The effects of fluorine and chlorine substitution on

Journal of Molecular Structure (Theochem) 500 (2000) 195–223 www.elsevier.nl/locate/theochem

The effects of fluorine and chlorine substitution on bond lengths in ethanes and disilanes: comparisons of ab initio and experimental information B. Fodi 1, D.C. McKean*, M.H. Palmer Chemistry Department, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, UK

Abstract Ab initio and some density functional theory calculations of bond lengths in fluoro- and chloro-ethanes and disilanes are ˚ under strictly comparable conditions. The resulting changes in MH and MX (M C, Si; reported with a precision of ^0.0001 A X F, Cl) bond length are analysed for the effects of halogens substituted in geminal (a), or vicinal (gauche or trans) positions. The shortening effect of a halogen on an MH bond is markedly reduced or even reversed by the introduction of electron correlation at the MP2 or B3LYP level. MX bonds are little affected. gauche halogen consistently shortens both MH and MX bonds, while trans halogen has no effect on an MH bond but a small and variable effect on the MX bond. The reality of these calculated changes in bond length is tested in two ways. MH bond lengths are plotted against experimental values of the isolated stretching frequencies n isMH, which themselves correlate well with experimental r0 bond lengths. Agreement on the resulting substituent effects is generally good for the gauche and trans effects of halogen but variable for a effects. Unobserved n isMH values are predicted from computed bond lengths in fluoroethanes, chloroethanes and chlorodisilanes. Calculated MX and MM bond lengths are compared with experimental values, notably those from electron diffraction studies amongst the ethanes. Most calculations underestimate the changes found experimentally in CF and CCl bond lengths. CC bond length changes are underestimated in fluoroethanes and overestimated in the chloro-compounds. The ‘offset’ value (re(calc) ⫺ re(true)) for a CH or SiH bond calculated with a given basis set and level of theory in most cases varies markedly throughout the series of compounds. The same is true for CF, CCl, CC and SiSi bonds if the corresponding offset values for the ra lengths are constant. The need is stressed for extended experimental work on many of the compounds, especially the disilanes. It is recommended that structures should be refined with ab initio derived constraints on the bond lengths involved and differences between spectroscopic and diffraction-based geometries reconciled through the calculation of rz structures. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Ab initio; Fluoro- and chloro-ethanes; Fluoro- and chloro-disilanes; Bond lengths; Off-set values

1. Introduction * Corresponding author. Tel.: ⫹ 44-131-650-4729; fax: ⫹ 44131-650-4743. E-mail addresses: [email protected] (D.C. McKean), [email protected] (M.H. Palmer). 1 Erasmus exchange student from the University of Kaiserslautern.

Changes in the structures of methanes and silanes due to substitution of halogen have been the subject of extensive investigation by both experimental and theoretical approaches, since the classic paper by

0166-1280/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(00)00378-X

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B. Fodi et al. / Journal of Molecular Structure (Theochem) 500 (2000) 195–223

Brockway on the contraction in the CF bond length on passing from CH3F to CF4 [1]. The contractions that are generally found in CX and SiX (X F,Cl) bond lengths have been attributed to ‘double bond-no bond resonances’ [1] or negative hyperconjugation, in valence bond terminology. 2 However more recent papers which have examined the phenomenon through ab initio calculations tend to favour a purely electrostatic or electronegativity effect [2,3]. The effects of halogen substitution on geminal and vicinal CH or SiH bond lengths have received much less attention, perhaps because the experimental uncertainty associated with these lengths is so great, while the changes in the lengths are small compared with those in the CX or SiX bonds. The ab initio calculation of molecular geometry is ideally suited to the determination of these small effects and many such calculations are in the literature. However high precision both in the determination and the reporting of such data is essential. In practice, in most papers bond lengths are quoted to ˚ , which obscures or markedly rounds up/ ^0.001 A down the small differences for particular bond types between molecules. A notable exception to this is the ab initio study by Ignacio and Schlegel of methanes and silanes where on the one hand, the lengths deter˚ and on the other, use mined are quoted to ^0.0001 A is made of the very close relationship between bond length and average CH or SiH bond stretching frequency [4]. 3 Here the influence of negative hyperconjugation in lengthening the CH bond from methane to methyl fluoride is discernable, although electron correlation is in fact needed for the full effect to be calculated by ab initio methods (cf. Ref. [10]). The interest in extending studies of this kind to ethanes and disilanes lies in the possibility of identi-

2 In molecular orbital terms, this would be described as the selective incorporation of CX p ⴱ- or s ⴱ-anti-bonding (virtual) MOs in the full CI expansion of the ground state. 3 Experimentally the average CH stretching frequency is derived from spectra of the normal species which in the case of CH3 and CH2 compounds are likely to be perturbed by Fermi resonances. A more appropriate quantity to use here is either the isolated CH stretching frequency n isCH measured in the partially deuterated compound, e.g. CHD2F, [5,6] or the local mode frequency derived from high overtone studies [7,8]. In the case of SiH compounds the average frequency is adequate provided only one type of SiH bond is present [9].

fying specific effects of halogen substitution in affecting bonds either gem (or a), as in the methane or silane series, or else vicinal (b ), in which case alternative gauche and trans (antiperiplanar) effects may be distinguished. The data available here from conventional experimental methods such as rotational spectroscopy or gas-phase electron diffraction is sparse. Where studies have been made, there is extreme difficulty at the present time of such methods being able to distinguish realistically between the non-equivalent CX or SiX bonds in a molecule such as M2HX5 or the similar CH or SiH bonds in an structure such as M2H5X. A further obstacle is the differing nature of the structures determined by the spectroscopic (e.g. r0, rs) and gas phase electron diffraction (GED) (e.g. ra, rg, ra) approaches, each of which represents a different type of average, so that markedly different values may be reported for the same bond in the same molecule by the two methods. In such a situation, a quantum-chemical (QC) approach has a crucial role to play. Amongst ethanes and disilanes, many such studies have been carried out on fluorinated ethanes [10–27], but only a few on chlorinated ethanes [28,29] and disilanes [29–33]. 4 Rarely have bond lengths been reported to more ˚ [22,28–32] and only in five of these, than ^0.001 A have the differing effects of b halogen been considered [28–32], although such effects can be seen in the other studies. Our own interest in such a study stems from early work on isolated CH stretching frequencies n isCH in the ethyl halides which showed that halogen substitution strengthened a gauche related CH bond but weakened or left unchanged a trans related one [34]. Later, similar effects on a smaller scale were found for SiH bonds from n isSiH studies in Si2H5X and 1,1Si2H4X2 compounds (X Cl, Br) [29] and in further chlorinated disilanes, 1,2-Si2H4Cl2, 1,1,2-Si2H4Cl3, 1,1,1-Si2H3Cl3 and 1,1,2,2-Si2H2Cl4 [30]. Qualitatively these changes in n isSiH were confirmed by HF/6-31G ⴱ calculations for mono-, di- and trichlorodisilanes of both SiH stretching frequency and SiH bond length [30]. These same calculations also indicated that a similar distinction between the gauche 4 Refs. [10,11,28] cover complete ranges of halogenated ethanes from C2H6 to C2X6.


and trans effects of chlorine was to be found in the SiCl bond lengths, a finding repeated in 1,1,2,2Si2H2Cl4 [31]. The present study was carried out with the object of extending our earlier HF/6-31G ⴱ calculations firstly to the complete range of chlorinated disilanes, and secondly to the corresponding fluorine derivatives and to the fluoro- and chloro-ethanes where existing data were inadequate for the precision we desired. Knowing the difference made by electron correlation to the prediction of gem effects of halogen in methanes, it seemed important to carry out MP2 calculations also. It then becomes necessary to explore the extent to which the ab initio bond length changes found can be regarded as realistic in cases where direct comparison with experimental structures is lacking. The problem is particularly acute for MH bonds on account of the high zero-point energy associated with hydrogen motion combined with the low scattering power of the hydrogen for electrons. Amongst all the compounds in the present study there is in fact only one MH bond length determined with reasonable precision, which is that in ethane itself [35]. In this situation, n isCH or n isSiH values constitute an important alternative source of experimental information. For both CH and SiH bonds n is correlates well with r0 lengths in cases where the latter have been well determined by experiment [6,36]. For a closely related series of compounds such as alkanes, ab initio CH bond lengths determined at SCF levels to the needful ˚ ) have been shown to degree of precision (^0.0001 A give excellent linear correlations with experimental n isCH values [37–39]. However since the gradients of these correlations differ both according to the size of the basis set and also from that of the experimental r0 versus n isCH graph, there is still doubt as to the accuracy of any particular bond length change calculated by ab initio methods [39], although the sequencing of such values is clearly excellent. It therefore seemed important to calculate structures and bond lengths at several levels of theory and with several basis sets for the limited number of ethanes and disilanes where experimental values of n isMH are available. In the course of this study it became evident that there are interesting correlations between bond length and atomic charges of various kinds and these and

197

their chemical interpretation will be treated in the following paper [40].

2. Ab initio calculations We used both of the commonly used QC packages Gamess-UK [41,42] and Gaussian94 [43]. Due to a variety of factors which could include differing levels of precision in integral evaluation, SCF/MP2 wavefunction convergence, criteria for convergence in the geometric variables and exponents in the wave functions themselves, these two programs do not always lead to identical results at the level of precision required here [30]. 5 Indeed, comparison of the bond lengths quoted in Refs. [10–27] with each other and with our own results, shows that differences of up to ˚ in a given bond length are not uncommon, 0.002 A even though the different determinations apparently use the same program, basis set and methodology. 6 Some of these variations might arise from differing approaches in rounding, and in most circumstances are unimportant. However for studies such as the present, it is important to use a single set of criteria for determination of these variables, within one package, and a single basis set. The structures of all four series of compounds, fluoro- and chloro-ethanes and disilanes MHnX6⫺n (M C, Si; X F, Cl) were optimized using the program Gamess-UK(V6.2). The selection of the 6-31G ⴱ basis enables immediate comparison to be made with our previous study [30]. Under these conditions, energies are static to ˚ , with 10 ⫺10 a.u., bond length changes were ⬍10 ⫺4 A ⫺4 changes in angles ⬍10 degrees. This was achieved by using integral evaluation and retention in the SCF step at 10 ⫺24 a.u. As a final check that the values of the parameters affecting convergence in the geometry optimisation were adequate to produce structures reproducible to the above order of accuracy, we performed test calculations, starting from very 5 In Table 10 of Ref. [30] the bond lengths quoted for Si2H5Cl and 1,1-Si2H4Cl2 were from the Gaussian program, when they should have been taken from the Gamess one. The data in the later Tables 12–14 in Ref. [30] were all calculated from the correct Gamess values, which are included here in Table 2. 6 Comparison of our Gaussian94 bond lengths for chloroethanes at the HF/6-31Gⴱ level with those of Ref. [28] show variations of up ˚. to 0.0009 A

