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Conformations of silicon-containing rings
Journal of Molecular Structure (Theochem) 454 (1998) 91–102
Conformations of silicon-containing rings Part 1. A conformational study on 1,3,5-trisilacyclohexane. Comparison of ab initio, semiempirical, and molecular mechanics calculations. Conformational energy surface of 1,3,5-trisilacyclohexane Ingvar Arnason a,*, Gudjon K. Thorarinsson a, Eberhard Matern b a Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland Institut fu¨r Anorganische Chemie der Universita¨t Karlsruhe, Engesserstr. Geb. 30.45, D-76128 Karlsruhe, Germany
b
Received 22 September 1997; received in revised form 24 April 1998; accepted 30 April 1998
Abstract The structure and relative energies for the basic conformations of 1,3,5-trisilacyclohexane (1) have been calculated by several methods and their performance compared. It is found that HF ab initio calculations using the basis set 6-31G*, the SV(P) basis set used by TURBOMOLE and the MM3 force field produce mutually fairly consistent results. MM2 performs not as well as MM3, but in many cases MM2 performs better than 3-21G. Three semiempirical methods (AM1, MNDO, and PM3) were tested. None of them was found to produce reliable results. It is found by ab initio (6-31G* and SV(P)) and MM3 calculations that the dihedral angles for the chair conformation are 52.7–53.1⬚, which makes (1) more flattened than cyclohexane, and thus (1) does not exhibit behaviour similar to cyclohexasilane, which is less flattened than cyclohexane. The ring flattening of (1) is mainly caused by the intrinsically large SiCSi bond angle (114.1–114.8⬚). The twist conformation of (1) is found by the same calculations to be 2.1–3.1 kcal mol −1 higher in energy than the chair conformation, and the boat form is found to be 0.3–0.4 kcal mol −1 higher than the twist form. These values are much closer to the values for cyclohexasilane than to those for cyclohexane. The conformational energy surface of (1) has been calculated by using MM3. The energy barrier from the chair to the twist conformation of (1) is found to be 5.5 kcal mol −1. 䉷 1998 Elsevier Science B.V. All rights reserved. Keywords: Conformational analysis; Ab initio calculations; Semiempirical calculations; Molecular mechanics; Conformational energy surface
1. Introduction The conformational behaviour of six-membered rings continues to be a fruitful field of research as is evident from a recent review [1]. The conformations * Corresponding author. Fax: +354 552 8911; e-mail: ingvara @raunvis.hi.is
of lowest energy for cyclohexane are well understood, and at room temperature the molecule exists almost entirely in the chair conformation (D 3d symmetry). From experimental and theoretical results it is generally accepted that the twist conformation (D 2) corresponds to a local minimum on the conformational energy surface (CES) about 5.5–7 kcal mol −1 above the chair form [2–4]. The boat conformation (C 2v)
0166-1280/98/$ - see front matter 䉷 1998 Elsevier Science B.V. All rights reserved. PII: S 01 66 - 12 8 0( 9 8) 0 02 3 4- 6
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corresponds to a transition state that is 1.0–1.1 kcal mol −1 above and between two twist minima on a pseudorotational pathway [3,4]. The interconversions chair–twist–chair and twist–boat–twist have been described in terms of ring puckering parameters [5–7]. Recently Ferguson et al. have compared the performance of ab initio (HF/3-21G), semiempirical (AM1) and molecular mechanics (MM2) methods for the conformational analysis of C 5 –C 8 alicyclic systems [4]. They concluded that MM and ab initio calculations produce mutually consistent results. The semiempirical calculations were capable of locating reasonable geometries (except for the five-membered ring), however the relative energies for the conformers were less reliable. The structure of cyclohexasilane has been determined by a gas-phase electron diffraction investigation and by a MM2 calculation [8,9]. At 130⬚C the molecule was found to exist predominantly in the chair form, but the conformational composition could not be uniquely determined. Three models were found to fit well to the experimental data (100% chair; 63 (8)% chair and 37 (8)% twist; 62 (7)% chair, 25 (7)% twist, and 13 (7)% boat; the values in parentheses are standard deviations). The energy differences between chair and twist were calculated to be between 1.7 and 2.2 kcal mol −1 and between twist and boat about 0.2–0.3 kcal mol −1. In a recent MM3 report these energy differences were calculated to be 1.8 and 0.2 kcal mol −1, respectively [10]. The 1,3,5-trisilacyclohexane (1) is an interesting intermediate between the parent molecules cyclohexane and cyclohexasilane, and (1) might be expected to show a comparable conformational behaviour and to possess energy differences between chair, twist, and boat conformations somewhere between those for cyclohexane and cyclohexasilane. However, in (1) the Si–C bonds are slightly polar in contrast to the C–C and Si–Si bonds in cyclohexane and cyclohexasilane, respectively. Also in (1) the hydrogen atoms bound to Si and C have different partial charges. Therefore, it is possible that some steric or energetic properties of (1) will not take a mediate position between cyclohexane and cyclohexasilane. The chemistry of (1) and its derivatives is an important part of the chemistry of carbosilanes as can be seen from an extensive review [11]. In a recent study we reported 1H NMR data of Si-alkylated derivatives
of (1) and found considerably lower A values [12] for alkyl groups bound to (1) than in the case of cyclohexane [13]. This prompted us to investigate the relative conformational energies of these compounds. To the best of our knowledge, no calculations have been reported for (1) and, therefore, we present in this paper the results of ab initio, semi-empirical, and molecular mechanics calculations for the basic conformations of molecule (1).
2. Computational methods 2.1. Choice of methods Allingers MM2 force field has been widely used as a standard force field since it was first introduced in 1977 [14]. In 1988 MM2 was extended to include silanes [9]. The new force field, MM3, is claimed to perform better than MM2 [10,15]. A recent comparative study of conformational energies calculated by several molecular mechanics methods has revealed that the Merck molecular force field (MMFF93) and force fields based on the MM2 or MM3 functional form perform significantly better than other force fields tested [16]. In this paper we use both MM2 and MM3. Ferguson and co-workers recently reported that AM1 predicts too low energies for the twist and boat conformations of cyclohexane as compared to the ab initio and MM2 values as well as to experimental values [4]. In a similar way, a comparison of results from semiempirical methods with those obtained by ab initio and/or molecular mechanics calculations for some heterocyclic systems has revealed poor performance of semiempirical methods [17,18]. There are, however, also recent contributions reporting good results from semiempirical methods for special tasks [19–22]. Therefore we found it justified to consider also semiempirical calculations. Because none of the semiempirical methods seems to be definitely the best, we decided to compare the three common methods, AM1 [23], MNDO [24], and PM3 [25]. The level for our ab initio calculations was chosen to give a reasonable compromise. On the one hand, we want to achieve reliable geometric parameters and relative energies for the basic conformations of (1).
I. Arnason et al. / Journal of Molecular Structure (Theochem) 454 (1998) 91–102
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the authentic MM2(91) [14] and MM3(92) [15] force fields. The conformational energy surface was mapped by varying two dihedral angles of the ring skeleton in steps of 2.0⬚ using the dihedral driver. Semiempirical calculations and ab initio calculations using the 3-21G and 6-31G* basis sets were carried out with the program package Spartan 3.0 on a SGI work station [30] and partly with MacSpartan on a Power Macintosh computer [31]. Ab initio calculations using the program system TURBOMOLE were run on IBM and SGI work stations. Default parameters were used for the semiempirical and ab initio calculations and no geometrical constraints were used for geometrical optimizations. Root mean square (RMS) analyses were performed using the program MacMimic. This is done by superimposing two or more structures, atom by atom, and then the RMS value of the distances of the fitted atoms is calculated for each superimposed structure. We present two sets of RMS values, one set where all atoms are compared, and another set where only the heavier atoms, C and Si, are considered.
