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A semiempirical AM1, MNDO and PM3 study of the rotational barriers of various ureas, thioureas, amides and thioamides
33
283 (1993) 33-48 0 1993 - Elsevier Science Publishers B.V. All rights reserved
Journal of Molecular Structure (Theochem), 01661280/93/$06.00
A semiempirical AM 1, MNDO and PM3 study of the rotational barriers of various ureas, thioureas, amides and thioamides M. Feigel*, T. Strassner Institut fir Organische Chemie, Universith’t Erlangen-Ntirnberg
Henkestrasse
42, D-8520 Erlangen, Germany
(Received 15 October 1992) Abstract AM1 proved to be the most useful method of MNDO, AM1 and PM3 for calculating rotational barriers of compounds containing a (R,R) N-CX-R linkage (amides, t ioamides, urea and thioureas). The barriers ! calculated with AM1 must be corrected using the equation AG,igtia = 1 6ADHy,,9 + 4 5 kcal mol-’ to obtain f + 2.05 kcalmol-’ the best coincidence with experimental values. Another equation, AHabinitio = 1.3JAH[,,,) reproduces recent ab initio data well.
Introduction Semiempirical calculations have been applied to nearly all areas of main group organic chemistry [l]. However, the calculated quantities are often inaccurate and should be checked against the results of experiment or the results of high-level ab initio calculations [2]. This deficiency is particularly obvious in compounds containing nitrogen where the lone pair interaction in saturated systems is questionable [3], and in heterocycles due to the electronic distribution [4]. In the present study we looked at urea and amide compounds containing the R2N-CX-R fragment (X = 0 or S) found in many biological systems. The commonly accepted picture of electron delocalization in the amide unit (from nitrogen to carbonyl oxygen) has been questioned in the light of recent ab initio calculations on formamide [5]. The present semiempirical calculations cannot * Corresponding
author.
contribute to this discussion, but have a more practical intention: do the widely distributed programs AM1 [6], MNDO [7] and PM3 [8] (with different versions in different program packages) reproduce the rotational flexibility of the unit in a large variety of substituted compounds (amides, ureas and their thio-analogues)? The increase in computational power means that it is now possible to study peptides, nucleotides and fragments of enzymes with semiempirical methods. The R2NCO-R unit is a basic constituent of the backbone of these large molecules. Is the use of semiempirical programs justified in all cases where the flexibility or rigidity of the unit is important? To check the value of the semiempirical calculations, we compared the results obtained with experimental data or with the most recent ab initio calculations. Calculational procedure We used the programs AMl, MNDO and PM3 in two computing packages: VAMP 4.40[9] (running
34
hi. Feigel and T. Strassner/J. Mol. Struct. (Theo&em) 283 (1993) 33-48
on a CONVEX C220 and an SGI-Indigo), and (running on a PC 486-33(256) with 8 Mbyte memory). The packages differ in two main aspects: the way in which the gradients are optimized (VAMP uses the EF method [l 11, whereas MOPAC uses the BFGS (for a summary see Ref. 12) gradient optimization); and MOPAC 6.0 detects -NH-COunits and adds an additional rotational barrier to this unit, if the keyword “MMOK” is used. Usually both packages gave identical results (the keyword “PRECISE” was generally used). Slight differences in the calculated energies probably result from the different optimization procedures. The only large differences seen (still less than 0.6 kcal mol-’ ) are restricted to compounds containing the sterically demanding t-butyl and i-propyl groups. All R,R’N-CORN (urea or amide) torsions were first calculated using the reaction coordinates. The dihedral angle w between the normals of the R-N-R’ and the O=C-R” planes was varied from 0” to 360” in steps of lo”, optimizing all other coordinates (see Scheme 1). The R,R’N-C unit usually becomes strongly pyramidal during the torsion which results in two different transition states for rotation, where the R,R’ groups are bent towards or away from the carbonyl oxygen atom. The values given in the tables illustrate the lower energy barrier found for the rotational trajectories. The geometries and energies of the stationary points derived from the reaction coordinates were checked with force calculations using the keywords “NLLSQ” and “FORCE” to ensure that they were MOPAC 6.0[lo]
Xl
x2
Scheme 1. Definition of the torsional angle w used in Figs. 4 to 9.
R”
Scheme 2. Definition of w and the bending angle 8 used in Figs. 1 to 3.
stationary points. Transition states can be distinguished from other stationary points by the fact that the Hessian matrix has only a single negative value for these states. The effect of pyramidalization at nitrogen during the torsion was investigated in more detail for formamide, N-methylacetamide (the parent peptide model) and N-methylurea. Energy surfaces with two and four dimensions were collected for the amides and the urea molecule, respectively, using as variables the dihedral angles w between the R”CO- and RNR’-planes (see above) and, in addition, varying the pyramidalization at the nitrogen atoms by the angle 8 defined in Scheme 2. Comparison of the AMl, MNDO and PM3 methods The energy surfaces shown in Figs. 1 to 3 give a first insight into the differences between the semiempirical methods, as applied to rotation about the CO-N bond in formamide and N-methylacetamide. The contours of equal energy spaced by 1 kcalmol-’ were obtained by varying both the angle of torsion w and the bending angle 19 (see the definition in Scheme 2). There are marked differences between the shapes of the surfaces obtained with AM1 and MNDO (Figs. 1 and 2), whereas the appearance of the corresponding PM3 surfaces (not shown) is similar to the MNDO plots. AM1 and MNDO show ground states for formamide at dihedral angles of 0”, 180” and 360”, but the methods give different pyramidalization at nitrogen. The MNDO results show the minimum energy at B = 35” whilst the
M. Feigel and T. StrassnerlJ.
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150 ‘Dihedral
200 angle
(Theochem)
250
300
283 (1993) 33-48
350
(to)’
AM 1 minimum-energy conformation is planar (13= 0.04”). The two transition states for rotation (TSt, and TS,; w = 90” and 270”, are respectively
70
60
50
6 P LB
40
d ._ 4 6 ?
30
20
10
0
0
50
100
150 ‘Dihedral
200 angle
0
50
100
150 ‘Dihedral
Fig. 1. The AM1 energy surface of formamide as a function of the torsion at the amide bond (w) and the pyramidalization at nitrogen (0). The lines are separated by 1 kcal mol-’ .
8
35
250
300
350
(co)
Fig. 2. The MNDO energy surface of formamide as a function of the torsion at the amide bond (w) and the pyramidalization at nitrogen (19). The lines are separated by 1 kcal mol-' .
200 mgk
250
300
350
(0)’
Fig. 3. The AM1 energy surface of N-methylacetamide as a function of the (C,-C-N-C) torsional angle (w) and the pyramidalization at nitrogen (0). The lines are separated by 1 kcalmol-t . The ground state at 180” corresponds to the more stable Z isomer.
shown to be strongly pyramidal by both methods; however, the actual rotation will follow the lowenergy path over TS2, where the NH2 group is bent towards the carbonyl oxygen atom (Scheme 3). These points are marked on the surface and the minimum-energy pathway is shown in the figures. Similar transition states for formamide have been described by Wiberg and Laidig [5] using high level ab initio calculations (MP3/6-3 1G**). Despite the fact that AM1 (and even more so MNDO) underestimates the height of the barrier (TS& the relative order of the stationary points calculated with the semiempirical methods is identical to the order found with ab initio calculations (Scheme 3). This fact is promising for calculations on larger systems (see below), where ab initio methods will require too much computational time. The basic shape of the surfaces is not changed by the addition of alkyl groups to the unit, as in N-methylacetamide (Fig. 3). Again, AM1 yields nearly planar ground states (models for cis and trans peptide bonds) and calculates bend transi-
M. Feigel and T. StrassnerlJ. Mol. Struct. (Theochem) 283 (1993) 33-48
36
R Ts2
d TSl
GS
R=H
TS2
TSI
GS
ab initio: (MP3/6-31G”)
15.34
17.6
0
AMl:
10.1
15.1
0
5.3
7.8
0
13.60
17.73
0
AMl:
7.79
10.71
0
MNDO:
1.3
4.21
0
MNDO: R=CH3 ab initio: (MP4(fc)SDTQ/6_3lG(d))
Scheme 3. The relative energies (kcalmol-‘) of the stationary points of formamide and dimethylacetamide. (See Refs. 5 and 23 for ab initio data.) tion states for rotation about C-N (Fig. 3), whereas MNDO and PM3 give a bent ground state for the molecule (not shown). For all the systems studied in this work, we calculated the trajectory of rotation, where pyramidalization at the nitrogen atom was not fixed. In the case of formamide this led to the curves shown in Fig. 4. Depending on the sense of torsion, MNDO and PM3 reach both transition states (TSi and T$), whereas the equal barrier heights (TS,) found with AM1 result from the nearly flat ground state with easy inversion. Three more examples of rotational trajectories are shown in Figs. 5 to 7, where all three hamiltonians are plotted together. Urea type molecules with quite ‘normal’ substituents were selected, but the shape of some of the curves is rather unexpected. The MNDO curves in Figs. 5 and 6 show an extreme at quite unusual torsional angles (minimum at 90” and maximum at ca. 0”). This is in contrast to X-ray structures where nearly planar ground states are found even in the presence of sterically demanding substituents [13]. PM3 yields very flat barriers, although the positions of
the extreme are the expected ones (Figs. 5 and 6). In the case of tetramethylurea (Fig. 7) PM3 gives a very scattered curve without any definite barrier. A careful investigation of the geometries on the rotational trajectory shows that the reason for these unexpected shapes is repulsive interactions between methyl groups attached to different nitrogen atoms. AM1 yields the highest barriers, which are closest to given experimental values (see Table l), but the absolute values are still too low. For example, comparing all three curves in Fig. 5, it is obvious that AM1 gives the closest value (3.7 kcalmol-‘) to the experimental value (9.7 kcalmol-i) (compound 69, Ref. 16). Both other methods give even smaller barriers. This seems to be due to the parameterization of nitrogen in the semiempirical hamiltonians, a problem which has recently been discussed for aromatic amines [ 141. The spike in the AM1 curve (Fig. 7) is not a plotting error, but shows the problems dealing with a one-dimensional trajectory. The rotational surface of methylated urea compounds probably has more than two dimensions - we expected that the rotation of one of the amide groups depends on the rotational orientation of the other R2N-CO bond. The most simple compound, i.e. that containing one methyl group (N-methylurea), was selected for the calculation of a two-dimensional surface, using both torsional angles (wi and w2) as coordinates (Fig. 8). The overall picture of the surface shown in Fig. 8 is as expected. Minima are found where both torsional angles w1 and wz are close to 0” or 180”, transition states appear when one coordinate is twisted to 90” or 270”, and maxima occur when both coordinates have values of 90” or 270”. However, some strange vertical textures appear in the graph. The discontinuity results from sudden inversion of either the NH2 or the NHCHj group during the forced rotation of one coordinate. Hence, the energy surface to be calculated should also contain the bending coordinates on both nitrogen atoms, which leads to a four-dimensional surface. Even if
M. Feigel and T. Strassner/J. Mol. Struct. (Theochem) 283 (1993) 33-48
37
Table 1 The activation enthalpies for bond rotation in amides and ureas calculated using different hamiltonians, data (free energies) for some dimethylamide?