198


different initial structures. One of these is shown in the Appendix. The MP2 correlated structures were obtained in the same way as the SCF restricted-Hartree–Fock (RHF) structures above; usually the input variables from the RHF study were used as input to the MP2 calculations to accelerate convergence, a result occurring from the coherent set of bond lengths, angles and force constants in the Hessian matrix. Similar Gaussian94 calculations were carried out with the 6-31G ⴱ basis set on all the fluoro- and chloroethanes and chlorodisilanes. However we quote below only those bond lengths for the cases where experimental values n isMH were available. Additional optimizations were carried out with the triple zeta basis function 6-311G ⴱⴱ at RHF and MP2 levels, togther with a density functional theory (DFT) treatment using the hybrid functional B3LYP [44–46]. For the fluoro- and chloro-ethanes only we also employed a mixed basis consisting of 6-311G ⴱ on hydrogen and carbon togther with 6-311⫹G ⴱ on the halogen. Precision of structures was enhanced by utilisation of the ‘tight’ option on the geometry optimization, with the SCF convergence condition set to 10 ⫺10 in most cases. However, variation of the latter between 10 ⫺10 and the default value of 10 ⫺8 had a negligible effect ˚ ) on bond lengths. In the Gaussian94 (⬍0.00002 A DFT calculations, a fine grid was employed consisting of 99 radial shells round each atom and 302 angular points in each shell. In the initial stages of this work, some ab initio values of n isMH were also calculated for comparison with those observed, as in our previous study [30], and results for these as well as other parameters of the optimizations are available from the authors. Two considerations suggest that a comparison of calculated and observed n isMH values may not be too helpful in assessing the accuracy of the calculated bond length changes. Firstly data for the fluoroethanes suggested that the correlation between ab initio bond length and ab initio n isMH value is not as precise as has been hitherto supposed, although we found it to be very close for both fluoro- and chloro-disilanes. Secondly, it is not obvious that the gradient of the linear correlation between these two quantities should be the same whether they are both determined ab initio or both experimentally. A direct comparison of ab initio bond length with experimental n isMH value avoids

these possible complications and has the merit of economy in CPU time. Of course the problem associated with the gradient of this plot remains. If the experimental bond lengths r0 employed for the correlations with n isMH differ by a constant amount, their ‘offset’ value, from the true equilbrium values re, then the hypothetical gradient of the plot of n isMH against re(true) should be the same as that of n isMH against r0. It is then plausible to suggest that the quality of a series of ab initio calculations of re may be judged in part by the extent to which the gradient of the re (QC) plot against n isMH(exp) agrees with that for r0 versus n isMH(exp). A difference in the gradients of the two plots would entail a variation in the QC offset value (re(QC) ⫺ re(true)) for a given level of theory and basis set. Both the extent of this variation as well as the actual magnitude of the offset value would then provide measures of the imperfection of the QC treatment. Previous discussions of offset values have presumed these to be constant for a given bond, basis set and level of theory, in a series of compounds [47,48]. Description of the structures needs a brief comment. In all cases these are staggered forms; however, test cases were performed which show that eclipsed structures are saddle points with a single negative frequency. Each molecule is identified by the number of halogen atoms present, and (if necessary) point group, as follows: M2H6 0(D3d); M2H5X 1(Cs); 1,1-M2H4X2 11(Cs); 1,2-M2H4X2 12T (trans, C2h) or 12G (gauche, C2); 1,1,1-M2H3X3 111(C3v); 1,1,2-M2H3X3 112Cs or 112C1; 1,1,1,2-M2H2X4 1112; 1,1,2,2,-M2H2X4 1122T (C2h) or 1122G (C2); 1,1,1,2,2-M2HX5 11122; M2X6 111222, where M C or Si. For brevity, in tables we designate the 6-31G ⴱ and 6-311G ⴱⴱ basis sets by ‘sv’ (split valence) and ‘tz’ (triple zeta) respectively, while the mixed 6-311G ⴱ/ 6-311⫹G ⴱ set is shown as ‘tz⫹’.

3. Results and discussion In Sections 3.1–3.4 we present the results of our bond length determinations and identify trends in the differences found. We then examine the extent to which the computed bond length changes can be supported by experimental evidence, firstly from n is


199

Table 1 ˚ ) in fluoro- and chloro-ethanes and disilanes Ab initio MH and MX bond lengths (A Na

Molecule

Bond b

M C (ethanes) XF

1 2 3 4 5 6 7 8 9 10 27 28 29 30 31 32 33 34 35 36 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 37 38 39 40 a b c d

1 11 12T 12G 112Cs 112Cs 112C1 112C1 112C1 111 1122T 1122G 1122G 1112 1112 1112 11122 11122 11122 111222 0 1 1 1 11 11 11 12T 12G 12G 112Cs 112Cs 112C1 112C1 112C1 111 1122T 1122G 1112 11122

MX MX x MXt MXg MXgx MXgg MXgx MXtx MXgt MX xx MXgtx x MXgg MXgtx MXgxx MXtxx MXggt xx MXgg MXgtxx x MXggt xx MXggt MH MH x MHg MHt MH xx MHgg MHgt MXgx MXgx MXtx MXtxx MXgtx MXgxx x MXgg MXgtx MHggt xx MXgg MXgtxx x MXggt xx MXggt

M Si (disilanes) X Cl

XF

X Cl

HF c

MP2 c

HF c

MP2 c

HF c

MP2 c

HF d

MP2 c

1.3726 1.3460 1.3685 1.3661 1.3393 1.3582 1.3384 1.3434 1.3622 1.3249 1.3358 1.3316 1.3379 1.3176 1.3238 1.3555 1.3113 1.3169 1.3304 1.3111 1.0856 1.0828 1.0841 1.0855 1.0790 1.0832 1.0832 1.0812 1.0817 1.0833 1.0803 1.0817 1.0781 1.0807 1.0807 1.0815 1.0777 1.0784 1.0797 1.0773

1.3990 1.3731 1.3948 1.3921 1.3660 1.3842 1.3644 1.3707 1.3881 1.3526 1.3624 1.3578 1.3649 1.3443 1.3519 1.3820 1.3378 1.3443 1.3574 1.3385 1.0929 1.0938 1.0916 1.0934 1.0928 1.0910 1.0911 1.0923 1.0931 1.0950 1.0945 1.0934 1.0918 1.0923 1.0922 1.0898 1.0917 1.0924 1.0916 1.0914

1.7988 1.7820 1.7915 1.7857 1.7728 1.7746 1.7709 1.7810 1.7814 1.7777 1.7728 1.7634 1.7744 1.7685 1.7815 1.7723 1.7623 1.7745 1.7671 1.7693 1.0856 1.0790 1.0832 1.0862 1.0745 1.0818 1.0833 1.0776 1.0781 1.0803 1.0764 1.0790 1.0743 1.0775 1.0777 1.0815 1.0748 1.0750 1.0774 1.0748

1.7881 1.7791 1.7825 1.7777 1.7707 1.7682 1.7681 1.7780 1.7741 1.7778 1.7698 1.7609 1.7715 1.7678 1.7806 1.7660 1.7604 1.7730 1.7639 1.7668 1.0929 1.0905 1.0914 1.0940 1.0885 1.0909 1.0920 1.0897 1.0903 1.0922 1.0907 1.0913 1.0888 1.0902 1.0901 1.0909 1.0897 1.0898 1.0902 1.0900

1.6041 1.5911 1.6047 1.6024 1.5886 1.5987 1.5891 1.5914 1.6017 1.5791 1.5881 1.5855 1.5883 1.5770 1.5789 1.5968 1.5735 1.5758 1.5835 1.5711 1.4804 1.4770 1.4790 1.4813 1.4711 1.4771 1.4788 1.4756 1.4755 1.4775 1.4717 1.4751 1.4694 1.4734 1.4749 1.4756 1.4671 1.4683 1.4718 1.4648

1.6281 1.6150 1.6292 1.6267 1.6130 1.6234 1.6133 1.6158 1.6261 1.6033 1.6125 1.6101 1.6127 1.6013 1.6037 1.6212 1.5982 1.6003 1.6078 1.5957 1.4887 1.4875 1.4876 1.4902 1.4828 1.4860 1.4875 1.4862 1.4863 1.4885 1.4839 1.4860 1.4814 1.4844 1.4857 1.4844 1.4793 1.4806 1.4824 1.4769

2.0830 2.0681 2.0798 2.0742 2.0599 2.0657 2.0597 2.0659 2.0714 2.0566 2.0576 2.0523 2.0588 2.0485 2.0555 2.0634 2.0434 2.0481 2.0509 2.0421 1.4804 1.4743 1.4774 1.4802 1.4683 1.4750 1.4770 1.4718 1.4718 1.4743 1.4686 1.4719 1.4661 1.4699 1.4714 1.4746 1.4646 1.4660 1.4696 1.4636

2.0713 2.0588 2.0691 2.0642 2.0521 2.0576 2.0518 2.0575 2.0621 2.0494 2.0505 2.0458 2.0513 2.0430 2.0489 2.0559 2.0378 2.0426 2.0450 2.0375 1.4887 1.4860 1.4866 1.4892 1.4827 1.4852 1.4868 1.4843 1.4843 1.4868 1.4837 1.4849 1.4814 1.4832 1.4845 1.4851 1.4806 1.4818 1.4832 1.4808

Datum number. x, g, t indicate halogen atoms in a, gauche or trans positions relative to the bond concerned. Gamess values, HF or MP2/sv, this work. Gamess values, HF/sv, for data numbers 0–26, this work for data numbers 27–40. Data for 1 and 11 were quoted incorrectly in Ref. [30].

200

Table 2 ˚ ) due to substitution of halogen X Contractions in CH and SiH bond lengths (A (A) Alpha halogen substitution Data no.

Nb

˚ )a ⫺Dr(CH) (A

˚ )a ⫺Dr(SiH) (A

XF

1 1 1 1 1 1 1 1

Average 15–12 21–20 23–19 37–24 38–22 38–25 40–39

2 2 2 2 2 2 2

Average

XF

X Cl

HF c

MP2 c

HF c

MP2 c

HF

MP2

HF

MP2 c

0.0028 0.0029 0.0024 0.0022 0.0015 0.0025 0.0025 0.0018

⫺0.0009 ⫺0.0007 ⫺0.0015 ⫺0.0016 ⫺0.0023 ⫺0.0013 ⫺0.0011 ⫺0.0018

0.0066 0.0056 0.0051 0.0059 0.0043 0.0043 0.0056 0.0041

0.0024 0.0017 0.0011 0.0018 0.0007 0.0007 0.0019 0.0007

0.0034 0.0034 0.0035 0.0038 0.0037 0.0037 0.0039 0.0038

0.0012 0.0014 0.0013 0.0017 0.0015 0.0016 0.0018 0.0020

0.0061 0.0056 0.0056 0.0059 0.0051 0.0051 0.0056 0.0050

0.0027 0.0023 0.0023 0.0024 0.0019 0.0020 0.0023 0.0019

0.0023(4)

⫺0.0014(5)

0.0052(8)

0.0014(6)

0.0037(2)

0.0016(3)

0.0055(4)

0.0022(3)

0.0038 0.0030 0.0036 0.0030 0.0033 0.0023 0.0024

0.0010 0.0005 0.0013 0.0006 0.0010 ⫺0.0002 0.0002

0.0045 0.0039 0.0038 0.0027 0.0040 0.0027 0.0026

0.0020 0.0015 0.0015 0.0005 0.0015 0.0003 0.0002

0.0059 0.0058 0.0061 0.0063 0.0068 0.0066 0.0070

0.0047 0.0046 0.0049 0.0051 0.0054 0.0051 0.0055

0.0060 0.0057 0.0057 0.0053 0.0059 0.0054 0.0060

0.0033 0.0031 0.0029 0.0026 0.0031 0.0027 0.0024

0.0035 (7)

0.0011(7)

0.0064(4)

0.0050(3)

0.0057(3)

0.0029(3)

0.0031(5)

0.0006(5)

(B) gauche halogen substitution Data no.

