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AM1 and PM3 semiempirical molecular orbital study of silatranes.
Journal of Molecular Structure (Theochem), 283 (1993) 251-259 0166-1280/93/%06.00 0 1993 - ElsevierScience.PublishersB.V. All rights reserved
251
AM1 and PM3 semiempirical molecular orbital study of silatranes. Part 2. The 1-methylsilatrane G.I. Csonka, P. Hencsei* Department
of Inorganic Chemistry,
Technical University
of Budapest, H-1521 Budapest, Hungary
(Received 29 June 1992 in final form 15 October 1992) Abstract
AM1 and PM3 semiempirical models have been employed to study the bonding and structure of l-methylsilatrane using full geometry optimization. Heats of formation were calculated at various Si-N distances between 220 and 360pm. Two minima were found on the energy profile when Cs symmetry was retained. A third local energy minimum was found, in a non-symmetrical conformation.
Introduction
A previous article reported the MNDO, AM1 and PM3 equilibrium conformations of l-fluorosilatrane [l]. Silatranes (RSi(OCH2CH2)sN, lorganyl-2,8,9-trioxa-5-aza-I-silatricyclo [3.3.3.0’.‘] undecanes) are biologically active, silicon-containing organic molecules (Fig. 1) [2-41. The most important structural feature of these molecules is the transannular Si-N donor-acceptor bond. Two forms of the structure may be assumed. The central silicon atom in the endo form is bonded to a nitrogen atom through three ethoxy bridges and via a dative bond; the lone electron pair on the nitrogen is turned towards the silicon and the Si-N distance is relatively short (Fig. 1). In the exo form the nitrogen lone pair is outside and the resulting Si-N distance is much longer (Fig. 2). In crystalline samples of many substituted silatranes, short Si-N distances were observed, indicating that the endo form exists in the solid state. Gas-phase electron diffraction (ED) measurements show longer Si-N distances in 1-fluorosilatrane: 204.2pm (X-ray) [5]; 232.4pm (ED) [6]; and in * Corresponding
author.
I-methylsilatrane: 217.5 pm (X-ray) [7]; 245 pm (ED) [8]. In I-chlorosilatrane the Si-N distance is 202.3pm (X-ray) [9]; this is the shortest Si-N distance measured and no ED data is available. The measured Si-N distances are longer than the sum of the covalent radii (187 pm or 189.5 pm) [lO,ll], but shorter than the sum of the appropriate non-bonded radii (269pm) [l l] and much shorter than the sum of the van der Waals radii (350pm) [lo]. The Si-N distance is also variable in solution, shortening in polar solvents and lengthening in non-polar solvents [8]. The Si-N distance has been found to be dependent on the nature of the substituent R. An electron-withdrawing substituent (R = fluorine or chlorine) shortens the Si-N distance by decreasing the electron density on silicon and thus increasing its electronacceptor potential and causing a stronger Si-N dative bond to be formed. This is in agreement with the experimental results. Methyl substitution has the opposite effect, resulting in a longer Si-N bond. This bond lengthening is about 13 pm in both types of measurements. The silatrane skeleton has been found to have approximately Cs symmetry in the solid state. The symmetry is only approximate because of
G.I. Csonka and P. HencseilJ. Mol. Strut. (Theo&em) 283 (1993) 251-259
(111.0 pm)
SI
.
Fig. 1. The molecular diagram, with the atoms labelled, of the endo C, form of I-methylsilatrane (AM1 (PM3) equilibrium geometry).
Fig. 2. The molecular diagram, with the hetero atoms labelled, of the exo C, form of 1-methylsilatrane (AM1 (PM3) equilibrium geometry).
the high flexibililty of the ethoxy links between silicon and nitrogen [5,7,9]. A partially disordered structure has been found in 1-fluorosilatrane [5]. NMR data also show very fast ring inversions in solution [12] for other substituted silatranes. The existence of different polymorphic moditications was explained by freezing of intramolecular movements. The high dipole moments of silatranes may play a role in their biological activity by facilitating penetration of membranes [ 1,2]. The experimental dipole moment of 1-methylsilatrane is 5.3 D [13]. The early theoretical investigations of silatranes were limited by the size of the molecule, by the lack of experimental geometries, by their conformational flexibility and by the limited methods for geometry optimization and computing power that were available. The nature of the Si-N bond was frequently discussed on the basis of sp3d hybridization. However, based on the existence of the corresponding boron compound, the boratrane [1,2],
the importance of d orbitals was questioned and another, so-called hypervalent model was also proposed [14]. The ab initio theory was also applied, but no geometry optimizations were performed. Only simple model compounds of neutral pentacoordinated adducts were calculated with full geometry optimization. The predicted stabilization energy of the NH3-SiF4 adduct was calculated to be 10.0 and 8.6 kcalmol-‘, respectively, with minimal and double-zeta basis sets [15,16]. The existence of the NH3-SiF4 adduct was proved by previous experiments [17]. A number of ab initio calculations show the existence and stability of neutral pentacoordinated compounds containing an Si-N bond [1820]. The axial bond was found to be a three-centre, four-electron bond, so that the strength of the axial Si-N bond is influenced by the ligand in the opposite axial position [20]. Gordon et al. [21] used the AM1 semiempirical method to fully optimize the geometry of
G.I. Csonka and P. HencseilJ. Mol. Strut.
(Theochem)
283 (1993) 251-259
1-hydroxysilatrane (R = OH) and related compounds and they performed single point HF/631G(d) ab initio calculations on the AM 1 equilibrium geometries. The geometries of some simpler model compounds were also optimized at the 6-31G(d) ab initio level. This made a direct comparison of ab initio and AM 1 optimized geometries possible. The performance of AM 1 has been found to be satisfactory. The predicted Si-N distances are 15-20 pm longer and the Si-0 distances are 6-9pm longer than the ab initio results, but the general trends are well reproduced. Utilizing the Bader electron density analysis [22], it was found that the Si-N bond critical point still exists at larger Si-N distances, only a small amount of energy is required to decrease the Si-N distance in I-hydroxysilatrane to reach a typical crystal geometry and as the number of ethoxy bridges increases, the Si-N bond weakens and the Si-O,, bond strengthens. Greenberg et al. [23] studied 1-methylsilatrane and model compounds by HF/3-21G(d) ab initio theory. No geometry optimization was performed. The calculations were carried out at two points; a solid-state and an approximate gas-phase geometry were applied. It was found that the Mulliken charges do not change much as the Si-N distance is varied, the silicon atom remains strongly positive and the nitrogen atom remains strongly negative. In the present study the calculations of l-methylsilatrane are included. Two recent semiempirical model hamiltonians were used in order to study the effects of parameterization, their utility and limitations. Computational methods All geometries were fully optimized using the semiempirical AM1 [24] and PM3 [25] methods and adapted versions of the MOPAC [26] program. The latest AM1 parameters for silicon were used [27] in the calculations. The calculations were carried out on an i486/33 MHz workstation and on an IBM RS/6000 model 320H. The PLUTO program was used to plot the geometries.
