Conformation and Charge Distribution of Bicyclic @-Lactams:Structure-Activity Relationships BERTA FERNANDEZ, LUiS CARBALLEIRA, and MICUEL A. RiOS Departamento de Quimica Fisica, Facultad de Quimica, Santiago de Compostela, E-15706 Spain
SYNOPSIS
The structures of 7-0x0-1-azabicyclo[ 3.2.01 heptane and its 4-oxa, 3-ethylene-4-oxa, and 3-ethylene-6-methyl-4-oxa derivatives, and of 8-0x0-1-azabicyclo[ 4.2.01 octane and its 5oxa derivative, were studied by ah initio methods. Conformations were refined without constraints using the 4-21G and the 4-21G* basis sets, and energies and charge distributions were improved by single-point6-31G*/4-21G* calculations.The results are interpreted in terms of structural trends related to B-lactamase inhibitor capability.
INTRODUCTION /3-Lactam antibiotics, which include penicillins and cephalosporins, inhibit the transpeptidases and carboxypeptidases involved in the biosynthesis of the peptidoglycan bacterial cell walls. Clavulanic acid and its derivatives are P-lactamase inhibitors whose administration in conjunction with P-lactam antibiotics allows the latter to be effective against 0-lactamase producing bacteria that would otherwise hydrolyze the antibiotic and s ~ r v i v eThe . ~ biological activity of both groups of compounds depends critically on the reactivity of the lactam ring, whose peptide bond is broken during inhibition of bacterial enzymes4s5:If the bond is too strong, as may occur in molecules in which the environment of the N atom is planar, the inhibition reaction is prevented; if the bond is too weak, which has been associated with the existence of a pyramidal N environment, the molecule may react before reaching its target enzyme. The 5- or 6-membered ring t o which the lactam ring is fused in both groups is believed to modify the reactivity of the otherwise planar lactam ring by orienting its active positions. In their M I N D 0 / 3 study of the structure of 4oxa-7-0x0-1-azabicyclo [ 3.2.01 heptane, which has the same skeleton a s clavulanic acid, Glidewell e t a1.' found t h a t the bond angles at the N atom summed to considerably less than 360" ( i n contrast ~~
Biopolymers, Vol. 32, 97-106 (1992) 0 1992 John Wiley & Sons, Inc.
CCC 0006-3525/92/010097-10$04.00
t o the planar structure of 2-azetidinone7), that this sum was very sensitive to the nature of substituents on the C atom next to the carbonyl carbon, and that the C -N bond lengths were longer and the C =0 bond length shorter than in 2-azetidinone. In a conformational study of a methyl derivative of 3-ethylene-4-oxa-7-oxo-l-azabicyclo [ 3.2.01 heptane in which the P-lactam ring was constrained t o remain planar, Vasudevan and Rao8 identified only a single, very rigid, conformation (whereas the 5-membered nonlactam ring of penicillin adopts two conformations), and emphasized that the biological activity of such systems may depend on structural features such a s the relative orientation of the two rings, the nonplanarity of the peptide bond fragment, and the configuration of the substituent a t the C5 atom (Figure 1) . Following the lead of the above studies, we have investigated the structures of 7-0x0-1-azabicyclo [ 3.2.01 heptane ( 1 ) , and its 4-oxa (3),3-ethylene-4-oxa ( 5 ) ,and 3-ethylene-6-methyl-4-oxa (6) derivatives, a n d of 8-0x0-1-azabicyclo [ 4.2.01 octane ( 2 )and its 5-oxa derivative ( 4 ) (Figure 1 ) . Since clavulanic acid analogues lacking the C3 carboxyl group were shown to be also potent P-lactamase inh i b i t o r ~ , ~we , ' considered in the choice of the compounds under study, for the sake of simplicity, compounds without the carboxyl group. We used the SCFHF method" and the 4-21G, 4-21G,* and 631G*" basis sets included in the GAUSSIAN 88 package." Geometries were calculated using the 497
98
FERNANDEZ, CARBALLEIRA, AND RIOS
H
H
Compound 2
Compound 1
H H
H
Compound 4
Compound 3
H
Compound
5
Compound 6
Figure 1. Atom numbering used for the molecules studied.
21G and the 4-21G* basis sets after checking that for 2-azetidinone the former gave results in keeping with 6-31G* * calculations and with the findings of electron diffraction, microwave, and x-ray s t u d i e ~ . ~ The skeletal starting coordinates were refined without constraints using the usual GAUSSIAN 88 convergence criteria; for 8-oxo-l-azabicyclo[ 4.2.01 octane, the "tight" option with stricter convergence thresholds was also employed at the 4-21G level, but i t was dispensed with for the remaining molecules
because in spite of using much more computer time it did not improve the calculated geometry significantly ( t h e maximum differences between the two 4-21G sets of results were 1 lop3A for bond lengths, 0.1" for bond angles and 0.5" for torsional angles (see Table 111). Once the final geometry had been obtained, Mulliken population analysis l 3 , I 4 was carried out and energies were recalculated by singlepoint 6-31G*/ /4-21G* calculations. Figure 1shows the atom numbering used for the molecules studied.
-
CONFORMATION AND CHARGE DISTRIBUTION OF P-LACTAMS
RESULTS AND DISCUSSION Table I lists our 4-21G results for 2-azetidinone together with published 6-31G* * results and experimental findings obtained by microwave spectroscopy, electron diffraction, and x-ray method^.^ Since the 4-21G geometry compared no worse with experiment than the 6-31G* * geometry, and in view of the difference in computer time between using 421G and using 6-31G* *, we felt justified in carrying out the main study with the former basis set and the 4-21G* one. Table I1 lists the calculated absolute energies and dipole moments of the molecules studied before and
after recalculation with the 6-31G * basis set, together with the absolute value of the greatest Cartesian component among all the residual forces on the atoms of each molecule.
Geometry
7-0xo-l-Azabicyclo[3.2.0]Heptane ( 1 ) and 8-Oxo-l-Azabicyclo[4.2.0]Octane ( 2 ) Comparing the 4-21G results with the 4-21G* ones (Table 111) , it can be seen that the geometrical features most affected by the introduction of polariza-
Table I Main Geometrical Features of 2-hetidinone (Bond lengths in Angstroms and Angles in Degrees) H\
H
H
,”
0
N-C2 C2-C3 c3-c4 N-C4 c2-0 N-H C3-H C4-H N-C2-C3 c2-c3-c4 C3-C4-N C4-N-C2 C2-N-H C4-N-H C3-C2-0 C2-C3-H N-C4-H C4-C3-H H-C3-H H-C3-C2-0 H-C4-N-H 0-C2-N-H C3- C2-N-
r (XR)”
r (6-31G**)”
r (4-21G)
1.380(2) 1.537(3) 1.553(5) 1.479(3) 1.201(1) .990(3) 1.105(5) 1.105(5)
1.331 1.522 1.538 1.467 1.225
1.358 1.533 1.549 1.455 1.186 .994 1.081 1.084
1.375 1.553 1.568 1.483 1.202 .995 1.079 1.079
91.1(2) 86.0(2) 87.6(1) 95.3(2)
91.7 85.9 86.2 96.2
91.2 85.6 87.0 96.2
91.0 86.2 86.4 96.4 131.3 132.2 136.4 114.0 114.0 115.2 110.6
64.8(10) 64,1(9) C4
l‘H
r (ED + MWPb
131.0(6) 136.6(3) 115.103) 114.4(9) 114.5(9) 110.0(3)
99
135.9
133.0 135.9 114.1 114.2
63.8 63.5
64.2 64.2 0.2 -0.2
a Electron diffraction (ED), microwave spectroscopy (Mw),x-ray (XR),and 6-31G** results were taken from Ref. 7 Bond lengths are rEvalues and angles r , obtained at 415 K, with standard deviations in parentheses.
