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

1. Molecular mechanics calculations

61

and MM3-92 (with the 19855 and 19906 amine parameters, respectively) were used to locate the stable conformers, as well as the transition structures connecting them. Energetic minima could be classified into two main families, chair/twist-chair (C/TC) and boat/twistboat (B/TB), while in each case the axial, equatorial or isoclinal orientation of the N H was also considered. Both force fields located the same collection of conformers, with similar geometries and general energetic picture, the most stable ones belonging to the TC family while the highest-energy ones belonged to the B family. The two force fields differ, however, in the relative stability of several conformers within each family. Four, energetically different, chair, four twist-chair, one boat and one twist-boat conformers were located, most having several isoenergetic counterparts leading to a total of 34 conformers (disregarding the N H orientation). MM3 calculations predict the TC1 conformation, with an axial N H to be the most stable one, closely followed by TC5 with an equatorial N H (relative energy < 0.02 kcal mol 1). The latter is calculated to be the most stable conformer according to MM2. The lowest-energy forms of each family, as found by both force fields, are shown in Figure 7 along with their calculated relative energies. Six transition states of boat type, divided into 2 energetically equal subgroups of 4 and 2, were found to separate the stable boat forms, completing a pseudorotational cycle of the B/TB family. The two main conformational families are connected by 14 TC $ B type transition states (divided into 4, energetically different, subgroups with 4, 4, 4 and 2 members) with energies (i.e. barriers) higher than 7 kcal mol 1. These structures are formed when 2 atoms interchange their relative positions with regard to a hypothetical equatorial ring plane, leading in the process to near-coplanarity of 5 of the 7 ring atoms. The main contribution to the transition state energies come from opening of the ring bond angles during this flattening process. The complete pseudorotational equilibrium, as a function of the two N C C C dihedral angles, is presented in Scheme 5. As previously discussed, the MM3 force field can treat nitrogen inversion. Barriers to such processes, leading to interconversion between the axial and equatorial forms of several

TC1, ax	TC5, eq			C1, eq
0.00 (0.82)	0.02 (0.00)			0.82 (1.69)

C3, ax	B1, eq	TB3, iso
2.00 (1.21)	1.87 (1.95)	4.27 (3.13)

FIGURE 7. The lowest-energy form of each of the conformational families of perhydroazepine 66 as calculated by MM2 and MM3 (MM2 relative energies in parentheses)

62			Pinchas Aped and Hanoch Senderowitz
ω1234
90	C3	TC2	C6		TC6

TC3		C2	TC5
				C7
	C4	C5	B5
60		TC4		TB3
		B6
		TC1		B2
30				TC7
		B7

C1 B8

0	B1
	C8

−30 TC14

B9

B14

TC8

B13

−60	B12	TC11	C11
C14		C12
	TB10	C9	TC10
		TC12

C13 −90 TC13

C10

TC9

−90	−60	−30	0	30	60	ω1765
						90

SCHEME 5. Schematic representation of the conformational equilibrium of perhydroazepine 66 as a function of the two dihedral angles ω1234 and ω1765. Continuous lines represent C/TC and B/TB families. TC $ B transitions are represented by broken lines. (ð) and (°) represent minimum and maximum energies, respectively. Reproduced with permission from Reference 105

were calculated by a full matrix Newton Raphson optimization of structures in which the N H bond and the C2 and C7 atoms lie in the same plane. The inversion transition states were characterized by one imaginary vibrational frequency in the range of 420 to 500 cm 1, demonstrating first-order saddle points. The calculated barrier values, in the 1.9 3.2 kcal mol 1 range, are quite low in comparison with that of ammonia (5.5 and 5.8 kcal mol 1 from MM3 calculations and experiment, respectively; see Section II.c.2), partly due to the energy height of the ground state considered as the process origin (the barrier was calculated as the difference between the flat transition state and the minimum with the highest-energy orientation of the N H bond).

4. Biologically active compounds

QCFF/PI and PCILO calculations106, as well as a combined MM3, NMR X-ray crystallography and structure comparison study107 109, were used to identify biologically active