and some experimental
R AH+(AMl) AH+(MNDO) AH’(PM3)
H 10.12 5.33 6.04
F 8.98 4.53 5.17
Cl 9.13 3.99 6.1
Br 10.8 4.84 5.49
J 10.48 4.93 4.6
H 9.61 5.39 5.11 19.4
F 7.21 2.51 3.76 17.1
Cl 6.79 1.77 4.12 15.4
Br 7.55 2.29 3.99 14.1
F F 9.16 4.62 5.54
Cl Cl 8.22 4.1 4.88
Br Br 5.47 3.99 5.21
J J
CH3
H
H 4.7 2.23 3.35
CHs 5.27 2.41 3.96
CH3
H HD-C6H4C 6.47 3.1 4.08
H H3CD-C6H4C 6.54 2.69 4.6
9.26 7.52 8.1
Et 9.7 4.12 6.07
n-Prop 9.63 4.09 6.01
7.8 1.3 2.92 15.6
FH$ 8.73 0.56 2.19 15.2
F2HC 9.46 0.98 3.21b 17.4
F3C 8.49 0.79 3.33 16.5
H F 9.82 5.01 5.65
H Cl 8.91 5.31 4.88
H Br 6.53 4.87 4.35
H J 4.84 1.66 4.44
H Et 5.86 2.22 3.23
H n-Prop 5.62 3.77 3.36
H i-Prop 5.69 2.56 3.18
H t-Bu 5.68 2.87 5.01
H H2N-C6H.,C 6.66 3.02 4.51
H 0aN-C6HaC 8.91 2.33 3.32
H3C
i-Prop 10.09 3.81 6.33
t-Bu 9.67 3.32 5.51
//
R-C,
%CH3)2 R AH+(AMl) AH+(MNDO) AH’(PM3) AG+(NMRsas)
RI
CH3
\N_C$
R2’
%H,
RI R2 AH+(AMl) AH+(MNDO) AH’(PM3)
AH+(AMl) AH+(MNDO) AH+(PM3)
H H 4.75 3.2 3.4
RI
H
C6HS
RZ
C6I-b
C6H5
RI R2
AH+(AMl) AH+(MNDO) AH’(PM3)
6.63 2.97 4.46
7.14 1.72 4.37
4.63 0.75 5.18 CH3
5.65 2.09 3.84
a Data for dimethylamides are from Ref. 17 (compounds b w = 80”; no convergence for w = 90”. ’ para-Substituted.
16-20 and 23-25).
is relatively easy to calculate such a surface, it is impossible to plot a four-dimensional surface, and so we selected the part which seemed of most interest in the present problem. The bending (et, 0,) combination of lowest energy was searched for in each torsional combination (q, ~2) in the fourdimensional surface. The energy of these structures is plotted in Fig. 9.
it
The surface shown in Fig. 9 has the same overall shape as that in Fig. 8, but the distortions are no longer seen. The sudden inversion at nitrogen, which causes the distortions in the twodimensional surface (Fig. 8) is now avoided, because the surface in Fig. 9, selected from the four-dimensional data set, shows only the optimum bending angle combinations.
38
M. Feigel and T. Strassner/J. Mol. Struct. (Theo&em) 283 (1993) 33-48
-42
-44
-46
I
-150
I
-100
Fig. 4. Energy (AHr in kcalmol-‘)
I
-50
I
I
0
50
I
100
150
of formamide, calculated using AM1 (-O-), MNDO (- + -) and PM3, (-Cl-), as a function of the torsion w (see Scheme 1).
Calculation of the four-dimensional surfaces of all the compounds studied in this work would, even with AMl, need so much computer time that such an exercise is impractical. We therefore restricted our study to one-dimensional trajectories (in w) and have proven the nature of the transition states by force calculations. For- N-methylurea this procedure yields the same barrier heights as found with the full four-dimensional approach. Table 1 shows the height of the barriers for some compounds, calculated with all three hamiltonians as described above. Comparison of the results of the calculations with experimental data (Table 1) proves that AM1 is the best choice. AM1 still underestimates the barriers, but the variation in values with substitution seems to be in line with the experimental data. Thus we decided to use AM1
for a more comprehensive (see below).
set of calculations
Rotational barriers of various compounds obtained witb the AM1 hamiltonian of different program packages (MOPAC and VAMP) The activation energies of rotation were obtained as explained above. The values given in Tables 2 to 5 prove that the results of VAMP and MOPAC (NOMM) are very similar. Small differences of up to 0.2 kcalmol-’ are due to the different methods of optimization. The keyword “MMOK” allows MOPAC to apply a molecular mechanics correction, so that the barrier of rotation is increased (to 14.00 kcal mol-’ in N-methylacetamide [15]). In general, when the option MMOK is used, values are obtained which
M. Feigel and T. Strassner/J. Mol. Strut.
(Theochem) 283 (1993) 33-48
39
-60
-65 -150 Fig. 5. Energy (A&
-100 kcalmol-‘)
-50
0
50
100
of (Z)-1-isopropyl-3,3-dimethylurea, calculated using AM1 (-O-), (-(I-), as a function of the torsion w (see Scheme 1).
150 MNDO (- + -) and PM3
do not carry a hydrogen atom on the nitrogen atom and thus it is not possible to use the keyword MMOK. Furthermore, applying this correction to urea units, the forced planarity at one of the
are 9.3 f 1.0 kcal mol-’ higher than the NOMM value. Thus the use of MMOK leads to an added increment for systems which contain -NH-COgroups. However, many natural amides and ureas
Table 2 AM1 calculated activation enthalpies of the C-N bond rotation in amides’
No. R VAMP MOPAC
5 J 10.48
6 HsC 9.26
7 Et 9.7
10.8 20.71
10.48 20.3
9.27 18.94
9.69
9.62
19.9
18.84
19.23
10 t-Bu 9.67
11 HO 4.05
12 CHO 11.69
13 HOOC 14.49
HzB 7.99
15 NC 10.68
9.89
4.04 13.86
11.69 21.49
14.5 24.35
8.58 18.22
10.68 20.52
2 F 8.98
3 Cl 9.73
10.12 19.91
8.97 18.96
9 i-Prop 10.09 10.04 19.71
19.87
8 n-Prop 9.63
6
NOMM MMOK No. R VAMP MOPAC
4 Br 10.8
1 H 10.12
9.73
14
6
NOMM MMOK
’ The program packages
VAMP
and
MOPAC
6
were used. gee text for the keywords “MMOK”
and “NOMM”.
hi. Feigel and T. Struner/J.
40
Mol. Strwt. (Theochem) 283 (1993) 33-48
3-E
215.5
214.5
214
213.5
213
212.5
i -150
Fig. 6. Energy (AI&, kcalmol-‘)
-100
-50
0
50
100
150
of (E)-1,3,3-trimethylthiourea, calculated using AM1 (-O-), MNDO (-+-) (-CL-), as a function of the torsion w (see.Scheme 1).
N-CO groups results in an out-of-plane bending of the second nitrogen atom. Thus it seems best to ignore this correction and to use instead the procedure described in the section on “How to get correct values”.
Comparism of calculated values and experimental data Barriers of rotation measured experimentally in the gas phase and in liquids are compared with AM1 calculated values in Table 6. Few of the compounds for which experimental gasphase data are available contain hydrogen atoms on the nitrogen atom, and thus the keyword MMOK could not be applied to these systems anyway. Figures 10 and 11 show data listed in Table 6 in
and PM3
graphical form. Obviously there is a correlation between rotational barriers measured in liquids and the AM 1 data (Fig. 10). There are some large deviations from this correlation (compounds 22 and 34). The line drawn in Fig. IO is the regression line without these points. The surprisingfy small deviation of most of the points from the correlation line (f2 kcal mol-‘) is due to various reasons such as: (a) the experimental free energies of activation (Act) are plotted against calculated enthalpies of activation (A&), so any correlation would imply that the activation entropy is nearly equal for all compounds; (b) solvents of different polarity were used for measuring the D NMR spectra - the increase of the barrier with increasing solvent polarity is undoubt~ly proven [ 191. Naturally, one would expect a better correlation between calculated barriers and
M. Fe&e! and T. Strassner/J. Mol. Stmct. (Themhem) 283 (1993) 33-48
41
-
3 -
1 -
<
9’
-24
-26
-28
,* ,’ Cl
11
-30 --__
-32 -150 Fig. 7. Energy (A&,
-100 kcalmol-‘)
-50
0
50
of tetramethylurea, calculated using AM1 (-O-), function of the torsion w (see Scheme 1).
expe~m~ntal results for the gas phase. However, the correlation between gas-phase NMR data and the AM1 calculations is less obvious (Fig. 11). The main reason for this is that the NMR measurements in the gas phase are restricted to a narrow temperature range and, therefore, the window in the activation energies is narrow too. Furthermore, there is the same problem of comparing AGt with AH+ as in Fig. 10. We corrected the AM1 activation data to free energy values at 298 K using the AM 1 options “THERMO” and “FORCE”. However, the correlation with experiment improved only slightly. The ab initio values (see Fig. 11) form a line which is almost parallel with the liquid regression line in Fig. 10. The second solid correlation line is built from a AHAM, ’ /A& ititio correlation. The fact, that the line is nearly
100 MNDO
(-+-)
150 and PM3 (-Cl-),
as a
parallel to the AG~~~~/AH~~, correlation indicates that solvent and entropy contributions are, with some scattering, “equal” for each compound and that these additional contributions to AG& do not systematically depend on the value of AH& Considering the range of different types of molecules calculated, the correlation between the values calculated with AM1 and the experimentally measured data is promising and is used below to estimate ex~~ental activation energies or “true” ab initio values from AM1 data. Influence of different substituents on the rotational barrier in ureas The influence of substituents on the rotational barriers of amides has been discussed based on experimental data [20]; others have discussed the
M. Feigel and T. StrassnerlJ. Mol. Siruct. (Theochem) 283 (1993) 33-48
42
theoretical background [21]. Our calculations cannot contribute much to this topic, but the large number of urea compounds studied here allows us to describe the influence of different substituents on nitrogen on the urea rotational barrier. We chose three different groups of substituents: halogens, various alkanes and aromatic rings.