3. Results and discussion Fig. 1. Chair (a), boat (b) and twist (c) conformations of 1,3,5trisilacyclohexane, (1).
On the other hand, we intend to use the same level of calculations for a series of alkylated derivatives of (1) (with up to 3 t-butyl groups) within reasonable CPU time. We started the ab initio calculations by using the standard Hartree–Fock (HF) 3-21G and 6-31G* basis sets [26]. For comparison we also carried out ab initio calculations on the HF level by using the program system TURBOMOLE [27,28], with the basis set split valence (SV) for C and H atoms and split valence polarization (SVP) for Si atoms, which can be expected to perform comparably with 6-31G*. In the text we will refer to the ab initio basis sets as 631G*, 3-21G, and SV(P), respectively. 2.2. Computational details For the molecular mechanics calculations we used MacMimic 3.0 [29], a Macintosh implementation of
3.1. Conformations of 1,3,5-trisilacyclohexane The chair, boat and twist conformations of (1) are shown in Fig. 1 (geometries calculated by 6-31G*) along with the atom numbering used. The results of the calculations are summarized in Tables 1–5. As can be seen from Table 5, all methods predict the chair conformation to be the global minimum, hence it will be treated as the dominant conformation. 3.1.1. Chair conformation Table 1 contains the optimized parameters for the chair conformation. Unfortunately there exists no direct experimental structure determination for (1); however, the crystal structures for some of its derivatives have been reported. The Si–C bond lengths determined by X-ray investigations fall in the range ˚ [11]. It is well known that the from 1.845 to 1.918 A reactivity of carbosilanes depends heavily on substituents. The Si–C skeleton in carbosilanes is stabilized by Si-chlorination whereas C-chlorination reduces its stability largely. Ab initio calculations by Ahlrichs
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Table 1 ˚ ), bond angles and dihedral angles (degree) for the chair conformation of 1,3,5-trisilacyclohexane Optimized bond lengths (A Element
Method of calculation 6-31G*
SiC SiH(eq) SiH(ax) CH(eq) CH(ax) CSiC SiCSi HSiH HCH CSiH(eq) CSiH(ax) SiCH(eq) SiCH(ax)
3-21G
1.891 1.480 1.480 1.089 1.090
SV(P)
1.917 1.492 1.494 1.088 1.089
MM2
1.892 1.489 1.490 1.099 1.101
MM3
1.881 1.488 1.491 1.114 1.115
1.878 1.483 1.484 1.113 1.113
AM1
MNDO
1.836 1.465 1.465 1.118 1.118
PM3
1.803 1.381 1.383 1.109 1.109
1.857 1.503 1.504 1.099 1.099
109.7 114.4 107.6 106.2 110.4 109.3 109.5 108.5
110.1 114.7 108.0 106.5 110.5 108.9 109.1 108.6
109.6 114.8 107.6 106.5 110.4 109.4 109.3 108.3
110.0 113.0 107.8 107.9 109.9 110.0 109.5 108.4
110.0 114.1 107.7 107.0 110.1 109.4 109.2 108.5
113.5 119.4 106.8 105.7 108.7 109.5 107.8 107.6
110.4 118.5 108.2 105.2 110.1 109.0 107.9 108.3
112.7 103.1 106.1 106.4 109.1 109.8 111.8 111.9
C6Si1C2Si3 53.1 HeqSi1C2Heq −61.7 HeqSi1C2Hax 53.8 HaxSi1C2Heq 56.5 HaxSi1C2Hax 172.0
52.1 −63.0 52.7 55.4 171.2
52.7 −62.2 53.4 56.1 171.7
54.7 −61.8 55.7 56.6 174.0
53.1 −62.8 53.5 55.4 171.7
36.5 −79.0 34.6 37.3 151.0
45.2 −70.2 43.2 48.3 161.7
63.9 −54.5 64.7 61.4 −179.4
et al. on chlorinated silaethanes and 1,3-disilapropanes support these findings in terms of Si–C-bond length variation as a function of chlorination [32]. In carbosilanes containing only Si, C and H atoms, the range of Si–C bond lengths narrows to 1.870– ˚ (X-ray results). 1.918 A
The Si–C bond lengths calculated by ab initio and molecular mechanics methods vary from 1.878 to ˚ in good agreement with the experimental 1.917 A values available. There is excellent agreement between the 6-31G* and SV(P) results (1.891 and ˚ , respectively), while the 3-21G basis set 1.892 A
Table 2 ˚ ) for the boat conformation of 1,3,5-trisilacyclohexane Optimized dihedral angles (degree) and some selected distances (A Method
Element qa12
6-31G* 3-21G SV(P) MM2 MM3 AM1 MNDO PM3 a
−52.8 −52.5 −53.0 −53.0 −51.7 −32.1 −42.8 −56.4
q 23 3.9 3.5 4.3 2.0 2.4 3.7 2.7 −7.0
q 34
q 45
48.1 48.2 47.9 51.2 49.8 28.1 42.5 62.9
−48.1 −48.2 −47.9 −51.2 −49.8 −29.0 −42.5 −62.9
q 56
Dihedral angle 6-1-2-3 is denoted q 12, the angle 1-2-3-4 q 23 etc. Bond length Si(1)–C(2) c Bond length C(2)–Si(3) d Distance between the ‘flagpole’ hydrogens; see Fig. 1(b) e Shortest distance between eclipsed hydrogens; see Fig. 1(b) b
−3.9 −3.5 −4.3 −2.0 −2.3 −1.9 −2.7 7.0
q 61
lb12
lc23
rd1
re2
52.8 52.5 53.0 53.0 51.6 31.1 42.8 56.4
1.890 1.915 1.889 1.880 1.878 1.836 1.802 1.857
1.902 1.925 1.902 1.881 1.879 1.839 1.805 1.863
2.971 3.004 2.961 2.849 2.932 4.049 3.289 2.459
2.767 2.790 2.775 2.742 2.742 2.655 2.615 2.797
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I. Arnason et al. / Journal of Molecular Structure (Theochem) 454 (1998) 91–102 Table 3 Optimized dihedral angles (degree) for the twist conformation of 1,3,5-trisilacyclohexane Method
6-31G 3-21G SV(P) MM2 MM3 AM1 MNDO PM3
Element q 12
q 23
q 34
q 45
q 56
q 61
−28.8 −28.5 −29.2 −30.1 −28.9 −10.5 −23.8 −37.0
−28.8 −28.5 −28.2 −28.7 −27.7 −22.2 −22.4 −37.0
61.6 61.0 61.5 62.5 60.5 35.3 50.4 73.7
−30.4 −30.0 −30.9 −31.2 −30.4 −14.1 −26.7 −32.3
−30.4 −30.1 −30.1 −30.0 −29.5 −21.6 −25.4 −32.2
61.6 61.0 61.6 62.6 60.6 33.7 50.4 73.7
˚ ). There is also a good predicts a longer bond (1.917 A agreement between MM2 and MM3 results (1.881 ˚ , respectively). The semiempirical and 1.878 A methods predict shorter Si–C bonds (1.803– ˚ ). This general pattern continues for other 1.857 A structural parameters in Table 1 and is confirmed by the RMS values given in Table 4, where optimized geometries calculated by the various methods are compared with the results of the 6-31G* calculation. We decided to use the HF/6-31G* calculations as reference because they result in a slightly lower energy than the SV(P) calculations indicating that 631G* is a better basis set for (1) than SV(P) used by TURBOMOLE; however, the energy difference is small and the geometries are quite similar. There is a small, but significant, structural difference found when 3-21G is compared with 6-31G*. Thus 3-21G predicts Si–C and Si–H bonds to be longer and the ring to be more flattened, which affects all dihedral
angles. Bond angles and C–H bond lengths, however, are predicted to be quite similar. The geometries calculated by MM2 and MM3 are similar to those obtained by ab initio methods. Of the two force-field methods, MM3 comes closer to the ab initio results, but remarkably, even the RMS value for MM2 (chair conformation) comes closer to 6-31G* than does that for 3-21G. The semiempirical methods predict structures which differ significantly from those obtained by the ab initio and MM methods. None of the three semiempirical methods tested performs well. In contrast to the other methods of calculations, they are also inconsistent when compared with each other. They all predict ordinary values for C–H bond lengths, HCH and CSiH bond angles, but other structural parameters deviate significantly from the ab initio and MM values as calculated by at least one of the semiempirical methods. The discrepancies are most pronounced
Table 4 ˚ ) of optimized geometries for 1,3,5-trisilacyclohexane compared to the results obtained by HF/6-31G* RMS values (A Method a
SV(P) 3-21G MM2 MM3 AM1 MNDO PM3 a b
Method b
Conformation Chair
Boat
Twist
0.011 0.035 0.032 0.018 0.265 0.154 0.204
0.010 0.028 0.046 0.031 0.367 0.175 0.230
0.012 0.031 0.029 0.030 0.426 0.200 0.212
All atoms considered Only C and Si atoms considered
SV(P) 3-21G MM2 MM3 AM1 MNDO PM3
Conformation Chair
Boat
Twist
0.003 0.029 0.021 0.013 0.098 0.085 0.126
0.003 0.025 0.028 0.019 0.162 0.096 0.141
0.005 0.027 0.019 0.015 0.186 0.103 0.141
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Table 5 Relative energies (kcal mol −1) of optimized conformations for 1,3,5-trisilacyclohexane Conformation
Method of calculation 6-31G*
Chair Twist Boat
a
0.0 2.15 2.54
3-21G b
0.0 1.19 1.46
SV(P) c
0.0 2.35 2.75
MM2 d
0.0 3.28 3.62
MM3 e
0.0 3.06 3.32
AM1 f
0.0 0.61 0.61
MNDO
PM3
g
0.0 h 1.62 2.08
0.0 0.88 0.88
a
Total energy: 987.379250 hartree Total energy: 982.177530 hartree c Total energy: 987.021609 hartree d Steric energy: 2.35 kcal mol −1 e Steric energy: 1.32 kcal mol −1 f DH f: 47.69 kcal mol −1 g DH f: 60.00 kcal mol −1 h DH f: 37.44 kcal mol −1 b
Fig. 2. Chair conformations of 1,3,5-trisilacyclohexane, (1), calculated by different methods. For comparison the four atoms in the plane of the chair have been superimposed. (a) AM1, MNDO, and PM3 compared; (b) 6-31G*, 3-21G, and MM2 compared; (c) 631G*, SV(P), and MM3 compared.