253
No symmetry constraints were imposed during the geometry optimizations and the “precise” keyword of MoPAchas always been used. A Cs-like and a completely non-symmetric geometry were optimized separately. The Si-N distance was varied between 220 and 360pm by steps of 20pm, and other geometrical parameters were fully optimized in each step. The lowest energy geometries were used to find the local minima’s points. The fully optimized geometries were always verified as minima by establishing that their Hessian matrices are definitely positive. Frequency analysis was performed, and zero-point energy was calculated at the minimum. The 0-Si-N-C dihedral angle was varied between -20” and 20” in steps of 10”. In this case the Si-N distance was relaxed together with the other geometrical parameters. The energy barrier of the ethoxy flip-flop was also calculated at the minimum, in order to study the flexibility of the three bridges linking the silicon and nitrogen. Mulliken charges, dipole moments, bond orders and energy partitioning were also calculated. Results and discussion The AM1 heats of formation Hr, dipole moments ~1and other important calculated values are listed in Table 1 for 1-methylsilatrane. The geometry has an approximate C3 symmetry (Figs. 1 and 2). The heat of formation shows two minima as a function of the Si-N distance. The equilibrium Si-N distances (endo and exo) are 7-8 pm longer than the corresponding distances calculated for I-fluorosilatrane (253.2 pm and 33 1.Opm respectively) [l]. This may be compared to the bond lengthening found in experiments (13 pm) [5-81. The average values of the three 0-Si-N-C dihedral angles are listed in Table 1 as a(Si-N). They are suitable for describing the conformation of the whole skeleton. As the Si-N distance decreases, this angle becomes more negative; at long distances it remains constant and positive. The value of the dipole moment decreases with the lengthening of the Si-N bond. The calculated
254
G.I. Csonka and P. HencseijJ. Mol. Siruct. (Theo&m) 283 (1993) 251-259
Table 1 AM1 results for 1-methylsilatrane R(Si-N) @m) 220.0 240.0 260.3 280.0 300.0 320.0 339.3 aa(Si-N)
Hf (kcal) -194.65 -199.72 -201.63 -200.81 -200.35 -201.62 -202.67
with approximate
C, symmetry, fully optimized geometry; variation of the Si-N
QW
a(Si-N)* (deg) -12.7 -5.6 0.2 6.8 8.7 8.5 8.0
Q(N)
P(Si-N)
i& 6.43 5.33 4.13 2.90 1.78 0.78 0.10
denotes the average of the three 0-Si-N-C
1.569 1.590 1.599 1.588 1.576 1.568 1.569
-0.281 -0.308 -0.346 -0.388 -0.405 -0.371 -0.308
0.226 0.152 0.094 0.053 0.026 0.012
dihedral angles around the Si-N
dipole moment agrees with the experimental one at the 240 pm Si-N distance. The atomic charge on silicon Q(Si) is calculated to be strongly positive and it has a very flat maximum at 26Opm, near to the optimum of the endo Si-N distance. The atomic charge on nitrogen Q(N) is strongly negative, with a more important variation. It has a minimum at 300pm and it increases rapidly at longer distances. The calculated positive charge on the silicon atom of lfluorosilatrane is higher by 0.14 charge unit, but the negative charge on the nitrogen atom shows no difference [l]. The existence of the strongly positive silicon and the strongly negative nitrogen is in agreement with ab initio 3-21G(d) Mulliken charges for 1-methylsilatrane [21]. The HF/321G(d) calculations have a tendency to give high charges. The Si-N bond order P(Si-N) is large at shorter Si-N distances (below 260pm). At longer distances the bond order is halved as the distance increases by 20pm. This behaviour may be compared to the non-bonding distance proposed by Glidewell [ 111. The energy partitioning shows a rather strong Si-N interaction even at large distances. A detailed analysis showed that the energy contribution of the resonance term was decreasing rapidly, but the sum of the electrostatic terms was high even at large Si-N distances due to high negative charge on the nitrogen. In the endo form the resonance term was equal to - 1.33 eV and the
distance
E(Si-N)
E(Si-C)
(ev)
(ev)
-6.03 -5.14 -4.43 -3.80 -3.10 -2.33
-16.15 -16.52 -16.78 -16.87 -16.91 -16.95 -17.05
bond.
electrostatic term was -3.10 eV. The opposite energetic behaviour of the two axial bonds (Si-N and Si-C) is in agreement with other AM1 and ab initio results for similar compounds [1,19,21]. The AM1 Si-N distance of the endo form is supposed to be 15 pm longer than the HF/631G(d) optimum [21]. If this overestimation is transferable, the HF/6-31G(d) Si-N distance of the endo form is predicted to be about 245pm. This value is in agreement with the ED experimental distance [8]. The energy hypersurface is very flat around the two minima. This result agrees with the earlier ones for I-hydroxysilatrane [20] and I-fluorosilatrane [l]. There is a very small energy barrier between the two local minima at 300pm; the exo form is more stable. These results suggest that the endo form may be easily transformed into the exo form and vice versa. Only a small amount of energy is required to change the Si-N distance between 240 and 340pm. The HF/3-21G(d) single point calculations in the solid-state geometry and in a hypothetical gas-phase geometry [22] may be well above the energy surface. According to those calculations the total energy at the 217.5 pm Si-N distance is lower by 22 kcal mol-’ than the total energy calculated at the 245 pm Si-N distance. This is in contradiction with the results presented here and with the tendencies of HF/6-31G(d) geometry optimizations on model compounds [22]. The value of the single point calculations is questionable from the point of view of energy comparisons.
255
G.I. Csonka and P. HencseijJ. Mol. Struct. (Theochem) 283 (1993) 251-259
Fig. 3. The molecular diagram, with the hetero atoms labelled, of the non-symmetric endo form of l-methylsilatrane (AM1 equilibrium geometry).