300
Steric effects of alkyl substituents 100
50
0 0
50
LOO
150 ‘Dihedral
200
250
300
350
angle (01)
Fig. 8. Energy of N-methylurea as a function of the torsion of the OC-NHCHs bond (q) and the HzN-CO bond (wZ). The lines are separated by 1 kcal mol-‘. The values were calculated from trajectories in wz while w, was fixed; all other degrees of freedom were variable and optimized. For w, , 0 corresponds to the E conformer with a transorientation of the C-O and N-CHs groups.
0
50
100
150 ‘Dihedral
200
250
300
350
angle (01)
Fig. 9. Energy of N-methylurea as a function of wr and wz. The lines are separated by 1 kcalmol-‘. The values were selected from a four-dimensional surface which also contains the bending at the nitrogen atoms. For the definition of wt and w2 see Fig. 8.
Comparing the effects of alkyl groups on the urea barrier, the effect of Z or E orientation of the substituent on the unrotated group is obvious. For example, the barrier in the parent urea 42 decreases only slightly if the rotating site is substituted with two methyl groups as in 64. However, if one additional methyl group is attached to 64 in the E position, the barrier drops from 3.8 kcal mol-’ (64) to only 1.8 kcalmol-’ (66), whereas the corresponding Z isomer (65) has almost the same barrier as 64. Addition of a methyl group to compound 42 does not change the rotational barrier of the sterically less demanding NH2 group by much (see 51/l and 52). The same trend is observed for i-propyl groups (see Tables 4 and 5) and even for t-butyl groups (58). The ground states of N-methylurea, N,N’dimethylurea and N, N, N’- 1,1,3-trimethylurea seem also to be sensitive to steric effects. The orientation of the NH(CHs) group obviously determined the stability of the conformers. The AM1 calculations show that N-methylurea is 0.9 kcal mol-’ more stable in the E conformation (52) than in the Z form (51/l), whereas for 1,1,3-trimethylurea the Z form (65) is the most stable conformer (AAGo = 1.96 kcal mol-‘). The -N(CH3)2 group destabilises the compound in which the NHCHs group is in the E geometry (66) by repulsion. The most stable form (by AMl) of N, N’dimethylurea is the Z,E form, the symmetrical Z,Z and E,E conformations being 0.89 and 1.33 kcal mol-’ higher in energy respectively.
43
M. Feigel and T. Strassner/J. Mol. Struct. (Theochem) 283 (1993) 33-48 Table 3 AM1 calculated activation enthalpies of the C-N bond rotation in dimethylamides
No. X R VAMP
and dimethylthioamide?
HzN 3.77
22 0 Cl,C 5.13
23 0 FCH2 8.73
24 0 F&H 9.46
7.76
3.8
5.23
8.67
9.48
28 0 CN 8.95
29 0 H3C0 6.44
30 0 H3CS 7.57 7.54
16 0 H 9.61
17 0 F 7.21
18 0 Cl 6.79
19 0 Br 7.55
9.59
7.0
6.7
7.54
20 0
21 0
HsC 7.8
MOPAC 6
NOMM No. X R VAMP
25 0
26 0
8.49
9.19
27 0 NC 5.63
F3C
Cd&
8.50
9.21
5.74
8.93
6.42
NHz 6.73
36 S F 9.63
37 S Cl 8.12
38 S NC 7.08
6.63
9.55
8.13
7.17
31 S H 14.1
32 S 12.46
33 S i-Prop 9.63
14.06
12.44
9.54
40 S CH,O 9.27
41 S CH,S 4.95
9.12
4.89
H3C
MOPAC 6
NOMM No. X R VAMP
3s S
34 S t-Bu 7.91
39 S CN 10.7
MOPAC 6
NOMM
8.56
aThe program packages
VAMP
and
MOPAC 6
10.68
were used. See text for the keyword “NOMM”.
__ 39
67 S . .
01
0
.
.. .. .. .. .. .
I
I
2
4
. . .. . . . . .. . .. .
I
. .. . .
I
I
6
10
.
I
12
Fig. 10. Plot of AM1 calculated activation enthalpies (A&, kcalmol-‘) against free activation energies in solution (AC+, kcal mol-‘) for ureas and amides. See Table 6 for corresponding data. The line given is the regression line calculated without compounds 22 and 34.
44
hf. Feigel and T. Strassner/J. Mol. Struct. (Theo&m)
Table 4 AM 1 calculated activation enthalpies of the C-N bond rotation in substituted
No. R2 VAMP MOPAC
ureasa
4.15
43 H F 9.82
44 H Cl 8.91
45 H Br 6.53
46 H J 4.84
41 F F 9.16
48 Cl Cl 8.22
49 Br Br 5.41
50 J J 4.63
4.15 13.48
9.83
19.0
8.83 18.68
6.54 15.6
4.84 14.36
9.16 19.11
8.1 18.35
5.41 15.33
4.63 14.29
52 H
53
CH3
CH3
55 H n-Prop 5.62
56 i-Prop H 4.81
57 H i-Prop 5.69
58 H t-Bu 5.68
4.82 13.43
5.12 14.45
5.5 14.38
42 H H
K1
6
NOMM MMOK No.
Sl/lb
Kr
CH3
5.21
5.65
54 H Et 5.86
4.14 13.4
5.21 14.62
5.61 14.81
5.63 14.15
5.63 14.46
RI
59 H
R2
CsH5
60 H HO-C,jHd’ 6.41
61 H HsCO-C6H4C 6.54
62 H H2N-C6HdC 6.66
63 H OZN-C~H~~ 8.91
6.45 11.19
6.51 15.9
6.58 11.58
8.92 15.61
H 4.1
R2 VAMP MOPAC
CH3
6
NOMM MMOK No.
6.63
VAMP MOPAC
283 (1993) 33-48
6
NOMM MMOK
6.63 16.02
a The program packages VAMP and MOPAC 6 were used. See text for the keywords “NOMM” and “MMOK”. b Values 51/l are valid for the rotation about the CO-NH2 bond, and values 51/2 are valid for the rotation about the NH-CH3 bond (see Table 6). ’ para-Substituted.
Ureas substituted with halogens Table 4 gives data for some urea compounds having different halogen substitution (compounds 43-50). Despite the fact that these compounds are unusual and no experimental data on them are available, the influence of the electronegativity of the substituents is obvious. As the most electronegative element, fluorine gives the greatest increase in the barrier compared with all other halogens up to iodine. There are two possible reasons for this. (1) It follows from the classical theory of resonance that the electronegative substituent at one nitrogen atom of the urea unit removes electrons from this atom, which contracts its p orbitals. Donation of electron density to the
carbonyl carbon atom is reduced and the second nitrogen atom is now more strongly fixed in the nearly planar ground state, due to increased r overlap of its p orbital. (2) The second explanation is that a stabilizing interaction occurs between the N-F dipole and the N-H dipole on the opposite nitrogen atom (a situation which may also be called a “F. . . H hydrogen bond”). Although data are given for the monosubstituted ureas 43-46 in Table 4 for the E conformation only, we also checked the Z conformers. The results (AGt: fluorine 5.5 kcalmol-‘; chlorine 6.1 kcal mol-‘; bromine 5.6 kcal mol-‘; iodine 5.46 kcal mol-‘) indicate that both arguments have some merit, i.e. the proposed X a.* H hydrogen bond and other influences of the
M. Feigel and T. Strassner/J. Mol. Strut.
(Theo&m)
283 (1993) 33-48
45
Table 5 AM1 calculated activation enthalpies of the C-N bond rotation in dimethylureas
No. X
64 0
RI RZ
H H
VAMP MOPAC
67 0
CH3
66 0 H
H
CH3
CH3
3.17
3.63
1.8
1.64
68 0 H i-Prop 2.9
3.8
3.66
1.83
1.47
4.98
1.5
73 S i-Prop H 5.86
74 S H i-Prop 2.97
2.03
5.38
2.51
65 0
CH3
69 0 i-Prop H 3.1 3.8
6
NOMM No. X
70 S H H 6.13
RI R2 VAMP MOPAC
and dimethylthioureasa
71 S
72 S
CH3
CH3
H 5.89
CH3
6
6.63
NOMM a The program pagackes
VAMP
5.85 and
MOPAC
6
were
used. For the keyword “NOMM” see text. 43-46. Thus it is obvious that there must be a certain degree of electronic balance in these ureas, where an increase in electronegativity does not lead to a further increase in the barrier of rotation.
electronegative group X on the urea resonance (in the E and Z orientations). Double substitution (compounds 47-50) leads to a slightly smaller barrier compared with the values for the monosubstituted compounds
20
i,,:r:.:: .....
. . . . . . ..____________...................................................................................
.2%-’
z
:s
75
76
.S
4 5
, S “‘.......‘...‘.“‘..................................................~;. :. .’ ,-
3
01
0
I
2
I
4
20
I
I
I
6
8
10
1
AH+(AMI)
Fig. 11. Plot of AM1 calculated activation enthalpies (AH’, kcal mol-‘) against free activation energies in the gas phase (AGt, kcal mol-’ ) for ureas and amides. The crosses show the four ab initio values. See Table 6 for corresponding data. The dotted line is the correlation line out of Fig. 10. The solid line gives the (AH~,,,,&/(AI&,) correlation.