1. Molecular mechanics calculations

63

compounds with respect to dopamine receptor agonism. In a typical work, Liljefors and Boegesoe109 have carried out conformational analysis of molecules containing piperidine and piperazine rings (67 69). Three degrees of freedom were considered, for example, in analyzing compound 68: (1) the rotation about the bond connecting the piperazine ring and the tricyclic ring system; (2) flip of the seven-membered ring via the C S C bridge; (3) pseudoaxial pseudoequatorial interconversion of the piperazine ring via rotation about the C C bond of the ethylene bridge. The global minimum was found to have a pseudoaxial piperazine ring and a tricyclic ring system in conformation A (Scheme 6). The complete lp N C H rotational curve, shown in Figure 8 for both the A and B groups, presents forms with a pseudoequatorial piperazine ring, and includes all other lowlying energy minima. It appears from Figure 8 that in addition to the global minimum (not shown in the graph) and to the conformer observed in the crystalline state110a,b (conformer a in Figure 8; MM2 relative energy of 0.4 kcal mol 1), only the conformer designated e (1.2 kcal mol 1) should be considered as a candidate for biological activity. All other stable forms were calculated to be 2.4 7.5 kcal mol 1 above the global minimum. Next, the lowest-energy calculated structures of compounds 67 69 were compared using a leastsquares molecular superimposition technique. The energetic cost of small variations in dihedral angles, needed to improve the overlap, was monitored by MM2. This comparison

F

F3 C

S

N

Cl

N

N

N

H3 C

HO

(67)

(68)

H H

N

i-Pr

HO

(69)

64	Pinchas Aped and Hanoch Senderowitz

N

S

N

Cl

Cl

N

S

N

A B

SCHEME 6. Reproduced with permission from J. H. Brown and C. H. Bushweller, J. Med. Chem., 31, 306 (1988)

15

− ∆E (kcal mol 1)

10
				f
5	d
		b		c
	a	e
0
0	90	180	270	360

Dihedral angle H-C-N-lp (deg)

FIGURE 8. MM2-85 calculated lp N C H rotational potential curve (C in the tricyclic ring system) for 68, with a pseudoequatorial piperazine ring. The conformations A (dashed line) and B (solid line) are defined in Scheme 6. Reproduced with permission from Reference 108

strongly suggested that the most probable candidate for the dopamine receptor active conformation is the e conformer.

In another work, a series of substituted 2-aminoindans was analyzed using MM285108. The calculated potential energy surface for rotation around the CH CH CH2 N and CH CH2 N lp in model compound 70 is presented in Figure 9 and shows 9 minima. These were scrutinized as potential candidates for dopamine receptor agonists, according to several criteria: The highest-energy conformation f (Erel D 7.3 kcal mol 1)

1. Molecular mechanics calculations

65

FIGURE 9. MM2-85 calculated torsional potential surface for the two-angle driver of the side chain of (S)-4-hydroxy-2-[(dimethylamino)methyl]indan 70. Reproduced with permission from Reference 108

OH

Me

CH2 N

Me

(70)

as well as conformers c and i, in which the nitrogen atom sticks out too far above the aromatic ring plane, were ruled out. Among the remaining conformers, only two, a and h (Erel D 2.1 and 0.0 kcal mol 1, respectively), satisfy the requirement of an N-lone pair directing downward and roughly perpendicular to the aromatic ring. These two conformers were fully minimized by MM2, and then fitted, by a least-squares method, to a known compound, used as a dopamine agonist template. Both gave reasonably good fits, and

66	Pinchas Aped and Hanoch Senderowitz

another parameter, namely the distance between the nitrogen and hydrogen bond donor group (the aromatic OH), could not assist in the distinction between them.

B. Spectroscopic Experiments and the Study of Chemical Effects

1. Nitrogen proton affinities and amine basicity

Alder and coworkers have used an early version of Allinger’s molecular mechanics program series, MM1, in their study of bicyclic amines and diamines with bridgehead nitrogens111. The work was aimed at rationalizing the measured proton affinities and ionization energies of such compounds, using a combination of computational (semiempirical, ab initio and force field calculations) and experimental (photoelectron spectra, proton affinities measurements and 1H and 13C NMR) data. Because of the inclusion of specific lone pairs on sp3 nitrogens in MM1 and MM2 and the consequent inability of these force fields to treat planar nitrogen atoms (see Section II.B.3), the molecular mechanics results for these systems are only qualitative. Experimental evidence, for example, supports nearly planar bridgehead nitrogens in the monoand diazabicyclo[3.3.3]undecane (71 and 72) while for 71, MM1 finds two conformers with inside and outside pyramidal nitrogens, the latter favored by only 3.75 kcal mol 1. The calculated relative energies, N. . .N distances and C N C bond angles for the three possible basic structures of the symmetrical diamines 72 and 73 are shown in Table 26. In diamines, the nitrogen lone pairs can interact in two ways: directly through-space, or through-bond, by mixing with other or bonds in the molecule. The calculated N C C C and C C C C dihedral angles, along the hydrocarbon bridges (near-gauche in 72 and 66 and 80° in 73), are far from the optimal values for through-bond coupling (0° and 180°), thus supporting the through-space mechanism. This is in contrast with the situation in the smaller bicyclic diamines ([2.2.2] and [2.3.3]), in which the shorter bridges are in favorable conformations for through-bond interactions. The strained structures of 72, 73 and their unsymmetrical analogs, [4.3.3] and [4.4.3], force the nitrogen atoms to be more flattened compared with the smaller systems, leading to generally lower lone-pair ionization energies. At the same time the nitrogens are pushed into close proximity, increasing the overlap between the lone pairs.