100
FERNANDEZ, CARBALLEIRA, AND RIOS
Table I1 Energies (au), Dipole Moments (Debye), and Residual Forces on the Atoms (Absolute Value of the Greatest Cartesian Component, in ua) Compound
2
3
4
5
6
-399.90564 -400.15065 -400.79288
-396.64967 -396.89455 -397.55979
-435.61919 -435.88258 -436.60737
-434.42503 -434.69386 -435.41171
-473.38351 -473.67305 -474.44922
1 ~~~
Energy
4-21G 4-21G* 6-31G*
P
4-21G 4-21G* 6-31G*
4.2019 3.4909 4.0638
4.2418 3.5916 4.1832
2.8274 2.5813 3.0142
3.8278 3.2788 3.7756
2.1682 1.9722 2.3197
2.1576 1.9463 2.2873
F
4-21G 4-21G*
.0000851 .0001772
.0000035 .0000639
.0000692 .0002157
.0000858 .0001863
.0001754 .0002353
.0003649 .00008 19
-360.93785 -361.16267 -361.74534
tion functions are the C =0 bond lengths ( 0.022 8, shorter in 1 and 0.023 8, shorter in 2 ) and the C -N -C bond angle between the two rings. Like the MIND0/3 study' of a compound of this type, our results (Table 111) show that the introduction of the second ring makes the p-lactam ring deviate from planarity, with a C5-N4-C7-C6 torsional angle of 12.0" in 1 and C6-N5-C8-C7 of 7.6" in 2 (4-21G* values). This changes the environment of the N atom from planar to pyramidal, the distance between the N atom and the plane of its three substituents being 0.464 8, in 1 and 0.223 A in 2 as against only 0.002 8, in 2-azetidinone. The torsional angles that reflect the relative configuration of the two rings are closer in 1 than in 2 because of the greater rigidity of the 5-membered ring. The 6membered ring has a chair conformation, with torsional angles deviating from those of the ideal chair at most by about 20'. In the 5-membered ring, atoms 4, 5 , 3, and 2 are almost coplanar. 4-Oxa-7-0x0-1 -Azabicyclo [ 3.2.01 Heptane ( 3 ) and 5-Oxa-8-0x0- 1-Aza-Bicyclo [ 4.2.01 Octane ( 4 )
From the comparison of the 4-21G values with the 4-21G* ones, it follows that in both compounds the greatest discrepancies are in the 01-C2 bond length and in the C -N -C angle between the two rings. Comparing the 4-21G - 4-21G* differences obtained for 1 with those obtained for 3, it can be Seen that they are smaller than 0.01 A for bond lengths and than 1.1' for bond angles. The substitution of 0 1 for C1 makes the environment of the N atom less planar, the 4-21G* distance from N to the plane of its neighbors being
0.518 8, in 3 and 0.298 8, in 4 as against 0.464 A in 1 and 0.223 A in 2. The departure of the N atom from planarity is also reflected in the C-N-C angles being narrower (Tables I11 and IV). The o-lactam ring is also less planar, with a C5 -N -C -C6 angle of 13.4" in 3 (as against 12.0" in 1 ) and a C6-N-C-C7 angle of 9.7" in 4 (as against 7.6" in 2 ) . In 4 the 6-membered ring has a chair conformation, the greatest deviation from the torsional angles of the perfect chair being 23.8'. The C -N bonds and the bonds of the nonlactam ring are longer in 3 than in 4, and the C-C distances of the plactam ring shorter. This reflects the greater strain of the 5-membered ring. Compound 4 exhibits anomeric effect, specifically the lengthening of the H-C2 bond trans to the oxygen lone pair in comparison with the gauche bond, and the widening of Hanti- C2 -01 in comparison with HgaLlche-C2-01 (Table V ) . Such effects have been explained as due to the stabilizing interaction between the lone pair and an antibonding orbital of the trans polar bond on the adjacent tetrahedral carbon atorn.l5 In 3 this interaction is much weaker. Comparing the results for 3 with those obtained for compounds like the amoxycillintrihydrate, bacmecillinamhydrochloride, and fluoroxacillin sodium salt monohydrate [these data have been obtained from the Cambridge Structural Database System (CSDS)],where the 01 atom has been substituted for S1, it can be seen that 3 is less planar at the Natom than the other molecules, being that the lactam ring is also less planar in 3. In the thiocompounds the conformation of the 5-membered ring differs from one molecule to the other, but the relative configuration of the two rings is the same,
o-
CONFORMATION AND CHARGE DISTRIBUTION OF 0-LACTAMS
101
for N -C7,0.024 A for C5 -N, 0.012 A for C3 -N, 0.021 A for 0 -C7,0.030 A for 0 -C5,0.036 A for 0 -C2, and 2.5' for C3 -N -C7. The torsional angles of 5 (Table 6 ) show that the C=C double bond changes the best 4-atom plane in the 5-membered ring from that formed by C2-C3-N-C5 in 3 to that formed bv C5-01 -C2-C3 in 5. These results agree with those reported by Brown et al. for the p-nitrobenzyl clavulanate, displaying this ester the same configuration as 5 and 6 . The double bond too lies almost