M. Feigel and T. Strassner/J. Mol. Struct. (Theochem) 283 (1993) 33-48
46
Table 6 Comparison of experimental and theoretical dataa Experimental No. 1 AGi AGS”“. 18-19 10.12 AH!;;
16 19.4 20.7’ 9.61
11 17.1 18.1C 7.21
18 15.4 16.5’ 6.79
19 14.1 15.7b 7.55
20 15.6 17.3m 7.8
No. AGi s
28 19.0
29 -
31 -
32 -
33 _
34 -
A&l AH!,,
21.4’ 8.95
14.8’ 6.44
24.18 14.1
21.6g 12.46
19.3s 9.63
No. AG+ AGY. +yd AH,,,
40 17.gg 9.27
41
67
69
71 10.6h 5.89
15.6g 4.95
High level ab initio calculations No. 1 Value 15.3 Basis set MP3/6-31G” A& 10.12
6.3i 1.64
9.7+ 3.7
23 15.2 16.4’ 8.73
24 17.4 18.3’ 9.46
25 16.5 17.8’ 8.49
35 _
36 -
37 -
39
13.0h 7.91
13.9’ 6.73
20.7’ 9.63
18.7 8.12
23.5g 10.7
75 18.7 20.4b 10.11
76 19.0 20.7s 10.86
20 13.6 MP4(fc)SDTQ/6-31G(d) 7.81
22 < 16 18.3’ 5.13
42 8.2 6-31G’ 4.75
5112 8.55 6-31G’ 4.37
“The structure of compounds l-71 is given in Tables 2 to 5. Compound 75 is H-CO-N(CH$H& and compound 76 is H-CO-N(CH(CHs)&. Experimental data are from Refs. 16 and 17. The ab initio data are from Ref. 18. bNeat solution. ’ In CC14. d In HsC-CO-CHs . ’ In DMF. f In (CBrF&. g In C12C6H4. h In CDCls . i In (ClsCH)s. j In CHClrF. ’ In CHCls. ’ In C*C&. mIn isooctane.
Aromatic substituents
How to get correct values
The substitution of one NH* group in urea by a NH(C6H5) group increases the rotational barrier on the opposite NH2 site by 2 kcal mol-' . This is consistent with the difference between ammonia and aniline where the phenyl ring reduces the pKa value [22]. The nitrogen lone pair in aromatic amines is less available for urea resonance and electron-donating para-substituents (60-62) thus have no significant effect, but the electron-withdrawing nitro group (63) increases the barrier further by about 2.3 kcal mol-’ to 8.91 kcalmol-’ . This is in line with the resonance argument mentioned above.
Here we refer to Figs. 10 and 11 which show the calculated values in comparison with experimental data. While it seems possible to reproduce the experimental free energy values in the gas phase by using high level ab initio calculations on small systems [23], a more practical approach which is also valid for large systems would be the following procedure, depending on the intention of the chemist. (1) If accurate AH+ values are desired, conduct a brief AM1 calculation to obtain AHf,,,) and use Eq. (1) to obtain a probably correct AZY&~~~,,
M. Feigel and T. Strassner/J. Mol. Struct. (Theochem) 283 (1993) 33-48
value: AHi.binitio = 1.35A$,,)
+ 2.05
(2) To obtain a rough estimate of the experimentally accessible barriers (AG&tid at 298K), use Eq. (2), which results from the correlation shown in Fig. 10: AGisuid = 1.6AZ&,,)
+ 4.5
(2)
These methods replace the artificial forcefield correction, available in MOPAC (MMOK). They are generally applicable to all types of systems, not only to those containing an NH-CO unit. Furthermore, MMOK is parameterized only on N-methylacetamide [15], whereas the correlation presented by Eq. (2) (and Eq. (1)) is obtained using a large set of experimental data. The best method for calculating rotational barriers will still be high-level ab initio calculations, but it will save years of computer time if Eq. (1) is used for large systems such as small peptides, proteins or even enzymes. A first project in this direction will be the calculation of the cis/trans isomerization in proline containing peptides in the presence of “rotamase” enzymes such as the binding proteins for FK 506 or cyclosporine A [24]. Acknowledgements
We thank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie for financial support. T.S. would like to thank the Studienstiftung des Deutschen Volkes for a grant. References (a) T. Clark, A Handbook of Computational Chemistry, Wiley-Interscience, New York, 1985. (b) D.F.V. Lewis, Chem. Rev., 86 (1986) 1111. (a) W.J. Hehre, L. Radom, P.v.R. Schleyer and J.A. Pople, Ab Initio Molecular Orbital Theory, WileyInterscience, New York, 1986. (b) M.J.S. Dewar, in E. Clementi (Ed.), MOTECC 91,
41
ESCOM, Leiden, 1991, p. 455. 3 J.C. Del Valle and J.L.G. De Paz, J. Mol. Struct. (Theochem), 86 (1991) 481. 4 (a) W.M.F. Fabian, J. Comput. Chem., 12 (1991) 17. (b) A.R. Katritzky, K. Yannakopoulou, E. Anders, J. Stevens and M. Szafran, J. Org. Chem., 55 (1990) 5683. (c) A.R. Katritzky, M. Szafran, N. Malhotra, U. Chaudry and E. Anders, Tetrahedron Comput. Methodol., 3 (1990) 247. K.B. Wiberg and K.E. Laidig, J. Am. Chem. Sot., 109 (1987) 5935. M.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P Stewart, J. Am. Chem. Sot., 107 (1985) 3902. (a) M.S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4899. (b) MS. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4907. 8 (a) J.J.P. Stewart, J. Comput. Chem., 10 (1989) 209. (b) J.J.P. Stewart, J. Comput. Chem., 10 (1989) 221. 9 (a) Program package VAMP 4.40 (Vector&d AMPAC) by T. Clark is used at the University Erlangen, Germany for semiempirical calculations. (b) J.J.P. Stewart, AMPAC, QCPE Bull., 6 (1986) 506. 10 J.J.P. Stewart, MOPAC 6.0, QCPE, No. 455/SGRW. 11 J. Baker, J. Comput. Chem., 7 (1986) 385. 12 D.F. Shanno, J. Optimization Theory Appl., 46 (1985) 87. 13 (a) U. Lepore, G.C. Lepore, P. Ganis and M. Goodman, Cryst. Struct. Commun., 4 (1975) 351. (b) J. Kopf, H. Rust and W. Dannecker, Cryst. Struct. Commun., 8 (1979) 429. (c) W.A. Brett, P. Rademacher and R. Boese, Acta Crystallogr., Sect. C, 46 (1990) 880. (d) C. Toniolo, G. Valle, G.M. Bonora, M. Crisma, V. Moretto, J. Izdebski, J. Pelka, D. Pawlak and C.H. Schneider, Int. J. Pept. Protein Res., 31 (1988) 77. 14 D.A. Smith, C.W. Ulmer II and M.J. Gilbert, J. Comput. Chem., 13 (1992) 640. 15 MOPAC 5.0 manual, QCPE No. 455, Indiana University, Bloomington, IN. to experimental values measured in 16 References solution: 16: T. Drake&erg, K. Dahlquist and S. Forsen, J. Phys. Chem., 76 (1972) 2178. 17: L.W. Reeves and K.N. Shaw, Can. J. Chem., 49 (1971) 3671. l&19: E.A. Allen, R.F. Hobson, L.W. Reeves and K.N. Shaw, J. Am. Chem. Sot., 94 (1972) 6604. 20: R.C. Neumann and V. Jonas, J. Org. Chem., 39 (1974) 929. 22: M.D. Wunderlich, L.K. Leung, J.A. Sandberg, K.D. Meyer and C.H. Yoder, J. Am. Chem. Sot., 100 (1978) 1500.
48
M. Feigel and T. StrassnerlJ. Mol. Strut. (Theochem) 283 (1993) 33-48
25: B.D. Ross, N.S. True and D. Decker, J. Phys. Chem., 87 (1983) 89. 23, 24, 28: B.D. Ross, L.T. Wong and N.S. True, J. Phys. Chem., 89 (1985) 836. 29: E. Lustig, W.R. Benson and N. Duy, J. Org. Chem., 32 (1967) 851. 31: A. Loewenstein, A. Melera, P. Rigny and W. Walter, J. Phys. Chem., 68 (1964) 1597. 32: J. Sandstrom, J. Phys. Chem., 71 (1967) 2318. 33: F. Conti and W.V. Philipsborn, Helv. Chim. Acta, 50 (1967) 603. 34: W. Walter, E. Schaumann and H. Paulsen, Liebigs Ann. Chem., 691 (1966) 25. 35, 36, 37, 39: R.F. Hobson, L.W. Reeves and K.N. Shaw, J. Phys. Chem., 77 (1973) 1228. 40,41: J. Sandstrom, J. Phys. Chem., 71 (1967) 2318. 67: F.A.L. Anet and M. Ghiaci, J. Am. Chem. Sot., 101 (1979) 6857. 69: P. Stilbs, Acta. Chem. Stand., 25 (1971) 2635. 71: G. Isaksson and J. Sandstrom, Acta. Chem. Stand., 24 (1970) 2565. 75: R.M. Hammaker and B.A. Gugler, J. Mol. Spectrosc., 17 (1965) 356. 76: T.H. Sidall, W.E. Stewart and F.D. Knight, J. Phys. Chem., 76 (1972) 2178. 17 References for experimental values measured in the gas phase. 16: C. Suarez, C.B. LeMaster, C.L. LeMaster, M.
18
19 20 21
22 23 24
Tafazzoli and N.S. True, J. Phys. Chem., 94( 17) (1990) 6679. 17, 18,20,25,75: M. Feigel, J. Phys. Chem., 87 (1983) 3054. 19,22,23,24,28: B.D. Ross, L.T. Wong and N.S. True, J. Phys. Chem., 89 (1985) 836. 76: C.B. LeMaster and N.S. True, J. Phys. Chem., 93 (1989) 1307. References for the ab initio values: 1: See Ref. 5. 20: See Ref. 23. 42,51,52: M. Kontoyianni and J.P. Bowen, J. Comput. Chem., 13 (1992) 657. M. Feigel, J. Phys. Chem., 87 (1983) 3054. M. Oki, Applications of Dynamic NMR Spectroscopy to Organic Chemistry, VCH, Weinheim. (a) L. Radom and N.V. Riggs, Aust. J. Chem., 35 (1986) 197. (b) P.G. Jasien, W.J. Stevens and M. Krauss, J. Mol. Struct., 139 (1986) 197. F.A.L. Anet and M. Ghiaci, J. Am. Chem. Sot., 101 (1979) 6857. E.M. Duffy, D.L. Severance and W.L. Jorgensen, J. Am. Chem. Sot., 114 (1992) 7535. (a) G. Fischer and F.X. Schmid, Biochemistry, 29 (1990) 2205. (b) S.L. Schreiber, Science, 251 (1991) 283. (c) M.K. Rosen and S.L. Schreiber, Angew. Chem., 104 (1992) 413.