The calculated AM1 zero-point energy in the endo minimum is 145.2 kcal mol-’ and in the exo minimum it is 145.7 kcal mol-‘. Frequency analysis shows that there is an Si-N stretching vibration at 271 cm-’ and it is combined with C-N (at 469 and 1542 cm-‘), Si-0 and Si-C (at 733 cm-‘) vibrations in the endo form. In the exo form no Si-N stretching vibration was found. It is presumed that the ethoxy links are very flexible. In order to study this flexibility another series of geometry optimizations were performed, with one of the links forced out of the Cs symmetry position (Fig. 3). Table 2 shows the results for the non-symmetric conformation. This conformation does not exist as a separate energy minimum at Table 2 AM1 results for I-methylsilatrane, R(Si-N)
the 220pm Si-N distance. It appears above 240 pm in a separate energy valley with a local minimum at 258.5pm. It disappears again at longer Si-N distances as the Cs form becomes more advantageous energetically. It is easier to “pull out” the nitrogen if the links are symmetrically ordered. The second (exo) energy minimum does not exist for the non-symmetric conformation. The energy required to make one of the Si-O-C-C-N rings planar was found to be 1.4 kcal mol-’ at the 260.3pm Si-N distance. This is the energy barrier between the C, and the non-symmetric conformation. The low amount of energy required supports the possible existence of disordered structures in the crystal phase [5] and is in accordance with the NMR observations related to the high flexibility of the silatrane skeleton [12]. The dihedral angles calculated by the AM1 method do not agree with the solid-phase results. The conformation of the whole silatrane skeleton can be represented by the 0-Si-N-C dihedral angle. The use of a second, dependent C-0-Si-N angle can also be helpful. In the solid-state geometry the average of the three C-0-Si-N dihedral angles is -7.7” and the average of the 0-Si-N-C angles is -17.4” [7]. In the calculated AM1 (C,, endo) geometry the C-0-Si-N angle is -27” and the 0-Si-N-C angle is 0”. If the Si-N distance is fixed at 220pm, the two equilibrium dihedral angles are -7.5” and -12.7”, respectively, which is comparable to the experimental results [7]. Table 3 shows the results of a geometry optimization in which the 0-Si-N-C angle was
fully optimized geometry, non-symmetrical
Hf (kcal)
p (D)
Q(Si)
(pm) 240 260 280 300 320 340
- 198.76 -200.61 -198.93 -196.88 -196.21 -195.00
5.35 4.26 3.22 2.24 1.31 0.92
1.589 1.604 1.613 1.609 1.606 1.617
Q(N) -0.305 -0.342 -0.382 -0.400 -0.362 -0.300
form; variation of the Si-N distance P(Si-N)
0.152 0.095 0.056 0.030 0.015 0.007
E(Si-N) (ev)
E(Si-C)
-5.13 -4.43 -3.84 -3.16 -2.34 -1.67
-16.50 -16.81 - 16.99 -17.07 -17.15 -17.30
(ev)
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G.I. Csonka and P. Hencsei/J. Mol. Struct. (Theochem) 283 (1993) 251-259
Table 3 AM1 results for 1-methylsilatrane dihedral angle a(Si-N)’
with approximate
&B-N)
Q(W
(deg)
Hr (k@
(pm)
?D)
-20 -10 0 10 20
-198.96 -200.84 -201.62 -201.16 -199.31
251.6 254.0 260.2 265.4 269.5
4.57 4.57 4.14 3.61 3.04
“a(Si-N)
Cs symmetry,
denotes the average of the three 0-Si-N-C
1.621 1.609 1.599 1.585 1.573
R(Si-N) (pm) 220.0 240.0 256.3 260.0 280.0 300.0 320.0 327.7 340.0 ‘a(Si-N)
Hf (kcal) -218.90 -222.37 -223.43 -223.38 -222.07 -222.69 -224.51 -225.22 -224.39
with approximate a(Si-N)a (deg) -9.4 -3.2 0.3 1.0 3.0 1.5 1.4 -6.8 -5.5
-0.339 -0.338 -0.346 -0.355 -0.363
P(Si-N)
0.118 0.111 0.094 0.08 1 0.071
of the 0-Si-N-C
E(Si-N)
E(Si-C)
(ev)
(ev)
-4.81 -4.69 -4.44 -4.21 -4.02
-16.83 -16.77 -16.78 -16.76 -16.77
bond.
action in the silatrane skeleton for the Si-N bond; (c) the closer the Si-N distance is to the solid-phase result, the closer are the calculated dihedral angles to the experimental values. Table 4 lists the MNDO-PM3 results for I-methylsilatrane; they can be compared with the results in Table 1. The heat of formation shows two minima as in the AM1 results. The equilibrium Si-N distances are shorter than the distances given by the AM1 method, but because of the flat energy surface this difference is not so important. The main difference is in the energy values. In the case of the PM3 method the exo form is even more stable. Despite the differences in shape, the energy hypersurface is very flat. The energy barrier is located between 280 and 300pm. The results are quantitatively different from the AM1 ones but they lead to similar conclusions. The average values of the three 0-Si-N-C
Cs symmetry, fully optimized geometry; variation of the Si-N
p (D)
Q(W
5.37 4.34 3.49 3.31 2.31 1.27 0.40 0.14 0.31
0.911 0.940 0.950 0.953 0.962 0.967 0.974 0.976 0.981
denotes the average of the three O-B-N-C
Q(N)
dihedral angles around the Si-N
changed in steps and the other geometric parameters were allowed to relax freely. It was found that 0.8 kcalmol-’ energy was required to rotate this angle by -lo”, while the Si-N distance was shortened by 6.2pm. The average of the three C-0-Si-N dihedral angles was changed to -14”. The Si-N bond order was increasing parallel with the Si-N diatomic energy contribution. 2.7 kcalmol-’ energy was required to rotate this angle further and the Si-N distance was shortened by 8.6pm. It is noteworthy that both axial bonds (Si-N and Si-C) were shortening and strengthening in the same time. Three conclusions can be drawn from these results: (a) the geometry found in the crystal structure is the preferred position for the Si-N and Si-C bonds; (b) as the nitrogen is pushed toward the silicon the torsional angles of the skeleton are changing and there is a stretching torsion interTable 4 PM3 results for 1-methylsilatrane
fully optimized geometry; variation
Q(N) 0.077 0.009 -0.043 -0.054 -0.115 -0.130 -0.104 -0.096 -0.085
P(Si-N)
distance
E(Si-N) (ev)
E(Si-C)
0.253 0.166 0.111 0.100 0.057 0.026 0.011
-3.13 -2.30 -1.79 -1.70 -1.25 -0.67 -0.32
-10.81 -11.03 -11.16 -11.17 -11.27 -11.31 -11.38
0.005
-0.14
-11.43
dihedral angles around the Si-N
bond.
(ev)
*
G.I. Csonka and P. HencseilJ.
Mol. Strut.