with respect to the ring dihedral and bond angles. The ab initio and MM methods predict dihedral angles in a narrow range from 52.1⬚ to 54.7⬚. PM3 predicts a rather puckered ring with a dihedral angle of 63.9⬚, while conversely, MNDO predicts a flattened ring and AM1 predicts a very flat ring with dihedral angles of 45.2⬚ and 36.5⬚, respectively. The reason for the variation in ring flattening is discussed at the end of this section. The effect of different dihedral angles is visualized in Fig. 2. The four atoms C(2), Si(3), Si(5), and C(6) in the plane of the chair have been superimposed. Fig. 2(a) shows a comparison of the three semi-empirical methods, in Fig. 2(b) the structures from 6-31G*, 3-21G and MM2 are compared, while in Fig. 2(c) the close alignment of 6-31G*, SV(P), and MM3 structures is shown. MNDO predicts an average CSiC bond angle of 110.4⬚, very close to the values obtained by the ab initio and MM methods (109.6– 110.1⬚), whereas the corresponding values from PM3 and AM1 are 112.7⬚ and 113.5⬚, respectively. Conversely, the SiCSi bond angles (113.0–114.8⬚ from ab initio and MM methods) are smaller according to PM3 (103.1⬚), but larger according to MNDO and AM1 (118.5⬚ and 119.4⬚, respectively). Reported experimental bond angles for the symmetrical rings cyclohexane and cyclohexasilane are 111.0⬚ and 110.3⬚, respectively [3,8]. The reported dihedral angles are 55.9⬚ and 57.9⬚, respectively. Calculated values agree well with the experimental ones. The fact that cyclohexasilane is less flattened than cyclohexane and hence closer in shape to an ‘ideal’ form, has been explained by the considerably longer
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I. Arnason et al. / Journal of Molecular Structure (Theochem) 454 (1998) 91–102 Table 6 Bond angles (degree) for propane analogues Propane analogue
CH 3 –CH 2 –CH 3 CH 3 –SiH 2 –CH 3 SiH 3 –CH 2 –SiH 3 SiH 3 –SiH 2 –SiH 3
Method of calculation 6-31G*
MM3
AM1
PM3
112.8 111.5 116.5 112.7
112.3 111.2 115.5 111.2
111.8 113.3 122.0 108.3
111.7 111.7 102.5 109.5
Si–Si bonds compared to the C–C bonds causing smaller repulsive gauche SiH 2…SiH 2 interactions than in the corresponding CH 2…CH 2 unit [8]. Therefore it may appear surprising that the ab initio values for (1) are as low as 53.1⬚ (6-31G*) and 52.7⬚ (SV(P)), supported by the MM3 value of 53.1⬚, which means that (1) is indeed found to be more flattened than cyclohexane. There is, however, a simple explanation for this. The extent of flattening of six-membered rings is determined first of all by the bond lengths and angles within the ring. In cyclohexane-like systems no special property of six-membered rings is required to explain the extent of flattening, but rather the intrinsic natural bond lengths and angles, as found in simple acyclic systems containing as few as three atoms, are often reproduced fairly well.1 This is illustrated by comparing the calculated bond angles for propane and its silicon-containing analogues with those in the corresponding six-membered rings. Table 6 contains the results of selected calculations of bond angles for propane analogues. In general the bond angles are calculated to be 0–2⬚ larger in the propane analogue than in the corresponding six-membered ring. The main reason for the ring flattening in 1,3,5-trisilacyclohexane as calculated ab initio (631G*) is the large SiCSi bond angle of 114.4⬚, which is intrinsically large as can be seen in SiH 3 – CH 2 –SiH 3, where it is 116.5⬚. The corresponding MM3 values are 114.1⬚ and 115.5⬚, respectively. The ring shape for the chair form of (1) as calculated by AM1 (very flat) and PM3 (puckered) is mainly caused by the extreme values predicted for the SiCSi bond angle in SiH 3 –CH 2 –SiH 3 by these methods (122.0⬚ and 102.5⬚, respectively).
1
A referee’s comment has drawn our attention to this relationship.
3.1.2. Twist and boat conformations The dihedral angles for the boat and twist conformations of (1) are presented in Tables 2 and 3, respectively. Table 2 also contains four characteristic distances for the boat conformation: the two different Si–C bond lengths (l 12 and l 23), the shortest distance between two eclipsed hydrogen atoms, and the distance between the two ‘flagpole’ hydrogens. Because regular boat (C s) and twist (C 1) conformations of (1) have lower symmetry than the corresponding conformations of cyclohexane, one needs three sets of values for the dihedral angles instead of two in the case of cyclohexane. In some cases the calculations predict less regular conformations (boat: AM1; twist: SV(P), MM2, MM3, AM1 and MNDO), in which cases all six dihedral angles are needed to describe the structure. The twist conformation can be viewed as being a relaxed boat form, and each method shows all Si–C bond lengths for it to be very similar. We will not, therefore, discuss any further structural parameters for these conformations. Notice, however, that the molecular coordinates and hence all parameters for the conformations calculated are available as supplementary material (see Section 5). An inspection of Table 2 reveals that the ab initio ˚ longer than methods calculate l 23 to be about 0.01 A l 12 (l 12 are practically the same as for the chair form). MM methods calculate all Si–C bond lengths to be practically equal. The semiempirical methods predict ˚ as compared to an elongation of l 23 by 0.003–0.006 A l 12. Ab initio calculations for the boat conformation of cyclohexane result in longer ‘in plane’ C–C bonds by ˚ as compared to the bonds to C atoms 1 and 4 0.018 A [3]. This bond lengthening is generally attributed to the repulsive interaction of the eclipsed CH 2 groups. It is understandable that the bond lengthening (l 23 ⬎ l 12) is smaller in (1) than in cyclohexane due to the longer
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Si–C bonds (and partly also due to longer Si–H bonds compared to C–H bonds) in (1) as compared to cyclohexane. Indeed, the shortest distance between eclipsed hydrogens in (1) is well beyond the sum of van der Waals radii for two hydrogen atoms [33]. The same holds for the distance between the ‘flagpole’ hydrogens of the boat form, except for the puckered boat conformation calculated by PM3, where this distance is found to be close to the van der Waals distance. 3.2. Relative conformational energies of 1,3,5trisilacyclohexane Relative energies for the chair, twist and boat conformations of (1) are given in Table 5. All methods tested agree on the chair conformation being the global minimum. The energy calculated by each method for the chair conformation is also given. The semiempirical methods, which give the heats of formation (DH f), predict quite different values. AM1 and MNDO (as well as all the other methods) are able to find different geometries for the twist and boat conformations, but each of them calculates the same energy for both conformations. In each case the starting geometries were those obtained by the conformation search mode and Sybyl force field provided by Spartan. Different structure for the twist conformation could be obtained by AM1 if the starting geometry was altered, however, the resulting energy turned out always to be the same. The energy difference between the chair and the twist conformations calculated by AM1 and MNDO is very small (0.61 and 0.88 kcal mol −1 respectively), considerably smaller than that reported for cyclohexasilane (1.7–2.2 kcal mol −1) [8]. The total energy calculated by HF/6-31G* is slightly lower than that calculated by TURBOMOLE using the SV(P) basis set. The energy difference between the chair and the twist forms is 2.15 kcal mol −1 for 6-31G* and 2.35 kcal mol −1 for SV(P). Both methods calculate the boat to be 0.4 kcal mol −1 higher in energy than the twist conformation. The values calculated according to 3-21G are 1.19 and 1.46 kcal mol −1 for the twist and boat forms, respectively. This suggests that 3-21G may not be a sufficient basis set for reliable conformational energy calculations for alkyl derivatives of (1). The MM methods calculate the twist conformation to be 3.28 kcal mol −1 (MM2) and 3.06 kcal mol −1 (MM3)
higher than the chair form. The difference from twist to boat is 0.34 kcal mol −1 (MM2) and 0.26 kcal mol −1 (MM3). PM3 predicts the twist form to be 1.62 kcal mol −1 higher than the chair form and the difference from twist to boat to be 0.46 kcal mol −1, values not far from those calculated ab initio. Because the conformational energy difference between the chair and twist forms increases from 1.19 to 2.15 kcal mol −1 as the basis set is improved from 3-21G to 6-31G*, and decreases from 3.28 to 3.06 kcal mol −1 as one uses the improved version MM3 instead of MM2, it may be concluded that the twist conformation for molecule (1) is approximately 2.1–3.1 kcal mol −1 higher in energy than the chair form and that the energy difference between the twist and boat conformations is about 0.3–0.4 kcal mol −1. Thus the relative conformational energies are much closer to those for cyclohexasilane than for cyclohexane. This is somewhat surprising, but Dixon and Komornicki concluded from their ab initio analysis of cyclohexane, that of the 8 kcal mol −1 energy difference between the chair and boat forms, 6 kcal mol −1 might be attributed to eclipsing interactions and that the remaining 2 kcal mol −1 is due to distortions that relieve the ‘flagpole’ interactions [3]. Our results indicate that in the case of (1) the ‘flagpole’ interactions can be neglected and that the eclipsing interactions are much smaller than in the case of cyclohexane. Therefore it might be that the increased bond length from C–C in cyclohexane to Si–C in (1) relaxes the twist and boat conformation efficiently and, thus, a further bond lengthening by Si–Si bonds in the case of cyclohexasilane does not induce much improvement. 3.3. Conformational energy surface of 1,3,5trisilacyclohexane Calculating the structure of the basic conformations of (1) and their relative energies is the first step in exploring the conformational behaviour of this ring system. The next step is to mark the pathway between the conformations and finally to map the conformational energy surface (CES). We have decided to construct the CES by using MM3. We conclude from our calculations that MM3 is capable of giving a reasonable picture of the structures and conformational energies of the most important conformations of (1).
