has a specific parameterization been reported in the literature. Several features of these systems are of particular importance and a challenge to molecular mechanics calculations and must be included in any critical evaluation of the force-field performance. For amino compounds these are the treatments of nitrogen inversion, the reproduction of changes in C H bond lengths when antiperiplanar to a nitrogen lone pair (lp) and the consequent calculation of the Bohlmann bands in the IR spectra, the reproduction of the shortening of C N bonds in tertiary amines, the treatment of interand intramolecular hydrogen bonds and the reproduction of structural and energetic manifestations of stereoelectronic effects such as the anomeric effect characterstic of N C X moieties and the gauche effect characteristic of N C C X moieties (X D electronegative atom/group). As for nitro compounds, the two most challenging aspects are the possible conjugation of the nitro group to other systems and the consequent geometry of the molecule and the barriers for rotation around the C N bond in aromatic and aliphatic nitro compounds.

In the following we will present the explicit form of the potential functions and the parameterization of most of the force fields used in molecular mechanics calculations of amino, nitro and nitroso compounds and evaluate their performance according to these criteria.

1. Molecular mechanics calculations

5

B. Specific Force Fields MM2

Several force fields have been used in molecular mechanics calculations of amino, nitro and nitroso compounds. The most intensive work has been done with MM2 and, in recent years, also with MM3, probably due to the generally recognized high performance of these force fields and since they are the only ones which have undergone extensive specific parameterization for these systems, however, several other calculations are also found in the literature (see below). We therefore start with the MM2 and MM3 force fields where we briefly outline the specific form of the potential functions and discuss, in some detail, the parameterization procedure for the type of compounds discussed in this chapter. We then turn to several other force fields which have not undergone specific parameterization but were nevertheless used in the calculations (AMBER, Tripos, DREIDING, UFF). We conclude with a brief comparison of the energetic performance of all force fields.

The MM2 force field3 is probably the most extensively parameterized and intensively used force field to date. It reproduces a variety of molecular properties such as geometry, dipole moments, conformational energies, barriers to rotation and heats of formation. Of particular importance for calculations of amines is that MM2 treats lone pairs on sp3 nitrogens (and oxygens) as pseudo atoms with a special atom type and parameters. A closely related force field, MM207, was derived from MM2 by Osawa and Jaime. MM20 uses the same potential functions as MM2, but employs a different set of parameters in an attempt to better reproduce barriers to rotation about single C C bonds.

1. MM2 potential functions1,3

Within the MM2 force field, the molecular steric energy is given by

Etotal D Estretch C Ebend C Estretch		bend C Etorsion C EVdW C Eelectrostatic	2
The stretching energy is given by a sum of quadratic (harmonic) and cubic terms:
Estretch i,j D K rij rij0 2 C K1 rij rij0 3			3

where rij and rij0 are the actual and ‘natural’ bond lengths between atoms i and j, respectively, and K and K1 are stretching force constants: rij0 is subjected to primary

electronegativity effects8 which allow for a better reproduction of experimental data such as, for example, the shortening of C N bonds along the series CH3NH2 ! (CH3)2NH ! (CH3)3N (see Section II.C.2 for more details).

The bending energy is given by

Ebend i,j,k D K ijk ijk0 2 C K1 ijk ijk0 6

4

where ijk and ijk0 are the actual and ‘natural’ i j k bond angles and K and K1 are bending force constants.

The stretch bend energy allows for the i j and j k bonds to stretch when the angle between them (i j k) closes and is given by

Estretch		bend D K[ rij rij0 C rjk rjk0 ] ijk ijk0	5

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

6	Pinchas Aped and Hanoch Senderowitz
	Torsional energy is given by

Etorsion i,j,k,l D 0.5V1 1 C cos ωijkl C 0.5V2 1 cos 2ωijkl C 0.5V3 1 C cos 3ωijkl6

where V1, V2 and V3 are adjustable parameters and ωijkl is the torsional angle. The VdW energy is given by a Buckingham type potential function9:

EVdW i,j

D

ε[2.9

ð

105 exp

12.5rŁ

/rij

2.25 rŁ

/rij 6]

rŁ /r

3.311

ij

ij

ε

ð

336.176 rŁ

/rij 2

rŁ /r > 3.311

(7)

ij

where rijŁ D ri C rj D sum of VdW radii of atoms i and j and ε D εiεj 0.5 is the well depth of the i j VdW potential curve.