being that the C6 -C5 -N -C3 and O / S -C5 -N -C7 torsional angles are smaller in 3 than in the sulfur analogues. 3-Ethylene-4-Oxa-7-0x0- 1-Azabicyclo [3.2.01Heptane ( 5 ) and Its 6-Methyl Derivative ( 6 )
The 4-21G and the 4-21G* sets of results for 5 and 6 differ appreciably only for C -N and C -0 bond lengths and for the C3 -N -C7 bond angle, being that the 4-21G values are greater by about 0.013 A
Table I11 4-21G and 4-21G* Geometric Results for 1 and 2" 1 4-21G
2 4-21G*
4-21G
4-21G*
N-C7 C5-N C6 -C7 C6 -C5 0-C7 C3-N C2-C3 Cl-C5 c1- c 2
1.3982 1.4965 1.5519 1.5617 1.1998 1.4714 1.5664 1.5367 1.5571
1.3900 1.4757 1.5426 1.5498 1.1781 1.4633 1.5539 1.5364 1.5465
N-C8 C6-N C7 -C8 C7 -C6 C4-N c 3 -c 4 C2 -C3 C1- C6 c1- c 2 0-C8
1.3735 (1.3732) 1.4803 (1.4797) 1.5543 (1.5546) 1.5664 (1.5666) 1.4486 (1.4482) 1.5448 (1.5449) 1.5475 (1.5476) 1.5270 (1.5270) 1.5489 (1.5491) 1.2041 (1.2042)
1.3671 1.4632 1.5455 1.5538 1.4445 1.5387 1.5412 1.5307 1.5414 1.1815
C5-N-C7 C6-C7-N C6- C5-N 0 -C7-C6 C3-N-C7 c 2 -c1- c 5 C2- C3-N C1- C5 -C6 c1- c 2 - c 3
93.59 91.76 87.77 136.71 126.74 102.85 102.87 118.09 105.07
92.82 91.98 88.50 136.52 123.39 102.35 103.39 118.74 104.56
C6- N-C8 C7 -C8-N C7- C6- N C4- N -C6 C3 -C4 -N c 2 -c3- c 4 C1-C6-N c1-c2-c3 C2 -C1 -C6 0-C8-N
96.16 (96.22) 91.00 (90.99) 86.69 (86.69) 125.61 (125.58) 108.67 (108.60) 111.04 (111.01) 109.73 (109.71) 111.06 (111.07) 109.07 (109.04) 132.08 (132.11)
95.62 91.04 87.22 125.59 109.95 111.19 111.10 110.91 109.67 132.19
C5 -N-C7-C6 C6- C5- N-C7 C5-C6-C7-N C7- C6- C5 -N
9.65 -9.59 -9.26 8.64
11.96 -11.90 -11.42 10.74
C6- N -C8-C7 C7 -C6N- C8 C6- C7-C8N C8-C7 -C6- N
4.55 -4.52 -4.28 3.98
C1 -C5-N-C3 C2 -C3 -NC5 C1 -C2 -C3N C2- C1- C5 -N c5-c1- c 2 -c3
-24.15 2.23 20.56 35.28 -35.24
-20.93 -1.67 23.59 34.28 -36.02
C1- C6 -N -C4 C3- C4 -N -C6 C2- C3 -C4-N c1-c2-c3-c4 C2-C1 -C6-N C6-C1 -C2-C3
C6- C5 -N -C3 C1 -C5 -NC7
-142.42 108.68
-140.13 107.30
-167.10
-167.01
C5-N
-C7 -0
C7C1-
C6-N -C4 C6 -N -C8
C6-N-
C8-
0
(4.16) (-4.13) (-3.91) (3.64)
7.57 -7.54 -7.12 6.66
-45.21 (-45.46) 43.10 (43.41) -46.75 (-46.79) 59.63 (59.66) 49.10 (49.14) -60.37 (-60.31)
-40.73 39.63 -45.86 59.23 46.75 -59.13
-163.79 (-164.14) 114.06 (114.54)
-159.54 111.27
-174.37 (-174.79)
-171.24
~~~
a
Bond lengths are in A and angles in degrees. For 2,values obtained using nontight convergence criteria are shown in parentheses.
102
FERNANDEZ, CARBALLEIRA, AND RIOS
Table IV 4-21G and 4-21G* Geometric Results for 3 and 4 (Bond Lengths Are in bi and Angles in Degrees 4
3 4-21G
4-21G
4-21G*
4-21G*
N-C7 C5-N C6-C7 C6-C5 0-C7 C3-N C2 -C3 01-C5 01-c 2
1.4176 1.4802 1.5495 1.5477 1.1953 1.4665 1.5747 1.4353 1.4604
1.4047 1.4612 1.5405 1.5397 1.1749 1.4589 1.5582 1.4002 1.4178
N-C8 C6-N C7 -C8 C7 -C6 C4-N c 3 -c4 C2 -C3 01-C6 01-c2 0-C8
1.3868 1.4666 1.5534 1.5518 1.4532 1.5465 1.5388 1.4248 1.4557 1.2002
1.3780 1.4519 1.5440 1.5431 1.4481 1.5388 1.5339 1.3951 1.4164 1.1788
C5-N-C7 C6-C7-N C5-C6C7 0-C7-N C3 -N -C7 C2 -01-C5 C2-C3-N 01-C5 -C6 01-C2-C3
92.54 91.35 85.10 130.92 123.86 108.89 102.22 112.08 106.18
91.73 91.81 83.81 130.94 120.83 107.00 101.68 112.70 105.75
C6- N- C8 C7-C8-N C6 -C7 -C8 C4-N-C8 C3-C4-N c 2 - c 3- c 4 01-C6-N 01-C2-C3 C2-01 -C6 0-C8-N
95.27 90.71 85.56 123.61 107.76 110.47 111.30 110.53 112.19 131.77
94.58 90.94 84.72 128.87 108.69 110.02 112.61 110.55 111.76 131.86
C5-NC7- C6 C5 -C6C7- N C7 -C6- C5 -N C6-C5-N-C7
10.77 -10.32 9.88 -10.78
13.37 -12.74 12.24 -13.37
C6 -NC8- C7 C6- C7 -C8-N C8- C7- C6- N C7-C6-N-C8
6.08 -5.74 5.43 -6.09
9.67 -9.10 8.64 -9.68
01-C5-N -C3 C2- C3 -N- C5 01-C2-C3-N C2-Ol-C5-N c 5 - 0 1 -c2-c3
-26.12 13.06 4.58 28.69 -21.15
-23.53 4.52 15.73 34.05 -31.30
01-C6- N -- C4 C3 -C4- N -- C6 C2 -C3- C4-N 01-c2-c3-c4 C2-01-C6-N C6-01 -C2-C3
-42.94 40.73 -46.06 59.31 50.24 -61.54
-40.02 36.17 -43.25 59.56 51.42 -63.74
-138.65 101.75
-137.01 100.11
C7-C6-N-C4 01-C6-N -C8
-155.89 106.86
-153.07 103.38
-166.58
-163.09
C6-N
-173.10
-169.33
C6-C5 -N-C3 01-C5-N -C7 c5-
c4-c7-
0
in the plane of atoms 5, 1, 2, and 3, the 4-21G* C5 -01-C2 =C torsional angles being about 176". The P-lactam ring is slightly more planar in 5 than in 3. The C7-N bond is larger in 5 than in 3,and in both cases shorter than that reported for the p -nitrobenzyl clavulanate.16 This bond distance is related to the reactivity of these compounds, which is greater for a larger, and consequently more labile, C7 -N bond. The introduction of the methyl substituent causes no appreciable effect on this bond distance.