Nb

˚ )a ⫺Dr(CH) (A

˚ )a ⫺Dr(SiH) (A

XF

13–11 17–14 18–12 19–12 22–20 23–15 25–20

1 1 1 1 1 1 1

X Cl

HF c

MP2

HF c

0.0015 0.0023 0.0016 0.0011 0.0016 0.0009 0.0026

0.0013 0.0023 0.0015 0.0007 0.0016 0.0010 0.0028

0.0024 0.0029 0.0014 0.0009 0.0013 0.0002 0.0026

XF MP2 c 0.0015 0.0020 0.0008 0.0002 0.0009 ⫺0.0003 0.0021

X Cl

HF

MP2

HF

MP2 c

0.0014 0.0025 0.0014 0.0015 0.0024 0.0017 0.0026

0.0011 0.0027 0.0013 0.0012 0.0025 0.0014 0.0028

0.0030 0.0032 0.0025 0.0025 0.0024 0.0022 0.0029

0.0021 0.0024 0.0017 0.0017 0.0019 0.0013 0.0023


12–11 18–13 19–13 20–14 22–17 24–16 25–17 39–26

X Cl

Table 2 (continued) (B) (A) gauche Alpha halogen substitution Data no.

Nb

˚ )a ⫺Dr(CH) (A

˚ )a ⫺Dr(SiH) (A

XF

X Cl

HF c

MP2 c

HF c

X Cl

HF

MP2

HF

MP2 c

0.0009 ⫺0.0001

0.0034 0.0031

0.0033 0.0033

0.0026 0.0018

0.0019 0.0013

1 1

0.0019 0.0010

0.0021 0.0006

Average 16–13 24–18 24–19 26–17 37–23 40–38

2 2 2 2 2 2

0.0016(5) 0.0009 0.0005 0.0010 0.0017 0.0004 0.0011

0.0015(7) 0.0006 0.0000 0.0008 0.0013 0.0001 0.0010

0.0015(9) 0.0014 0.0001 0.0006 0.0018 ⫺0.0005 0.0002

0.0009(8) 0.0005 ⫺0.0005 0.0001 0.0011 ⫺0.0009 ⫺0.0002

0.0022(7) 0.0019 0.0022 0.0021 0.0032 0.0023 0.0035

0.0022(9) 0.0016 0.0018 0.0019 0.0031 0.0021 0.0037

0.0026(4) 0.0024 0.0019 0.0019 0.0024 0.0015 0.0024

0.0018(4) 0.0014 0.0011 0.0011 0.0017 0.0008 0.0010

0.0009(4)

0.0006(5)

0.0006(8)

0.0000(7)

0.0025(6)

0.0024(8)

0.0021(3)

0.0012(3)

(C) trans halogen substitution Data no.

˚ )a ⫺Dr(CH) (A

˚ )a ⫺Dr(SiH) (A

XF

14–11 17–13 20–12 21–15 22–18 22–19 25–18 25–19 26–16 38–23 39–24 40–37 Average a

c

XF

X Cl

HF c

MP2 c

HF c

MP2 c

HF

MP2

HF

MP2 c

0.0001 0.0009 ⫺0.0005 ⫺0.0013 ⫺0.0005 0.0000 0.0005 0.0010 0.0017 ⫺0.0003 0.0010 0.0004

⫺0.0005 0.0005 ⫺0.0012 ⫺0.0017 ⫺0.0011 ⫺0.0003 0.0000 0.0009 0.0012 ⫺0.0006 0.0007 0.0003

⫺0.0006 ⫺0.0001 ⫺0.0013 ⫺0.0019 ⫺0.0014 ⫺0.0009 ⫺0.0001 0.0004 0.0003 ⫺0.0007 0.0001 0.0000

⫺0.0011 ⫺0.0006 ⫺0.0017 ⫺0.0022 ⫺0.0016 ⫺0.0010 ⫺0.0004 0.0002 0.0000 ⫺0.0010 0.0000 ⫺0.0003

⫺0.0009 0.0002 ⫺0.0005 ⫺0.0006 0.0005 0.0004 0.0007 0.0006 0.0015 0.0011 0.0016 0.0023

⫺0.0015 0.0001 ⫺0.0010 ⫺0.0011 0.0002 0.0003 0.0005 0.0006 0.0016 0.0008 0.0020 0.0024

0.0002 0.0004 0.0000 ⫺0.0003 ⫺0.0001 ⫺0.0001 0.0004 0.0004

⫺0.0005 ⫺0.0002 ⫺0.0008 ⫺0.0010 ⫺0.0006 ⫺0.0006 ⫺0.0002 ⫺0.0002

0.0001 0.0003 0.0010

⫺0.0004 0.0000 ⫺0.0002

⫺0.0001(9)

⫺0.0005(7)

⫺0.0008(7)

0.0002(3)

⫺0.0004(3)

0.0003(8)

From the appropriate columns in Table 2. No. of substituent halogens in the a (part A) or gauche (part B) positions. ˚. Gaussian94 calculations give average values agreeing within 0.0001 A

0.0006(9)

⫺0.0004(12)

201

b

X Cl


MP2 c

38–21 39–25

Average

0.0014 0.0003

XF

202


Table 3 Contractions in CX and SiX bond lengths due to substitution of halogen X (A) Alpha halogen substitution Data no.

Nb

˚ )a ⫺Dr(CX) (A

˚ )a ⫺Dr(SiX) (A

XF HF c 2–1 8–3 7–4 5–4 27–9 28–6 29–9 35–32

1 1 1 1 1 1 1 1

Average 10–2 30–5 30–7 31–8 33–28 34–27 34–29 36–35

2 2 2 2 2 2 2 2

Average

X Cl MP2 c

HF c

XF MP2 c

HF

X Cl MP2

HF

MP2 c

0.0149 0.0139 0.0145 0.0143 0.0138 0.0134 0.0126 0.0125

0.0125 0.0116 0.0124 0.0121 0.0116 0.0118 0.0108 0.0109

0.0266 0.0251 0.0277 0.0268 0.0264 0.0266 0.0243 0.0251

0.0259 0.0241 0.0277 0.0261 0.0257 0.0264 0.0232 0.0246

0.0168 0.0105 0.0148 0.0129 0.0086 0.0112 0.0070 0.0052

0.0090 0.0045 0.0096 0.0070 0.0043 0.0073 0.0026 0.0021

0.0130 0.0133 0.0133 0.0138 0.0136 0.0132 0.0134 0.0133

0.0131 0.0134 0.0134 0.0137 0.0136 0.0133 0.0134 0.0134

0.0261(11)

0.0255(13)

0.0109(37)

0.0058(27)

0.0134 (2)

0.0134 (2) 0.0137 (8)

0.0117(6)

0.0211 0.0217 0.0208 0.0196 0.0203 0.0189 0.0210 0.0193

0.0205 0.0217 0.0201 0.0188 0.0200 0.0181 0.0206 0.0189

0.0013 0.0029 0.0003 ⫺0.0026 0.0005 ⫺0.0032 ⫺0.0015 ⫺0.0029

0.0120 0.0116 0.0121 0.0125 0.0120 0.0123 0.0125 0.0124

0.0117 0.0117 0.0120 0.0121 0.0119 0.0122 0.0124 0.0121

0.0094 0.0091 0.0088 0.0086 0.0080 0.0079 0.0087 0.0075

0.0203(9)

0.0198(11)

⫺0.0007(21)

0.0122 (3)

0.0120(2) 0.0103 (10)

0.0043 0.0043 0.0024 ⫺0.0005 0.0011 ⫺0.0017 ⫺0.0001 ⫺0.0022 0.0010(24)

0.0115 0.0114 0.0112 0.0104 0.0089 0.0095 0.0107 0.0088

0.0085(6)

(B) gauche halogen substitution Data no.

Nb

˚ )a ⫺Dr(CX) (A

˚ )a ⫺Dr(SiX) (A

XF HF c 4–1 5–2 7–2 9–3 27–8 29–8 30–10 34–31

1 1 1 1 1 1 1 1

Average 6–4 28–5 28–7 32–9 33–30 35–27 35–29 36–34 Average

2 2 2 2 2 2 2 2

X Cl MP2 c

HF c

XF MP2 c

HF

X Cl MP2

HF

MP2 c

0.0088 0.0082 0.0084 0.0084 0.0083 0.0071 0.0081 0.0074

0.0071 0.0067 0.0070 0.0070 0.0070 0.0062 0.0064 0.0063

0.0065 0.0067 0.0076 0.0063 0.0076 0.0055 0.0073 0.0069

0.0069 0.0071 0.0087 0.0067 0.0083 0.0058 0.0083 0.0076

0.0131 0.0092 0.0111 0.0101 0.0082 0.0066 0.0092 0.0070

0.0104 0.0084 0.0110 0.0084 0.0082 0.0065 0.0100 0.0076

0.0017 0.0025 0.0020 0.0030 0.0033 0.0031 0.0021 0.0031

0.0014 0.0020 0.0017 0.0031 0.0033 0.0031 0.0020 0.0034

0.0068(7)

0.0074(9)

0.0093(20)

0.0088(14)

0.0026(6)

0.0025(8) 0.0081(5)

0.0067(3)

0.0079 0.0077 0.0068 0.0067 0.0063 0.0054 0.0075 0.0058

0.0079 0.0082 0.0066 0.0061 0.0065 0.0050 0.0075 0.0058

0.0111 0.0094 0.0075 0.0091 0.0062 0.0057 0.0073 0.0052

0.0095 0.0098 0.0072 0.0081 0.0074 0.0059 0.0076 0.0062

0.0037 0.0031 0.0036 0.0049 0.0035 0.0046 0.0048 0.0047

0.0033 0.0029 0.0032 0.0049 0.0031 0.0047 0.0049 0.0046

0.0066 0.0063 0.0060 0.0062 0.0052 0.0055 0.0063 0.0051

0.0068(8)

0.0067(10)

0.0077(19)

0.0077(13)

0.0041 (7)

0.0040(8) 0.0072(11)

0.0085 0.0076 0.0074 0.0080 0.0051 0.0067 0.0079 0.0060

0.0059(5)


203

Table 3 (continued) (C) (A) trans Alphahalogen halogensubstitution substitution Data no.