(Theochem)
283 (1993) 251-259
dihedral angles (a(%N) in Table 4) agree well with the dihedral angles obtained by the AM1 method at shorter distances (below 260pm), but there is considerable disagreement above 300pm (see Table 1). This different conformation stabilizes the PM3 geometry at longer Si-N distances. Further geometry parameters are given in Figs. 1 and 2. The Si-0 distances calculated by the PM3 method are shorter and the C-N distances are longer than the corresponding AM1 distances and they agree better with experimental results [5]. The PM3 C-H distances are shorter and more realistic. The N-Si-C angles were in each case very close to 180”. The value of the dipole moment decreases with the lengthening of the Si-N bond as in the AM1 method, but the predicted values are considerably smaller. The calculated dipole moment agrees with the experimental one at the 220 pm Si-N distance. The atomic charge on silicon (Q(Si) in Table 4) is strongly positive, but much less than the AM1 atomic charge. The charge on the silicon atom increases as the Si-N distance increases. In 1-fluorosilatrane, the calculated positive charge on silicon is higher by 0.16 charge unit [ 11.The atomic charge on nitrogen Q(N) is slightly positive at shorter Si-N distances (below 220pm) and at longer distances it is slightly negative. This is one of the most important differences between the PM3 and AM1 results and it is reflected in the differences in the other calculated properties (dipole moments, energy partitioning). This difference was also Table 5 PM3 results for 1-methylsilatrane, R(Si-N) (pm) 220.0 240.0
Hr (kcal) -218.30 -221.79 -222.61
260.0 280.0
-220.94
300.0 316.2 320.0
-220.90 -221.51 -221.52
340.0
-219.12
found between the AM1 and PM3 methods in the case of 1-fluorosilatrane [I]. The values of the Si-N bond order P(Si-N) are larger than those calculated using the AM1 method, but they indicate the same tendency. The energy partitioning shows that the Si-N interaction starts to diminish rapidly above 280pm. The absolute values are much smaller than those calculated using the AM1 method. A detailed analysis shows that the energy contribution of the resonance term is practically the same for the two different methods. The origin of the difference is the electrostatic term. The electrostatic contribution in the endo form is practically zero, -0.26eV, using the PM3 method while it is -3.10 eV using the AM1 method. This difference can be explained by the much smaller PM3 charge on the nitrogen atom. The calculated PM3 zero-point energy of the endo geometry is 139.5 kcal mol-’ . Frequency analysis shows that there is an Si-N stretching vibration at 286cm-’ which is combined with C-N (at 439cm-i) and Si-0 and Si-C (at 710 cm-‘) vibrations in the endo form. Table 5 lists the results calculated using the PM3 method in the same way as Table 2 summarizes the AM1 results. The non-symmetric form has two minima. This is the essential difference between the AM1 and PM3 energy surfaces. The PM3 parametrization gives extra stability to the exo form. Otherwise the calculated values show the same tendencies concluded from Tables 2 and 4. The
fully optimized geometry, non-symmetrical iJ (D)
QWI
5.40
0.911
4.38 3.38 2.49
0.938 0.954
1.57 1.Ol 0.98 0.88
0.966 0.972 0.981 0.983 0.993
251
c?(N) 0.083 0.015 -0.054 -0.113 -0.123 -0.101 -0.096 -0.075
form; variation of the Si-N P(B-N)
distance
E(Si-N)
E(Si-C)
(ev)
(ev)
0.253
-3.12
0.168 0.101 0.059
-2.29 -1.70 -1.24
-10.81 -11.02 -11.17
0.027
-0.66
-11.30
0.013 0.006
-0.30
-11.36 -11.42
-0.13
-11.26
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Table 6 PM3 results for I-methylsilatrane dihedral angle
with approximate
a(Si-N)a
Hi
R(Si-N)
(deg)
@Cal)
(Pm)
-20 -10 0 10 20
-220.09 -222.44 -223.43 -222.68 -220.74
244.9 250.2 255.9 257.9 255.0
C, symmetry,
p (D)
QW
4.02 3.86 3.51 3.26 3.16
aa(Si-N) denotes the average of the three O-B-N-C
0.952 0.950 0.950 0.950 0.948
fully optimized
Q(N) -0.028 -0.028 -0.042 -0.040 -0.026
geometry; variation
P(Si-N)
0.152 0.132 0.112 0.105 0.113
dihedral angles around the Si-N
dipole moments, the absolute values of atomic charges and the diatomic energy contributions are systematically smaller when using the PM3 method. The same kind of flexibility was found as above. The energy profile is extremely flat between 240 and 320 pm. The endo form is lower in energy. The energy barrier is at about 290pm. The energy barrier to transform an out-ofsymmetry ethoxy link back into the symmetrical position was calculated to be 1 kcalmol-‘. The ethoxy link is calculated to be even more flexible by the PM3 method. Table 6 lists the PM3 results obtained by rotating the O-%-C-N dihedral angle. There is qualitative agreement between the PM3 and AM1 results in Table 3. 1 kcalmol-’ energy was required to rotate this angle by -lo”, while the Si-N distance was shortened by 5.7 pm (Table 6). The average of the three C-0-Si-N dihedral angles was changed to - 15”. The Si-N bond order increased, parallel with the Si-N diatomic energy contribution. 3.3 kcal mol-’ energy was required to rotate this angle further. The rotation in the opposite direction requires even less energy (in agreement with the AM1 results) and causes Si-N bond shortening (in disagreement with the AM1 results). The other calculated values show the characteristic differences between the PM3 and AM1 parametrization. However, there is considerable agreement in the tendencies, which seem to be model independent. The geometries of the three energy minima agree well and the most important findings based on the AM1 results are
283 (1993) 2Sl-259
of the 0-Si-N-C
E(Si-N)
E(Si-C)
(ev)
(ev)
-2.15 -1.99 -1.81 -1.71 -1.75
-11.09 -11.11 -11.15 -11.18 -11.18
bond.
supported by the PM3 results. The existence of a fourth, non-symmetric exo minimum is supported by the PM3 but not by the AM1 results. The Si-N distance in I-methylsilatrane is 6-7 pm longer than in I-fluorosilatrane according to both methods. The experimental methods (ED and XD) show an increase in the 13 pm distance [1,5-81. Conclusions The main findings of this paper are as follows: (1) two minima were found on the energy profile when C, symmetry was retained by both semiempirical methods with two different Si-N distances (endo C, and exo C, forms); (2) there exists a third, non-symmetrical conformation in a separate minimum in which the Si-N distance is nearly identical to the Si-N distance found in the endo C, conformation. The PM3 results show the possible existence of a fourth minimum; (3) the calculated endo Si-N distances are longer by 1 1- 15 pm than the gas-phase experimental value. The predicted Si-N distance agrees with the gas-phase result if the Si-N distance is corrected by a factor (- 15 pm) originating from HF/6-3 1G(d) analogies; (4) the Si-N distance in 1-methylsilatrane was predicted to be 6-7 pm longer than in l-fluorosilatrane, in agreement with experimental results; (5) the Si-N distance was found to be dependent on the 0-Si-N-C dihedral angle, turning this
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283 (1993) 251-259
angle closer to the crystal-phase results as the equilibrium Si-N distance is decreasing. The energy required to turn this dihedral angle by 20” is 2.7-3.3 kcal mol-‘; (6) the energy cost of shortening the Si-N distance has been found to be small, the energy hypersurface is rather flat and the silatrane skeleton is flexible. The calculations show that the crystal forces could easily distort the gas-phase structure; (7) the calculated Si-N bond orders and energy partitioning show an existing Si-N bond at distances below 260-270 pm.
10 11 12 13 14
Acknowledgement 15
This work was supported by the OTKA fund (No. 382 and 644) of the Government of Hungary.