-C8-0
Table V 4-2 lG* Geometric Features of 3 and 4 Related to Anomeric Trends (Bond Lengths Are in bi and Angles in Degrees) Compound Hanti-C2 C2 Honti- C2 -01 HgaUck -C2 -01 HgOMhe-
3
4
1.0896 1.0842 110.63 108.06
1.0935 1.0846 110.48 106.33
CONFORMATION AND CHARGE DISTRIBUTION OF P-LACTAMS
The greatest differences between 3 and 5 in regard to bond lengths and angles involve the oxygen of the &membered ring, the length of the 0-C2 bond decreasing by 0.049 A and the O-C2-C3 and C2 -01-C5 angles increasing by about 3.4". The distance from the N atom to the plane of its three neighbors is 0.519 A in 5 and 0.524 A in 6 as against 0.518 A in 3,showing that both the double bond and the methyl group decrease the planarity of the N atom environment. Comparing the results for 5 with those obtained through the x-ray analysis of 4-nitrobenzyl-3-ben-
103
zylidene-7-oxo-4-thia-l-azabicyclo [ 3.2.0 ] heptane2-carboxylate ( A )and 4-nitrobenzyl- [ 3SR,5RS,Z]2 - (2-phenylthioethylidene)-penam-3-carboxylate (B; these data have been obtained from the CSDS; Figure a ) , it follows that as in the case of 3, the sulfur analogues are more planar at the N atoms. The torsional angles that give insight into the relative conformation of the two rings are smaller in 5 , and the C5 -01-C2 -C3 environment is much more planar in 5 than in the sulfur analogues (absolute values of 3.6" in 5 against 8.4" in A and 6.9" in B ) . These result supports the fact that the
Table VI 4-21G and 4-21G* Geometric Results for 5 and 6 (Bond Lengths are in hi and Angles in Degrees) 6
5
4-21G
4-21G*
4-21G
4-21G* ~
N-C7 C5-N C6-C7 C6 -C5 0-C7 C3-N C2 -C3 c=c2 01-C5 01-c2
1.4225 1.4808 1.5492 1.5466 1.1939 1.4672 1.5342 1.3094 1.4419 1.4040
1.4091 1.4565 1.5404 1.5411 1.1734 1.4545 1.5284 1.3138 1.4113 1.3684
1.4215 1.4807 1.5468 1.5541 1.1953 1.4668 1.5339 1.3094 1.4420 1.4055
1.4090 1.4568 1.5400 1.5479 1.1747 1.4546 1.5279 1.3137 1.4120 1.3694
C5-N-C7 C6-C7-N C6- C5 -N 0-C7-N C3-N-C7 C2-C3-N c=c2-c3 01-C5-C6 01-C2C3 C2-01-C5
92.57 91.37 89.31 130.84 123.33 101.60 128.79 113.14 109.11 110.51
92.10 91.68 89.87 130.82 120.89 101.79 128.04 113.77 109.16 110.39
92.38 91.66 89.16 130.88 123.10 101.65 128.91 113.94 109.05 110.51
91.77 91.94 89.82 130.89 120.48 101.86 128.18 114.19 109.09 110.40
C5-N-C7-C6 C6- C5-N -C7 C7-C6-C5-N C5 -C6C7-N
9.14 -9.15 8.42 -8.77
11.83 -11.82 10.85 -11.22
10.50 -10.45 9.62 -10.03
13.31 -13.23 12.16 -12.59
-22.42 19.88 -10.15 15.36 -3.34
-20.80 17.85 -8.94 14.83 -3.62
-22.62 19.61 -9.46 16.01 -4.21
-21.20 18.01 -8.76 15.36 -4.07
-136.14 104.56
-135.53 102.91
-137.11
104.05
-136.35 101.91
-168.63 176.70
-165.20 176.55
-165.34 175.70
-162.46 176.09
01-C5-NC3 C2-C3-N-C5 01-C2-C3-N C2-01 -C5-N c 5 -01 -c2 -c3 C6- C5- N01-C5-N-C7 C5 -Nc5-01
C3
C7- 0 -c2 =c
104
FERNANDEZ, CARBALLEIRA, AND RIOS
N02
0
H
H
Compound A
H
0-
H
H
Compound 8 Figure 2.
Compounds A and B (see text).
activity of clavulanic acid is higher than that of its sulfur a n a I ~ g u e s . l ~ - ~ ~ The torsional angles most affected by the introduction of the methyl group in 5 to give 6 are those involving C6 -H. Of the skeletal torsional angles, the most affected are those involving the C = O bond. In keeping with these alterations, the bond length to change most is C6-Cc5 and the most altered bond angles are the H -C6- C. The introduction of the methyl substituent has no significant effect in the configuration of the bicyclic ring system. Charge Distributions
Figure 3 displays the net atomic charges on the skeleta1 atoms as calculated by Mulliken population a n a l y ~ i sat~ the ~,~ ~ 6-31G*//4-21G* level. It should
be borne in mind, of course, that the results of the Mulliken population method depend heavily on the basis set used, but through a qualitative analysis it can be seen that in all the molecules the most positively charged atom-the one most exposed to nucleophilic attack-is the P-lactam carbonyl carbon. The most negative-the center for electrophilic attack-is N in 1, 2, and 4, and the intracyclic 0 in the other molecules.
Conclusions From the obtained results it follows that the closer the structure is to that of the clavulanic acid, the smaller the planarity at the N-atom environments and the longer the C7 -N bond length; therefore the compound should be more active as a p-lactam-
CONFORMATION AND CHARGE DISTRIBUTION OF (3-LACTAMS
Compound 1
Compound 3
Compound 5
105
Compound 2
Compound
4
Compound 6
Figure 3. Net atomic charges on the skeletal atoms for the molecules studied.
ase inhibitor. In 6 this planarity is even smaller, and if the methyl group is oriented toward the face of the molecule where it will not interfere the fitting with the enzyme,' 6 would be more active than the other studied systems. The sulfur compounds are much more planar than the clavulanic acid analogues, with larger torsional angles between the two rings, more planar 4- and 5-membered rings, and more planar N-atom environments. These results explain why the sulfur analogues are much less active than the clavulanic acid derivative^.^^-^^
The authors are grateful to the Xunta de Galicia for financial support. BF received an FPI grant from the Spanish Ministry of Education and Science.