Nb

˚ )a ⫺Dr(CX) (A

˚ )a ⫺Dr(SiX) (A

XF

X Cl

XF

X Cl

HF c

MP2 c

HF c

MP2 c

HF

MP2

HF

MP2 c

3–1 8–2 9–4 27–5 27–7 29–5 29–7 31–10 32–6 34–30 35–28 36–33

0.0041 0.0026 0.0039 0.0035 0.0026 0.0014 0.0005 0.0011 0.0027 0.0007 0.0012 0.0002

0.0042 0.0024 0.0040 0.0036 0.0020 0.0011 ⫺0.0005 0.0007 0.0022 0.0000 0.0004 ⫺0.0007

0.0073 0.0010 0.0043 0.0000 ⫺0.0019 ⫺0.0016 ⫺0.0035 ⫺0.0038 0.0023 ⫺0.0060 ⫺0.0035 ⫺0.0070

0.0056 0.0011 0.0036 0.0009 ⫺0.0017 ⫺0.0008 ⫺0.0034 ⫺0.0028 0.0022 ⫺0.0052 ⫺0.0030 ⫺0.0064

⫺0.0006 ⫺0.0003 0.0007 0.0005 0.0010 0.0003 0.0008 0.0002 0.0019 0.0012 0.0020 0.0024

⫺0.0011 ⫺0.0008 0.0006 0.0005 0.0008 0.0003 0.0006 ⫺0.0004 0.0022 0.0010 0.0023 0.0025

0.0032 0.0022 0.0028 0.0023 0.0021 0.0011 0.0009 0.0011 0.0023 0.0004 0.0014 0.0013

0.0022 0.0013 0.0021 0.0016 0.0013 0.0008 0.0005 0.0005 0.0017 0.0004 0.0008 0.0003

Average

0.0020(13)

⫺0.0011(40)

⫺0.0008(35)

a b c

0.0016(16)

0.0008 (9)

0.0007(11)0.0018 (8)

0.0011(6)

From Gaussian94 calculations. is Sr, Sn represent the changes in rSiH or n SiH from that of Si2H6. ˚ (CF) or 0.0003 A ˚ (CCl, SiCl). Gaussian94 calculations give average values agreeing within 0.0001 A

data (Section 3.5) and secondly from direct experimental determinations of structure (Section 3.6). 3.1. MH and MX bond lengths and method of analysis In Table 1 we list the ab initio MH and MX bond lengths determined by the Gamess program in this or in the previous study [30], using the 6-31G ⴱ basis. Our method of extracting information on the a, gauche and trans effects of a given halogen substitution has been described earlier [30] and involves characterising each bond in each molecule by a superscript X indicating the number of a (gem) X atoms (X F,Cl), and by a subscript giving the number of trans (t) or gauche (g) halogens. This nomenclature is illustrated by the Newman diagrams in Fig. 1, representing the twelve members of a series of halogenated ethanes or disilanes. In this way the change in bond length given by a single a, gauche or trans effect can be obtained by appropriate subtractions of one datum in Table 1 from another. Identification of a particular subtraction is facilitated by assigning a datum number to each of the entries in this table. The resulting a, gauche and trans effects of halogen substitution are then compiled in Table 2 for the

effects on CH and SiH bond distances and in Table 3 for CX and SiX lengths. Because there is evidence from both bond length studies in methanes and silanes and also n is data that a and gauche effects vary with the number of substitutions made, we separate in Tables 2 and 3 the a and gauche effects resulting from the first halogen substitution from those due to a second one. The average value of each a or gauche effect at the first or second substitution is then given. There can of course only be one halogen atom trans to any MH or MX bond. Within each group of data corresponding to a given substitution, the number of halogens present increases with descent in the table, which in itself facilitates the identification of trends. All the changes listed are negative ones. This emphasises the point that in nearly every cases we are concerned with bond contraction as the result of halogen substitution. 3.2. CH and SiH bond length changes due to halogen substitution 3.2.1. a effects Table 2 shows that at the Hartree–Fock level, we

204


Fig. 1. Newman diagrams for the twelve M2H6⫺NXN type molecules. Superscripts x and subscripts g and t indicate the numbers of halogen atoms a, gauche or trans to each bond.


205

Fig. 1. (continued)

find contractions in both CH and SiH bonds due to a halogen which are roughly constant for a given substitution although a slight diminution with the total number of halogens present can be seen in most cases. Correspondingly in three of the four cases, the contractions change but little from the first to the second substitution. However for the SiH bond in fluorodisilanes there is a marked increase in the contraction from the first to the second substitution of fluorine. For both CH and SiH bonds the contraction due to chlorine is rather greater that that due to fluorine. The main effect of introducing electron correlation is to lessen the contraction markedly. Indeed in the fluoroethanes the first substitution of fluorine leads instead to a lengthening of the CH bond. This repeats the effect found in fluoromethane [10] where it is reflected in the fall in n isCH from methane to CH3F [5]. It would be natural to invoke negative hyperconjugation as the common explanation for these effects, but the generality of the effect suggests a need for caution. The second substitution of fluorine in the ethanes leaves the CH length almost unchanged. The shortening effect of fluorine on the SiH bond is reduced at the MP2 level to a smaller extent than in the ethanes. However when the substituent is chlorine,

the MP2-HF difference is nearly as great as that in the fluoroethanes. Since hyperconjugation is unlikely to be important here, these MP2-HF differences may arise from another source.

3.2.2. gauche effects At the HF level, contractions are found in all cases but one. Those in the SiH bonds due to chlorine, determined previously as far as the tri-substituted derivatives [30], continue up to 11122 with only a slight reduction. A similar effect of fluorine increases the contraction slightly with increase in substitution. Introduction of electron correlation reduces the contraction to a modest extent in the chloro compounds and leaves it unchanged in the fluoro series. With the CH bond, the introduction of the first fluorine or chlorine has a similar effect within the spread of the data at both HF and MP2 levels, but in both cases the second halogen tends to exert a smaller effect. It is noticeable that the more marked deviations from the averages occur in both HF and MP2 data for the same subtraction, suggesting that such deviations reflect structural properties of one or both of the

206


molecules concerned and not defects of the particular QC approach. 3.2.3. trans effects On average these are all zero within the spread, which tends to be higher than that for the a or gauche effects. The very small lengthenings predicted for chloroethanes and chlorodisilanes at the MP2 level may just be significant. However the SiH bond shows a clear tendency to contract as the number of fluorine atoms substituted increases, at both HF and MP2 levels. Comparing these trans effects with the above gauche ones, we therefore see a sharp distinction. The gauche bonds are significantly strengthened by halogen substitution whereas the trans ones are not. This parallels the similar finding from n is values [5,29,30]. 3.3. CX and SiX bond length changes due to halogen substitution 3.3.1. a effects Table 3 shows that a effects are the source of the largest bond shortenings occurring in these compounds. A noteworthy feature is the agreement between the contractions calculated at the SCF and MP2 levels of theory, for both CF and SiF bonds upon fluorine substitution. There is a slight drop in the average value from the first to the second substitution. For the CCl bond the results are much more variable, the contraction tending to fall to zero as the number of chlorine atoms present increases, becoming negative in some instances, particularly for the second substitution at the MP2 level. Contractions for the SiCl bond are more uniform but also display a trend towards diminishing values as the number of chlorines increase. In contrast to what is found with the CF and SiF bonds, the contractions in the CCl and SiCl bonds diminish from the HF to the MP2 level. Steric factors are of course likely to be more prominent in the chloroethanes. 3.3.2. gauche effects Throughout all four series, the level of theory has little effect on the smaller contractions here found. For the CF bond the contractions are quite well defined and constant over the first and second substitutions.

The CCl ones are much more variable and fall markedly with increase in number of chlorines substituted. Contractions in both the SiF and the SiCl bonds are quite well defined: the former increases slightly with the number of fluorines, the latter, if anything diminishes with chlorine substitution. It is noteworthy that the gauche effect on the SiCl bond is markedly greater than that on the SiF one. 3.3.3. trans effects These are all small and rather variable, especially for the CCl bond, where the trend towards lengthening of the bond with increasing number of chlorines is particularly strong, the resulting average being undefined. The overall variablity seen here and also in the gauche and a effects for chlorine is likely to arise from steric effects. However, the latter can hardly be involved in the large contraction from 1 to ˚ , HF). In the fluoroethanes there is a 12T (0.0073 A similar but less pronounced trend in the CF distance, which leaves the average just positive. The fluorodisilanes exhibit a different kind of behaviour. An initial lengthening of the CF length gives way to a a marked contraction with descent in the table. The chlorodisilanes however behave like the chloroethanes, with an initial marked contraction which diminishes slowly with increasing substitution. Steric effects should be of less importance in these disilanes. 3.4. CC and SiSi bonds Table 4 lists the values calculated for these bonds. Figs. 2 and 3 show plots of the CC and SiSi bond lengths, respectively, determined at the MP2/6-31G ⴱ level against N, the number of halogens substituted. The corresponding plots for the HF data are very similar. The presence of minima in the CC distances around N 2 in the fluoro- and chloro-ethanes has been noted earlier [10,28]: that in the fluorocompounds is shallower. By contrast there is a steady fall in the SiSi distance with increase in N for fluorodisilanes, which may or may not be linear. However in the chlorodisilanes only a very slight fall occurs. 3.5. Comparison of ab initio bond length changes with experiment: use of isolated MH stretching frequencies 3.5.1. Precision of the experimental n is data The accuracy of this kind of datum must first be


207

Table 4 ˚ ), from Gamess calculations Ab initio (sv) values of CC and SiSi bond lengths (A CC(F)

0 1 11 12T 12G 111 112Cs 112C1 1112 1122T 1122G 11122 111222

CC(Cl)

SiSi(F)

SiSi(Cl)

HF

MP2

HF

MP2

HF

MP2

HF

MP2

1.5273 1.5121 1.5023 1.5118 1.5036 1.4995 1.5046 1.5059 1.5075 1.5103 1.5118 1.5172 1.5265

1.5248 1.5089 1.4986 1.5109 1.5009 1.4954 1.5040 1.5048 1.5065 1.5107 1.5134 1.5186 1.5277

1.5273 1.5172 1.5157 1.5159 1.5149 1.5207 1.5206 1.5206 1.5322 1.5355 1.5323 1.5529 1.5818

1.5248 1.5143 1.5111 1 5134 1.5121 1.5138 1.5175 1.5169 1.5269 1.5316 1.5291 1.5486 1.5778

2.3535 2.3487 2.3423 2.3485 2.3472 2.3308 2.3433 2.3433 2.3341 2.3402 2.3420 2.3317 2.3207

2.3358 2.3331 2.3278 2.3360 2.3339 2.3157 2.3320 2.3317 2.3216 2.3293 2.3313 2.3202 2.3080

2.3535 2.3501 2.3474 2.3480 2.3502 2.3448 2.3499 2.3476 2.3465 2.3484 2.3496 2.3481 2.3489