H	N	N	N	N
			N
	(71)		(72)	(73)

In a later work112, Alder has used molecular-mechanics-like arguments to analyze and rationalize trends in amine basicity resulting from strain effects. The suggested model assumes that changes in (Brønsted) basicity or proton affinity (PA) result from differences in steric energy between the amine and its protonated ion. The steric energy may be divided, as is done in molecular mechanics, to contributions of bond stretching, bondangle bending, torsional strain and nonbonded interactions. In series of analog compounds, it is sometimes possible to isolate one such term as the main source of strain effecting the basicity. The quantitative application of this model requires the calculation of steric

		1. Molecular mechanics calculations				67
TABLE 26. Force		field (MM1) calculations of	1,5-diazabicyclo[3.3.3]undecane			72 and 1,6-
		˚	bond	angles in	degrees, relative energies in
diazabicyclo[4.4.4]tetradecan 73 (distances in A,
kcal mol 1)111
			C N C		N N
Structure		Symmetry	angle		distance	Erel
N	N	C3h	114.8		3.34	0.00
N	N	C3	116.2	(out)	2.61	5.56
			116.9	(in)
N	N	C3h	119.6		2.44	23.01
N	N	D3	117.2		4.27	40.37
N	N	C3	118.2	(out)	3.34	26.97
			111.8	(in)
N	N	D3	113.8		2.61	0.00

energies of amines and their protonated analogs. Since at that time, reliable force field parameters for ammonium ions were not available, only a qualitative discussion could be held. The steric energy term which is most likely to affect amine basicity is the bending one. It is reasonable to assume that the bending potential of protonated amines resembles that of the corresponding hydrocarbons, and is much more rigid than the potential of the neutral amines, which readily inverts via a planar geometry with a relatively low energy (i.e. barrier). Thus, deviations of the C N C angle from its ideal geometry (close to tetrahedral) increases the strain difference between the amine and its protonated form, leading to a reduced basicity. Indeed, in the small-ring cyclic amine series, azetidine, aziridine and 1-azabicyclo[1.1.0]butane, the measured PA values, 222.7, 215.7 and 212 kcal mol 1, decrease in reverse proportionality to the strain of the system (an alternative explanation involves the change in hybridization around the nitrogen atom,

68	Pinchas Aped and Hanoch Senderowitz

leading to a greater s-character of the lone pair as the size of the ring is reduced). Relatively small increases in N C N bond angles are observed in the bicyclic amines series, discussed in the previous work. The measured PA values for 1-azabicyclo[2.2.2]octane (74), which has a normal pyramidal nitrogen, and for 1-azabicyclo[3.3.3]undecane (71), with an almost flat nitrogen, are almost identical (ca 233 kcal mol 1). On the other hand, in 1-azabicyclo[4.4.4]tetradecane (75), where the bridgehead nitrogen is pyramidalized inward (according to MM1 and MM2 calculations), there is a 16.5 kcal mol 1 decrease in the PA (relative to 71 and 74). This difference matches almost exactly the surplus steric energy of 18.5 kcal mol 1 calculated by MM2 for the conformer with an outwarddirected lone pair, suggesting that the decreased basicity of 75 comes almost entirely from the increase in steric energy as the nitrogen inverts outward to accept the proton.

N H

N H

(74)	(75)
While all strain effects in monoamines	are basicity weakening, it is possible to

find cases in diand polyamines where strain is relieved upon protonation, leading to increased basicity. This phenomenon is observed in 1,4-diaminobutane derivatives where an almost linear N. . .H (NC) hydrogen bond in the mono-protonated derivatives leads to a stable, seven-membered ring structure. Thus, for example, the measured PA of 1,6-diazabicyclo[4.4.4]tetradecane (73) is 228.3 kcal mol 1, about 11 kcal mol 1 higher than its monoamine analog 75, despite the similar, inwardly pyramidalized, nitrogen conformation of both neutral amines.