283 (1993) 33-48 0 1993 - Elsevier Science Publishers B.V. All rights reserved
Journal of Molecular Structure (Theochem), 01661280/93/$06.00
A semiempirical AM 1, MNDO and PM3 study of the rotational barriers of various ureas, thioureas, amides and thioamides M. Feigel*, T. Strassner Institut fir Organische Chemie, Universith’t Erlangen-Ntirnberg
Henkestrasse
42, D-8520 Erlangen, Germany
(Received 15 October 1992) Abstract AM1 proved to be the most useful method of MNDO, AM1 and PM3 for calculating rotational barriers of compounds containing a (R,R) N-CX-R linkage (amides, t ioamides, urea and thioureas). The barriers ! calculated with AM1 must be corrected using the equation AG,igtia = 1 6ADHy,,9 + 4 5 kcal mol-’ to obtain f + 2.05 kcalmol-’ the best coincidence with experimental values. Another equation, AHabinitio = 1.3JAH[,,,) reproduces recent ab initio data well.
Introduction Semiempirical calculations have been applied to nearly all areas of main group organic chemistry [l]. However, the calculated quantities are often inaccurate and should be checked against the results of experiment or the results of high-level ab initio calculations [2]. This deficiency is particularly obvious in compounds containing nitrogen where the lone pair interaction in saturated systems is questionable [3], and in heterocycles due to the electronic distribution [4]. In the present study we looked at urea and amide compounds containing the R2N-CX-R fragment (X = 0 or S) found in many biological systems. The commonly accepted picture of electron delocalization in the amide unit (from nitrogen to carbonyl oxygen) has been questioned in the light of recent ab initio calculations on formamide [5]. The present semiempirical calculations cannot * Corresponding
author.
contribute to this discussion, but have a more practical intention: do the widely distributed programs AM1 [6], MNDO [7] and PM3 [8] (with different versions in different program packages) reproduce the rotational flexibility of the unit in a large variety of substituted compounds (amides, ureas and their thio-analogues)? The increase in computational power means that it is now possible to study peptides, nucleotides and fragments of enzymes with semiempirical methods. The R2NCO-R unit is a basic constituent of the backbone of these large molecules. Is the use of semiempirical programs justified in all cases where the flexibility or rigidity of the unit is important? To check the value of the semiempirical calculations, we compared the results obtained with experimental data or with the most recent ab initio calculations. Calculational procedure We used the programs AMl, MNDO and PM3 in two computing packages: VAMP 4.40[9] (running
34
hi. Feigel and T. Strassner/J. Mol. Struct. (Theo&em) 283 (1993) 33-48
on a CONVEX C220 and an SGI-Indigo), and (running on a PC 486-33(256) with 8 Mbyte memory). The packages differ in two main aspects: the way in which the gradients are optimized (VAMP uses the EF method [l 11, whereas MOPAC uses the BFGS (for a summary see Ref. 12) gradient optimization); and MOPAC 6.0 detects -NH-COunits and adds an additional rotational barrier to this unit, if the keyword “MMOK” is used. Usually both packages gave identical results (the keyword “PRECISE” was generally used). Slight differences in the calculated energies probably result from the different optimization procedures. The only large differences seen (still less than 0.6 kcal mol-’ ) are restricted to compounds containing the sterically demanding t-butyl and i-propyl groups. All R,R’N-CORN (urea or amide) torsions were first calculated using the reaction coordinates. The dihedral angle w between the normals of the R-N-R’ and the O=C-R” planes was varied from 0” to 360” in steps of lo”, optimizing all other coordinates (see Scheme 1). The R,R’N-C unit usually becomes strongly pyramidal during the torsion which results in two different transition states for rotation, where the R,R’ groups are bent towards or away from the carbonyl oxygen atom. The values given in the tables illustrate the lower energy barrier found for the rotational trajectories. The geometries and energies of the stationary points derived from the reaction coordinates were checked with force calculations using the keywords “NLLSQ” and “FORCE” to ensure that they were MOPAC 6.0[lo]
Xl
x2
Scheme 1. Definition of the torsional angle w used in Figs. 4 to 9.
R”
Scheme 2. Definition of w and the bending angle 8 used in Figs. 1 to 3.
stationary points. Transition states can be distinguished from other stationary points by the fact that the Hessian matrix has only a single negative value for these states. The effect of pyramidalization at nitrogen during the torsion was investigated in more detail for formamide, N-methylacetamide (the parent peptide model) and N-methylurea. Energy surfaces with two and four dimensions were collected for the amides and the urea molecule, respectively, using as variables the dihedral angles w between the R”CO- and RNR’-planes (see above) and, in addition, varying the pyramidalization at the nitrogen atoms by the angle 8 defined in Scheme 2. Comparison of the AMl, MNDO and PM3 methods The energy surfaces shown in Figs. 1 to 3 give a first insight into the differences between the semiempirical methods, as applied to rotation about the CO-N bond in formamide and N-methylacetamide. The contours of equal energy spaced by 1 kcalmol-’ were obtained by varying both the angle of torsion w and the bending angle 19 (see the definition in Scheme 2). There are marked differences between the shapes of the surfaces obtained with AM1 and MNDO (Figs. 1 and 2), whereas the appearance of the corresponding PM3 surfaces (not shown) is similar to the MNDO plots. AM1 and MNDO show ground states for formamide at dihedral angles of 0”, 180” and 360”, but the methods give different pyramidalization at nitrogen. The MNDO results show the minimum energy at B = 35” whilst the
M. Feigel and T. StrassnerlJ.
LOO
Mol. Struct.
150 ‘Dihedral
200 angle
(Theochem)
250
300
283 (1993) 33-48
350
(to)’
AM 1 minimum-energy conformation is planar (13= 0.04”). The two transition states for rotation (TSt, and TS,; w = 90” and 270”, are respectively
70
60
50
6 P LB
40
d ._ 4 6 ?
30
20
10
0
0
50
100
150 ‘Dihedral
200 angle
0
50
100
150 ‘Dihedral
Fig. 1. The AM1 energy surface of formamide as a function of the torsion at the amide bond (w) and the pyramidalization at nitrogen (0). The lines are separated by 1 kcal mol-’ .
8
35
250
300
350
(co)
Fig. 2. The MNDO energy surface of formamide as a function of the torsion at the amide bond (w) and the pyramidalization at nitrogen (19). The lines are separated by 1 kcal mol-' .
200 mgk
250
300
350
(0)’
Fig. 3. The AM1 energy surface of N-methylacetamide as a function of the (C,-C-N-C) torsional angle (w) and the pyramidalization at nitrogen (0). The lines are separated by 1 kcalmol-t . The ground state at 180” corresponds to the more stable Z isomer.
shown to be strongly pyramidal by both methods; however, the actual rotation will follow the lowenergy path over TS2, where the NH2 group is bent towards the carbonyl oxygen atom (Scheme 3). These points are marked on the surface and the minimum-energy pathway is shown in the figures. Similar transition states for formamide have been described by Wiberg and Laidig [5] using high level ab initio calculations (MP3/6-3 1G**). Despite the fact that AM1 (and even more so MNDO) underestimates the height of the barrier (TS& the relative order of the stationary points calculated with the semiempirical methods is identical to the order found with ab initio calculations (Scheme 3). This fact is promising for calculations on larger systems (see below), where ab initio methods will require too much computational time. The basic shape of the surfaces is not changed by the addition of alkyl groups to the unit, as in N-methylacetamide (Fig. 3). Again, AM1 yields nearly planar ground states (models for cis and trans peptide bonds) and calculates bend transi-
M. Feigel and T. StrassnerlJ. Mol. Struct. (Theochem) 283 (1993) 33-48
36
R Ts2
d TSl
GS
R=H
TS2
TSI
GS
ab initio: (MP3/6-31G”)
15.34
17.6
0
AMl:
10.1
15.1
0
5.3
7.8
0
13.60
17.73
0
AMl:
7.79
10.71
0
MNDO:
1.3
4.21
0
MNDO: R=CH3 ab initio: (MP4(fc)SDTQ/6_3lG(d))
Scheme 3. The relative energies (kcalmol-‘) of the stationary points of formamide and dimethylacetamide. (See Refs. 5 and 23 for ab initio data.) tion states for rotation about C-N (Fig. 3), whereas MNDO and PM3 give a bent ground state for the molecule (not shown). For all the systems studied in this work, we calculated the trajectory of rotation, where pyramidalization at the nitrogen atom was not fixed. In the case of formamide this led to the curves shown in Fig. 4. Depending on the sense of torsion, MNDO and PM3 reach both transition states (TSi and T$), whereas the equal barrier heights (TS,) found with AM1 result from the nearly flat ground state with easy inversion. Three more examples of rotational trajectories are shown in Figs. 5 to 7, where all three hamiltonians are plotted together. Urea type molecules with quite ‘normal’ substituents were selected, but the shape of some of the curves is rather unexpected. The MNDO curves in Figs. 5 and 6 show an extreme at quite unusual torsional angles (minimum at 90” and maximum at ca. 0”). This is in contrast to X-ray structures where nearly planar ground states are found even in the presence of sterically demanding substituents [13]. PM3 yields very flat barriers, although the positions of
the extreme are the expected ones (Figs. 5 and 6). In the case of tetramethylurea (Fig. 7) PM3 gives a very scattered curve without any definite barrier. A careful investigation of the geometries on the rotational trajectory shows that the reason for these unexpected shapes is repulsive interactions between methyl groups attached to different nitrogen atoms. AM1 yields the highest barriers, which are closest to given experimental values (see Table l), but the absolute values are still too low. For example, comparing all three curves in Fig. 5, it is obvious that AM1 gives the closest value (3.7 kcalmol-‘) to the experimental value (9.7 kcalmol-i) (compound 69, Ref. 16). Both other methods give even smaller barriers. This seems to be due to the parameterization of nitrogen in the semiempirical hamiltonians, a problem which has recently been discussed for aromatic amines [ 141. The spike in the AM1 curve (Fig. 7) is not a plotting error, but shows the problems dealing with a one-dimensional trajectory. The rotational surface of methylated urea compounds probably has more than two dimensions - we expected that the rotation of one of the amide groups depends on the rotational orientation of the other R2N-CO bond. The most simple compound, i.e. that containing one methyl group (N-methylurea), was selected for the calculation of a two-dimensional surface, using both torsional angles (wi and w2) as coordinates (Fig. 8). The overall picture of the surface shown in Fig. 8 is as expected. Minima are found where both torsional angles w1 and wz are close to 0” or 180”, transition states appear when one coordinate is twisted to 90” or 270”, and maxima occur when both coordinates have values of 90” or 270”. However, some strange vertical textures appear in the graph. The discontinuity results from sudden inversion of either the NH2 or the NHCHj group during the forced rotation of one coordinate. Hence, the energy surface to be calculated should also contain the bending coordinates on both nitrogen atoms, which leads to a four-dimensional surface. Even if
M. Feigel and T. Strassner/J. Mol. Struct. (Theochem) 283 (1993) 33-48
37
Table 1 The activation enthalpies for bond rotation in amides and ureas calculated using different hamiltonians, data (free energies) for some dimethylamide?