2.3358 2.3338 2.3307 2.3330 2.3349 2.3263 2.3347 2.3321 2.3289 2.3324 2.3335 2.3296 2.3261

considered. In contrast to the type of QC calculation here employed, which determines an equilibrium structure and a harmonic force field, n is values represent transitions among anharmonic oscillator energy levels derived from motions which incorporate small amounts of stretching of other bonds such as CD ones and to a lesser extent, bending of bond angles. Since bond length is expected to relate directly to the individual bond stretching force constant, it is important that contributions to the potential energy distribution from other motions should remain small. 7 The evidence is that this is generally the case [5,6]. Of more concern is the presence of anharmonicity, especially that which results in Fermi resonances. Careful study of CH local mode behaviour suggests that the intrinsic anharmonicity associated with CH stretching is a function primarily of the valence type of the molecule, rather than of the magnitude of the frequency concerned [49]. This would suggest that in a series of closely related compounds such as halogenated ethanes or disilanes, the influence of anharmonicity in the stretching motion will be uniform and therefore will contribute only to the scale factor for the level of QC theory applied. Of more concern is the presence of Fermi resonance. This has been assumed to be negligible in nearly all cases of isolated CH 7 These contributions are likely to be well calculated in an ab initio determination of n is.

stretching transitions [5]. However the work of Quack and co-workers on substituted methanes of the type CHXYZ has identified a small resonance between the single CH stretching motion in this molecule and the first overtone of the CH bend [50]. The latter frequency tends to be unusually high where the substituent is fluorine, as in CHF3 which will tend to enhance Fermi resonances of the above kind. This might give cause for concern in the fluoroethanes. However examination of the local mode frequencies n sCH quoted for CHD3 (3048 cm ⫺1) [50] and CHD2F (3027 cm ⫺1) [51] shows a frequency shift of 21 cm ⫺1 which is close to that of 17 cm ⫺1 in the observed frequencies (2993, 2976 cm ⫺1), suggesting that this shift is insensitive to the resonance present. The ab initio studies of CH bond lengths in alkanes cited above strongly suggest that neither anharmonicty nor Fermi resonances present significant sources of uncertainty in these compounds [38–40]. In the case of SiH bond stretching motion, no Fermi resonances greater than about 0.5 cm ⫺1 have been detected in silyl halides [52] and such evidence as is available suggests that there is little variation in the intrinsic anharmonicity. Moreover the greater weight of the silicon atom results in a ‘purer’ stretching motion. These considerations suggest that the error in the experimental shift in n is lies in the range 2–5 cm ⫺1 for CH bonds, while for SiH ones it arises almost wholly

208


Fig. 2. Plot of C–C bond lengths, calculated at the MP2/6-31G ⴱ level for fluoro- and chloro-ethanes, versus the number of halogen atoms present. Data from Table 4.

from uncertainties in the band centres concerned, for which about ^1 cm ⫺1 is a reasonable estimate. 3.5.2. Comparison of calculations of re with n is values Since there exist eighteen experimental n is data for chlorodisilanes (Table 5), but only nine for chloro-

ethanes (Table 6) and six for fluoroethanes (Table 7) it is appropriate to consider the three classes of compound in order of decreasing numbers of data. Included also are the changes in length for each bond from that of the parent molecule, designated as a substituent effect Sr These permit a ready

Fig. 3. Plot of Si–Si bond lengths calculated at the MP2/6-31G ⴱ level, for fluoro- and chloro-disilanes, versus the number of halogen atoms present. Data from Table 4.


209

Table 5 is and substituent effects Sr, Sn in Computed SiH bond lengths r (from Gaussian94 calculations), observed isolated stretching frequencies n SiH chlorodisilanes Species

0 1 1 1 1 1 1 11 11 11 11 11 11 12T 12T 12G 12G 12G 12G 111 111 112Cs 112Cs 112Cs 112Cs 112C1 112C1 112C1 112C1 112C1 112C1 1122T 1122T 1122G 1122G a b c d

Bond, S a

SiH SiH x SiHg SiHt Sx Sg St SiH xx SiHgg SiHgt S xx Sgg Sgt SiHgx Sgx SiHgx SiHtx Sgx Stx SiHggt Sggt SiHtxx SiHgtx Stxx Sgtx SiHgxx x SiHgg SiHgtx Sgxx x Sgg Sgtx xx SiHgg xx Sgg SiHgtxx Sgtxx

˚) r (A HF/sv

HF/tz

MP2/sv

MP2/tz

B3LYP/tz

1.47827 1.47188 1.47801 1.47523 ⫺0.0064 ⫺0.0030 ⫺0.0003 1.46549 1.47286 1.47487 ⫺0.0128 ⫺0.0054 ⫺0.0034 1.46929 ⫺0.0090 1.46932 1.47193 ⫺0.0090 ⫺0.0063 1.47245 ⫺0.0058 1.46583 1.46941 ⫺0.0124 ⫺0.0089 1.46343 1.46741 1.46893 ⫺0.0148 ⫺0.0109 ⫺0.0093 1.46202 ⫺0.0163 1.46339 ⫺0.0149

1.48017 1.47285 1.47713 1.47971 ⫺0.0073 ⫺0.0030 ⫺0.0005 1.46566 1.47486 1.47663 ⫺0.0145 ⫺0.0053 ⫺0.0035 1.47026 ⫺0.0099 1.47034 1.47269 ⫺0.0098 ⫺0.0075 1.47432 ⫺0.0059 1.46577 1.47026 ⫺0.0144 ⫺0.0099 1.46357 1.46855 1.46979 ⫺0.0166 ⫺0.0116 ⫺0.0104 1.46223 ⫺0.0179 1.46340 ⫺0.0168

1.48700 1.48403 1.48486 1.48738 ⫺0.0030 ⫺0.0021 0.0004 1.48061 1.48337 1.48495 ⫺0.0064 ⫺0.0021 ⫺0.0021 1.48222 ⫺0.0048 1.48228 1.48472 ⫺0.0047 ⫺0.0023 1.48323 ⫺0.0038 1.48155 1.48270 ⫺0.0055 ⫺0.0043 1.47928 1.48107 1.48239 ⫺0.0077 ⫺0.0059 ⫺0.0046 1.47847 ⫺0.0085 1.47970 ⫺0.0073

1.47790 1.47333 1.47583 1.47799 ⫺0.0046 ⫺0.0021 0.0001 1.46816 1.47447 1.47570 ⫺0.0097 ⫺0.0034 ⫺0.0022 1.47158 ⫺0.0063 1.47169 1.47369 ⫺0.0062 ⫺0.0042 1.47403 ⫺0.0039 1.46869 1.47180 ⫺0.0092 ⫺0.0061 1.46681 1.47058 1.47153 ⫺0.0111 ⫺0.0073 ⫺0.0064 1.46605 ⫺0.0119 1.46690 ⫺0.0110

1.48688 1.48290 1.48426 1.48711 ⫺0.0040 ⫺0.0026 0.0002 1.47806 1.48233 1.48418 ⫺0.0088 ⫺0.0046 ⫺0.0027 1.48066 ⫺0.0062 1.48075 1.48338 ⫺0.0061 ⫺0.0035 1.48197 ⫺0.0049 1.47867 1.48097 ⫺0.0082 ⫺0.0059 1.47625 1.47917 1.48053 ⫺0.0106 ⫺0.0077 ⫺0.0064 1.47504 ⫺0.0119 1.47620 ⫺0.0107

n is,Sn (cm ⫺1) (obs) b

˚) r0, Sr c (A

2162.6 2176.5 d 2174.3 2160.6 13.9 11.7 ⫺2.0 2191.9 2179.7 2172.3 29.2 17.1 9.7 2184.5 d 21.9 2184.4 d 2171.6 d 21.8 9.0 2178.6 d 16.0 2184.6 2181.4 22.0 18.8 2199.2 2188.9 2181.4 36.6 26.3 18.8 2204.5 41.9 2198.4 d 35.8

1.4840 1.4816 1.4820 1.4844 ⫺0.0025 ⫺0.0021 0.0004 1.4788 1.4810 1.4823 ⫺0.0053 ⫺0.0031 ⫺0.0017 1.4801 ⫺0.0039 1.4801 1.4825 ⫺0.0039 ⫺0.0016 1.4812 ⫺0.0029 1.4801 1.4807 ⫺0.0040 ⫺0.0034 1.4775 1.4793 1.4807 ⫺0.0066 ⫺0.0047 ⫺0.0034 1.4765 ⫺0.0075 1.4776 ⫺0.0064

is Sr, Sn represent the changes in rSiH or n SiH from that of Si2H6. From Ref. [30]. is ˚ ) 1.8729⫺0.0001798 n SiH From the correlation equation r0SiH(A (cm ⫺1) Ref. [36]. Derived from frequencies of the undeuterated species using energy factored force fields.

comparison of the differences arising from basis set and level of theory and with that expected from n is. Since the parallel study of bond length in relation to atomic charge [40] indicates that the relationships involved may vary according to the number of a (gem) halogen atoms, we distinguish in each figure, plots for MH bonds with no a halogen (H) from those

with one such halogen (H x) or two (H xx). In any complete series, which includes the parent ethane or disilane, there are six H, eight H x and six H xx type bonds. Fig. 4 for the chlorodisilanes shows that re determined at the MP2/sv level correlates quite well with n isSiH. However, the plots for the H xx bonds lie on a