The electrostatic energy is given by charge charge or dipole dipole interactions:

Echarge		charge i,j D qiqj/εrij		(8)
Edipole			dipole ij D i j/εrij3 cos 3 cos ˛i cos ˛j	(9)

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

µi

αi

	χ	rij
		µj
		αj

(1)

2. MM2 parameterization of amines5

The parameterization of the MM2 force field for amines5 was originally based on experimental data with occasional references to quantum mechanical calculations mainly to evaluate conformational energies. Missing parameters (bond lengths and angles) for several unique amino functionalities were later evaluated from ab initio calculations and incorporated into the force field10. As in the case of alcohols it was found necessary to include explicit lp on sp3 nitrogens. The main disadvantage of this treatment is that ammonia, for example, does not invert through a symmetrical transition state. However, apart from this shortcoming, the lp formalism seems to reproduce well the structural and energetic characteristics of amines. A complete list of amine parameters is provided in Reference 5.

a. Acyclic amines. An initial set of amine parameters was based on the microwave (MW) structures of ammonia and methylamines. A comparison of MM2, ab initio, MW and infrared (IR) structures for these model compounds is provided in Table 1. Four discrepancies between calculations and experiment are apparent: (1) MM2 calculations do not reproduce the decrease in C N bond lengths on going from primary to secondary

1. Molecular mechanics calculations

7

TABLE 1. Calculated (MM2, MM3 and ab initio) and observed structural parameters for ammonia and methylamines (bond lengths in A,˚ bond angles and tilt angles in degrees, dipole moments in Debye)5,6. Reprinted with permission from Refs. 5 and 6. Copyright (1985, 1990) American Chemical Society

Parameter				MM2		MM3a	Ab initiob		MW				ED
Ammonia									1.0144 š 0.002
N H				1.013		1.015	1.003
H N H				107.6		107.1	107.2		107.1 š		0.9
dipole moment				1.43		1.49	1.92		1.47
Methylamine									1.093 š
C H				1.114		1.110	1.095	(a)			0.006
C N							1.086	(s)	1.474 š				1.467 š 0.002
				1.454		1.463	1.484				0.005
N H				1.015	c	1.014	1.010		1.014
H C H				109.0	(a)c	108.71	108.4	(a)	109.47 š 0.8
C N H				109.1	(s)	107.79	107.5	(s)	112.1 š
				111.3		112.29	110.0				0.8
H		N	H			106.42	105.9		.85			0.6
				105.4		111.01			105 d š
N C H									110.3
						110.27
CH3 tilt				0.19			3.9		3.5
dipole moment				1.33		1.29			1.336
Dimethylamine (2)									1.019 š				1.00 š 0.2
N H				1.017		1.018	0.999				0.007
C N				1.460		1.462	1.461		1.463 š		0.005		1.455 š 0.002
C H				1.115		1.110	1.080		1.084 š		0.005		1.106 š 0.002
C		H0		1.115		1.110	1.081		1.098	š	0.004		1.106	š	0.002
		H00		1.115		1.110	1.090		1.098		0.004		1.106		0.002
C										š				š
C N H				109.5		109.83	112.3		108.9 š		0.3		107 š 2.0
C N C				112.1		112.42	115.1		112.2 š		0.2		111.8 š 0.6
N C H				109.4		110.28	109.4		109.7 š		0.3		112.0		0.8
N		C	H0	110.7		110.47	109.2		108.2	š	0.3			š
			H00	110.7		110.22	114.0		113.8		0.3
N		C								š
H			H0	108.2		107.65	108.0		109.0		0.2		106.8		0.8
		C								š				š
			H00	108.3		108.48	108.5		109.2		0.2		106.8		0.8
H		C								š				š
H0 C H00				109.4		109.64	107.6		107.2 š		0.3		106.8 š 0.8
CH3 tilt				0.9					3.4
dipole moment				1.10		1.07			1.03
Trimethylamine									1.454 š				1.454 š 0.002
C N				1.465		1.460	1.445				0.003
C N C				110.9		111.20	111.9		110.9 š		0.6		e
N C H						111.37	113.0						110.2
						110.54	109.8						110.2
						110.30							110.2
dipole moment				0.64		0.62	0.75		0.63

aMM3 data for ammonia were calculated for this work with MM3-94.

bab initio data for ammonia (HF/6-31GŁ ) were taken from P. C. Hariharan and J. A. Pople, Mol. Phys., 27, 209 (1974). Ab initio data for trimethylamine (HF/6-31GŁ ) were calculated for this work.

c(a) D one hydrogen is anti to the nitrogen’s lp and the other is gauche to the nitrogen’s lp; (s) D both hydrogens are gauche to the nitrogen’s lp.

dTaken from Reference 11. eTaken from Reference 12.