2. Magnetic anisotropy of cyclopropane and cyclobutane

Aromatic amino and nitro compounds were calculated using the MM2 force field in a study of the magnetic anisotropy of the cyclopropane and cyclobutane ring systems113. A series of fluorenes in which position 9 was unsubstituted, or part of a three-, fouror five-membered ring leading to a spiro system, and position 2 was substituted by H, NO2 or NH2 groups (76a c to 79a c) was synthesized and analyzed by NMR. The chemical shift of the peri hydrogens, H-1 and H-8, was used as a probe and assumed to depend on the sum of contributions from the substituted fluorene (where the contribution of the aromatic system was assumed to be constant) and the spirocycloalkanes. The two extreme cases, 76a c and 79a c, served as unperturbed, reference models. In order to isolate the special contributions from the small rings, a method developed by Allinger114 was used, which correlates proton chemical shifts with the sum of the VdW interaction energies related to these protons. For this purpose, structures 76a c to 79a c were calculated using a PCModel implementation of MM2 (MMX115), and all possible conformers and their relative populations were determined. A significant deviation from the VdW energies/chemical shift correlation in the case of the three-membered ring clearly confirmed the assumption of an upfield chemical shift induced by cyclopropane on protons located over the face of the ring.

1. Molecular mechanics calculations				69
	H	H	H
H
H			Y
H	X		H
(76)	(77)	(78)	(79)
X = CH2	C	C	C

(a)Y = H; (b) Y = NO2 ; (c) Y = NH2

3.CD spectra of N -nitrosopyrrolidines

Polonski and coworkers have used the MM2 force field in their study of the conformational dependence of Circular Dichroism (CD) of N-nitrosopyrrolidines17,116. Since no parameters were available for the N-nitroso system, preliminary parameterization work had to be done (see Section II.B.3). The bicyclic and

tricyclic N-nitrosopyrrolidine derivatives,				82		86, were synthesized and their CD
spectra recorded and			compared with that	of the related, more flexible, monocyclic
systems, 80 and 81.			The MM2 calculated geometries and conformational energies
of 80		86 compare	favorably with the available experimental data. Thus the
energy	difference between the Z and E stereoisomers for the 3-substituted pyrrolidines

(80 84) was calculated, as expected, to be very low (<0.05 kcal mol 1). The lowestenergy conformation of 81 was calculated by MM2 to be the E isomer with an equatorial phenyl substituent, a half-chair conformation of the five-membered ring and a close-to- planar NNO group, all in good agreement with the crystal structure (Table 27). The vicinal

coupling constants, 3JHCCH, between the C-alpha and C-beta protons of 82 86 were calculated for each minimum energy conformation using an improved Karplus equation

TABLE 27. A comparison of selected torsional angles (degrees) of 3-phenyl-N-nitrosopyrrolidine, 81, as calculated by MM2 and measured by X-ray crystallographya

				MM2
Torsional angleb	X-ray		E-eqc	E-ax
2-3-4-5	38.4	41.5		40.2
1-2-3-4	31.1	36.0		33.7
3-4-5-1	30.0	29.9		30.0
1-2-3-Ph	155.3	162.1		85.9
2-1-6-7	179.4	179.1		178.5
Erel (kcal mol 1)		0.00		1.28

aThe enantiomeric form was calculated by MM2. bFor numbering, see structure 81.

cEquatorial and axial phenyl groups.

70			Pinchas Aped and Hanoch Senderowitz
		R
4	3	H
5 1	2
N
6
N
7			N			N
O
(80) R =		Me		NO		ON
(81) R = Ph			exo-(82)			endo-(82)

NO

N

N

NO

exo-(83)		endo-(83)
	R
	(84)	R = Me
	(85)	R = Ph
N	(86) R = Pri

NO

(Gandour and coworkers117) and the appropriate dihedral angles obtained by MM2, and were compared with the values measured by NMR in solution. For the bicyclic derivatives, 84 86, which in solution exist in a single conformation, the calculated and experimental values agree to within 5% (standard deviation). For 82 and 83, the observed coupling constants result from the exo endo equilibrium, and the comparison with the calculated values for each conformer demonstrated the predominance of the latter form in each case. The geometry of the five-membered ring and the conformational composition in solution, established by the combined NMR MM2 study, were later used to rationalize the CD spectra of these systems. It was shown that the skeleton (five-membered ring) geometry is indeed the major factor in determining the sign of the n- Ł Cotton effect, and that the CD curve can be correctly explained using the ‘lower symmetry’ sector rule earlier proposed by these authors118.

4. 17O and 15N NMR spectra of N -nitrosamines

Cerioni has used MM2 calculations in a comparative analysis of 17O and 15N NMR spectra of a series of aliphatic and aromatic N-nitrosamines119 (no computational details were given in this work). In particular, two groups of aliphatic (87 89 and 90 92) and