and some experimental
R AH+(AMl) AH+(MNDO) AH’(PM3)
H 10.12 5.33 6.04
F 8.98 4.53 5.17
Cl 9.13 3.99 6.1
Br 10.8 4.84 5.49
J 10.48 4.93 4.6
H 9.61 5.39 5.11 19.4
F 7.21 2.51 3.76 17.1
Cl 6.79 1.77 4.12 15.4
Br 7.55 2.29 3.99 14.1
F F 9.16 4.62 5.54
Cl Cl 8.22 4.1 4.88
Br Br 5.47 3.99 5.21
J J
CH3
H
H 4.7 2.23 3.35
CHs 5.27 2.41 3.96
CH3
H HD-C6H4C 6.47 3.1 4.08
H H3CD-C6H4C 6.54 2.69 4.6
9.26 7.52 8.1
Et 9.7 4.12 6.07
n-Prop 9.63 4.09 6.01
7.8 1.3 2.92 15.6
FH$ 8.73 0.56 2.19 15.2
F2HC 9.46 0.98 3.21b 17.4
F3C 8.49 0.79 3.33 16.5
H F 9.82 5.01 5.65
H Cl 8.91 5.31 4.88
H Br 6.53 4.87 4.35
H J 4.84 1.66 4.44
H Et 5.86 2.22 3.23
H n-Prop 5.62 3.77 3.36
H i-Prop 5.69 2.56 3.18
H t-Bu 5.68 2.87 5.01
H H2N-C6H.,C 6.66 3.02 4.51
H 0aN-C6HaC 8.91 2.33 3.32
H3C
i-Prop 10.09 3.81 6.33
t-Bu 9.67 3.32 5.51
//
R-C,
%CH3)2 R AH+(AMl) AH+(MNDO) AH’(PM3) AG+(NMRsas)
RI
CH3
\N_C$
R2’
%H,
RI R2 AH+(AMl) AH+(MNDO) AH’(PM3)
AH+(AMl) AH+(MNDO) AH+(PM3)
H H 4.75 3.2 3.4
RI
H
C6HS
RZ
C6I-b
C6H5
RI R2
AH+(AMl) AH+(MNDO) AH’(PM3)
6.63 2.97 4.46
7.14 1.72 4.37
4.63 0.75 5.18 CH3
5.65 2.09 3.84
a Data for dimethylamides are from Ref. 17 (compounds b w = 80”; no convergence for w = 90”. ’ para-Substituted.
16-20 and 23-25).
is relatively easy to calculate such a surface, it is impossible to plot a four-dimensional surface, and so we selected the part which seemed of most interest in the present problem. The bending (et, 0,) combination of lowest energy was searched for in each torsional combination (q, ~2) in the fourdimensional surface. The energy of these structures is plotted in Fig. 9.
it
The surface shown in Fig. 9 has the same overall shape as that in Fig. 8, but the distortions are no longer seen. The sudden inversion at nitrogen, which causes the distortions in the twodimensional surface (Fig. 8) is now avoided, because the surface in Fig. 9, selected from the four-dimensional data set, shows only the optimum bending angle combinations.
38
M. Feigel and T. Strassner/J. Mol. Struct. (Theo&em) 283 (1993) 33-48
-42
-44
-46
I
-150
I
-100
Fig. 4. Energy (AHr in kcalmol-‘)
I
-50
I
I
0
50
I
100
150
of formamide, calculated using AM1 (-O-), MNDO (- + -) and PM3, (-Cl-), as a function of the torsion w (see Scheme 1).
Calculation of the four-dimensional surfaces of all the compounds studied in this work would, even with AMl, need so much computer time that such an exercise is impractical. We therefore restricted our study to one-dimensional trajectories (in w) and have proven the nature of the transition states by force calculations. For- N-methylurea this procedure yields the same barrier heights as found with the full four-dimensional approach. Table 1 shows the height of the barriers for some compounds, calculated with all three hamiltonians as described above. Comparison of the results of the calculations with experimental data (Table 1) proves that AM1 is the best choice. AM1 still underestimates the barriers, but the variation in values with substitution seems to be in line with the experimental data. Thus we decided to use AM1
for a more comprehensive (see below).
set of calculations
Rotational barriers of various compounds obtained witb the AM1 hamiltonian of different program packages (MOPAC and VAMP) The activation energies of rotation were obtained as explained above. The values given in Tables 2 to 5 prove that the results of VAMP and MOPAC (NOMM) are very similar. Small differences of up to 0.2 kcalmol-’ are due to the different methods of optimization. The keyword “MMOK” allows MOPAC to apply a molecular mechanics correction, so that the barrier of rotation is increased (to 14.00 kcal mol-’ in N-methylacetamide [15]). In general, when the option MMOK is used, values are obtained which
M. Feigel and T. Strassner/J. Mol. Strut.
(Theochem) 283 (1993) 33-48
39
-60
-65 -150 Fig. 5. Energy (A&
-100 kcalmol-‘)
-50
0
50
100
of (Z)-1-isopropyl-3,3-dimethylurea, calculated using AM1 (-O-), (-(I-), as a function of the torsion w (see Scheme 1).
150 MNDO (- + -) and PM3
do not carry a hydrogen atom on the nitrogen atom and thus it is not possible to use the keyword MMOK. Furthermore, applying this correction to urea units, the forced planarity at one of the
are 9.3 f 1.0 kcal mol-’ higher than the NOMM value. Thus the use of MMOK leads to an added increment for systems which contain -NH-COgroups. However, many natural amides and ureas
Table 2 AM1 calculated activation enthalpies of the C-N bond rotation in amides’
No. R VAMP MOPAC
5 J 10.48
6 HsC 9.26
7 Et 9.7
10.8 20.71
10.48 20.3
9.27 18.94
9.69
9.62
19.9
18.84
19.23
10 t-Bu 9.67
11 HO 4.05
12 CHO 11.69
13 HOOC 14.49
HzB 7.99
15 NC 10.68
9.89
4.04 13.86
11.69 21.49
14.5 24.35
8.58 18.22
10.68 20.52
2 F 8.98
3 Cl 9.73
10.12 19.91
8.97 18.96
9 i-Prop 10.09 10.04 19.71
19.87
8 n-Prop 9.63
6
NOMM MMOK No. R VAMP MOPAC
4 Br 10.8
1 H 10.12
9.73
14
6
NOMM MMOK
’ The program packages
VAMP
and
MOPAC
6
were used. gee text for the keywords “MMOK”
and “NOMM”.
hi. Feigel and T. Struner/J.
40
Mol. Strwt. (Theochem) 283 (1993) 33-48
3-E
215.5
214.5
214
213.5
213
212.5
i -150
Fig. 6. Energy (AI&, kcalmol-‘)
-100
-50
0
50
100
150
of (E)-1,3,3-trimethylthiourea, calculated using AM1 (-O-), MNDO (-+-) (-CL-), as a function of the torsion w (see.Scheme 1).
N-CO groups results in an out-of-plane bending of the second nitrogen atom. Thus it seems best to ignore this correction and to use instead the procedure described in the section on “How to get correct values”.
Comparism of calculated values and experimental data Barriers of rotation measured experimentally in the gas phase and in liquids are compared with AM1 calculated values in Table 6. Few of the compounds for which experimental gasphase data are available contain hydrogen atoms on the nitrogen atom, and thus the keyword MMOK could not be applied to these systems anyway. Figures 10 and 11 show data listed in Table 6 in
and PM3
graphical form. Obviously there is a correlation between rotational barriers measured in liquids and the AM 1 data (Fig. 10). There are some large deviations from this correlation (compounds 22 and 34). The line drawn in Fig. IO is the regression line without these points. The surprisingfy small deviation of most of the points from the correlation line (f2 kcal mol-‘) is due to various reasons such as: (a) the experimental free energies of activation (Act) are plotted against calculated enthalpies of activation (A&), so any correlation would imply that the activation entropy is nearly equal for all compounds; (b) solvents of different polarity were used for measuring the D NMR spectra - the increase of the barrier with increasing solvent polarity is undoubt~ly proven [ 191. Naturally, one would expect a better correlation between calculated barriers and
M. Fe&e! and T. Strassner/J. Mol. Stmct. (Themhem) 283 (1993) 33-48
41
-
3 -
1 -
<
9’
-24
-26
-28
,* ,’ Cl
11
-30 --__
-32 -150 Fig. 7. Energy (A&,
-100 kcalmol-‘)
-50
0
50
of tetramethylurea, calculated using AM1 (-O-), function of the torsion w (see Scheme 1).
expe~m~ntal results for the gas phase. However, the correlation between gas-phase NMR data and the AM1 calculations is less obvious (Fig. 11). The main reason for this is that the NMR measurements in the gas phase are restricted to a narrow temperature range and, therefore, the window in the activation energies is narrow too. Furthermore, there is the same problem of comparing AGt with AH+ as in Fig. 10. We corrected the AM1 activation data to free energy values at 298 K using the AM 1 options “THERMO” and “FORCE”. However, the correlation with experiment improved only slightly. The ab initio values (see Fig. 11) form a line which is almost parallel with the liquid regression line in Fig. 10. The second solid correlation line is built from a AHAM, ’ /A& ititio correlation. The fact, that the line is nearly
100 MNDO
(-+-)
150 and PM3 (-Cl-),
as a
parallel to the AG~~~~/AH~~, correlation indicates that solvent and entropy contributions are, with some scattering, “equal” for each compound and that these additional contributions to AG& do not systematically depend on the value of AH& Considering the range of different types of molecules calculated, the correlation between the values calculated with AM1 and the experimentally measured data is promising and is used below to estimate ex~~ental activation energies or “true” ab initio values from AM1 data. Influence of different substituents on the rotational barrier in ureas The influence of substituents on the rotational barriers of amides has been discussed based on experimental data [20]; others have discussed the
M. Feigel and T. StrassnerlJ. Mol. Siruct. (Theochem) 283 (1993) 33-48
42
theoretical background [21]. Our calculations cannot contribute much to this topic, but the large number of urea compounds studied here allows us to describe the influence of different substituents on nitrogen on the urea rotational barrier. We chose three different groups of substituents: halogens, various alkanes and aromatic rings.