REFERENCES 1. Boyd, D. B. (1982) in Chemistry and Biology of pLuctum Antibiotics Vol. 1, Morin, R. B. & Gorman, M., Eds., Academic Press, New York, pp. 500-545. 2. Cole, M. (1984) in Antimicrobial Agriculture, Pro-
106
FERNANDEZ, CARBALLEIRA, AND RIOS
ceedings of the International Symposium on Antibiotic Agriculture: Benefits Malefits, Vol. 4, Woodbine, Malcolm, Eds., Butterworth, London, pp. 5-29. 3. Brooks, G., Bruton, G., Finn, M. J., Harbridge, J. B., Harris, M. A., Howarth, T. J., Hunt, E., Stirling, I. & Zomaya, 1. I. ( 1985) Recent Advances in Chemistry of the &Lactam Antibiotics Vol. 52, Special PublicationRoyal Society of Chemistry, London, pp. 222-241. 4. Roberts, S. M. & Price, B. J. (1985) in Medicinal Chemistry: The Role of Organic Chemistry in Drug Research, Academic Press, London, pp. 227-248. 5. Boyd, D. B. (1977) Int. J. Quantum Chem. Quantum Biol. Sympos. 4, 161-167. 6. Glidewell, C. & Mollison, G. S. M. (1981) J. Mol. Struct. 72,203-208. 7. Marstokk, K. M., Mollendal, H., Samdal, S. & Uggerud, E. (1989) Acta Chem. Scand. 43, 351-363. 8. Vasudevan, T. K. & Rao, V. S. R. ( 1981)Biopolymers 20,865-877. 9. Mak, C. P., Prasad, K. & Turnowsky, F. (1983) J. Antibiot. 36, 398-406. 10. Szabo, A. & Ostlund, N. S. (1989) Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, McGraw-Hill, New York, pp. 131152. 11. Hehre, W. J., Radom, L., Schleyer, P. v. R. & Pople, J. A. ( 1986) Ab Znitio Molecular Orbital Theory, John Wiley & Sons, Inc., New York, pp. 80-82. 12. Frisch, M. J., Head-Gordon, M., Schlegel, H. B., Ra-
ghavachari, K., Binkley, J. S., Gonzalez, C., Defrees, D. J., Fox, D. J., Whiteside, R. A., Seeger, R., Melius, C. F., Baker, J., Martin, R. L., Kahn, L. R., Stewart, J. J. P., Fluder, E. M., Topiol, S. & Pople, J. A. (1988) Gaussian 88, Gaussian, Inc., Pittsburgh, PA. 13. Baker, J. (1985) Theor. Chim. Actu 68,221-229. 14. Hunizaga, S. & Narita, S. (1980) Isr. J . Chem. 19, 242-254. 15. Schafer, L., Van Alsenoy, C., Williams, J. O., Scarsdale, J. N. & Geise, H. J. (1981) J. Mol. Struct. (Theochem.) 7 6 , 349-361. 16. Brown, A. G., Corbett, D. F., Goodacre, J., Harbridge, J. B., Howarth, T. T., Ponsford, R. J., Stirling, I. & King, T. J. (1984) J. Chem. SOC.Perkin Trans. I635650. 17. Cherry, P. C., Evans, D. N., Newall, C. E., Watson, N. S., Murray-Rust, P. & Murray-Rust, J. (1980) Tetrahedr. Lett. 21,561-564. 18. Brain, E. G., Broom, N. J. P. & Hickling, R. I. (1981) J. Chem. SOC.Perkin Z 892-896. 19. Arrowsmith, J. E. & Greengrass, C . W. (1982) Tetrahedr. Lett. 23, 357-360. 20. Douglas, J. L., Martel, A., Caron, G., MBnard, M., Silveira, L. & Clardy, J. (1984) Can. J. Chem. 62, 2282-2286.
Received March 4, 1991 Accepted August 15, 1991
SYNOPSIS
The structures of 7-0x0-1-azabicyclo[ 3.2.01 heptane and its 4-oxa, 3-ethylene-4-oxa, and 3-ethylene-6-methyl-4-oxa derivatives, and of 8-0x0-1-azabicyclo[ 4.2.01 octane and its 5oxa derivative, were studied by ah initio methods. Conformations were refined without constraints using the 4-21G and the 4-21G* basis sets, and energies and charge distributions were improved by single-point6-31G*/4-21G* calculations.The results are interpreted in terms of structural trends related to B-lactamase inhibitor capability.
INTRODUCTION /3-Lactam antibiotics, which include penicillins and cephalosporins, inhibit the transpeptidases and carboxypeptidases involved in the biosynthesis of the peptidoglycan bacterial cell walls. Clavulanic acid and its derivatives are P-lactamase inhibitors whose administration in conjunction with P-lactam antibiotics allows the latter to be effective against 0-lactamase producing bacteria that would otherwise hydrolyze the antibiotic and s ~ r v i v eThe . ~ biological activity of both groups of compounds depends critically on the reactivity of the lactam ring, whose peptide bond is broken during inhibition of bacterial enzymes4s5:If the bond is too strong, as may occur in molecules in which the environment of the N atom is planar, the inhibition reaction is prevented; if the bond is too weak, which has been associated with the existence of a pyramidal N environment, the molecule may react before reaching its target enzyme. The 5- or 6-membered ring t o which the lactam ring is fused in both groups is believed to modify the reactivity of the otherwise planar lactam ring by orienting its active positions. In their M I N D 0 / 3 study of the structure of 4oxa-7-0x0-1-azabicyclo [ 3.2.01 heptane, which has the same skeleton a s clavulanic acid, Glidewell e t a1.' found t h a t the bond angles at the N atom summed to considerably less than 360" ( i n contrast ~~
Biopolymers, Vol. 32, 97-106 (1992) 0 1992 John Wiley & Sons, Inc.
CCC 0006-3525/92/010097-10$04.00
t o the planar structure of 2-azetidinone7), that this sum was very sensitive to the nature of substituents on the C atom next to the carbonyl carbon, and that the C -N bond lengths were longer and the C =0 bond length shorter than in 2-azetidinone. In a conformational study of a methyl derivative of 3-ethylene-4-oxa-7-oxo-l-azabicyclo [ 3.2.01 heptane in which the P-lactam ring was constrained t o remain planar, Vasudevan and Rao8 identified only a single, very rigid, conformation (whereas the 5-membered nonlactam ring of penicillin adopts two conformations), and emphasized that the biological activity of such systems may depend on structural features such a s the relative orientation of the two rings, the nonplanarity of the peptide bond fragment, and the configuration of the substituent a t the C5 atom (Figure 1) . Following the lead of the above studies, we have investigated the structures of 7-0x0-1-azabicyclo [ 3.2.01 heptane ( 1 ) , and its 4-oxa (3),3-ethylene-4-oxa ( 5 ) ,and 3-ethylene-6-methyl-4-oxa (6) derivatives, a n d of 8-0x0-1-azabicyclo [ 4.2.01 octane ( 2 )and its 5-oxa derivative ( 4 ) (Figure 1 ) . Since clavulanic acid analogues lacking the C3 carboxyl group were shown to be also potent P-lactamase inh i b i t o r ~ , ~we , ' considered in the choice of the compounds under study, for the sake of simplicity, compounds without the carboxyl group. We used the SCFHF method" and the 4-21G, 4-21G,* and 631G*" basis sets included in the GAUSSIAN 88 package." Geometries were calculated using the 497
98
FERNANDEZ, CARBALLEIRA, AND RIOS
H
H
Compound 2
Compound 1
H H
H
Compound 4
Compound 3
H
Compound
5
Compound 6
Figure 1. Atom numbering used for the molecules studied.
21G and the 4-21G* basis sets after checking that for 2-azetidinone the former gave results in keeping with 6-31G* * calculations and with the findings of electron diffraction, microwave, and x-ray s t u d i e ~ . ~ The skeletal starting coordinates were refined without constraints using the usual GAUSSIAN 88 convergence criteria; for 8-oxo-l-azabicyclo[ 4.2.01 octane, the "tight" option with stricter convergence thresholds was also employed at the 4-21G level, but i t was dispensed with for the remaining molecules
because in spite of using much more computer time it did not improve the calculated geometry significantly ( t h e maximum differences between the two 4-21G sets of results were 1 lop3A for bond lengths, 0.1" for bond angles and 0.5" for torsional angles (see Table 111). Once the final geometry had been obtained, Mulliken population analysis l 3 , I 4 was carried out and energies were recalculated by singlepoint 6-31G*/ /4-21G* calculations. Figure 1shows the atom numbering used for the molecules studied.
-
CONFORMATION AND CHARGE DISTRIBUTION OF P-LACTAMS
RESULTS AND DISCUSSION Table I lists our 4-21G results for 2-azetidinone together with published 6-31G* * results and experimental findings obtained by microwave spectroscopy, electron diffraction, and x-ray method^.^ Since the 4-21G geometry compared no worse with experiment than the 6-31G* * geometry, and in view of the difference in computer time between using 421G and using 6-31G* *, we felt justified in carrying out the main study with the former basis set and the 4-21G* one. Table I1 lists the calculated absolute energies and dipole moments of the molecules studied before and
after recalculation with the 6-31G * basis set, together with the absolute value of the greatest Cartesian component among all the residual forces on the atoms of each molecule.