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G. Forgacs, M. Kolonits and I. Hargittai, Struct. Chem., 1 (1990) 245. L. Pbrkanyi, L. Bihatsi and P. Hencsei, Cryst. Struct. Commun., 7 (1978) 435. Q. Shen and R.L. Hilderbrandt, J. Mol. Struct., 64 (1980) 257. A.A. Kemme, Ya.Ya. Bleidelis, V.A. Pestunovich, V.P. Baryshok and M.G. Voronkov, Dokl. Akad. Nauk SSSR, 243 (1978) 688. L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY, 1960. C. Glidewell, Inorg. Chim. Acta, 20 (1976) 113. M.G. Voronkov and V.M. Dyakov, Silatrani, Izd. Nauka, Novosibirsk, 1978. M.G. Voronkov, I.B. Mazeika and G.I. Zelcans, Khim. Geterosikl. Soedin., (1958) 58. V.F. Sidorkin, V.A. Pestunovich and M.G. Voronkov, Dokl. Akad. Nauk SSSR, 235 (1977) 1363. J.M. Cheyhaber, S.T. Nagy and C.S. Lin, Can. J. Chem., 62 (1984) 27. C.J. Mardsen, Inorg. Chem., 22 (1983) 3177. B.S. Ault, Inorg. Chem., 20 (1981) 2817. W.J. Hehre, R. Ditchfield and J.A. Pople, J. Chem. Phys., 67 (1972) 2257. M.S. Gordon, Chem. Phys. Lett., 76 (1980) 163. M.S. Gordon, L.P. Davies and L.W. Burggraf, Chem. Phys. Lett., 163 (1989) 371. M.S. Gordon, M.T. Carroll, J.H. Jensen, L.P. Davis, L.W. Burggraf and R.M. Guidey, Organometallics, 10 (1991) 2657. R.F. Bader, Act. Chem. Res., 18 (1985) 9. A. Greenberg, C. Plant and CA. Venanzi, J. Mol. Struct. (Theochem), 234 (1991) 291. M.J.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P. Stewart, J. Am. Chem. Sot., 107 (1985) 3902. J.J.P. Stewart, J. Comput. Chem., 10 (1989) 209. J.J.P. Stewart, MOPAC, QCPE No. 455, 1983. M.J.S. Dewar and C.X. Jie, Organometallics, 6 (1987) 1486.
251
AM1 and PM3 semiempirical molecular orbital study of silatranes. Part 2. The 1-methylsilatrane G.I. Csonka, P. Hencsei* Department
of Inorganic Chemistry,
Technical University
of Budapest, H-1521 Budapest, Hungary
(Received 29 June 1992 in final form 15 October 1992) Abstract
AM1 and PM3 semiempirical models have been employed to study the bonding and structure of l-methylsilatrane using full geometry optimization. Heats of formation were calculated at various Si-N distances between 220 and 360pm. Two minima were found on the energy profile when Cs symmetry was retained. A third local energy minimum was found, in a non-symmetrical conformation.
Introduction
A previous article reported the MNDO, AM1 and PM3 equilibrium conformations of l-fluorosilatrane [l]. Silatranes (RSi(OCH2CH2)sN, lorganyl-2,8,9-trioxa-5-aza-I-silatricyclo [3.3.3.0’.‘] undecanes) are biologically active, silicon-containing organic molecules (Fig. 1) [2-41. The most important structural feature of these molecules is the transannular Si-N donor-acceptor bond. Two forms of the structure may be assumed. The central silicon atom in the endo form is bonded to a nitrogen atom through three ethoxy bridges and via a dative bond; the lone electron pair on the nitrogen is turned towards the silicon and the Si-N distance is relatively short (Fig. 1). In the exo form the nitrogen lone pair is outside and the resulting Si-N distance is much longer (Fig. 2). In crystalline samples of many substituted silatranes, short Si-N distances were observed, indicating that the endo form exists in the solid state. Gas-phase electron diffraction (ED) measurements show longer Si-N distances in 1-fluorosilatrane: 204.2pm (X-ray) [5]; 232.4pm (ED) [6]; and in * Corresponding
author.
I-methylsilatrane: 217.5 pm (X-ray) [7]; 245 pm (ED) [8]. In I-chlorosilatrane the Si-N distance is 202.3pm (X-ray) [9]; this is the shortest Si-N distance measured and no ED data is available. The measured Si-N distances are longer than the sum of the covalent radii (187 pm or 189.5 pm) [lO,ll], but shorter than the sum of the appropriate non-bonded radii (269pm) [l l] and much shorter than the sum of the van der Waals radii (350pm) [lo]. The Si-N distance is also variable in solution, shortening in polar solvents and lengthening in non-polar solvents [8]. The Si-N distance has been found to be dependent on the nature of the substituent R. An electron-withdrawing substituent (R = fluorine or chlorine) shortens the Si-N distance by decreasing the electron density on silicon and thus increasing its electronacceptor potential and causing a stronger Si-N dative bond to be formed. This is in agreement with the experimental results. Methyl substitution has the opposite effect, resulting in a longer Si-N bond. This bond lengthening is about 13 pm in both types of measurements. The silatrane skeleton has been found to have approximately Cs symmetry in the solid state. The symmetry is only approximate because of
G.I. Csonka and P. HencseilJ. Mol. Strut. (Theo&em) 283 (1993) 251-259
(111.0 pm)
SI
.
Fig. 1. The molecular diagram, with the atoms labelled, of the endo C, form of I-methylsilatrane (AM1 (PM3) equilibrium geometry).
Fig. 2. The molecular diagram, with the hetero atoms labelled, of the exo C, form of 1-methylsilatrane (AM1 (PM3) equilibrium geometry).
the high flexibililty of the ethoxy links between silicon and nitrogen [5,7,9]. A partially disordered structure has been found in 1-fluorosilatrane [5]. NMR data also show very fast ring inversions in solution [12] for other substituted silatranes. The existence of different polymorphic moditications was explained by freezing of intramolecular movements. The high dipole moments of silatranes may play a role in their biological activity by facilitating penetration of membranes [ 1,2]. The experimental dipole moment of 1-methylsilatrane is 5.3 D [13]. The early theoretical investigations of silatranes were limited by the size of the molecule, by the lack of experimental geometries, by their conformational flexibility and by the limited methods for geometry optimization and computing power that were available. The nature of the Si-N bond was frequently discussed on the basis of sp3d hybridization. However, based on the existence of the corresponding boron compound, the boratrane [1,2],
the importance of d orbitals was questioned and another, so-called hypervalent model was also proposed [14]. The ab initio theory was also applied, but no geometry optimizations were performed. Only simple model compounds of neutral pentacoordinated adducts were calculated with full geometry optimization. The predicted stabilization energy of the NH3-SiF4 adduct was calculated to be 10.0 and 8.6 kcalmol-‘, respectively, with minimal and double-zeta basis sets [15,16]. The existence of the NH3-SiF4 adduct was proved by previous experiments [17]. A number of ab initio calculations show the existence and stability of neutral pentacoordinated compounds containing an Si-N bond [1820]. The axial bond was found to be a three-centre, four-electron bond, so that the strength of the axial Si-N bond is influenced by the ligand in the opposite axial position [20]. Gordon et al. [21] used the AM1 semiempirical method to fully optimize the geometry of
G.I. Csonka and P. HencseilJ. Mol. Strut.
(Theochem)
283 (1993) 251-259
1-hydroxysilatrane (R = OH) and related compounds and they performed single point HF/631G(d) ab initio calculations on the AM 1 equilibrium geometries. The geometries of some simpler model compounds were also optimized at the 6-31G(d) ab initio level. This made a direct comparison of ab initio and AM 1 optimized geometries possible. The performance of AM 1 has been found to be satisfactory. The predicted Si-N distances are 15-20 pm longer and the Si-0 distances are 6-9pm longer than the ab initio results, but the general trends are well reproduced. Utilizing the Bader electron density analysis [22], it was found that the Si-N bond critical point still exists at larger Si-N distances, only a small amount of energy is required to decrease the Si-N distance in I-hydroxysilatrane to reach a typical crystal geometry and as the number of ethoxy bridges increases, the Si-N bond weakens and the Si-O,, bond strengthens. Greenberg et al. [23] studied 1-methylsilatrane and model compounds by HF/3-21G(d) ab initio theory. No geometry optimization was performed. The calculations were carried out at two points; a solid-state and an approximate gas-phase geometry were applied. It was found that the Mulliken charges do not change much as the Si-N distance is varied, the silicon atom remains strongly positive and the nitrogen atom remains strongly negative. In the present study the calculations of l-methylsilatrane are included. Two recent semiempirical model hamiltonians were used in order to study the effects of parameterization, their utility and limitations. Computational methods All geometries were fully optimized using the semiempirical AM1 [24] and PM3 [25] methods and adapted versions of the MOPAC [26] program. The latest AM1 parameters for silicon were used [27] in the calculations. The calculations were carried out on an i486/33 MHz workstation and on an IBM RS/6000 model 320H. The PLUTO program was used to plot the geometries.