Fig. 3. 3-D presentation of a part of the conformational energy surface of 1,3,5-trisilacyclohexane, (1). Steric energy, calculated by MM3, shown as a function of the two dihedral angles, q 23 and q 65. For clarity the steric energy has been cut off at 6.0 kcal mol −1.
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Fig. 4. Lowest energy pathway for the conversion chair–twist–boat–twist–chair for 1,3,5-trisilacyclohexane, (1). Steric energy, calculated by MM3, shown relative to the chair conformation.
It is convenient to use the dihedral driver (a built-in feature of MacMimic/MM3) to change two dihedral angles of the ring in small steps and to calculate the steric energy for each step as shown by Burkert and Allinger for cyclohexane [34]. We have varied q 23 and q 65 (see Table 2 and Fig. 1 for definition of dihedral angles) in steps of 2.0⬚ from +90⬚ to −90⬚. The result is shown as a 3-dimensional picture in Fig. 3. For clarity, steric energies larger than 6 kcal mol −1 are omitted in the figure. Steric energies of this magnitude are because of ring distortions that are not part of the conformational equilibrium described here. Notice, however, that in reality the CES of a puckered six-membered ring is that of a globe and not a two-dimensional map as has been pointed out by Pickett and Strauss [6], Cremer and Pople [5], and Zefirov et al. [7]. It is not difficult, however, given a knowledge of the nature of the global surface (the two chair conformations are at the north and south poles and a belt of alternating twist and boat conformations on a pseudorotational pathway along the equator), to connect the results shown in Fig. 3 to the global surface. One can easily locate the two poles (chairs) and a ‘valley’ with four local minima (twist) connected by saddle points (boats) between them along the ‘visible’ part of the equator (diagonal from +90⬚; +90⬚ to −90⬚; −90⬚). On the global surface there are six boat and six twist conformations along the equator. The remaining twist and boat conformations are located on the ‘invisible
remote’ side of the globe. They would become visible if one used another pair of dihedral angles, that is q 12 and q 54, or q 34 and q 16. This would be equivalent to a rotation of 120⬚ (clockwise or anticlockwise) around the axis which connects the two poles of the globe. By mapping the conformational results as a function of two dihedral angles, many of the same problems are encountered as when representing the earths surface on a two-dimensional map. Thus, for example, the twist conformations do not all have the same appearance, depending on their location on the equator. The most important conversion of a chair conformation to a twist–boat–twist pseudorotation and back to the chair or the inverted chair conformation is quite evident, however. The lowest energy pathway for this conversion is shown in Fig. 4. It should be noted that the direction connecting the chair to the twist is essentially orthogonal to the motion connecting two twist forms via the boat conformation. The energy barrier from the chair to the twist conformation amounts to 5.5 kcal mol −1 and that from twist to chair only 2.4 kcal mol −1. It is also remarkable to see that the transition ridge between the chair and the valley of twist and boat conformations is almost constant in energy (0.2 kcal mol −1 between the highest and lowest value on the ridge). Therefore a precise location of a transition conformation is not very meaningful as Dixon and Komornicki have pointed out [3]. However, the transition state on the lowest energy pathway, as calculated by MM3, corresponds to a
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‘sofa’ with approximate C s symmetry. The three Si atoms and two of the C atoms of (1) are nearly coplanar and the third C atom has a flap angle of 127.4⬚ to the plane. The corresponding flap angle to the plane of four atoms in the chair conformation is 131.3⬚ as calculated by MM3.
4. Conclusions The aim of this work was to calculate the structure and relative conformational energies for 1,3,5-trisilacyclohexane, (1), and to explore its conformational energy surface. Several methods of calculation were used and tested for this purpose. None of the three semi-empirical methods, AM1, MNDO, and PM3 was found to be suitable for calculating the structure and relative energies of the basic conformations of (1) and their use is not recommended for further work on related compounds. Ab initio calculations at the HF/631G* level and the almost equivalent SV(P) basis set used by TURBOMOLE are considered to give reliable results both for structure and relative energies. The results obtained by using the lower-quality basis set 3-21G are significantly different which makes us believe that it is unsuitable for this purpose. The two force fields tested, MM2 and MM3, were found to give results somewhere between those obtained by 6-31G* and 3-21G. MM3 was found to perform better than MM2, hence MM3 was considered capable of giving a reasonable CES for (1). The results indicate that (1) shows qualitatively a similar conformational behaviour as cyclohexane and cyclohexasilane. Its energy differences between the chair, twist, and boat conformations were found to be much closer to those for cyclohexasilane than for cyclohexane. On the other hand, however, the ring of (1) is more flattened than that of cyclohexane, and in that sense (1) does not exhibit behaviour similar to cyclohexasilane, which is less flattened than cyclohexane. The ring flattening of (1) was found to be caused by the intrinsically large SiCSi bond angle.
5. WWW supplementary material The following material is available via the THEOCHEM HomePage at http://www.elsevier.nl/locate/
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theochem. 1. Molecular coordinates for the chair, twist, and boat conformation of (1), calculated by each method used, in PDB format. 2. Fig. 3 as a colour picture. 3. Conformational energy surface of 1,3,5-trisilacyclohexane as a table, giving the steric energy calculated by MM3 as a function of the coordinates q 23 and q 65.
Acknowledgements We wish to thank Professor H. Jonsson at the University of Washington, Seattle, and Priv. Doz. Dr. M. Ha¨ser at the University of Karlsruhe for useful discussions and for their help with the calculations. A research assistance grant for G.K. Thorarinsson by the University of Iceland is acknowledged. At the time of completion of this work, our friend Dr. M. Ha¨ser died as a result of a tragic climbing accident. We wish to dedicate this publication to his memory. References [1] E. Juaristi (Ed.), Conformational Behavior of Six-Membered Rings, Methods in Stereochemical Analysis, VCH Publishers, New York, 1995. [2] M. Squillacote, R.S. Sheridan, O.L. Chapman, F.A.L. Anet, J. Am. Chem. Soc. 97 (1975) 3244. [3] D.A. Dixon, A. Komornicki, J. Phys. Chem. 94 (1990) 5630. [4] D.M. Ferguson, I.R. Gould, W.A. Glauser, S. Schroeder, P.A. Kollman, J. Comput. Chem. 13 (1992) 525. [5] D. Cremer, J.A. Pople, J. Am. Chem. Soc. 97 (1975) 1354. [6] H.M. Pickett, H.L. Strauss, J. Am. Chem. Soc. 92 (1970) 7281. [7] N.S. Zefirov, V.A. Palyulin, E.E. Dashevskaya, J. Phys. Org. Chem. 3 (1990) 147. [8] Z. Smith, A. Almenningen, E. Hengge, D. Kovar, J. Am. Chem. Soc. 104 (1982) 4362. [9] M.R. Frierson, M.R. Iman, V.B. Zalkow, N.L. Allinger, J. Org. Chem. 53 (1988) 5248. [10] K. Chen, N.L. Allinger, J. Phys. Org. Chem. 10 (1997) 697. [11] G. Fritz, E. Matern, Carbosilanes, Springer-Verlag, Heidelberg, 1986. [12] C.H. Bushweller, in: E. Juaristi (Ed.), Conformational Behavior of Six-Membered Rings, VCH Publishers, New York, 1995, p. 25. [13] I. Arnason, A. Kvaran, Z. anorg. allg. Chem. 624 (1998) 65. [14] N.L. Allinger, J. Am. Chem. Soc. 99 (1977) 8127. [15] N.L. Allinger, Y.H. Yuh, J.-H. Lii, J. Am. Chem. Soc. 111 (1989) 8551.
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[16] K. Gundertofte, T. Liljefors, P.-O. Norrby, I. Pettersson, J. Comput. Chem. 17 (1996) 429. [17] C.W. Jefford, G. Bernardinelli, M.C. Josso, P.-Y. Morgantini, J. Weber, J. Mol. Struct. (Theochem) 337 (1995) 31. [18] M. Giordan, R. Custodio, J.R. Trigo, J. Comput. Chem. 17 (1996) 156. [19] C. Alhambra, F.J. Luque, M. Orozco, J. Comput. Chem. 15 (1994) 12. [20] R.A. Barrett, R.J. Meier, J. Mol. Struct. (Theochem) 363 (1996) 203. [21] R. Janoschek, W.M.F. Fabian, G. Kollenz, C.O. Kappe, J. Comput. Chem. 15 (1994) 132. ¨ gretir, S. Yarligan, J. Mol. Struct. (Theochem) 366 (1996) [22] C. O 227. [23] M.S.J. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [24] M.J.S. Dewar, W.J. Thiel, J. Am. Chem. Soc. 99 (1977) 4899. [25] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 221.