8	Pinchas Aped and Hanoch Senderowitz

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

′H	H
CH3	H
	Η′′
	(2)

The torsional parameters for the methylamine fragment were chosen to reproduce the barriers to rotation in methylamine, dimethylamine and trimethylamine. The calculated values, 1.90, 3.04 and 4.22 kcal mol 1 for the three methylamines, respectively, are in good agreement with the experimental ones (1.98, 3.22 and 4.35 kcal mol 1). The torsional parameters for the C C N H and C C N lp fragments were chosen to reproduce the axial/equatorial energy difference in piperidine (0.30 and 0.25 0.74 kcal mol 1 in favour of the equatorial hydrogen conformation from MM2 calculations and NMR experiments, respectively) at the expense of ethylamine (0.13 and 0.6 kcal mol 1 in favor of the C C N lp gauche conformation from MM2 calculations and experiment, respectively), since it was not possible to fit both molecules with the same set of torsional parameters. Finally, the C N C C fragment was chosen to reproduce the experimental free-energy difference between the trans and gauche conformations of methylethylamine (>1.3 and

1.14kcal mol 1 from MW and MM2, respectively).

b. Cyclic amines. The smallest cyclic amine considered during MM2 parameterization is the four-membered ring azetidine (3). As customary with MM2 treatments of 4-membered rings, unique bending and torsional parameters were applied to this molecule. A far-IR

study has shown azetidine to be puckered with a planar barrier height of 1.26 kcal mol 1

and an equatorial hydrogen preference of 0.27 kcal mol 113 . An electron diffraction (ED) study confirmed the nonplanarity of the system with an observed puckering angle (see

structure 3) of 33°14 . The MM2 numbers are 1.09 and 0.05 kcal mol 1 for the barrier height and equatorial hydrogen preference, respectively, and 36.2° for the puckering angle. While the calculated barrier and puckering angle are in good agreement with the experimental values, MM2 overestimates the stability of the H-axial conformer, probably due to

N

H

q

ω

Φ

(3)

1. Molecular mechanics calculations

9

TABLE 2. Calculated (MM2 and MM3) and observed (ED and MW/ED) structure of azetidine (bond lengths in A,˚ bond angles, , q and ω, in degrees; see structure 3 for the definition of , q and ω)5,6. Reprinted with permission from Refs. 5 and 6. Copyright (1985, 1990) American Chemical Society

Structural feature	MM2a	MM3b	ED	MW/ED
C N	1.471	1.475	1.482 š 0.006	1.473
C C	1.549	1.563	1.553 š 0.009	1.563
C H	1.116		1.107 š 0.003
N H	1.014		1.002 š 0.014
C N C	92.5	91.26	92.2 š 0.4	91.2
C C C	86.6	84.85	86.9 š 0.4	84.6
C C N	86.4	88.24	85.8 š 0.4	88.2
H C H	114.3		110.0 š 0.7
	36.2	29.0	33.1 š 2.4	29.7
q	0.311
ω	10.7

aThe MM2 force field was parameterized to reproduce the ED values.

bThe MM3 force field was parameterized to reproduce the MW/ED values.

a lp effect which prevents a realistic inversion of the nitrogen and thus stabilizes this form (in the ‘real world’ this minima may vanish due to repulsion between the axial hydrogen and the C3 methylene which leads to nitrogen inversion). A comparison of MW and MM2 structures for azetidine is provided in Table 2 and shows good agreement between theory and experiment.

Not much information is available for the five-membered ring pyrrolidine (4). MM2 calculations predicted that the 2-half-chair form is preferred over a host of other conformers by an average of 0.3 kcal mol 1 with a 4.37 kcal mol 1 barrier to planarity. The ‘equatorial’ hydrogen is calculated to be favored by E D 0.20 kcal mol 1 over the axial one.

Much controversy is found in the literature regarding the conformational preference of the six-membered ring piperidine (5)5. However, most experimental evidence is consistent with a predominance of the H-equatorial conformer by 0.25 0.74 kcal mol 1. As noted above, the C C N H and C C N lp torsional parameters were adjusted to reproduce an intermediate value of 0.30 kcal mol 1. MM2 calculations of this system have revealed, perhaps contrary to chemical intuition, that most of the energy difference between the H- axial and H-equatorial conformers results from torsional energy while the 1,3-diaxial interactions have only a negligible contribution5.