Geometry
7-0xo-l-Azabicyclo[3.2.0]Heptane ( 1 ) and 8-Oxo-l-Azabicyclo[4.2.0]Octane ( 2 ) Comparing the 4-21G results with the 4-21G* ones (Table 111) , it can be seen that the geometrical features most affected by the introduction of polariza-
Table I Main Geometrical Features of 2-hetidinone (Bond lengths in Angstroms and Angles in Degrees) H\
H
H
,”
0
N-C2 C2-C3 c3-c4 N-C4 c2-0 N-H C3-H C4-H N-C2-C3 c2-c3-c4 C3-C4-N C4-N-C2 C2-N-H C4-N-H C3-C2-0 C2-C3-H N-C4-H C4-C3-H H-C3-H H-C3-C2-0 H-C4-N-H 0-C2-N-H C3- C2-N-
r (XR)”
r (6-31G**)”
r (4-21G)
1.380(2) 1.537(3) 1.553(5) 1.479(3) 1.201(1) .990(3) 1.105(5) 1.105(5)
1.331 1.522 1.538 1.467 1.225
1.358 1.533 1.549 1.455 1.186 .994 1.081 1.084
1.375 1.553 1.568 1.483 1.202 .995 1.079 1.079
91.1(2) 86.0(2) 87.6(1) 95.3(2)
91.7 85.9 86.2 96.2
91.2 85.6 87.0 96.2
91.0 86.2 86.4 96.4 131.3 132.2 136.4 114.0 114.0 115.2 110.6
64.8(10) 64,1(9) C4
l‘H
r (ED + MWPb
131.0(6) 136.6(3) 115.103) 114.4(9) 114.5(9) 110.0(3)
99
135.9
133.0 135.9 114.1 114.2
63.8 63.5
64.2 64.2 0.2 -0.2
a Electron diffraction (ED), microwave spectroscopy (Mw),x-ray (XR),and 6-31G** results were taken from Ref. 7 Bond lengths are rEvalues and angles r , obtained at 415 K, with standard deviations in parentheses.
100
FERNANDEZ, CARBALLEIRA, AND RIOS
Table I1 Energies (au), Dipole Moments (Debye), and Residual Forces on the Atoms (Absolute Value of the Greatest Cartesian Component, in ua) Compound
2
3
4
5
6
-399.90564 -400.15065 -400.79288
-396.64967 -396.89455 -397.55979
-435.61919 -435.88258 -436.60737
-434.42503 -434.69386 -435.41171
-473.38351 -473.67305 -474.44922
1 ~~~
Energy
4-21G 4-21G* 6-31G*
P
4-21G 4-21G* 6-31G*
4.2019 3.4909 4.0638
4.2418 3.5916 4.1832
2.8274 2.5813 3.0142
3.8278 3.2788 3.7756
2.1682 1.9722 2.3197
2.1576 1.9463 2.2873
F
4-21G 4-21G*
.0000851 .0001772
.0000035 .0000639
.0000692 .0002157
.0000858 .0001863
.0001754 .0002353
.0003649 .00008 19
-360.93785 -361.16267 -361.74534
tion functions are the C =0 bond lengths ( 0.022 8, shorter in 1 and 0.023 8, shorter in 2 ) and the C -N -C bond angle between the two rings. Like the MIND0/3 study' of a compound of this type, our results (Table 111) show that the introduction of the second ring makes the p-lactam ring deviate from planarity, with a C5-N4-C7-C6 torsional angle of 12.0" in 1 and C6-N5-C8-C7 of 7.6" in 2 (4-21G* values). This changes the environment of the N atom from planar to pyramidal, the distance between the N atom and the plane of its three substituents being 0.464 8, in 1 and 0.223 A in 2 as against only 0.002 8, in 2-azetidinone. The torsional angles that reflect the relative configuration of the two rings are closer in 1 than in 2 because of the greater rigidity of the 5-membered ring. The 6membered ring has a chair conformation, with torsional angles deviating from those of the ideal chair at most by about 20'. In the 5-membered ring, atoms 4, 5 , 3, and 2 are almost coplanar. 4-Oxa-7-0x0-1 -Azabicyclo [ 3.2.01 Heptane ( 3 ) and 5-Oxa-8-0x0- 1-Aza-Bicyclo [ 4.2.01 Octane ( 4 )
From the comparison of the 4-21G values with the 4-21G* ones, it follows that in both compounds the greatest discrepancies are in the 01-C2 bond length and in the C -N -C angle between the two rings. Comparing the 4-21G - 4-21G* differences obtained for 1 with those obtained for 3, it can be Seen that they are smaller than 0.01 A for bond lengths and than 1.1' for bond angles. The substitution of 0 1 for C1 makes the environment of the N atom less planar, the 4-21G* distance from N to the plane of its neighbors being
0.518 8, in 3 and 0.298 8, in 4 as against 0.464 A in 1 and 0.223 A in 2. The departure of the N atom from planarity is also reflected in the C-N-C angles being narrower (Tables I11 and IV). The o-lactam ring is also less planar, with a C5 -N -C -C6 angle of 13.4" in 3 (as against 12.0" in 1 ) and a C6-N-C-C7 angle of 9.7" in 4 (as against 7.6" in 2 ) . In 4 the 6-membered ring has a chair conformation, the greatest deviation from the torsional angles of the perfect chair being 23.8'. The C -N bonds and the bonds of the nonlactam ring are longer in 3 than in 4, and the C-C distances of the plactam ring shorter. This reflects the greater strain of the 5-membered ring. Compound 4 exhibits anomeric effect, specifically the lengthening of the H-C2 bond trans to the oxygen lone pair in comparison with the gauche bond, and the widening of Hanti- C2 -01 in comparison with HgaLlche-C2-01 (Table V ) . Such effects have been explained as due to the stabilizing interaction between the lone pair and an antibonding orbital of the trans polar bond on the adjacent tetrahedral carbon atorn.l5 In 3 this interaction is much weaker. Comparing the results for 3 with those obtained for compounds like the amoxycillintrihydrate, bacmecillinamhydrochloride, and fluoroxacillin sodium salt monohydrate [these data have been obtained from the Cambridge Structural Database System (CSDS)],where the 01 atom has been substituted for S1, it can be seen that 3 is less planar at the Natom than the other molecules, being that the lactam ring is also less planar in 3. In the thiocompounds the conformation of the 5-membered ring differs from one molecule to the other, but the relative configuration of the two rings is the same,