[26] W.J. Hehre, L. Radom, P.v.R. Schleyer, J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986. [27] R. Ahlrichs, M. Ba¨r, M. Ha¨ser, H. Horn, C. Ko¨lmel, Chem. Phys. Lett. 162 (1989) 165. [28] A. Scha¨fer, H. Horn, R. Ahlrichs, J. Chem. Phys. 97 (1992) 2571. [29] MacMimic, Version 3.0, InStar Software AB, IDEON Research Park, S-233 70 Lund, Sweden. [30] Spartan, Version 3.0, Wavefunction, Inc., 18401 Von Karman Avenue, Suite 370, Irvine, CA 92612, USA. [31] MacSpartan, Version 1.0, Wavefunction, Inc., 18401 Von Karman Avenue, Suite 370, Irvine, CA 92612, USA. [32] H. Schiffer, R. Ahlrichs, Theor. Chim. Acta 75 (1989) 99. [33] A. Bondi, J. Phys. Chem. 68 (1964) 441. [34] U. Burkert, N.L. Allinger, Molecular Mechanics. ACS Monographs, M.C. Caserio (Ed.), Vol. 177, American Chemical Society, Washington, DC, 1982.
Conformations of silicon-containing rings Part 1. A conformational study on 1,3,5-trisilacyclohexane. Comparison of ab initio, semiempirical, and molecular mechanics calculations. Conformational energy surface of 1,3,5-trisilacyclohexane Ingvar Arnason a,*, Gudjon K. Thorarinsson a, Eberhard Matern b a Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland Institut fu¨r Anorganische Chemie der Universita¨t Karlsruhe, Engesserstr. Geb. 30.45, D-76128 Karlsruhe, Germany
b
Received 22 September 1997; received in revised form 24 April 1998; accepted 30 April 1998
Abstract The structure and relative energies for the basic conformations of 1,3,5-trisilacyclohexane (1) have been calculated by several methods and their performance compared. It is found that HF ab initio calculations using the basis set 6-31G*, the SV(P) basis set used by TURBOMOLE and the MM3 force field produce mutually fairly consistent results. MM2 performs not as well as MM3, but in many cases MM2 performs better than 3-21G. Three semiempirical methods (AM1, MNDO, and PM3) were tested. None of them was found to produce reliable results. It is found by ab initio (6-31G* and SV(P)) and MM3 calculations that the dihedral angles for the chair conformation are 52.7–53.1⬚, which makes (1) more flattened than cyclohexane, and thus (1) does not exhibit behaviour similar to cyclohexasilane, which is less flattened than cyclohexane. The ring flattening of (1) is mainly caused by the intrinsically large SiCSi bond angle (114.1–114.8⬚). The twist conformation of (1) is found by the same calculations to be 2.1–3.1 kcal mol −1 higher in energy than the chair conformation, and the boat form is found to be 0.3–0.4 kcal mol −1 higher than the twist form. These values are much closer to the values for cyclohexasilane than to those for cyclohexane. The conformational energy surface of (1) has been calculated by using MM3. The energy barrier from the chair to the twist conformation of (1) is found to be 5.5 kcal mol −1. 䉷 1998 Elsevier Science B.V. All rights reserved. Keywords: Conformational analysis; Ab initio calculations; Semiempirical calculations; Molecular mechanics; Conformational energy surface
1. Introduction The conformational behaviour of six-membered rings continues to be a fruitful field of research as is evident from a recent review [1]. The conformations * Corresponding author. Fax: +354 552 8911; e-mail: ingvara @raunvis.hi.is
of lowest energy for cyclohexane are well understood, and at room temperature the molecule exists almost entirely in the chair conformation (D 3d symmetry). From experimental and theoretical results it is generally accepted that the twist conformation (D 2) corresponds to a local minimum on the conformational energy surface (CES) about 5.5–7 kcal mol −1 above the chair form [2–4]. The boat conformation (C 2v)
0166-1280/98/$ - see front matter 䉷 1998 Elsevier Science B.V. All rights reserved. PII: S 01 66 - 12 8 0( 9 8) 0 02 3 4- 6
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corresponds to a transition state that is 1.0–1.1 kcal mol −1 above and between two twist minima on a pseudorotational pathway [3,4]. The interconversions chair–twist–chair and twist–boat–twist have been described in terms of ring puckering parameters [5–7]. Recently Ferguson et al. have compared the performance of ab initio (HF/3-21G), semiempirical (AM1) and molecular mechanics (MM2) methods for the conformational analysis of C 5 –C 8 alicyclic systems [4]. They concluded that MM and ab initio calculations produce mutually consistent results. The semiempirical calculations were capable of locating reasonable geometries (except for the five-membered ring), however the relative energies for the conformers were less reliable. The structure of cyclohexasilane has been determined by a gas-phase electron diffraction investigation and by a MM2 calculation [8,9]. At 130⬚C the molecule was found to exist predominantly in the chair form, but the conformational composition could not be uniquely determined. Three models were found to fit well to the experimental data (100% chair; 63 (8)% chair and 37 (8)% twist; 62 (7)% chair, 25 (7)% twist, and 13 (7)% boat; the values in parentheses are standard deviations). The energy differences between chair and twist were calculated to be between 1.7 and 2.2 kcal mol −1 and between twist and boat about 0.2–0.3 kcal mol −1. In a recent MM3 report these energy differences were calculated to be 1.8 and 0.2 kcal mol −1, respectively [10]. The 1,3,5-trisilacyclohexane (1) is an interesting intermediate between the parent molecules cyclohexane and cyclohexasilane, and (1) might be expected to show a comparable conformational behaviour and to possess energy differences between chair, twist, and boat conformations somewhere between those for cyclohexane and cyclohexasilane. However, in (1) the Si–C bonds are slightly polar in contrast to the C–C and Si–Si bonds in cyclohexane and cyclohexasilane, respectively. Also in (1) the hydrogen atoms bound to Si and C have different partial charges. Therefore, it is possible that some steric or energetic properties of (1) will not take a mediate position between cyclohexane and cyclohexasilane. The chemistry of (1) and its derivatives is an important part of the chemistry of carbosilanes as can be seen from an extensive review [11]. In a recent study we reported 1H NMR data of Si-alkylated derivatives
of (1) and found considerably lower A values [12] for alkyl groups bound to (1) than in the case of cyclohexane [13]. This prompted us to investigate the relative conformational energies of these compounds. To the best of our knowledge, no calculations have been reported for (1) and, therefore, we present in this paper the results of ab initio, semi-empirical, and molecular mechanics calculations for the basic conformations of molecule (1).
2. Computational methods 2.1. Choice of methods Allingers MM2 force field has been widely used as a standard force field since it was first introduced in 1977 [14]. In 1988 MM2 was extended to include silanes [9]. The new force field, MM3, is claimed to perform better than MM2 [10,15]. A recent comparative study of conformational energies calculated by several molecular mechanics methods has revealed that the Merck molecular force field (MMFF93) and force fields based on the MM2 or MM3 functional form perform significantly better than other force fields tested [16]. In this paper we use both MM2 and MM3. Ferguson and co-workers recently reported that AM1 predicts too low energies for the twist and boat conformations of cyclohexane as compared to the ab initio and MM2 values as well as to experimental values [4]. In a similar way, a comparison of results from semiempirical methods with those obtained by ab initio and/or molecular mechanics calculations for some heterocyclic systems has revealed poor performance of semiempirical methods [17,18]. There are, however, also recent contributions reporting good results from semiempirical methods for special tasks [19–22]. Therefore we found it justified to consider also semiempirical calculations. Because none of the semiempirical methods seems to be definitely the best, we decided to compare the three common methods, AM1 [23], MNDO [24], and PM3 [25]. The level for our ab initio calculations was chosen to give a reasonable compromise. On the one hand, we want to achieve reliable geometric parameters and relative energies for the basic conformations of (1).
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the authentic MM2(91) [14] and MM3(92) [15] force fields. The conformational energy surface was mapped by varying two dihedral angles of the ring skeleton in steps of 2.0⬚ using the dihedral driver. Semiempirical calculations and ab initio calculations using the 3-21G and 6-31G* basis sets were carried out with the program package Spartan 3.0 on a SGI work station [30] and partly with MacSpartan on a Power Macintosh computer [31]. Ab initio calculations using the program system TURBOMOLE were run on IBM and SGI work stations. Default parameters were used for the semiempirical and ab initio calculations and no geometrical constraints were used for geometrical optimizations. Root mean square (RMS) analyses were performed using the program MacMimic. This is done by superimposing two or more structures, atom by atom, and then the RMS value of the distances of the fitted atoms is calculated for each superimposed structure. We present two sets of RMS values, one set where all atoms are compared, and another set where only the heavier atoms, C and Si, are considered.