H

N

NH

(4)(5)

The conformational behavior of N-methyl-piperidine (6) had been extensively studied. Most researchers now agree that the Me-equatorial conformer is favored by about

2.7 kcal mol 15 . The C N C C torsional parameter was adjusted to produce an energy difference, E, of 2.50 kcal mol 1, most of which comes from torsional and bending contributions. A comparison of calculated and observed conformational energies in simple mono-cyclic amines is given in Table 3. In most cases the agreement between MM2 and experimental values is very good. One notable exception is cis-2,6-di-t-butylpiperidine,

10	Pinchas Aped and Hanoch Senderowitz

TABLE 3. Calculated (MM2) and observed conformational energies (kcal mol 1) in monocyclic amines5. Reprinted with permission from Ref. 5. Copyright (1985) American Chemical Society

Compound	Stable conformer			Ecalculated	Eexperimental
Azetidine	puckered, N H eq			0.05	0.27			0.04
Pyrrolidine	2-env. or	half-chair		0.24	0.20		š
Cyclobutylamine			a	0.15	0.16
	NH2 eq (gg)
Cyclohexylamine	NH2 eq (gg)a			1.37	1.1		1.8
1-Amino-1-methylcyclohexane	Methyl eq			0.64
eq-1-Amino-2-methylcyclohexane	Methyl eq			1.45
1-Amino-eq-2-methylcyclohexane	NH2 eq			1.28
1-Amino-2,2-dimethylcyclohexane	NH2 eq			1.12			0.8
Piperidine	N H eq			0.30	0.3
eq-2-Methylpiperidine	N H eq			0.29
ax-2-Methylpiperidine	N H eq			0.23
3-Methylpiperidine	CH3 eq			1.62	1.6, 1.65
eq-3-Methylpiperidine	N H eq			0.30
ax-3-Methylpiperidine	N H eq			0.49
4-Methylpiperidine	CH3 eq			1.75	1.9, 1.93
2,2,6,6-Tetramethylpiperdine	N H eq			0.40
cis-2,6-Di-t-butylpiperidine	N H ax			0.65	0.65
N-Methylpiperidine	CH3 eq			2.50	0.4		3.15
2-Methylpiperidine (N H eq)	CH3 eq			2.11	b
					2.5b
eq-2-Methyl-N-methylpiperidine	N CH3 eq			1.68	2.5b
eq-3-Methyl-N-methylpiperidine	N CH3 eq			2.57	2.5b
eq-4-Methyl-N-methylpiperidine	N CH3 eq			2.47	2.5b
eq-4-t-Butyl-N-methylpiperidine	N CH3 eq			2.52	2.5
1,2,2,6-Tetramethylpiperidine	N CH3 eq			1.70	1.95 š 0.2
1-eq,2-Dimethylpiperidine	2-CH3 eq			1.68	1.5, 1.9, 1.7
1-eq,3-Dimethylpiperidine	3-CH3 eq			1.62	1.5, 1.77, 1.6
1-eq,4-Dimethylpiperidine	4-CH3 eq			1.72	1.98, 1.8
2,3,3-Trimethylpiperidine	2-CH3 eq			1.24
2,2,3-Trimethylpiperidine	3-CH3 eq			1.13
1-eq,2,3,3-Tetramethylpiperidine	2-CH3 eq			0.60

aEach C C N lp torsion is qauche.

bThis approximate value was taken as an average from analogous systems.

where MM2 calculations favor the H-axial conformation (axial:equatorial ratio of 3:1) in contrast with experiment (axial:equatorial ratio of 1:3). One possible explanation to this discrepancy is an inverted assignment of the IR bands to the two conformers.

The last molecule considered in this parameterization study was 1,5,9,13tetraazacyclohexadecane (7). A comparison between MM2 and X-ray results (see structure 7)5 reveals good fit between theory and experiment (the X-ray C C bond lengths are shorter than the MM2 corresponding ones, partly since the data were collected at room temperature with no corrections for thermal motion).

c. Heats of formation. The parameters used in the calculation of heats of formation for aliphatic amines are C N, N H, N Me, N CHR2, R2NH, R3N and N CR3. These were obtained according to the following method: Using bond enthalpies from the hydrocarbon part of the force field, the sum of the hydrocarbon fragment contributions, torsional increments (necessary to account for the thermal excitation of the rotation about bonds with low rotational barriers), conformational population increments (necessary to account for any additional conformations), translation-rotation increments (4kT) and steric energy was