253
No symmetry constraints were imposed during the geometry optimizations and the “precise” keyword of MoPAchas always been used. A Cs-like and a completely non-symmetric geometry were optimized separately. The Si-N distance was varied between 220 and 360pm by steps of 20pm, and other geometrical parameters were fully optimized in each step. The lowest energy geometries were used to find the local minima’s points. The fully optimized geometries were always verified as minima by establishing that their Hessian matrices are definitely positive. Frequency analysis was performed, and zero-point energy was calculated at the minimum. The 0-Si-N-C dihedral angle was varied between -20” and 20” in steps of 10”. In this case the Si-N distance was relaxed together with the other geometrical parameters. The energy barrier of the ethoxy flip-flop was also calculated at the minimum, in order to study the flexibility of the three bridges linking the silicon and nitrogen. Mulliken charges, dipole moments, bond orders and energy partitioning were also calculated. Results and discussion The AM1 heats of formation Hr, dipole moments ~1and other important calculated values are listed in Table 1 for 1-methylsilatrane. The geometry has an approximate C3 symmetry (Figs. 1 and 2). The heat of formation shows two minima as a function of the Si-N distance. The equilibrium Si-N distances (endo and exo) are 7-8 pm longer than the corresponding distances calculated for I-fluorosilatrane (253.2 pm and 33 1.Opm respectively) [l]. This may be compared to the bond lengthening found in experiments (13 pm) [5-81. The average values of the three 0-Si-N-C dihedral angles are listed in Table 1 as a(Si-N). They are suitable for describing the conformation of the whole skeleton. As the Si-N distance decreases, this angle becomes more negative; at long distances it remains constant and positive. The value of the dipole moment decreases with the lengthening of the Si-N bond. The calculated
254
G.I. Csonka and P. HencseijJ. Mol. Siruct. (Theo&m) 283 (1993) 251-259
Table 1 AM1 results for 1-methylsilatrane R(Si-N) @m) 220.0 240.0 260.3 280.0 300.0 320.0 339.3 aa(Si-N)
Hf (kcal) -194.65 -199.72 -201.63 -200.81 -200.35 -201.62 -202.67
with approximate
C, symmetry, fully optimized geometry; variation of the Si-N
QW
a(Si-N)* (deg) -12.7 -5.6 0.2 6.8 8.7 8.5 8.0
Q(N)
P(Si-N)
i& 6.43 5.33 4.13 2.90 1.78 0.78 0.10
denotes the average of the three 0-Si-N-C
1.569 1.590 1.599 1.588 1.576 1.568 1.569
-0.281 -0.308 -0.346 -0.388 -0.405 -0.371 -0.308
0.226 0.152 0.094 0.053 0.026 0.012
dihedral angles around the Si-N
dipole moment agrees with the experimental one at the 240 pm Si-N distance. The atomic charge on silicon Q(Si) is calculated to be strongly positive and it has a very flat maximum at 26Opm, near to the optimum of the endo Si-N distance. The atomic charge on nitrogen Q(N) is strongly negative, with a more important variation. It has a minimum at 300pm and it increases rapidly at longer distances. The calculated positive charge on the silicon atom of lfluorosilatrane is higher by 0.14 charge unit, but the negative charge on the nitrogen atom shows no difference [l]. The existence of the strongly positive silicon and the strongly negative nitrogen is in agreement with ab initio 3-21G(d) Mulliken charges for 1-methylsilatrane [21]. The HF/321G(d) calculations have a tendency to give high charges. The Si-N bond order P(Si-N) is large at shorter Si-N distances (below 260pm). At longer distances the bond order is halved as the distance increases by 20pm. This behaviour may be compared to the non-bonding distance proposed by Glidewell [ 111. The energy partitioning shows a rather strong Si-N interaction even at large distances. A detailed analysis showed that the energy contribution of the resonance term was decreasing rapidly, but the sum of the electrostatic terms was high even at large Si-N distances due to high negative charge on the nitrogen. In the endo form the resonance term was equal to - 1.33 eV and the
distance
E(Si-N)
E(Si-C)
(ev)
(ev)
-6.03 -5.14 -4.43 -3.80 -3.10 -2.33
-16.15 -16.52 -16.78 -16.87 -16.91 -16.95 -17.05
bond.
electrostatic term was -3.10 eV. The opposite energetic behaviour of the two axial bonds (Si-N and Si-C) is in agreement with other AM1 and ab initio results for similar compounds [1,19,21]. The AM1 Si-N distance of the endo form is supposed to be 15 pm longer than the HF/631G(d) optimum [21]. If this overestimation is transferable, the HF/6-31G(d) Si-N distance of the endo form is predicted to be about 245pm. This value is in agreement with the ED experimental distance [8]. The energy hypersurface is very flat around the two minima. This result agrees with the earlier ones for I-hydroxysilatrane [20] and I-fluorosilatrane [l]. There is a very small energy barrier between the two local minima at 300pm; the exo form is more stable. These results suggest that the endo form may be easily transformed into the exo form and vice versa. Only a small amount of energy is required to change the Si-N distance between 240 and 340pm. The HF/3-21G(d) single point calculations in the solid-state geometry and in a hypothetical gas-phase geometry [22] may be well above the energy surface. According to those calculations the total energy at the 217.5 pm Si-N distance is lower by 22 kcal mol-’ than the total energy calculated at the 245 pm Si-N distance. This is in contradiction with the results presented here and with the tendencies of HF/6-31G(d) geometry optimizations on model compounds [22]. The value of the single point calculations is questionable from the point of view of energy comparisons.
255
G.I. Csonka and P. HencseijJ. Mol. Struct. (Theochem) 283 (1993) 251-259
Fig. 3. The molecular diagram, with the hetero atoms labelled, of the non-symmetric endo form of l-methylsilatrane (AM1 equilibrium geometry).