o-
CONFORMATION AND CHARGE DISTRIBUTION OF 0-LACTAMS
101
for N -C7,0.024 A for C5 -N, 0.012 A for C3 -N, 0.021 A for 0 -C7,0.030 A for 0 -C5,0.036 A for 0 -C2, and 2.5' for C3 -N -C7. The torsional angles of 5 (Table 6 ) show that the C=C double bond changes the best 4-atom plane in the 5-membered ring from that formed by C2-C3-N-C5 in 3 to that formed bv C5-01 -C2-C3 in 5. These results agree with those reported by Brown et al. for the p-nitrobenzyl clavulanate, displaying this ester the same configuration as 5 and 6 . The double bond too lies almost
being that the C6 -C5 -N -C3 and O / S -C5 -N -C7 torsional angles are smaller in 3 than in the sulfur analogues. 3-Ethylene-4-Oxa-7-0x0- 1-Azabicyclo [3.2.01Heptane ( 5 ) and Its 6-Methyl Derivative ( 6 )
The 4-21G and the 4-21G* sets of results for 5 and 6 differ appreciably only for C -N and C -0 bond lengths and for the C3 -N -C7 bond angle, being that the 4-21G values are greater by about 0.013 A
Table I11 4-21G and 4-21G* Geometric Results for 1 and 2" 1 4-21G
2 4-21G*
4-21G
4-21G*
N-C7 C5-N C6 -C7 C6 -C5 0-C7 C3-N C2-C3 Cl-C5 c1- c 2
1.3982 1.4965 1.5519 1.5617 1.1998 1.4714 1.5664 1.5367 1.5571
1.3900 1.4757 1.5426 1.5498 1.1781 1.4633 1.5539 1.5364 1.5465
N-C8 C6-N C7 -C8 C7 -C6 C4-N c 3 -c 4 C2 -C3 C1- C6 c1- c 2 0-C8
1.3735 (1.3732) 1.4803 (1.4797) 1.5543 (1.5546) 1.5664 (1.5666) 1.4486 (1.4482) 1.5448 (1.5449) 1.5475 (1.5476) 1.5270 (1.5270) 1.5489 (1.5491) 1.2041 (1.2042)
1.3671 1.4632 1.5455 1.5538 1.4445 1.5387 1.5412 1.5307 1.5414 1.1815
C5-N-C7 C6-C7-N C6- C5-N 0 -C7-C6 C3-N-C7 c 2 -c1- c 5 C2- C3-N C1- C5 -C6 c1- c 2 - c 3
93.59 91.76 87.77 136.71 126.74 102.85 102.87 118.09 105.07
92.82 91.98 88.50 136.52 123.39 102.35 103.39 118.74 104.56
C6- N-C8 C7 -C8-N C7- C6- N C4- N -C6 C3 -C4 -N c 2 -c3- c 4 C1-C6-N c1-c2-c3 C2 -C1 -C6 0-C8-N
96.16 (96.22) 91.00 (90.99) 86.69 (86.69) 125.61 (125.58) 108.67 (108.60) 111.04 (111.01) 109.73 (109.71) 111.06 (111.07) 109.07 (109.04) 132.08 (132.11)
95.62 91.04 87.22 125.59 109.95 111.19 111.10 110.91 109.67 132.19
C5 -N-C7-C6 C6- C5- N-C7 C5-C6-C7-N C7- C6- C5 -N
9.65 -9.59 -9.26 8.64
11.96 -11.90 -11.42 10.74
C6- N -C8-C7 C7 -C6N- C8 C6- C7-C8N C8-C7 -C6- N
4.55 -4.52 -4.28 3.98
C1 -C5-N-C3 C2 -C3 -NC5 C1 -C2 -C3N C2- C1- C5 -N c5-c1- c 2 -c3
-24.15 2.23 20.56 35.28 -35.24
-20.93 -1.67 23.59 34.28 -36.02
C1- C6 -N -C4 C3- C4 -N -C6 C2- C3 -C4-N c1-c2-c3-c4 C2-C1 -C6-N C6-C1 -C2-C3
C6- C5 -N -C3 C1 -C5 -NC7
-142.42 108.68
-140.13 107.30
-167.10
-167.01
C5-N
-C7 -0
C7C1-
C6-N -C4 C6 -N -C8
C6-N-
C8-
0
(4.16) (-4.13) (-3.91) (3.64)
7.57 -7.54 -7.12 6.66
-45.21 (-45.46) 43.10 (43.41) -46.75 (-46.79) 59.63 (59.66) 49.10 (49.14) -60.37 (-60.31)
-40.73 39.63 -45.86 59.23 46.75 -59.13
-163.79 (-164.14) 114.06 (114.54)
-159.54 111.27
-174.37 (-174.79)
-171.24
~~~
a
Bond lengths are in A and angles in degrees. For 2,values obtained using nontight convergence criteria are shown in parentheses.
102
FERNANDEZ, CARBALLEIRA, AND RIOS
Table IV 4-21G and 4-21G* Geometric Results for 3 and 4 (Bond Lengths Are in bi and Angles in Degrees 4
3 4-21G
4-21G
4-21G*
4-21G*
N-C7 C5-N C6-C7 C6-C5 0-C7 C3-N C2 -C3 01-C5 01-c 2
1.4176 1.4802 1.5495 1.5477 1.1953 1.4665 1.5747 1.4353 1.4604
1.4047 1.4612 1.5405 1.5397 1.1749 1.4589 1.5582 1.4002 1.4178
N-C8 C6-N C7 -C8 C7 -C6 C4-N c 3 -c4 C2 -C3 01-C6 01-c2 0-C8
1.3868 1.4666 1.5534 1.5518 1.4532 1.5465 1.5388 1.4248 1.4557 1.2002
1.3780 1.4519 1.5440 1.5431 1.4481 1.5388 1.5339 1.3951 1.4164 1.1788
C5-N-C7 C6-C7-N C5-C6C7 0-C7-N C3 -N -C7 C2 -01-C5 C2-C3-N 01-C5 -C6 01-C2-C3
92.54 91.35 85.10 130.92 123.86 108.89 102.22 112.08 106.18
91.73 91.81 83.81 130.94 120.83 107.00 101.68 112.70 105.75
C6- N- C8 C7-C8-N C6 -C7 -C8 C4-N-C8 C3-C4-N c 2 - c 3- c 4 01-C6-N 01-C2-C3 C2-01 -C6 0-C8-N
95.27 90.71 85.56 123.61 107.76 110.47 111.30 110.53 112.19 131.77
94.58 90.94 84.72 128.87 108.69 110.02 112.61 110.55 111.76 131.86
C5-NC7- C6 C5 -C6C7- N C7 -C6- C5 -N C6-C5-N-C7
10.77 -10.32 9.88 -10.78
13.37 -12.74 12.24 -13.37
C6 -NC8- C7 C6- C7 -C8-N C8- C7- C6- N C7-C6-N-C8
6.08 -5.74 5.43 -6.09
9.67 -9.10 8.64 -9.68
01-C5-N -C3 C2- C3 -N- C5 01-C2-C3-N C2-Ol-C5-N c 5 - 0 1 -c2-c3
-26.12 13.06 4.58 28.69 -21.15
-23.53 4.52 15.73 34.05 -31.30
01-C6- N -- C4 C3 -C4- N -- C6 C2 -C3- C4-N 01-c2-c3-c4 C2-01-C6-N C6-01 -C2-C3
-42.94 40.73 -46.06 59.31 50.24 -61.54
-40.02 36.17 -43.25 59.56 51.42 -63.74
-138.65 101.75
-137.01 100.11
C7-C6-N-C4 01-C6-N -C8
-155.89 106.86
-153.07 103.38
-166.58
-163.09
C6-N
-173.10
-169.33
C6-C5 -N-C3 01-C5-N -C7 c5-
c4-c7-
0
in the plane of atoms 5, 1, 2, and 3, the 4-21G* C5 -01-C2 =C torsional angles being about 176". The P-lactam ring is slightly more planar in 5 than in 3. The C7-N bond is larger in 5 than in 3,and in both cases shorter than that reported for the p -nitrobenzyl clavulanate.16 This bond distance is related to the reactivity of these compounds, which is greater for a larger, and consequently more labile, C7 -N bond. The introduction of the methyl substituent causes no appreciable effect on this bond distance.