300
Steric effects of alkyl substituents 100
50
0 0
50
LOO
150 ‘Dihedral
200
250
300
350
angle (01)
Fig. 8. Energy of N-methylurea as a function of the torsion of the OC-NHCHs bond (q) and the HzN-CO bond (wZ). The lines are separated by 1 kcal mol-‘. The values were calculated from trajectories in wz while w, was fixed; all other degrees of freedom were variable and optimized. For w, , 0 corresponds to the E conformer with a transorientation of the C-O and N-CHs groups.
0
50
100
150 ‘Dihedral
200
250
300
350
angle (01)
Fig. 9. Energy of N-methylurea as a function of wr and wz. The lines are separated by 1 kcalmol-‘. The values were selected from a four-dimensional surface which also contains the bending at the nitrogen atoms. For the definition of wt and w2 see Fig. 8.
Comparing the effects of alkyl groups on the urea barrier, the effect of Z or E orientation of the substituent on the unrotated group is obvious. For example, the barrier in the parent urea 42 decreases only slightly if the rotating site is substituted with two methyl groups as in 64. However, if one additional methyl group is attached to 64 in the E position, the barrier drops from 3.8 kcal mol-’ (64) to only 1.8 kcalmol-’ (66), whereas the corresponding Z isomer (65) has almost the same barrier as 64. Addition of a methyl group to compound 42 does not change the rotational barrier of the sterically less demanding NH2 group by much (see 51/l and 52). The same trend is observed for i-propyl groups (see Tables 4 and 5) and even for t-butyl groups (58). The ground states of N-methylurea, N,N’dimethylurea and N, N, N’- 1,1,3-trimethylurea seem also to be sensitive to steric effects. The orientation of the NH(CHs) group obviously determined the stability of the conformers. The AM1 calculations show that N-methylurea is 0.9 kcal mol-’ more stable in the E conformation (52) than in the Z form (51/l), whereas for 1,1,3-trimethylurea the Z form (65) is the most stable conformer (AAGo = 1.96 kcal mol-‘). The -N(CH3)2 group destabilises the compound in which the NHCHs group is in the E geometry (66) by repulsion. The most stable form (by AMl) of N, N’dimethylurea is the Z,E form, the symmetrical Z,Z and E,E conformations being 0.89 and 1.33 kcal mol-’ higher in energy respectively.
43
M. Feigel and T. Strassner/J. Mol. Struct. (Theochem) 283 (1993) 33-48 Table 3 AM1 calculated activation enthalpies of the C-N bond rotation in dimethylamides
No. X R VAMP
and dimethylthioamide?
HzN 3.77
22 0 Cl,C 5.13
23 0 FCH2 8.73
24 0 F&H 9.46
7.76
3.8
5.23
8.67
9.48
28 0 CN 8.95
29 0 H3C0 6.44
30 0 H3CS 7.57 7.54
16 0 H 9.61
17 0 F 7.21
18 0 Cl 6.79
19 0 Br 7.55
9.59
7.0
6.7
7.54
20 0
21 0
HsC 7.8
MOPAC 6
NOMM No. X R VAMP
25 0
26 0
8.49
9.19
27 0 NC 5.63
F3C
Cd&
8.50
9.21
5.74
8.93
6.42
NHz 6.73
36 S F 9.63
37 S Cl 8.12
38 S NC 7.08
6.63
9.55
8.13
7.17
31 S H 14.1
32 S 12.46
33 S i-Prop 9.63
14.06
12.44
9.54
40 S CH,O 9.27
41 S CH,S 4.95
9.12
4.89
H3C
MOPAC 6
NOMM No. X R VAMP
3s S
34 S t-Bu 7.91
39 S CN 10.7
MOPAC 6
NOMM
8.56
aThe program packages
VAMP
and
MOPAC 6
10.68
were used. See text for the keyword “NOMM”.
__ 39
67 S . .
01
0
.
.. .. .. .. .. .
I
I
2
4
. . .. . . . . .. . .. .
I
. .. . .
I
I
6
10
.
I
12
Fig. 10. Plot of AM1 calculated activation enthalpies (A&, kcalmol-‘) against free activation energies in solution (AC+, kcal mol-‘) for ureas and amides. See Table 6 for corresponding data. The line given is the regression line calculated without compounds 22 and 34.
44
hf. Feigel and T. Strassner/J. Mol. Struct. (Theo&m)
Table 4 AM 1 calculated activation enthalpies of the C-N bond rotation in substituted
No. R2 VAMP MOPAC
ureasa
4.15
43 H F 9.82
44 H Cl 8.91
45 H Br 6.53
46 H J 4.84
41 F F 9.16
48 Cl Cl 8.22
49 Br Br 5.41
50 J J 4.63
4.15 13.48
9.83
19.0
8.83 18.68
6.54 15.6
4.84 14.36
9.16 19.11
8.1 18.35
5.41 15.33
4.63 14.29
52 H
53
CH3
CH3
55 H n-Prop 5.62
56 i-Prop H 4.81
57 H i-Prop 5.69
58 H t-Bu 5.68
4.82 13.43
5.12 14.45
5.5 14.38
42 H H
K1
6
NOMM MMOK No.
Sl/lb
Kr
CH3
5.21
5.65
54 H Et 5.86
4.14 13.4
5.21 14.62
5.61 14.81
5.63 14.15
5.63 14.46
RI
59 H
R2
CsH5
60 H HO-C,jHd’ 6.41
61 H HsCO-C6H4C 6.54
62 H H2N-C6HdC 6.66
63 H OZN-C~H~~ 8.91
6.45 11.19
6.51 15.9
6.58 11.58
8.92 15.61
H 4.1
R2 VAMP MOPAC
CH3
6
NOMM MMOK No.
6.63
VAMP MOPAC
283 (1993) 33-48
6
NOMM MMOK
6.63 16.02
a The program packages VAMP and MOPAC 6 were used. See text for the keywords “NOMM” and “MMOK”. b Values 51/l are valid for the rotation about the CO-NH2 bond, and values 51/2 are valid for the rotation about the NH-CH3 bond (see Table 6). ’ para-Substituted.
Ureas substituted with halogens Table 4 gives data for some urea compounds having different halogen substitution (compounds 43-50). Despite the fact that these compounds are unusual and no experimental data on them are available, the influence of the electronegativity of the substituents is obvious. As the most electronegative element, fluorine gives the greatest increase in the barrier compared with all other halogens up to iodine. There are two possible reasons for this. (1) It follows from the classical theory of resonance that the electronegative substituent at one nitrogen atom of the urea unit removes electrons from this atom, which contracts its p orbitals. Donation of electron density to the
carbonyl carbon atom is reduced and the second nitrogen atom is now more strongly fixed in the nearly planar ground state, due to increased r overlap of its p orbital. (2) The second explanation is that a stabilizing interaction occurs between the N-F dipole and the N-H dipole on the opposite nitrogen atom (a situation which may also be called a “F. . . H hydrogen bond”). Although data are given for the monosubstituted ureas 43-46 in Table 4 for the E conformation only, we also checked the Z conformers. The results (AGt: fluorine 5.5 kcalmol-‘; chlorine 6.1 kcal mol-‘; bromine 5.6 kcal mol-‘; iodine 5.46 kcal mol-‘) indicate that both arguments have some merit, i.e. the proposed X a.* H hydrogen bond and other influences of the
M. Feigel and T. Strassner/J. Mol. Strut.
(Theo&m)
283 (1993) 33-48
45
Table 5 AM1 calculated activation enthalpies of the C-N bond rotation in dimethylureas
No. X
64 0
RI RZ
H H
VAMP MOPAC
67 0
CH3
66 0 H
H
CH3
CH3
3.17
3.63
1.8
1.64
68 0 H i-Prop 2.9
3.8
3.66
1.83
1.47
4.98
1.5
73 S i-Prop H 5.86
74 S H i-Prop 2.97
2.03
5.38
2.51
65 0
CH3
69 0 i-Prop H 3.1 3.8
6
NOMM No. X
70 S H H 6.13
RI R2 VAMP MOPAC
and dimethylthioureasa
71 S
72 S
CH3
CH3
H 5.89
CH3
6
6.63
NOMM a The program pagackes
VAMP
5.85 and
MOPAC
6
were
used. For the keyword “NOMM” see text. 43-46. Thus it is obvious that there must be a certain degree of electronic balance in these ureas, where an increase in electronegativity does not lead to a further increase in the barrier of rotation.
electronegative group X on the urea resonance (in the E and Z orientations). Double substitution (compounds 47-50) leads to a slightly smaller barrier compared with the values for the monosubstituted compounds
20
i,,:r:.:: .....
. . . . . . ..____________...................................................................................
.2%-’
z
:s
75
76
.S
4 5
, S “‘.......‘...‘.“‘..................................................~;. :. .’ ,-
3
01
0
I
2
I
4
20
I
I
I
6
8
10
1
AH+(AMI)
Fig. 11. Plot of AM1 calculated activation enthalpies (AH’, kcal mol-‘) against free activation energies in the gas phase (AGt, kcal mol-’ ) for ureas and amides. The crosses show the four ab initio values. See Table 6 for corresponding data. The dotted line is the correlation line out of Fig. 10. The solid line gives the (AH~,,,,&/(AI&,) correlation.