The calculated AM1 zero-point energy in the endo minimum is 145.2 kcal mol-’ and in the exo minimum it is 145.7 kcal mol-‘. Frequency analysis shows that there is an Si-N stretching vibration at 271 cm-’ and it is combined with C-N (at 469 and 1542 cm-‘), Si-0 and Si-C (at 733 cm-‘) vibrations in the endo form. In the exo form no Si-N stretching vibration was found. It is presumed that the ethoxy links are very flexible. In order to study this flexibility another series of geometry optimizations were performed, with one of the links forced out of the Cs symmetry position (Fig. 3). Table 2 shows the results for the non-symmetric conformation. This conformation does not exist as a separate energy minimum at Table 2 AM1 results for I-methylsilatrane, R(Si-N)
the 220pm Si-N distance. It appears above 240 pm in a separate energy valley with a local minimum at 258.5pm. It disappears again at longer Si-N distances as the Cs form becomes more advantageous energetically. It is easier to “pull out” the nitrogen if the links are symmetrically ordered. The second (exo) energy minimum does not exist for the non-symmetric conformation. The energy required to make one of the Si-O-C-C-N rings planar was found to be 1.4 kcal mol-’ at the 260.3pm Si-N distance. This is the energy barrier between the C, and the non-symmetric conformation. The low amount of energy required supports the possible existence of disordered structures in the crystal phase [5] and is in accordance with the NMR observations related to the high flexibility of the silatrane skeleton [12]. The dihedral angles calculated by the AM1 method do not agree with the solid-phase results. The conformation of the whole silatrane skeleton can be represented by the 0-Si-N-C dihedral angle. The use of a second, dependent C-0-Si-N angle can also be helpful. In the solid-state geometry the average of the three C-0-Si-N dihedral angles is -7.7” and the average of the 0-Si-N-C angles is -17.4” [7]. In the calculated AM1 (C,, endo) geometry the C-0-Si-N angle is -27” and the 0-Si-N-C angle is 0”. If the Si-N distance is fixed at 220pm, the two equilibrium dihedral angles are -7.5” and -12.7”, respectively, which is comparable to the experimental results [7]. Table 3 shows the results of a geometry optimization in which the 0-Si-N-C angle was
fully optimized geometry, non-symmetrical
Hf (kcal)
p (D)
Q(Si)
(pm) 240 260 280 300 320 340
- 198.76 -200.61 -198.93 -196.88 -196.21 -195.00
5.35 4.26 3.22 2.24 1.31 0.92
1.589 1.604 1.613 1.609 1.606 1.617
Q(N) -0.305 -0.342 -0.382 -0.400 -0.362 -0.300
form; variation of the Si-N distance P(Si-N)
0.152 0.095 0.056 0.030 0.015 0.007
E(Si-N) (ev)
E(Si-C)
-5.13 -4.43 -3.84 -3.16 -2.34 -1.67
-16.50 -16.81 - 16.99 -17.07 -17.15 -17.30
(ev)
256
G.I. Csonka and P. Hencsei/J. Mol. Struct. (Theochem) 283 (1993) 251-259
Table 3 AM1 results for 1-methylsilatrane dihedral angle a(Si-N)’
with approximate
&B-N)
Q(W
(deg)
Hr (k@
(pm)
?D)
-20 -10 0 10 20
-198.96 -200.84 -201.62 -201.16 -199.31
251.6 254.0 260.2 265.4 269.5
4.57 4.57 4.14 3.61 3.04
“a(Si-N)
Cs symmetry,
denotes the average of the three 0-Si-N-C
1.621 1.609 1.599 1.585 1.573
R(Si-N) (pm) 220.0 240.0 256.3 260.0 280.0 300.0 320.0 327.7 340.0 ‘a(Si-N)
Hf (kcal) -218.90 -222.37 -223.43 -223.38 -222.07 -222.69 -224.51 -225.22 -224.39
with approximate a(Si-N)a (deg) -9.4 -3.2 0.3 1.0 3.0 1.5 1.4 -6.8 -5.5
-0.339 -0.338 -0.346 -0.355 -0.363
P(Si-N)
0.118 0.111 0.094 0.08 1 0.071
of the 0-Si-N-C
E(Si-N)
E(Si-C)
(ev)
(ev)
-4.81 -4.69 -4.44 -4.21 -4.02
-16.83 -16.77 -16.78 -16.76 -16.77
bond.
action in the silatrane skeleton for the Si-N bond; (c) the closer the Si-N distance is to the solid-phase result, the closer are the calculated dihedral angles to the experimental values. Table 4 lists the MNDO-PM3 results for I-methylsilatrane; they can be compared with the results in Table 1. The heat of formation shows two minima as in the AM1 results. The equilibrium Si-N distances are shorter than the distances given by the AM1 method, but because of the flat energy surface this difference is not so important. The main difference is in the energy values. In the case of the PM3 method the exo form is even more stable. Despite the differences in shape, the energy hypersurface is very flat. The energy barrier is located between 280 and 300pm. The results are quantitatively different from the AM1 ones but they lead to similar conclusions. The average values of the three 0-Si-N-C
Cs symmetry, fully optimized geometry; variation of the Si-N
p (D)
Q(W
5.37 4.34 3.49 3.31 2.31 1.27 0.40 0.14 0.31
0.911 0.940 0.950 0.953 0.962 0.967 0.974 0.976 0.981
denotes the average of the three O-B-N-C
Q(N)
dihedral angles around the Si-N
changed in steps and the other geometric parameters were allowed to relax freely. It was found that 0.8 kcalmol-’ energy was required to rotate this angle by -lo”, while the Si-N distance was shortened by 6.2pm. The average of the three C-0-Si-N dihedral angles was changed to -14”. The Si-N bond order was increasing parallel with the Si-N diatomic energy contribution. 2.7 kcalmol-’ energy was required to rotate this angle further and the Si-N distance was shortened by 8.6pm. It is noteworthy that both axial bonds (Si-N and Si-C) were shortening and strengthening in the same time. Three conclusions can be drawn from these results: (a) the geometry found in the crystal structure is the preferred position for the Si-N and Si-C bonds; (b) as the nitrogen is pushed toward the silicon the torsional angles of the skeleton are changing and there is a stretching torsion interTable 4 PM3 results for 1-methylsilatrane
fully optimized geometry; variation
Q(N) 0.077 0.009 -0.043 -0.054 -0.115 -0.130 -0.104 -0.096 -0.085
P(Si-N)
distance
E(Si-N) (ev)
E(Si-C)
0.253 0.166 0.111 0.100 0.057 0.026 0.011
-3.13 -2.30 -1.79 -1.70 -1.25 -0.67 -0.32
-10.81 -11.03 -11.16 -11.17 -11.27 -11.31 -11.38
0.005
-0.14
-11.43
dihedral angles around the Si-N
bond.
(ev)
*
G.I. Csonka and P. HencseilJ.
Mol. Strut.