3. Results and discussion Fig. 1. Chair (a), boat (b) and twist (c) conformations of 1,3,5trisilacyclohexane, (1).
On the other hand, we intend to use the same level of calculations for a series of alkylated derivatives of (1) (with up to 3 t-butyl groups) within reasonable CPU time. We started the ab initio calculations by using the standard Hartree–Fock (HF) 3-21G and 6-31G* basis sets [26]. For comparison we also carried out ab initio calculations on the HF level by using the program system TURBOMOLE [27,28], with the basis set split valence (SV) for C and H atoms and split valence polarization (SVP) for Si atoms, which can be expected to perform comparably with 6-31G*. In the text we will refer to the ab initio basis sets as 631G*, 3-21G, and SV(P), respectively. 2.2. Computational details For the molecular mechanics calculations we used MacMimic 3.0 [29], a Macintosh implementation of
3.1. Conformations of 1,3,5-trisilacyclohexane The chair, boat and twist conformations of (1) are shown in Fig. 1 (geometries calculated by 6-31G*) along with the atom numbering used. The results of the calculations are summarized in Tables 1–5. As can be seen from Table 5, all methods predict the chair conformation to be the global minimum, hence it will be treated as the dominant conformation. 3.1.1. Chair conformation Table 1 contains the optimized parameters for the chair conformation. Unfortunately there exists no direct experimental structure determination for (1); however, the crystal structures for some of its derivatives have been reported. The Si–C bond lengths determined by X-ray investigations fall in the range ˚ [11]. It is well known that the from 1.845 to 1.918 A reactivity of carbosilanes depends heavily on substituents. The Si–C skeleton in carbosilanes is stabilized by Si-chlorination whereas C-chlorination reduces its stability largely. Ab initio calculations by Ahlrichs
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Table 1 ˚ ), bond angles and dihedral angles (degree) for the chair conformation of 1,3,5-trisilacyclohexane Optimized bond lengths (A Element
Method of calculation 6-31G*
SiC SiH(eq) SiH(ax) CH(eq) CH(ax) CSiC SiCSi HSiH HCH CSiH(eq) CSiH(ax) SiCH(eq) SiCH(ax)
3-21G
1.891 1.480 1.480 1.089 1.090
SV(P)
1.917 1.492 1.494 1.088 1.089
MM2
1.892 1.489 1.490 1.099 1.101
MM3
1.881 1.488 1.491 1.114 1.115
1.878 1.483 1.484 1.113 1.113
AM1
MNDO
1.836 1.465 1.465 1.118 1.118
PM3
1.803 1.381 1.383 1.109 1.109
1.857 1.503 1.504 1.099 1.099
109.7 114.4 107.6 106.2 110.4 109.3 109.5 108.5
110.1 114.7 108.0 106.5 110.5 108.9 109.1 108.6
109.6 114.8 107.6 106.5 110.4 109.4 109.3 108.3
110.0 113.0 107.8 107.9 109.9 110.0 109.5 108.4
110.0 114.1 107.7 107.0 110.1 109.4 109.2 108.5
113.5 119.4 106.8 105.7 108.7 109.5 107.8 107.6
110.4 118.5 108.2 105.2 110.1 109.0 107.9 108.3
112.7 103.1 106.1 106.4 109.1 109.8 111.8 111.9
C6Si1C2Si3 53.1 HeqSi1C2Heq −61.7 HeqSi1C2Hax 53.8 HaxSi1C2Heq 56.5 HaxSi1C2Hax 172.0
52.1 −63.0 52.7 55.4 171.2
52.7 −62.2 53.4 56.1 171.7
54.7 −61.8 55.7 56.6 174.0
53.1 −62.8 53.5 55.4 171.7
36.5 −79.0 34.6 37.3 151.0
45.2 −70.2 43.2 48.3 161.7
63.9 −54.5 64.7 61.4 −179.4
et al. on chlorinated silaethanes and 1,3-disilapropanes support these findings in terms of Si–C-bond length variation as a function of chlorination [32]. In carbosilanes containing only Si, C and H atoms, the range of Si–C bond lengths narrows to 1.870– ˚ (X-ray results). 1.918 A
The Si–C bond lengths calculated by ab initio and molecular mechanics methods vary from 1.878 to ˚ in good agreement with the experimental 1.917 A values available. There is excellent agreement between the 6-31G* and SV(P) results (1.891 and ˚ , respectively), while the 3-21G basis set 1.892 A
Table 2 ˚ ) for the boat conformation of 1,3,5-trisilacyclohexane Optimized dihedral angles (degree) and some selected distances (A Method
Element qa12
6-31G* 3-21G SV(P) MM2 MM3 AM1 MNDO PM3 a
−52.8 −52.5 −53.0 −53.0 −51.7 −32.1 −42.8 −56.4
q 23 3.9 3.5 4.3 2.0 2.4 3.7 2.7 −7.0
q 34
q 45
48.1 48.2 47.9 51.2 49.8 28.1 42.5 62.9
−48.1 −48.2 −47.9 −51.2 −49.8 −29.0 −42.5 −62.9
q 56
Dihedral angle 6-1-2-3 is denoted q 12, the angle 1-2-3-4 q 23 etc. Bond length Si(1)–C(2) c Bond length C(2)–Si(3) d Distance between the ‘flagpole’ hydrogens; see Fig. 1(b) e Shortest distance between eclipsed hydrogens; see Fig. 1(b) b
−3.9 −3.5 −4.3 −2.0 −2.3 −1.9 −2.7 7.0
q 61
lb12
lc23
rd1
re2
52.8 52.5 53.0 53.0 51.6 31.1 42.8 56.4
1.890 1.915 1.889 1.880 1.878 1.836 1.802 1.857
1.902 1.925 1.902 1.881 1.879 1.839 1.805 1.863
2.971 3.004 2.961 2.849 2.932 4.049 3.289 2.459
2.767 2.790 2.775 2.742 2.742 2.655 2.615 2.797
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I. Arnason et al. / Journal of Molecular Structure (Theochem) 454 (1998) 91–102 Table 3 Optimized dihedral angles (degree) for the twist conformation of 1,3,5-trisilacyclohexane Method
6-31G 3-21G SV(P) MM2 MM3 AM1 MNDO PM3
Element q 12
q 23
q 34
q 45
q 56
q 61
−28.8 −28.5 −29.2 −30.1 −28.9 −10.5 −23.8 −37.0
−28.8 −28.5 −28.2 −28.7 −27.7 −22.2 −22.4 −37.0
61.6 61.0 61.5 62.5 60.5 35.3 50.4 73.7
−30.4 −30.0 −30.9 −31.2 −30.4 −14.1 −26.7 −32.3
−30.4 −30.1 −30.1 −30.0 −29.5 −21.6 −25.4 −32.2
61.6 61.0 61.6 62.6 60.6 33.7 50.4 73.7
˚ ). There is also a good predicts a longer bond (1.917 A agreement between MM2 and MM3 results (1.881 ˚ , respectively). The semiempirical and 1.878 A methods predict shorter Si–C bonds (1.803– ˚ ). This general pattern continues for other 1.857 A structural parameters in Table 1 and is confirmed by the RMS values given in Table 4, where optimized geometries calculated by the various methods are compared with the results of the 6-31G* calculation. We decided to use the HF/6-31G* calculations as reference because they result in a slightly lower energy than the SV(P) calculations indicating that 631G* is a better basis set for (1) than SV(P) used by TURBOMOLE; however, the energy difference is small and the geometries are quite similar. There is a small, but significant, structural difference found when 3-21G is compared with 6-31G*. Thus 3-21G predicts Si–C and Si–H bonds to be longer and the ring to be more flattened, which affects all dihedral
angles. Bond angles and C–H bond lengths, however, are predicted to be quite similar. The geometries calculated by MM2 and MM3 are similar to those obtained by ab initio methods. Of the two force-field methods, MM3 comes closer to the ab initio results, but remarkably, even the RMS value for MM2 (chair conformation) comes closer to 6-31G* than does that for 3-21G. The semiempirical methods predict structures which differ significantly from those obtained by the ab initio and MM methods. None of the three semiempirical methods tested performs well. In contrast to the other methods of calculations, they are also inconsistent when compared with each other. They all predict ordinary values for C–H bond lengths, HCH and CSiH bond angles, but other structural parameters deviate significantly from the ab initio and MM values as calculated by at least one of the semiempirical methods. The discrepancies are most pronounced
Table 4 ˚ ) of optimized geometries for 1,3,5-trisilacyclohexane compared to the results obtained by HF/6-31G* RMS values (A Method a
SV(P) 3-21G MM2 MM3 AM1 MNDO PM3 a b
Method b
Conformation Chair
Boat
Twist
0.011 0.035 0.032 0.018 0.265 0.154 0.204
0.010 0.028 0.046 0.031 0.367 0.175 0.230
0.012 0.031 0.029 0.030 0.426 0.200 0.212
All atoms considered Only C and Si atoms considered
SV(P) 3-21G MM2 MM3 AM1 MNDO PM3
Conformation Chair
Boat
Twist
0.003 0.029 0.021 0.013 0.098 0.085 0.126
0.003 0.025 0.028 0.019 0.162 0.096 0.141
0.005 0.027 0.019 0.015 0.186 0.103 0.141
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Table 5 Relative energies (kcal mol −1) of optimized conformations for 1,3,5-trisilacyclohexane Conformation
Method of calculation 6-31G*
Chair Twist Boat
a
0.0 2.15 2.54
3-21G b
0.0 1.19 1.46
SV(P) c
0.0 2.35 2.75
MM2 d
0.0 3.28 3.62
MM3 e
0.0 3.06 3.32
AM1 f
0.0 0.61 0.61
MNDO
PM3
g
0.0 h 1.62 2.08
0.0 0.88 0.88
a
Total energy: 987.379250 hartree Total energy: 982.177530 hartree c Total energy: 987.021609 hartree d Steric energy: 2.35 kcal mol −1 e Steric energy: 1.32 kcal mol −1 f DH f: 47.69 kcal mol −1 g DH f: 60.00 kcal mol −1 h DH f: 37.44 kcal mol −1 b
Fig. 2. Chair conformations of 1,3,5-trisilacyclohexane, (1), calculated by different methods. For comparison the four atoms in the plane of the chair have been superimposed. (a) AM1, MNDO, and PM3 compared; (b) 6-31G*, 3-21G, and MM2 compared; (c) 631G*, SV(P), and MM3 compared.