-C8-0
Table V 4-2 lG* Geometric Features of 3 and 4 Related to Anomeric Trends (Bond Lengths Are in bi and Angles in Degrees) Compound Hanti-C2 C2 Honti- C2 -01 HgaUck -C2 -01 HgOMhe-
3
4
1.0896 1.0842 110.63 108.06
1.0935 1.0846 110.48 106.33
CONFORMATION AND CHARGE DISTRIBUTION OF P-LACTAMS
The greatest differences between 3 and 5 in regard to bond lengths and angles involve the oxygen of the &membered ring, the length of the 0-C2 bond decreasing by 0.049 A and the O-C2-C3 and C2 -01-C5 angles increasing by about 3.4". The distance from the N atom to the plane of its three neighbors is 0.519 A in 5 and 0.524 A in 6 as against 0.518 A in 3,showing that both the double bond and the methyl group decrease the planarity of the N atom environment. Comparing the results for 5 with those obtained through the x-ray analysis of 4-nitrobenzyl-3-ben-
103
zylidene-7-oxo-4-thia-l-azabicyclo [ 3.2.0 ] heptane2-carboxylate ( A )and 4-nitrobenzyl- [ 3SR,5RS,Z]2 - (2-phenylthioethylidene)-penam-3-carboxylate (B; these data have been obtained from the CSDS; Figure a ) , it follows that as in the case of 3, the sulfur analogues are more planar at the N atoms. The torsional angles that give insight into the relative conformation of the two rings are smaller in 5 , and the C5 -01-C2 -C3 environment is much more planar in 5 than in the sulfur analogues (absolute values of 3.6" in 5 against 8.4" in A and 6.9" in B ) . These result supports the fact that the
Table VI 4-21G and 4-21G* Geometric Results for 5 and 6 (Bond Lengths are in hi and Angles in Degrees) 6
5
4-21G
4-21G*
4-21G
4-21G* ~
N-C7 C5-N C6-C7 C6 -C5 0-C7 C3-N C2 -C3 c=c2 01-C5 01-c2
1.4225 1.4808 1.5492 1.5466 1.1939 1.4672 1.5342 1.3094 1.4419 1.4040
1.4091 1.4565 1.5404 1.5411 1.1734 1.4545 1.5284 1.3138 1.4113 1.3684
1.4215 1.4807 1.5468 1.5541 1.1953 1.4668 1.5339 1.3094 1.4420 1.4055
1.4090 1.4568 1.5400 1.5479 1.1747 1.4546 1.5279 1.3137 1.4120 1.3694
C5-N-C7 C6-C7-N C6- C5 -N 0-C7-N C3-N-C7 C2-C3-N c=c2-c3 01-C5-C6 01-C2C3 C2-01-C5
92.57 91.37 89.31 130.84 123.33 101.60 128.79 113.14 109.11 110.51
92.10 91.68 89.87 130.82 120.89 101.79 128.04 113.77 109.16 110.39
92.38 91.66 89.16 130.88 123.10 101.65 128.91 113.94 109.05 110.51
91.77 91.94 89.82 130.89 120.48 101.86 128.18 114.19 109.09 110.40
C5-N-C7-C6 C6- C5-N -C7 C7-C6-C5-N C5 -C6C7-N
9.14 -9.15 8.42 -8.77
11.83 -11.82 10.85 -11.22
10.50 -10.45 9.62 -10.03
13.31 -13.23 12.16 -12.59
-22.42 19.88 -10.15 15.36 -3.34
-20.80 17.85 -8.94 14.83 -3.62
-22.62 19.61 -9.46 16.01 -4.21
-21.20 18.01 -8.76 15.36 -4.07
-136.14 104.56
-135.53 102.91
-137.11
104.05
-136.35 101.91
-168.63 176.70
-165.20 176.55
-165.34 175.70
-162.46 176.09
01-C5-NC3 C2-C3-N-C5 01-C2-C3-N C2-01 -C5-N c 5 -01 -c2 -c3 C6- C5- N01-C5-N-C7 C5 -Nc5-01
C3
C7- 0 -c2 =c
104
FERNANDEZ, CARBALLEIRA, AND RIOS
N02
0
H
H
Compound A
H
0-
H
H
Compound 8 Figure 2.
Compounds A and B (see text).
activity of clavulanic acid is higher than that of its sulfur a n a I ~ g u e s . l ~ - ~ ~ The torsional angles most affected by the introduction of the methyl group in 5 to give 6 are those involving C6 -H. Of the skeletal torsional angles, the most affected are those involving the C = O bond. In keeping with these alterations, the bond length to change most is C6-Cc5 and the most altered bond angles are the H -C6- C. The introduction of the methyl substituent has no significant effect in the configuration of the bicyclic ring system. Charge Distributions
Figure 3 displays the net atomic charges on the skeleta1 atoms as calculated by Mulliken population a n a l y ~ i sat~ the ~,~ ~ 6-31G*//4-21G* level. It should
be borne in mind, of course, that the results of the Mulliken population method depend heavily on the basis set used, but through a qualitative analysis it can be seen that in all the molecules the most positively charged atom-the one most exposed to nucleophilic attack-is the P-lactam carbonyl carbon. The most negative-the center for electrophilic attack-is N in 1, 2, and 4, and the intracyclic 0 in the other molecules.
Conclusions From the obtained results it follows that the closer the structure is to that of the clavulanic acid, the smaller the planarity at the N-atom environments and the longer the C7 -N bond length; therefore the compound should be more active as a p-lactam-
CONFORMATION AND CHARGE DISTRIBUTION OF (3-LACTAMS
Compound 1
Compound 3
Compound 5
105
Compound 2
Compound
4
Compound 6
Figure 3. Net atomic charges on the skeletal atoms for the molecules studied.
ase inhibitor. In 6 this planarity is even smaller, and if the methyl group is oriented toward the face of the molecule where it will not interfere the fitting with the enzyme,' 6 would be more active than the other studied systems. The sulfur compounds are much more planar than the clavulanic acid analogues, with larger torsional angles between the two rings, more planar 4- and 5-membered rings, and more planar N-atom environments. These results explain why the sulfur analogues are much less active than the clavulanic acid derivative^.^^-^^
The authors are grateful to the Xunta de Galicia for financial support. BF received an FPI grant from the Spanish Ministry of Education and Science.
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106
FERNANDEZ, CARBALLEIRA, AND RIOS
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Received March 4, 1991 Accepted August 15, 1991