(Theochem)
283 (1993) 251-259
dihedral angles (a(%N) in Table 4) agree well with the dihedral angles obtained by the AM1 method at shorter distances (below 260pm), but there is considerable disagreement above 300pm (see Table 1). This different conformation stabilizes the PM3 geometry at longer Si-N distances. Further geometry parameters are given in Figs. 1 and 2. The Si-0 distances calculated by the PM3 method are shorter and the C-N distances are longer than the corresponding AM1 distances and they agree better with experimental results [5]. The PM3 C-H distances are shorter and more realistic. The N-Si-C angles were in each case very close to 180”. The value of the dipole moment decreases with the lengthening of the Si-N bond as in the AM1 method, but the predicted values are considerably smaller. The calculated dipole moment agrees with the experimental one at the 220 pm Si-N distance. The atomic charge on silicon (Q(Si) in Table 4) is strongly positive, but much less than the AM1 atomic charge. The charge on the silicon atom increases as the Si-N distance increases. In 1-fluorosilatrane, the calculated positive charge on silicon is higher by 0.16 charge unit [ 11.The atomic charge on nitrogen Q(N) is slightly positive at shorter Si-N distances (below 220pm) and at longer distances it is slightly negative. This is one of the most important differences between the PM3 and AM1 results and it is reflected in the differences in the other calculated properties (dipole moments, energy partitioning). This difference was also Table 5 PM3 results for 1-methylsilatrane, R(Si-N) (pm) 220.0 240.0
Hr (kcal) -218.30 -221.79 -222.61
260.0 280.0
-220.94
300.0 316.2 320.0
-220.90 -221.51 -221.52
340.0
-219.12
found between the AM1 and PM3 methods in the case of 1-fluorosilatrane [I]. The values of the Si-N bond order P(Si-N) are larger than those calculated using the AM1 method, but they indicate the same tendency. The energy partitioning shows that the Si-N interaction starts to diminish rapidly above 280pm. The absolute values are much smaller than those calculated using the AM1 method. A detailed analysis shows that the energy contribution of the resonance term is practically the same for the two different methods. The origin of the difference is the electrostatic term. The electrostatic contribution in the endo form is practically zero, -0.26eV, using the PM3 method while it is -3.10 eV using the AM1 method. This difference can be explained by the much smaller PM3 charge on the nitrogen atom. The calculated PM3 zero-point energy of the endo geometry is 139.5 kcal mol-’ . Frequency analysis shows that there is an Si-N stretching vibration at 286cm-’ which is combined with C-N (at 439cm-i) and Si-0 and Si-C (at 710 cm-‘) vibrations in the endo form. Table 5 lists the results calculated using the PM3 method in the same way as Table 2 summarizes the AM1 results. The non-symmetric form has two minima. This is the essential difference between the AM1 and PM3 energy surfaces. The PM3 parametrization gives extra stability to the exo form. Otherwise the calculated values show the same tendencies concluded from Tables 2 and 4. The
fully optimized geometry, non-symmetrical iJ (D)
QWI
5.40
0.911
4.38 3.38 2.49
0.938 0.954
1.57 1.Ol 0.98 0.88
0.966 0.972 0.981 0.983 0.993
251
c?(N) 0.083 0.015 -0.054 -0.113 -0.123 -0.101 -0.096 -0.075
form; variation of the Si-N P(B-N)
distance
E(Si-N)
E(Si-C)
(ev)
(ev)
0.253
-3.12
0.168 0.101 0.059
-2.29 -1.70 -1.24
-10.81 -11.02 -11.17
0.027
-0.66
-11.30
0.013 0.006
-0.30
-11.36 -11.42
-0.13
-11.26
258
G.I. Csonka and P. Hencsei/J. Mol. Struct. (Theochem)
Table 6 PM3 results for I-methylsilatrane dihedral angle
with approximate
a(Si-N)a
Hi
R(Si-N)
(deg)
@Cal)
(Pm)
-20 -10 0 10 20
-220.09 -222.44 -223.43 -222.68 -220.74
244.9 250.2 255.9 257.9 255.0
C, symmetry,
p (D)
QW
4.02 3.86 3.51 3.26 3.16
aa(Si-N) denotes the average of the three O-B-N-C
0.952 0.950 0.950 0.950 0.948
fully optimized
Q(N) -0.028 -0.028 -0.042 -0.040 -0.026
geometry; variation
P(Si-N)
0.152 0.132 0.112 0.105 0.113
dihedral angles around the Si-N
dipole moments, the absolute values of atomic charges and the diatomic energy contributions are systematically smaller when using the PM3 method. The same kind of flexibility was found as above. The energy profile is extremely flat between 240 and 320 pm. The endo form is lower in energy. The energy barrier is at about 290pm. The energy barrier to transform an out-ofsymmetry ethoxy link back into the symmetrical position was calculated to be 1 kcalmol-‘. The ethoxy link is calculated to be even more flexible by the PM3 method. Table 6 lists the PM3 results obtained by rotating the O-%-C-N dihedral angle. There is qualitative agreement between the PM3 and AM1 results in Table 3. 1 kcalmol-’ energy was required to rotate this angle by -lo”, while the Si-N distance was shortened by 5.7 pm (Table 6). The average of the three C-0-Si-N dihedral angles was changed to - 15”. The Si-N bond order increased, parallel with the Si-N diatomic energy contribution. 3.3 kcal mol-’ energy was required to rotate this angle further. The rotation in the opposite direction requires even less energy (in agreement with the AM1 results) and causes Si-N bond shortening (in disagreement with the AM1 results). The other calculated values show the characteristic differences between the PM3 and AM1 parametrization. However, there is considerable agreement in the tendencies, which seem to be model independent. The geometries of the three energy minima agree well and the most important findings based on the AM1 results are
283 (1993) 2Sl-259
of the 0-Si-N-C
E(Si-N)
E(Si-C)
(ev)
(ev)
-2.15 -1.99 -1.81 -1.71 -1.75
-11.09 -11.11 -11.15 -11.18 -11.18
bond.
supported by the PM3 results. The existence of a fourth, non-symmetric exo minimum is supported by the PM3 but not by the AM1 results. The Si-N distance in I-methylsilatrane is 6-7 pm longer than in I-fluorosilatrane according to both methods. The experimental methods (ED and XD) show an increase in the 13 pm distance [1,5-81. Conclusions The main findings of this paper are as follows: (1) two minima were found on the energy profile when C, symmetry was retained by both semiempirical methods with two different Si-N distances (endo C, and exo C, forms); (2) there exists a third, non-symmetrical conformation in a separate minimum in which the Si-N distance is nearly identical to the Si-N distance found in the endo C, conformation. The PM3 results show the possible existence of a fourth minimum; (3) the calculated endo Si-N distances are longer by 1 1- 15 pm than the gas-phase experimental value. The predicted Si-N distance agrees with the gas-phase result if the Si-N distance is corrected by a factor (- 15 pm) originating from HF/6-3 1G(d) analogies; (4) the Si-N distance in 1-methylsilatrane was predicted to be 6-7 pm longer than in l-fluorosilatrane, in agreement with experimental results; (5) the Si-N distance was found to be dependent on the 0-Si-N-C dihedral angle, turning this
G.I. Csonka and P. Hencsei/J. Mol. Strut.
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283 (1993) 251-259
angle closer to the crystal-phase results as the equilibrium Si-N distance is decreasing. The energy required to turn this dihedral angle by 20” is 2.7-3.3 kcal mol-‘; (6) the energy cost of shortening the Si-N distance has been found to be small, the energy hypersurface is rather flat and the silatrane skeleton is flexible. The calculations show that the crystal forces could easily distort the gas-phase structure; (7) the calculated Si-N bond orders and energy partitioning show an existing Si-N bond at distances below 260-270 pm.
10 11 12 13 14
Acknowledgement 15
This work was supported by the OTKA fund (No. 382 and 644) of the Government of Hungary.
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