210


line with slightly different gradient from those for the H and H x bonds. Fig. 4 also shows that at the HF level all three plots are well separated from each other and this is found to be true as well for the MP2/tz and B3LYP/tz calculations. The parameters for all these correlations are collected in Part A of Table 8. The slope of the H xx correlation is consistently less than those for the H and H x ones. Since each individual line expresses variations only due to gauche and trans effects, we see that the trends due to the latter are well represented in all cases, whereas separations between the lines indicate that the a effects of chlorine are poorly reproduced.The only effect of changing the basis set from split valence to triple zeta is to diminish the gradient slightly at the MP2 level and to worsen the fit in all cases by a small amount. Comparing the values of the gradients with that observed experimentally, ⫺0:180 × 10⫺3 A cm [36], we see that the HF and B3LYP values tend to be substantially greater than, whereas the MP2 ones are closer to, that observed. The slope of the line fitting all 18 points of the MP2/sv data, 0:208 × 10⫺3 A cm; is just 15% greater than the experimental value. The overall superiority of the MP2/sv calculations is most clearly seen in the comparisons in Table 5 of the re substituent effects Sr with those from r0. The correlations for the MP2/sv data plot allow predictions from the corresponding bond lengths of the following hitherto unobserved values of n isSiH: H x and H xx in in 1112 (2189 cm ⫺1; re 1:48105 A ⫺1 11122 (2204 cm ; re 1:47860 A: Table 6 lists the nine data for the chloroethanes, which include six H, one H x and two H xx values. As an additional feature, gauche–trans differences for 1 and 11 are included. Fig. 5 shows that at the HF/tz level the six plots for the bonds H correlate excellently with each other, whereas those for the H x and H xx types lie well below the linear regression line. The same is true for the HF/sv, B3LYP/tz, B3LYP/tz⫹ and MP2/tz bond length data (not shown). 8 This suggests that when the requisite n is data become available, the remaining H x and H xx points will be found to Very large and quite unacceptable changes in n is (⬎45 cm ⫺1) would be needed to bring these low-lying points on to the line. A measure of their displacement from the line is provided by the increase in the gradient seen in Table 8 when all nine points are involved in the correlation. 8

lie on lines of similar slope but displaced from that for the H bonds. The gradients of the HF and B3LYP plots for the six H type bonds all lie close to, or concident with, that of the r0 versus n isCH line, which is encouraging, but it is disappointing to find a marked drop below unity for all three MP2 calculations, as shown in Table 8, Part B. A feature of the MP2/sv and MP2/tz⫹ data is the tolerable fit obtained for all nine points, as seen in Fig. 5, with little change in gradient from six points fitted to nine. Either of these overall correlations can provide a basis for the prediction of the unobserved H x and H xx n isCH values from their calculated bond lengths.The relevant data in Table 9 employ the results of the MP2/tz⫹ calculations. The accuracy of the predictions as measured by the standard error for the regression, 6.5 cm ⫺1, is not very high, but the results may be of assistance in the analysis of observed spectra. The overall picture, then, is of a rather satisfactory account of the gauche and trans effects of halogen given by HF or B3LYP treatments, which however fail seriously on geminal ones. By contrast, the latter are better reproduced by MP2 treatments, however, at the expense of poorer vicinal ones. The only noticeable effect of change of basis set is the deterioration in reproduction of a effects which results in the MP2 calculations when the split valence basis is replaced by the triple zeta (tz) one. However this does not occur when a diffuse function is present on the chlorine (tz⫹). Table 7 shows the bond length and n isCH data for fluoroethanes. For convenience, CC distances for ethane itself are here included, together with the offset values for reCH and reCC which derive from the experimentally-based equilibrium geometry of re CC Duncan et al., who found re CH 1:0877 A; 1:5280 A; in this molecule [35]. The sparse data include those for four H, one H x and one H xx type bonds. Fig. 6 shows that at the HF/sv level, the H x and H xx plots lie well below the correlation for the four H ones, but that the correlation for all six MP2/tz data is quite good. For the latter, exclusion of the H x and H xx points makes only a small difference to the parameters, as seen in Table 8. In this respect the MP2/tz calculation is considerably better than the MP2/sv, MP2/tz⫹ and B3LYP/tz ones, where the H x and H xx points tend to lie on the high side. Part of the

Table 6 is Computed CH bond lengths r (from Gaussian94 calculations), observed isolated stretching frequencies n CH and substituent effects Sr, Sn in chloroethanes

0 1 1 1 1 1 1 1 11 11 11 11 11 11 11 111 111 11122 11122 a b c d

Bond, S

CH CH x CHg CHt Sx Sg St St⫺Sg CH xx CHgg CHgt S xx Sgg Sgt St⫺Sg CHggt Sggt xx CHggt xx Sggt

˚) r (A HF/sv

HF/tz

MP2/sv

MP2/tz

MP2/tz⫹

B3LYP/tz

B3LYP/tz⫹

1.08558 1.07889 1.08315 1.08617 ⫺0.0067 ⫺0.0024 0.0006 0.0030 1.07448 1.08182 1.08327 ⫺0.0111 ⫺0.0038 ⫺0.0023 0.0015 1.08147 ⫺0.0041 1.07483 ⫺0.0108

1.08619 1.07897 1.08366 1.08690 ⫺0.0072 ⫺0.0025 0.0007 0.0032 1.07423 1.08227 1.08380 ⫺0.0024 ⫺0.0120 ⫺0.0039 0.0015 1.08186 ⫺0.0043 1.07408 ⫺0.0121

1.09326 1.09068 1.09178 1.09438 ⫺0.0026 ⫺0.0015 0.0011 0.0026 1.08866 1.09120 1.09234 ⫺0.0046 ⫺0.0021 ⫺0.0009 0.0011 1.09125 ⫺0.0020 1.09021 ⫺0.0031

1.09334 1.09021 1.09187 1.09453 ⫺0.0031 ⫺0.0015 0.0012 0.0027 1.08779 1.09119 1.09228 ⫺0.0056 ⫺0.0022 ⫺0.0011 0.0011 1.09097 ⫺0.0024 1.08833 ⫺0.0050

1.09244 1.08990 1.09106 1.09385 ⫺0.0025 ⫺0.0014 0.0014 0.0028 1.08832 1.09054 1.09167 ⫺0.0041 ⫺0.0019 ⫺0.0008 0.0011 1.09052 ⫺0.0019 1.08974 ⫺0.0027

1.09356 1.08846 1.09148 1.09500 ⫺0.0051 ⫺0.0021 0.0014 0.0035 1.08503 1.09037 1.09206 ⫺0.0085 ⫺0.0032 ⫺0.0015 0.0017 1.09030 ⫺0.0033 1.08538 ⫺0.0082

1.09379 1.08882 1.09162 1.09517 ⫺0.0050 ⫺0.0022 0.0014 0.0036 1.08540 1.09043 1.09220 ⫺0.0084 ⫺0.0034 ⫺0.0016 0.0018 1.09040 ⫺0.0034 1.08585 ⫺0.0079

is ˚ ) 1.3982⫺0.0001023 n CH From the correlation equation r0CH (A (cm ⫺1) Ref. [6]. Ref. [35]. Ref. [34]. Ref. [53].

n is, Sn /cm ⫺1 (obs.)

˚) r0, Sr a (A

2951.3 b 2983.2 c 2972.4 c 2945.0 c 31.9 21.1 ⫺6.3 27.4 3006.3 d 2983.7 d 2971.3 d 55.0 32.4 20.0 12.4 2988 d 37 3002 d 51

1.0963 1.0930 1.0941 1.0969 ⫺0.0033 ⫺0.0022 0.0006 0.0028 1.0907 1.0930 1.0942 ⫺0.0056 ⫺0.0033 ⫺0.0020 0.0013 1.0925 ⫺0.0038 1.0911 ⫺0.0052


Species

211

212

Species

0 0 0 0 1 1 1 1 1 1 1 111 111 11122 11122 a b c d e

Bond, S

CH d CH c CC d CC c CH x CHg CHt Sx Sg St St⫺Sg CHggt Sggt xx CHggt xx Sggt

is n CH, Sn (cm ⫺1) (obs.)

˚) r (A HF/sv

HF/tz

MP2/sv

MP2/tz

MP2/tz ⫹

B3LYP/tz

B3LYP/tz⫹

1.08558 ⫺0.0021 1.52738 ⫺0.0062 1.08275 1.08414 1.08553 ⫺0.0028 ⫺0.0014 ⫺0.0001 0.0014 1.08150 ⫺0.0041 1.07729 ⫺0.0083

1.08619 ⫺0.0015 1.52704 ⫺0.0096 1.08346 1.08469 1.08634 ⫺0.0027 ⫺0.0015 0.0002 0.0017 1.08202 ⫺0.0042 1.07910 ⫺0.0071

1.09326 0.0056 1.52597 ⫺0.0020 1.09415 1.09191 1.09374 ⫺0.0009 ⫺0.0014 0.0005 0.0018 1.09012 ⫺0.0031 1.09169 ⫺0.0016

1.09334 0.0056 1.52889 ⫺0.0089 1.09349 1.09200 1.09379 0.0002 ⫺0.0013 0.0005 0.0018 1.08966 ⫺0.0037 1.09047 ⫺0.0029

1.09244 0.0047 1.52801 0.0000 1.09226 1.09110 1.09338 ⫺0.0002 ⫺0.0013 0.0009 0.0023 1.08944 ⫺0.0030 1.09175 ⫺0.0007

1.09356 0.0059 1.53045 0.0025 1.09406 1.09226 1.09406 0.0005 ⫺0.0013 0.0005 0.0018 1.08982 ⫺0.0037 1.09221 ⫺0.0014

1.09379 0.0061 1.52929 0.0013 1.09301 1.09224 1.09431 ⫺0.0008 ⫺0.0016 0.0005 0.0021 1.08988 ⫺0.0039 1.09166 ⫺0.0021

is ˚ ) 1.3982⫺0.0001023 n CH From the correlation equation r0CH (A (cm ⫺1) Ref. [6]. As in Table 6. Offset values re QC ⫺ re exp Ref. [35]. Ref. [54]. Ref. [55].

˚) r0, Sr a (A

2951.3 b

1.0963

2950.2 b 2973.5 b 2957.0 b ⫺1.1 22.2 5.7

1.0964 1.0940 1.0957 0.0001 ⫺0.0023 ⫺0.0006 0.0017 1.0903 ⫺0.0060 1.0911 ⫺0.0052

3010 d 59 3002 e 51


Table 7 is Computed CH bond lengths r (from Gaussian94), observed isolated stretching frequencies n CH and substituent effects Sr, Sn in fluoroethanes


213

Fig. 4. Correlations between reSiH and n isSiH for chlorodisilanes. Data from Table 5.

poor performance of the tz⫹ basis set lies in an overestimate of the gauche–trans difference, St ⫺ Sg for 1, which in turn appears to stem from the bond length for the trans CH bond. The presence of a diffuse function on fluorine in the basis set is clearly unhelpful. Apart from the tz⫹ value, the computed values of St ⫺ Sg in 1 are pleasingly close to that from r0. However, we note that all of the values of the gradients calculated are substantially less than that for the r0 correlation. Predictions of unobserved n isCH values are made in Table 9 using the MP2/tz correlation for six points in Table 8. Although the n isCH information available for the fluoro- and chloro-ethanes is admittedly limited, it is apparent that they do not exhibit the pleasing uniformity of behaviour found in alkanes at the SCF level [37–39], especially with regard to the a effects of halogen where a common offset value is clearly impossible in most cases. In the few situations where an overall fit to the data is roughly possible, the resulting gradients are much less than the value of 0:1023 × 10⫺3 A cm for the r0 correlation, which in turn suggests a significant variation in offset value throughout each series of compounds. For example, the gradient of 0:065 × 10⫺3 A cm for the MP2/tz plot for the fluoro-compounds suggests that a variation in ˚ occurs over the range offset value for re of 0.0023 A

from 1 to 11122, which is not negligible when ˚ in 0 compared with the absolute value of 0.0056 A for this basis set and level of theory (Table 7). The extent to which the above a effects can be ascribed to negative hyperconjugation must remain conjectural until such time as some independent means of assessing the latter can be found. 3.6. Comparison with experimental bond lengths 3.6.1. CF and CC bonds in fluoroethanes The general lack of comprehensive investigation, together with the changes that occur from one type of average geometry to another, means that there is effectively only one consistent set of experimental data that can be currently employed for the testing of the accuracy of QC calculations. This set is composed of the ra geometries determined by the GED method for all the fluoroethanes [56–64] as well as ethane itself [65]. The ra values chosen are listed in Table 10. Of these geometries, the more reliable ones are those from samples where only one conformer is present and even with these, inevitably assumptions have had to be made about the identity of non-equivalent bonds. Fig. 7 shows the plot of re for the CF bond determined at the MP2/6-31G ⴱ level against the ra value from the above GED studies.