M. Feigel and T. Strassner/J. Mol. Struct. (Theochem) 283 (1993) 33-48
46
Table 6 Comparison of experimental and theoretical dataa Experimental No. 1 AGi AGS”“. 18-19 10.12 AH!;;
16 19.4 20.7’ 9.61
11 17.1 18.1C 7.21
18 15.4 16.5’ 6.79
19 14.1 15.7b 7.55
20 15.6 17.3m 7.8
No. AGi s
28 19.0
29 -
31 -
32 -
33 _
34 -
A&l AH!,,
21.4’ 8.95
14.8’ 6.44
24.18 14.1
21.6g 12.46
19.3s 9.63
No. AG+ AGY. +yd AH,,,
40 17.gg 9.27
41
67
69
71 10.6h 5.89
15.6g 4.95
High level ab initio calculations No. 1 Value 15.3 Basis set MP3/6-31G” A& 10.12
6.3i 1.64
9.7+ 3.7
23 15.2 16.4’ 8.73
24 17.4 18.3’ 9.46
25 16.5 17.8’ 8.49
35 _
36 -
37 -
39
13.0h 7.91
13.9’ 6.73
20.7’ 9.63
18.7 8.12
23.5g 10.7
75 18.7 20.4b 10.11
76 19.0 20.7s 10.86
20 13.6 MP4(fc)SDTQ/6-31G(d) 7.81
22 < 16 18.3’ 5.13
42 8.2 6-31G’ 4.75
5112 8.55 6-31G’ 4.37
“The structure of compounds l-71 is given in Tables 2 to 5. Compound 75 is H-CO-N(CH$H& and compound 76 is H-CO-N(CH(CHs)&. Experimental data are from Refs. 16 and 17. The ab initio data are from Ref. 18. bNeat solution. ’ In CC14. d In HsC-CO-CHs . ’ In DMF. f In (CBrF&. g In C12C6H4. h In CDCls . i In (ClsCH)s. j In CHClrF. ’ In CHCls. ’ In C*C&. mIn isooctane.
Aromatic substituents
How to get correct values
The substitution of one NH* group in urea by a NH(C6H5) group increases the rotational barrier on the opposite NH2 site by 2 kcal mol-' . This is consistent with the difference between ammonia and aniline where the phenyl ring reduces the pKa value [22]. The nitrogen lone pair in aromatic amines is less available for urea resonance and electron-donating para-substituents (60-62) thus have no significant effect, but the electron-withdrawing nitro group (63) increases the barrier further by about 2.3 kcal mol-’ to 8.91 kcalmol-’ . This is in line with the resonance argument mentioned above.
Here we refer to Figs. 10 and 11 which show the calculated values in comparison with experimental data. While it seems possible to reproduce the experimental free energy values in the gas phase by using high level ab initio calculations on small systems [23], a more practical approach which is also valid for large systems would be the following procedure, depending on the intention of the chemist. (1) If accurate AH+ values are desired, conduct a brief AM1 calculation to obtain AHf,,,) and use Eq. (1) to obtain a probably correct AZY&~~~,,
M. Feigel and T. Strassner/J. Mol. Struct. (Theochem) 283 (1993) 33-48
value: AHi.binitio = 1.35A$,,)
+ 2.05
(2) To obtain a rough estimate of the experimentally accessible barriers (AG&tid at 298K), use Eq. (2), which results from the correlation shown in Fig. 10: AGisuid = 1.6AZ&,,)
+ 4.5
(2)
These methods replace the artificial forcefield correction, available in MOPAC (MMOK). They are generally applicable to all types of systems, not only to those containing an NH-CO unit. Furthermore, MMOK is parameterized only on N-methylacetamide [15], whereas the correlation presented by Eq. (2) (and Eq. (1)) is obtained using a large set of experimental data. The best method for calculating rotational barriers will still be high-level ab initio calculations, but it will save years of computer time if Eq. (1) is used for large systems such as small peptides, proteins or even enzymes. A first project in this direction will be the calculation of the cis/trans isomerization in proline containing peptides in the presence of “rotamase” enzymes such as the binding proteins for FK 506 or cyclosporine A [24]. Acknowledgements
We thank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie for financial support. T.S. would like to thank the Studienstiftung des Deutschen Volkes for a grant. References (a) T. Clark, A Handbook of Computational Chemistry, Wiley-Interscience, New York, 1985. (b) D.F.V. Lewis, Chem. Rev., 86 (1986) 1111. (a) W.J. Hehre, L. Radom, P.v.R. Schleyer and J.A. Pople, Ab Initio Molecular Orbital Theory, WileyInterscience, New York, 1986. (b) M.J.S. Dewar, in E. Clementi (Ed.), MOTECC 91,
41
ESCOM, Leiden, 1991, p. 455. 3 J.C. Del Valle and J.L.G. De Paz, J. Mol. Struct. (Theochem), 86 (1991) 481. 4 (a) W.M.F. Fabian, J. Comput. Chem., 12 (1991) 17. (b) A.R. Katritzky, K. Yannakopoulou, E. Anders, J. Stevens and M. Szafran, J. Org. Chem., 55 (1990) 5683. (c) A.R. Katritzky, M. Szafran, N. Malhotra, U. Chaudry and E. Anders, Tetrahedron Comput. Methodol., 3 (1990) 247. K.B. Wiberg and K.E. Laidig, J. Am. Chem. Sot., 109 (1987) 5935. M.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P Stewart, J. Am. Chem. Sot., 107 (1985) 3902. (a) M.S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4899. (b) MS. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4907. 8 (a) J.J.P. Stewart, J. Comput. Chem., 10 (1989) 209. (b) J.J.P. Stewart, J. Comput. Chem., 10 (1989) 221. 9 (a) Program package VAMP 4.40 (Vector&d AMPAC) by T. Clark is used at the University Erlangen, Germany for semiempirical calculations. (b) J.J.P. Stewart, AMPAC, QCPE Bull., 6 (1986) 506. 10 J.J.P. Stewart, MOPAC 6.0, QCPE, No. 455/SGRW. 11 J. Baker, J. Comput. Chem., 7 (1986) 385. 12 D.F. Shanno, J. Optimization Theory Appl., 46 (1985) 87. 13 (a) U. Lepore, G.C. Lepore, P. Ganis and M. Goodman, Cryst. Struct. Commun., 4 (1975) 351. (b) J. Kopf, H. Rust and W. Dannecker, Cryst. Struct. Commun., 8 (1979) 429. (c) W.A. Brett, P. Rademacher and R. Boese, Acta Crystallogr., Sect. C, 46 (1990) 880. (d) C. Toniolo, G. Valle, G.M. Bonora, M. Crisma, V. Moretto, J. Izdebski, J. Pelka, D. Pawlak and C.H. Schneider, Int. J. Pept. Protein Res., 31 (1988) 77. 14 D.A. Smith, C.W. Ulmer II and M.J. Gilbert, J. Comput. Chem., 13 (1992) 640. 15 MOPAC 5.0 manual, QCPE No. 455, Indiana University, Bloomington, IN. to experimental values measured in 16 References solution: 16: T. Drake&erg, K. Dahlquist and S. Forsen, J. Phys. Chem., 76 (1972) 2178. 17: L.W. Reeves and K.N. Shaw, Can. J. Chem., 49 (1971) 3671. l&19: E.A. Allen, R.F. Hobson, L.W. Reeves and K.N. Shaw, J. Am. Chem. Sot., 94 (1972) 6604. 20: R.C. Neumann and V. Jonas, J. Org. Chem., 39 (1974) 929. 22: M.D. Wunderlich, L.K. Leung, J.A. Sandberg, K.D. Meyer and C.H. Yoder, J. Am. Chem. Sot., 100 (1978) 1500.
48
M. Feigel and T. StrassnerlJ. Mol. Strut. (Theochem) 283 (1993) 33-48
25: B.D. Ross, N.S. True and D. Decker, J. Phys. Chem., 87 (1983) 89. 23, 24, 28: B.D. Ross, L.T. Wong and N.S. True, J. Phys. Chem., 89 (1985) 836. 29: E. Lustig, W.R. Benson and N. Duy, J. Org. Chem., 32 (1967) 851. 31: A. Loewenstein, A. Melera, P. Rigny and W. Walter, J. Phys. Chem., 68 (1964) 1597. 32: J. Sandstrom, J. Phys. Chem., 71 (1967) 2318. 33: F. Conti and W.V. Philipsborn, Helv. Chim. Acta, 50 (1967) 603. 34: W. Walter, E. Schaumann and H. Paulsen, Liebigs Ann. Chem., 691 (1966) 25. 35, 36, 37, 39: R.F. Hobson, L.W. Reeves and K.N. Shaw, J. Phys. Chem., 77 (1973) 1228. 40,41: J. Sandstrom, J. Phys. Chem., 71 (1967) 2318. 67: F.A.L. Anet and M. Ghiaci, J. Am. Chem. Sot., 101 (1979) 6857. 69: P. Stilbs, Acta. Chem. Stand., 25 (1971) 2635. 71: G. Isaksson and J. Sandstrom, Acta. Chem. Stand., 24 (1970) 2565. 75: R.M. Hammaker and B.A. Gugler, J. Mol. Spectrosc., 17 (1965) 356. 76: T.H. Sidall, W.E. Stewart and F.D. Knight, J. Phys. Chem., 76 (1972) 2178. 17 References for experimental values measured in the gas phase. 16: C. Suarez, C.B. LeMaster, C.L. LeMaster, M.
18
19 20 21
22 23 24
Tafazzoli and N.S. True, J. Phys. Chem., 94( 17) (1990) 6679. 17, 18,20,25,75: M. Feigel, J. Phys. Chem., 87 (1983) 3054. 19,22,23,24,28: B.D. Ross, L.T. Wong and N.S. True, J. Phys. Chem., 89 (1985) 836. 76: C.B. LeMaster and N.S. True, J. Phys. Chem., 93 (1989) 1307. References for the ab initio values: 1: See Ref. 5. 20: See Ref. 23. 42,51,52: M. Kontoyianni and J.P. Bowen, J. Comput. Chem., 13 (1992) 657. M. Feigel, J. Phys. Chem., 87 (1983) 3054. M. Oki, Applications of Dynamic NMR Spectroscopy to Organic Chemistry, VCH, Weinheim. (a) L. Radom and N.V. Riggs, Aust. J. Chem., 35 (1986) 197. (b) P.G. Jasien, W.J. Stevens and M. Krauss, J. Mol. Struct., 139 (1986) 197. F.A.L. Anet and M. Ghiaci, J. Am. Chem. Sot., 101 (1979) 6857. E.M. Duffy, D.L. Severance and W.L. Jorgensen, J. Am. Chem. Sot., 114 (1992) 7535. (a) G. Fischer and F.X. Schmid, Biochemistry, 29 (1990) 2205. (b) S.L. Schreiber, Science, 251 (1991) 283. (c) M.K. Rosen and S.L. Schreiber, Angew. Chem., 104 (1992) 413.