with respect to the ring dihedral and bond angles. The ab initio and MM methods predict dihedral angles in a narrow range from 52.1⬚ to 54.7⬚. PM3 predicts a rather puckered ring with a dihedral angle of 63.9⬚, while conversely, MNDO predicts a flattened ring and AM1 predicts a very flat ring with dihedral angles of 45.2⬚ and 36.5⬚, respectively. The reason for the variation in ring flattening is discussed at the end of this section. The effect of different dihedral angles is visualized in Fig. 2. The four atoms C(2), Si(3), Si(5), and C(6) in the plane of the chair have been superimposed. Fig. 2(a) shows a comparison of the three semi-empirical methods, in Fig. 2(b) the structures from 6-31G*, 3-21G and MM2 are compared, while in Fig. 2(c) the close alignment of 6-31G*, SV(P), and MM3 structures is shown. MNDO predicts an average CSiC bond angle of 110.4⬚, very close to the values obtained by the ab initio and MM methods (109.6– 110.1⬚), whereas the corresponding values from PM3 and AM1 are 112.7⬚ and 113.5⬚, respectively. Conversely, the SiCSi bond angles (113.0–114.8⬚ from ab initio and MM methods) are smaller according to PM3 (103.1⬚), but larger according to MNDO and AM1 (118.5⬚ and 119.4⬚, respectively). Reported experimental bond angles for the symmetrical rings cyclohexane and cyclohexasilane are 111.0⬚ and 110.3⬚, respectively [3,8]. The reported dihedral angles are 55.9⬚ and 57.9⬚, respectively. Calculated values agree well with the experimental ones. The fact that cyclohexasilane is less flattened than cyclohexane and hence closer in shape to an ‘ideal’ form, has been explained by the considerably longer
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I. Arnason et al. / Journal of Molecular Structure (Theochem) 454 (1998) 91–102 Table 6 Bond angles (degree) for propane analogues Propane analogue
CH 3 –CH 2 –CH 3 CH 3 –SiH 2 –CH 3 SiH 3 –CH 2 –SiH 3 SiH 3 –SiH 2 –SiH 3
Method of calculation 6-31G*
MM3
AM1
PM3
112.8 111.5 116.5 112.7
112.3 111.2 115.5 111.2
111.8 113.3 122.0 108.3
111.7 111.7 102.5 109.5
Si–Si bonds compared to the C–C bonds causing smaller repulsive gauche SiH 2…SiH 2 interactions than in the corresponding CH 2…CH 2 unit [8]. Therefore it may appear surprising that the ab initio values for (1) are as low as 53.1⬚ (6-31G*) and 52.7⬚ (SV(P)), supported by the MM3 value of 53.1⬚, which means that (1) is indeed found to be more flattened than cyclohexane. There is, however, a simple explanation for this. The extent of flattening of six-membered rings is determined first of all by the bond lengths and angles within the ring. In cyclohexane-like systems no special property of six-membered rings is required to explain the extent of flattening, but rather the intrinsic natural bond lengths and angles, as found in simple acyclic systems containing as few as three atoms, are often reproduced fairly well.1 This is illustrated by comparing the calculated bond angles for propane and its silicon-containing analogues with those in the corresponding six-membered rings. Table 6 contains the results of selected calculations of bond angles for propane analogues. In general the bond angles are calculated to be 0–2⬚ larger in the propane analogue than in the corresponding six-membered ring. The main reason for the ring flattening in 1,3,5-trisilacyclohexane as calculated ab initio (631G*) is the large SiCSi bond angle of 114.4⬚, which is intrinsically large as can be seen in SiH 3 – CH 2 –SiH 3, where it is 116.5⬚. The corresponding MM3 values are 114.1⬚ and 115.5⬚, respectively. The ring shape for the chair form of (1) as calculated by AM1 (very flat) and PM3 (puckered) is mainly caused by the extreme values predicted for the SiCSi bond angle in SiH 3 –CH 2 –SiH 3 by these methods (122.0⬚ and 102.5⬚, respectively).
1
A referee’s comment has drawn our attention to this relationship.
3.1.2. Twist and boat conformations The dihedral angles for the boat and twist conformations of (1) are presented in Tables 2 and 3, respectively. Table 2 also contains four characteristic distances for the boat conformation: the two different Si–C bond lengths (l 12 and l 23), the shortest distance between two eclipsed hydrogen atoms, and the distance between the two ‘flagpole’ hydrogens. Because regular boat (C s) and twist (C 1) conformations of (1) have lower symmetry than the corresponding conformations of cyclohexane, one needs three sets of values for the dihedral angles instead of two in the case of cyclohexane. In some cases the calculations predict less regular conformations (boat: AM1; twist: SV(P), MM2, MM3, AM1 and MNDO), in which cases all six dihedral angles are needed to describe the structure. The twist conformation can be viewed as being a relaxed boat form, and each method shows all Si–C bond lengths for it to be very similar. We will not, therefore, discuss any further structural parameters for these conformations. Notice, however, that the molecular coordinates and hence all parameters for the conformations calculated are available as supplementary material (see Section 5). An inspection of Table 2 reveals that the ab initio ˚ longer than methods calculate l 23 to be about 0.01 A l 12 (l 12 are practically the same as for the chair form). MM methods calculate all Si–C bond lengths to be practically equal. The semiempirical methods predict ˚ as compared to an elongation of l 23 by 0.003–0.006 A l 12. Ab initio calculations for the boat conformation of cyclohexane result in longer ‘in plane’ C–C bonds by ˚ as compared to the bonds to C atoms 1 and 4 0.018 A [3]. This bond lengthening is generally attributed to the repulsive interaction of the eclipsed CH 2 groups. It is understandable that the bond lengthening (l 23 ⬎ l 12) is smaller in (1) than in cyclohexane due to the longer
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Si–C bonds (and partly also due to longer Si–H bonds compared to C–H bonds) in (1) as compared to cyclohexane. Indeed, the shortest distance between eclipsed hydrogens in (1) is well beyond the sum of van der Waals radii for two hydrogen atoms [33]. The same holds for the distance between the ‘flagpole’ hydrogens of the boat form, except for the puckered boat conformation calculated by PM3, where this distance is found to be close to the van der Waals distance. 3.2. Relative conformational energies of 1,3,5trisilacyclohexane Relative energies for the chair, twist and boat conformations of (1) are given in Table 5. All methods tested agree on the chair conformation being the global minimum. The energy calculated by each method for the chair conformation is also given. The semiempirical methods, which give the heats of formation (DH f), predict quite different values. AM1 and MNDO (as well as all the other methods) are able to find different geometries for the twist and boat conformations, but each of them calculates the same energy for both conformations. In each case the starting geometries were those obtained by the conformation search mode and Sybyl force field provided by Spartan. Different structure for the twist conformation could be obtained by AM1 if the starting geometry was altered, however, the resulting energy turned out always to be the same. The energy difference between the chair and the twist conformations calculated by AM1 and MNDO is very small (0.61 and 0.88 kcal mol −1 respectively), considerably smaller than that reported for cyclohexasilane (1.7–2.2 kcal mol −1) [8]. The total energy calculated by HF/6-31G* is slightly lower than that calculated by TURBOMOLE using the SV(P) basis set. The energy difference between the chair and the twist forms is 2.15 kcal mol −1 for 6-31G* and 2.35 kcal mol −1 for SV(P). Both methods calculate the boat to be 0.4 kcal mol −1 higher in energy than the twist conformation. The values calculated according to 3-21G are 1.19 and 1.46 kcal mol −1 for the twist and boat forms, respectively. This suggests that 3-21G may not be a sufficient basis set for reliable conformational energy calculations for alkyl derivatives of (1). The MM methods calculate the twist conformation to be 3.28 kcal mol −1 (MM2) and 3.06 kcal mol −1 (MM3)
higher than the chair form. The difference from twist to boat is 0.34 kcal mol −1 (MM2) and 0.26 kcal mol −1 (MM3). PM3 predicts the twist form to be 1.62 kcal mol −1 higher than the chair form and the difference from twist to boat to be 0.46 kcal mol −1, values not far from those calculated ab initio. Because the conformational energy difference between the chair and twist forms increases from 1.19 to 2.15 kcal mol −1 as the basis set is improved from 3-21G to 6-31G*, and decreases from 3.28 to 3.06 kcal mol −1 as one uses the improved version MM3 instead of MM2, it may be concluded that the twist conformation for molecule (1) is approximately 2.1–3.1 kcal mol −1 higher in energy than the chair form and that the energy difference between the twist and boat conformations is about 0.3–0.4 kcal mol −1. Thus the relative conformational energies are much closer to those for cyclohexasilane than for cyclohexane. This is somewhat surprising, but Dixon and Komornicki concluded from their ab initio analysis of cyclohexane, that of the 8 kcal mol −1 energy difference between the chair and boat forms, 6 kcal mol −1 might be attributed to eclipsing interactions and that the remaining 2 kcal mol −1 is due to distortions that relieve the ‘flagpole’ interactions [3]. Our results indicate that in the case of (1) the ‘flagpole’ interactions can be neglected and that the eclipsing interactions are much smaller than in the case of cyclohexane. Therefore it might be that the increased bond length from C–C in cyclohexane to Si–C in (1) relaxes the twist and boat conformation efficiently and, thus, a further bond lengthening by Si–Si bonds in the case of cyclohexasilane does not induce much improvement. 3.3. Conformational energy surface of 1,3,5trisilacyclohexane Calculating the structure of the basic conformations of (1) and their relative energies is the first step in exploring the conformational behaviour of this ring system. The next step is to mark the pathway between the conformations and finally to map the conformational energy surface (CES). We have decided to construct the CES by using MM3. We conclude from our calculations that MM3 is capable of giving a reasonable picture of the structures and conformational energies of the most important conformations of (1).