214


Table 8 is a ⫹ b nisMH cm⫺1 : re MHA Linear regression data for correlation between reMH and n MH (A) Chlorodisilanes Level

HF HF HF MP2 MP2 MP2 MP2 B3LYP B3LYP B3LYP

Bond type

H Hx H xx H Hx H xx All H Hx H xx

Na

6 7 5 6 7 5 18 6 7 5

6-31G ⴱ(sv)

6-311G ⴱⴱ(tz)

a

⫺b × 10⫺3

⫺R b

a

⫺b × 10⫺3

⫺R b

2.124(75) 2.053(99) 1.904(70) 1.955(31) 1.944(35) 1.819(22) 1.936(14)

0.299(34) 0.267(46) 0.200(32) 0.216(14) 0.212(16) 0.155(10) 0.208(6)

0.975 0.935 0.964 0.991 0.986 0.994 0.992

2.108(82) 2.015(108) 1.882(81) 1.917(44) 1.874(51) 1.771(29)

0.291(38) 0.250(50) 0.190(37) 0.203(20) 0.185(24) 0.138(13)

0.968 0.914 0.948 0.981 0.962 0.987

2.064(51) 2.018(68) 1.894(49)

0.267(24) 0.246(31) 0.190(22)

0.985 0.962 0.980

(B) Fluoro- and chloro-ethanes Level/basis

Bond type

Fluoroethanes Na

HF/sv HF/tz MP2/sv MP2/sv MP2/tz MP2/tz MP2/tz⫹ MP2/tz⫹ B3LYP/tz B3LYP/tz B3LYP/tz⫹ B3LYP/tz ⫹ a b

H H H All H All H All H All H H

4 4 4 6 4 6 4 6 4 6 4 6

Chloroethanes

a

⫺b × 103

⫺R b

Na

a

⫺b × 103

⫺R b

1.299(12) 1.307(19) 1.269(31) 1.252(31) 1.297(29) 1.285(18) 1.272(48) 1.211(48) 1.301(30) 1.258(40) 1.311(34) 1.256(39)

0.072(4) 0.075(7) 0.060(11) 0.054(10) 0.069(10) 0.065(6) 0.061(16) 0.040(16) 0.070(10) 0.056(13) 0.073(11) 0.055(13)

0.997 0.993 0.970 0.932 0.981 0.984 0.935 0.779 0.980 0.902 0.977 0.902

6 6 6 9 6 9 6 9 6 9 6 9

1.415(5) 1.436(3) 1.302(25) 1.326(24) 1.322(22) 1.397(28) 1.304(32) 1.315(25) 1.406(26) 1.557(55) 1.416(26) 1.549(48)

0.112(2) 0.119(1) 0.071(9) 0.079(8) 0.078(7) 0.103(9) 0.072(11) 0.075(8) 0.106(9) 0.157(18) 0.109(9) 0.154(16)

1.000 1.000 0.972 0.966 0.983 0.972 0.959 0.958 0.986 0.955 0.988 0.963

Number of points. Correlation coefficient.

Every GED observation has been included. The scatter is better than might have been expected from the experimental uncertainties, with an R value of 0.978. The gradient of 0.769 indicates that overall the MP2 calculation is underestimating the effect of fluorine in changing the CF bond length. The MP2/tz and HF/sv gradients agree with the above value well within the standard error. The values of these gradients have the following significance. If the offset values for both re and ra were constant over the range of compounds, the gradient of each correlation plot would be unity. If the ra offset value alone is constant, which seems plausible at this stage, then the departure

from unity is due to variation in that for re, in which ˚ (MP2/sv) or case the latter decreases by 0.018 A ˚ 0.017 A (HF/sv) on passing from 1 to 111222. The precision of the experimental data makes it difficult to discriminate between a, gauche and trans effects. A partial remedy is to employ the alternative approach of comparing the larger changes of length which occur from one end of the series of compounds to the other. Since this on the experimental side will involve error in only two data, the proportionate effect of the latter is reduced due to the larger change in length involved. Table 11 shows the overall changes in rCF between the compounds 1, 111 and


215

Fig. 5. Correlations between reCH and n isCH for chloroethanes. Data from Table 6.

11122, for all of which calculations were available at the MP2/tz and B3LYP/tz levels. Between 1 and 111 we have the influence of two a effects, between 111 and 111222, that of one trans and

two gauche effects. The underestimate of both a and ggt effects on the CF bond at both HF and MP2 levels seems clear from the GED data. The B3LYP/tz calculations are marginally better than the others.

Table 9 is Predictions of n CH in fluoro- and chloro-ethanes Molecule

11 11 11 12T 12G 12G 112Cs 112Cs 112C1 112C1 112C1 1112 1122T 1122G a b c

Bond

CH xx CHgg CHgt CHgx CHgx CHtx CHtxx CHgtx CHgxx x CHgg CHgtx x CHggt CHgtxx CHgtxx

Fluoroethanes

Chloroethanes

˚) re(MP2/tz) (A

is n CH (pred) a (cm ⫺1)

˚) re(MP2/tz⫹) (A

is n CH (pred) b (cm ⫺1)

1.09208 1.09124 1.09117 1.09196 1.09272 1.09459 1.09386 1.09280 1.09111 1.09179 1.09159 1.09085 1.09084 1.09146

2975 2988 c 2989 c 2977 2965 2936 2947 2964 2990 2979 2982 2994 2994 2984

1.08919 1.08983 1.09182 1.09059 1.09085 1.08870 1.08974 1.08973 1.08968 1.08963 1.08956

3001 2992 2966 2982 2979 3007 2993 2994 2994 2995 2996

From re MP2=tz 1:28464 ⫺ 0:00006473nisCH ; s d 5:4 cm ⫺1 . From re MP2=tz⫹ 1:31455 ⫺ 0:00007510nisCH ; s d 6:5 cm ⫺1 . HF/tz values: 2987 cm ⫺1, Hgg; 2987 cm ⫺1, Hgt, s d 2:5 cm ⫺1 .

216


Fig. 6. Correlations between reCH and n isCH for fluoroethanes. Data from Table 7.

˚ The microwave 1–111 difference of 0.039 A derives from two different types of structure, rs and r0 [66,67] and its accuracy is likely to be very low.

Fig. 8 shows a similar plot for the CC bond in the fluoroethanes. The scatter here was somewhat greater than in that in Fig. 7 for the CF bond, with an R value of 0.940. With a gradient of 0.589, the MP2/sv bond

Fig. 7. Correlation between MP2/6-31G ⴱ(Gamess) re and GED ra values for the CF bond length in fluoroethanes. Analogous relationships are: re(HF/sv, Gamess) 0.275(50) ⫹ 0.784(37) ra, with R 0:981; re(MP2/tz, Gaussian94) 0.335(54) ⫹ 0.754(40) ra, with R 0:976:


217

Table 10 ˚ ) in fluoro- and chloro-ethanes Electron diffraction bond lengths ra (A Compound

CF

CC

Ref.

0 1 11 12T,G

– 1.397(4) 1.364(2) 1.389(2) b 1.384(1) 1.340(2) 1.387(8) 1.353(4) 1.389(6) 1.334(4) 1.350(2) 1.347 1.327 1.3246(20) a

1.5324(11) a 1.502(5) 1.498(4) 1.503(3) b 1.502(3) 1.494(3) 1.500(5)

[65] [56] [57] [58] [59] [60] [61]

1.501(4)

[62]

1.518(5) 1.525(4) 1.544(6) a

111 112Cs,C1 1112 1122T,G 11122 111222 a b

CCl

CC

Ref.

1.796(5) a

1.521(8) a

[68]

1.790(2)

1.531(3)

[69]

1.776(1)

1.58(ass)

[70]

[63] [56]

1.772(1)

1.542(3)

[71]

[64]

1.770(12)

1.566(20)

[72]

From rg ⫺ 12 =rg ; where rg is from electron diffraction data only. Values utilised.

length changes are only just over one half of those from the GED experiment. The corresponding HF/sv gradient is slightly lower at 0.506, the MP2/tz one a little higher, at 0.680. With the same assumption of

constancy of the offset value for ra, the re offset value ˚ (MP2/sv) or 0.027 A ˚ (HF/sv) on decreases by 0.021 A passing from 0 to 111. This is particularly striking when it is realised that the absolute values of the

Table 11 ˚) Overall changes in MX bond lengths (A Compounds

Bond

Method

Type

Source

1–111 a

111–111222 b

1–111222

Fluoroethanes

CF

HF/sv MP2/sv MP2/tz B3LYP/tz ED MW

re re re re ra rs / r0

Table 1 Table 1 This work c This work c Table 10 [66,67]

0.0477 0.0464 0.0455 0.0481 0.057(4) 0.039(?)

0.0138 0.0141 0.0147 0.0162 0.015(3)

0.0615 0.0605 0.0602 0.0643 0.072(4)

Chloroethanes

CCl

HF/sv MP2/sv MP2/tz⫹ B3LYP/tz ED MW

re re re re ra rs /r0


0.0211 0.0103 0.0110 0.0198 – 0.018(?)

0.0084 0.0110 0.0109 0.0136 –

0.0295 0.0213 0.0218 0.0334 0.026(13)

Fluorodisilanes

SiF

HF/sv MP2/sv ED/MW

re re rs,r0 /ra0

Table 1 Table 1 [79,80]

0.0250 0.0248

0.0080 0.0076

0.0330 0.0324 0.034(?)

Chlorodisilanes

SiCl

HF/sv MP2/sv MP2/tz B3LYP/tz

re re re re

Table 1 Table 1 This work c This work c

0.0264 0.0219 0.0257 0.0263

0.0145 0.0119 0.0131

0.0409 0.0338 0.0389

a b c

Effect of two a halogens. Effect of one trans and two gauche halogens. From Gaussian94 calculations.

218


Table 12 ˚) Overall changes in CC and SiSi bond lengths (A Compounds

Bond

Method

Type

Source.

0–111

111–111222

0–111222

Fluoroethanes

CC

HF/sv MP2/sv MP2/tz B3LYP/tz ED IR/MW

re re re re ra r0/rs


0.0278 0.0294 0.0294 0.0280 0.038(3) 0.0215(?)

⫺0.0270 ⫺0.0323 ⫺0.0380 ⫺0.0467 ⫺0.051(7)

0.0008 ⫺0.0029 ⫺0.0086 ⫺0.0187 ⫺0.013(6)

Chloroethanes

CC

HF/sv MP2/sv MP2/tz⫹ B3LYP/tz ED IR/MW

re re re re ra r0 / rs

Table 7 Table 7 This work a This work a Table 10 [35,74]

0.0066 0.0110 0.0145 0.0153

⫺0.0611 ⫺0.0640 ⫺0.0649 ⫺0.0763

⫺0.0545 ⫺0.0530 ⫺0.0505 ⫺0.0610 ⫺0.034(20)

HF/sv MP2/sv B3LYP/tz ED

re re

0.0227 0.0201

0.0101 0.0077

ra

Table 7 Table 7 This work a [77,78]

HF/sv MP2/sv MP2/tz B3LYP/tz ED

re re re re ra

Table 7 Table 7 This work a This work a [77,81]

0.0087 0.0095 0.0105 0.0066

⫺0.0041 0.0002 0.0024

Fluorodisilanes

Chlorodisilanes

a

SiSi

SiSi

0.0175(?) 0.0328 0.0278 0.0306 0.007(7) 0.0046 0.0097 0.0129 0.011(30)

From Gaussian94 calculations.

˚ (MP2/sv) or rCC offset value in 0 are only 0.012 A ˚ (HF/sv) (Table 7). 0.004 A The overall changes in the CC and SiSi bonds in the series 0, 111, 111222 are examined in Table 12. The calculated 0–111 changes in the fluoro-compounds are all less than those observed by the GED method, but the latter’s result for the 111–11122 change is bracketed by the MP2/tz and B3LYP/tz values. 3.6.2. CCl and CC bonds in chloroethanes Amongst the chloroethanes, GED rg or ra geometries are available for 1 [68], 12 [69], 112 [70], 1122 [71] and 111222 [72], Table 10. These are barely adequate to define a meaningful correlation. However plots for the MP2/6-31G ⴱ data similar to those in Figs. 7 and 8 but for the CCl and CC lengths are shown in Figs. 9 and 10. The gradients differ from unity in opposite directions, again suggesting significant changes in offset value, both negative and positive. While the gradient for the CCl bond at the HF level is unity within the standard error, the latter is so large in these chloro-compounds that more experimental

data will be needed before much reliance can be placed on these correlation parameters. Spectroscopic geometries have been determined recently for 1 (rs) [73], 11 (rs, r0) [74], and 12G (rs, r0) [74]. Older r0 structures are available for 111 [75,76]. The CC length in 111 is particularly difficult to define [74]. The overall changes in the CCl and CC lengths in the series 0, 1, 111, 111222 are shown in Tables 11 and 12. In neither the electron diffraction nor the spectroscopic bond lengths is there sufficient precision to evaluate the QC calculations. We note a substantial difference between the MP2 and B3LYP contractions in the CCl distances, but a fair agreement between these two calculations over the changes in the CC ones. 3.6.3. SiF and SiSi bond lengths in fluorodisilanes Table 13 lists the very few existing experimental studies of fluoro and chlorodisilanes. GED structures are reported for 0 [77] and 111222 [78,79], while spectroscopic data are available for 0 (r0) [36] and 1 (r0/rs) [80]. From these data we can at this stage only


219

Fig. 8. Correlation between the MP2/6-31Gⴱ(Gamess) re and GED ra values for the CC bond length in fluoroethanes. Analogous relationships are: re(HF/sv, Gamess) 0.746(101) ⫹ 0.506(67) ra, with R 0:917; re(MP2/tz, Gaussian94) 0.488(99) ⫹ 0.680(65) ra, with R 0:953:

compare the GED and ab initio changes in the SiSi distance from 0 to 111222, as in Table 12. All three QC calculations predict a greater lengthening than is found experimentally, which indicates that marked increases in offset value are occurring.

3.6.4. SiCl and SiSi bond lengths in chlorodisilanes The only data here are from the solitary GED study of 111222 [81]. The SiSi distance in this compound is too inaccurate for a change from 0 to be defined.

Fig. 9. Correlation between the MP2/6-31G ⴱ(Gamess) re and GED ra values for the CCl bond length in chloroethanes. Analogous relationships are: re(HF/sv, Gamess) 0.125(278) ⫹ 1.070(156) ra, with R 0:908; re(MP2/tz⫹, Gaussian94) 0.359(251) ⫹ 0.796(141) ra, with R 0:872:

220


Fig. 10. Correlation between the MP2/6-31G ⴱ(Gamess) re and GED ra values for the CC bond length in chloroethanes. Analogous relationships are: re(HF/sv, Gamess) ⫺0.860(338) ⫹ 1.556(220); ra, with R 0:954; re(MP2/tz⫹, Gaussian94) ⫺0.757(380) ⫹ 1.487(247) ra, with R 0:937:

4. Conclusions The principal impression left by this survey of four series of comparatively simple and well-known compounds must be the lack of suitable experimental data with which the validity of our QC calculations can be quantitatively tested. Not only are there many of these molecules for which no structural work has yet been reported, but for a number where such studies have been made, rz geometries which reconcile spectroscopic and GED measurements are lacking. With the ready availability of good scaled QC force fields, there is a strong case for the reworking of data already Table 13 ˚ ) in fluoro- and chloroExperimental SiX and SiSi bond lengths (A disilanes Compound

Geometry type

Si–Si

Si–X

Ref.

0

ra r0

2.331(3) 2.3317(15)

– –

[77] [36]

1

r0,rs

2.332(5)

1.598(8)

[80]

111222 (F)

ra rao

2.324(6) 2.317(6)

1.569(2) 1.564(2)

[78] [79]

111222 (Cl)

ra

2.32(3)

2.009(4)

[81]

in the literature. A very desirable objective is the replacment of the older correlations between r0 and n is [6,36] with similar ones between rz and n is. This would permit incorporation of structural data from molecules which have previously been excluded, for example, dichloromethane [82]. The opportunity should also be taken of building into each structure determination constraints from parallel QC calculations [83]. This applies particularly to GED studies of molecules such as 1,2-dihalogeno-, 1,1,2- trihalogeno- or 1,1,2,2-tetrahalogenocompounds, where several conformers are present, but could also be useful in spectroscopic studies, especially those involving the monoisotopic element fluorine. Constraints of this kind should be fine-tuned using correlations such as those in Figs. 4–10. For the study of CH and SiH bonds, it seems likely that isolated stretching frequencies will continue to be a major source of information concerning the validity of QC predictions and here there is also an urgent need for new data, particularly for fluoro-compounds.9 While the preparative problems involved in obtaining such data for CH bonds can be considerable, for SiH ones the 9 For the precision needed, FTIR spectra should be obtained using a resolution of at least 0.5 cm ⫺1.


221

Table 14 Optimization tests for Si2Cl6 using Gamess and Gaussian94 (HF/sv level) Start a

Refined geometry Gamess

Gaussian94

a

b

c

a

b

c

a

b

c

2.347 2.300

1.468 2.500

114.6 114.0

2.348847 2.348849

2.042141 2.042138

109.70259 109.70261

1.800

2.100

114.0

2.348839

2.042137

109.70254

2.800 2.000

2.100 1.800

114.0 105.0

2.348833 2.348835

2.042138 2.042147

109.70294 109.70280

2.000

1.800

118.0

2.348846

2.045138

109.70261

2.348324 2.348340 2.348335 b 2.348370 c 2.348404 b 2.348329 2.348336 2.348282 b 2.348273 c 2.348263 b

2.040390 2.040389 2.040389 b 2.040387 c 2.040384 b 2.040390 2.040391 2.040387 b 2.040389 c 2.040391 b

109.6837 109.6837 109.6836 b 109.6834 c 109.6831 b 109.6837 109.6836 109.6840 b 109.6839 c 109.6838 b

a b c

˚ ); b r(SiCl) (A ˚ ); c ⬔SiSiCl (⬚). a r(SiSi) (A Oscillatory finish. Average of penultimate and last steps.

infrared bands required are normally readily identified in the spectra of fully deuterated materials and even when these are highly impure, identification through ab initio calculations can be straightforward [30]. Within the limitations imposed by our existing information, the present study establishes the following points: 1. There is clear evidence for distinctive a, gauche and trans effects of halogen on CH and SiH distances. The contraction predicted at the HF level due to an a halogen is markedly reduced when electron correlation is introduced, even reversed in the case of fluoroethanes. gauche effects lead to small well-defined contractions in both fluoro- series and in chlorodisilanes. In chloroethanes, the contractions are smaller, particularly with electron correlation, and are more variable. The trans effect of halogen is usually negligible throughout all four series of compounds. 2. For MX bonds, contractions due to a halogen are large and well-defined except in the case of chloroethanes. gauche effects produce significant contractions which are well-defined in all four series, chlorine consistently producing a larger effect than fluorine. trans halogen produces changes which are variable, especially in the chloroethanes, and except in the latter, negative.

3. Evidence from experimental n is values confirms the trends in CH and SiH distances due to gauche and trans halogen substitution computed at all levels, and also the corresponding a effects at the MP2 level, when the appropriate basis is used. The quantitative success of the QC calculations is variable. Changes in CH distances in fluoroethanes are likely to be underestimated as substitution increases. 4. Computed changes in CF and CCl distances are smaller than those observed experimentally, while those for the CC bond are either too low, as in the fluoroethanes, or too high, as in the chloroethanes. 5. On the assumption that offset values (exp.–true) of r0 and ra for a given type of bond are constant, the offset values (calc.–true) for the re distances calculated here using a given basis set and level of theory, with a few possible exceptions, vary markedly over the range of compounds.

5. Note added in proof An important paper bearing on the question of constancy of re and ro values for the CH bond has been brought to our attention. A correlation between recent experimental values of reCH and n isCH has the

222

B. Fodi et al. / Journal of Molecular Structure (Theochem) 500 (2000) 195–223 ⫺5

˚ cm [84]. Some of the gradient 7.18(17) × 10 A gradients in Table 8B lie close to this value indicating that in these cases, the reCH(QC) offset value is not varying. However, it follows from the gradient of the roCH ˚ cm, that the offset versus n isCH plot, 10.23 × 10 ⫺5 A value for r0CH must itself be varying.

[8] [9] [10] [11]

Acknowledgements

[15] [16]

We thank Dr R. Stolevik and Dr K. Kuchitsu for helpful information, and Dr B.A. Smart and Dr C.A. Morrison for generous assistance in using the Gaussian94 program on the Edinburgh ab initio facility, supported by EPSRC grant GR/K/04194. We thank the EPSRC also for a work station on which some of the Gamess calculations were performed and Edinburgh University for time on the Cray T3D computer for the remainder.

[12] [13] [14]

[17] [18] [19] [20] [21] [22]

[23]

Appendix Table 14 shows the structural parameters for Si2Cl6 optimized in the Gamess and Gaussian94 programs, starting from widely differing geometries. The reproducibilities found in the SiCl bond length and SiSiCl angle are comparable. However the Gamess results for the SiSi length are slightly less variable than the Gaussian94 ones. The oscillatory nature of some of the latter was a rare occurrence amongst all the compounds studied. The small, consistent differences between the Gamess and Gaussian94 values mirror those reported previously in chlorodisilanes [30] and seen in comparisons of the data in Table 1 with those in Tables 5–7, for the same level and basis set.

[24] [25] [26] [27] [28] [29]

[30]

[31] [32] [33] [34] [35]

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