Fig. 3. 3-D presentation of a part of the conformational energy surface of 1,3,5-trisilacyclohexane, (1). Steric energy, calculated by MM3, shown as a function of the two dihedral angles, q 23 and q 65. For clarity the steric energy has been cut off at 6.0 kcal mol −1.
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Fig. 4. Lowest energy pathway for the conversion chair–twist–boat–twist–chair for 1,3,5-trisilacyclohexane, (1). Steric energy, calculated by MM3, shown relative to the chair conformation.
It is convenient to use the dihedral driver (a built-in feature of MacMimic/MM3) to change two dihedral angles of the ring in small steps and to calculate the steric energy for each step as shown by Burkert and Allinger for cyclohexane [34]. We have varied q 23 and q 65 (see Table 2 and Fig. 1 for definition of dihedral angles) in steps of 2.0⬚ from +90⬚ to −90⬚. The result is shown as a 3-dimensional picture in Fig. 3. For clarity, steric energies larger than 6 kcal mol −1 are omitted in the figure. Steric energies of this magnitude are because of ring distortions that are not part of the conformational equilibrium described here. Notice, however, that in reality the CES of a puckered six-membered ring is that of a globe and not a two-dimensional map as has been pointed out by Pickett and Strauss [6], Cremer and Pople [5], and Zefirov et al. [7]. It is not difficult, however, given a knowledge of the nature of the global surface (the two chair conformations are at the north and south poles and a belt of alternating twist and boat conformations on a pseudorotational pathway along the equator), to connect the results shown in Fig. 3 to the global surface. One can easily locate the two poles (chairs) and a ‘valley’ with four local minima (twist) connected by saddle points (boats) between them along the ‘visible’ part of the equator (diagonal from +90⬚; +90⬚ to −90⬚; −90⬚). On the global surface there are six boat and six twist conformations along the equator. The remaining twist and boat conformations are located on the ‘invisible
remote’ side of the globe. They would become visible if one used another pair of dihedral angles, that is q 12 and q 54, or q 34 and q 16. This would be equivalent to a rotation of 120⬚ (clockwise or anticlockwise) around the axis which connects the two poles of the globe. By mapping the conformational results as a function of two dihedral angles, many of the same problems are encountered as when representing the earths surface on a two-dimensional map. Thus, for example, the twist conformations do not all have the same appearance, depending on their location on the equator. The most important conversion of a chair conformation to a twist–boat–twist pseudorotation and back to the chair or the inverted chair conformation is quite evident, however. The lowest energy pathway for this conversion is shown in Fig. 4. It should be noted that the direction connecting the chair to the twist is essentially orthogonal to the motion connecting two twist forms via the boat conformation. The energy barrier from the chair to the twist conformation amounts to 5.5 kcal mol −1 and that from twist to chair only 2.4 kcal mol −1. It is also remarkable to see that the transition ridge between the chair and the valley of twist and boat conformations is almost constant in energy (0.2 kcal mol −1 between the highest and lowest value on the ridge). Therefore a precise location of a transition conformation is not very meaningful as Dixon and Komornicki have pointed out [3]. However, the transition state on the lowest energy pathway, as calculated by MM3, corresponds to a
I. Arnason et al. / Journal of Molecular Structure (Theochem) 454 (1998) 91–102
‘sofa’ with approximate C s symmetry. The three Si atoms and two of the C atoms of (1) are nearly coplanar and the third C atom has a flap angle of 127.4⬚ to the plane. The corresponding flap angle to the plane of four atoms in the chair conformation is 131.3⬚ as calculated by MM3.
4. Conclusions The aim of this work was to calculate the structure and relative conformational energies for 1,3,5-trisilacyclohexane, (1), and to explore its conformational energy surface. Several methods of calculation were used and tested for this purpose. None of the three semi-empirical methods, AM1, MNDO, and PM3 was found to be suitable for calculating the structure and relative energies of the basic conformations of (1) and their use is not recommended for further work on related compounds. Ab initio calculations at the HF/631G* level and the almost equivalent SV(P) basis set used by TURBOMOLE are considered to give reliable results both for structure and relative energies. The results obtained by using the lower-quality basis set 3-21G are significantly different which makes us believe that it is unsuitable for this purpose. The two force fields tested, MM2 and MM3, were found to give results somewhere between those obtained by 6-31G* and 3-21G. MM3 was found to perform better than MM2, hence MM3 was considered capable of giving a reasonable CES for (1). The results indicate that (1) shows qualitatively a similar conformational behaviour as cyclohexane and cyclohexasilane. Its energy differences between the chair, twist, and boat conformations were found to be much closer to those for cyclohexasilane than for cyclohexane. On the other hand, however, the ring of (1) is more flattened than that of cyclohexane, and in that sense (1) does not exhibit behaviour similar to cyclohexasilane, which is less flattened than cyclohexane. The ring flattening of (1) was found to be caused by the intrinsically large SiCSi bond angle.
5. WWW supplementary material The following material is available via the THEOCHEM HomePage at http://www.elsevier.nl/locate/
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theochem. 1. Molecular coordinates for the chair, twist, and boat conformation of (1), calculated by each method used, in PDB format. 2. Fig. 3 as a colour picture. 3. Conformational energy surface of 1,3,5-trisilacyclohexane as a table, giving the steric energy calculated by MM3 as a function of the coordinates q 23 and q 65.
Acknowledgements We wish to thank Professor H. Jonsson at the University of Washington, Seattle, and Priv. Doz. Dr. M. Ha¨ser at the University of Karlsruhe for useful discussions and for their help with the calculations. A research assistance grant for G.K. Thorarinsson by the University of Iceland is acknowledged. At the time of completion of this work, our friend Dr. M. Ha¨ser died as a result of a tragic climbing accident. We wish to dedicate this publication to his memory. References [1] E. Juaristi (Ed.), Conformational Behavior of Six-Membered Rings, Methods in Stereochemical Analysis, VCH Publishers, New York, 1995. [2] M. Squillacote, R.S. Sheridan, O.L. Chapman, F.A.L. Anet, J. Am. Chem. Soc. 97 (1975) 3244. [3] D.A. Dixon, A. Komornicki, J. Phys. Chem. 94 (1990) 5630. [4] D.M. Ferguson, I.R. Gould, W.A. Glauser, S. Schroeder, P.A. Kollman, J. Comput. Chem. 13 (1992) 525. [5] D. Cremer, J.A. Pople, J. Am. Chem. Soc. 97 (1975) 1354. [6] H.M. Pickett, H.L. Strauss, J. Am. Chem. Soc. 92 (1970) 7281. [7] N.S. Zefirov, V.A. Palyulin, E.E. Dashevskaya, J. Phys. Org. Chem. 3 (1990) 147. [8] Z. Smith, A. Almenningen, E. Hengge, D. Kovar, J. Am. Chem. Soc. 104 (1982) 4362. [9] M.R. Frierson, M.R. Iman, V.B. Zalkow, N.L. Allinger, J. Org. Chem. 53 (1988) 5248. [10] K. Chen, N.L. Allinger, J. Phys. Org. Chem. 10 (1997) 697. [11] G. Fritz, E. Matern, Carbosilanes, Springer-Verlag, Heidelberg, 1986. [12] C.H. Bushweller, in: E. Juaristi (Ed.), Conformational Behavior of Six-Membered Rings, VCH Publishers, New York, 1995, p. 25. [13] I. Arnason, A. Kvaran, Z. anorg. allg. Chem. 624 (1998) 65. [14] N.L. Allinger, J. Am. Chem. Soc. 99 (1977) 8127. [15] N.L. Allinger, Y.H. Yuh, J.-H. Lii, J. Am. Chem. Soc. 111 (1989) 8551.
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