2222
J . Phys. Chem. 1989, 93, 2222-2230
strength and decreasing the C-0 bond strength. The high quality of the EXAFS data obtained in this work allows more than a determination of differences in C-0 distance with respect to the reference compound; the data also provide information about the differences in the M-C-0 angles. As the enhancement of the M-O* contribution is a function of M-C-0 angle (the enhancement being stronger when the M-C-0 angle approaches 180°3),enlargement of the M-C-O angle with respect to the Os-C-0 angle in the reference compound O S ~ ( C O )is, ~ indicated in the EXAFS data analysis by a larger N and/or a smaller Ao2 for the M-O* contribution with respect to the M-C contribution. From theoretical calculations3 it may be concluded that in the case of low-Z scatterers like oxygen, a change in M-C-O angle may well be approximated by a change in A$ only. For both the H3Re3(CO)12and the [H2Re,(C0)12]-clusters, the Debye-Waller factors characterizing the Re-C and Re-O* shells do not differ beyond the accuracy of fO.OO1 AZ(Table 11). This result implies that the mean Re-C-0 angle in these complexes is approximately equal to the Os-C-O angle in O S ~ ( C O ) , ~ ,
viz. 169'. In the XRD structure determination Gf [HRe3(C0),,]*a mean Re-C-0 angle of 1 6 9 O was found as well.lz Thus, we infer that there is only very little influence of the overall charge on the cluster (and thus the extent of s-back-bonding) on the Re-C-0 angle. In summary, with the aid of good reference compounds, it is very possible to do a rather complete structure determination of a metal carbonyl with EXAFS. Special attention must be paid to the choice of references for the metal-carbonyl contributions because of the multiple scattering effect.
Acknowledgment. This research was supported by the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the Exxon Education Foundation. The assistance of the staffs of the Stanford Synchrotron Radiation Laboratory and the Brookhaven National Synchrotron Light Source is gratefully acknowledged. Registry No. H3Re3(cO),,, 73463-62-4; [H2Re3(C0),,]-,51779-06-7; [(C,H,),As] [H,Re3(CO),,], 12406-79-0; Re, 7440- 15-5.
Ab Initio Computation of Silicon-29 Nuclear Magnetic Resonance Chemical Shifts for a Range of Representative Compounds John R. Van Wazer,* Carl S. Ewig, and Robert Ditchfield+ Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235 (Received: March 12, 1988)
29SiNMR shielding tensors (and the chemical shifts derived therefrom) were calculated for 28 representativesilicon compounds, employing optimized molecular structures and a split-valence contracted basis set, both with and without d functions on the silicon, in a gauge-invariant representation. The larger of these two basis sets, 6-3 lG(*), agreed with experimentalchemical-shift data as well or slightly better than did reported computations employing larger basis sets. The following substituent-substitution series of compounds were investigated: SiH4/SiF4,SiH4/Si(CH3)4.Si(CH3)4/SiF4,and part of two series involving the SiCI4 molecule. Since these series of molecules show a wide range of "Si chemical shifts, with the shift values plotted for some series exhibiting a pronounced hump rather than a linear form, they represent a good test of the theoretical approach employed. Within these series and within a group of silyl derivatives, the calculated and experimental chemical-shift data agreed quite well. A group of disilicon compounds, H$i-X-SiH3 with X = nothing, 0, NH, and CH2, were also studied, as was the SiF2- anion and some other structures considered to be exemplifications. The effects on the shielding of rotational isomerization as well as of induced geometrical and electronic changes were investigated for several molecules. The paramagnetic and diamagnetic contributions to the magnetic shielding were analyzed, and an apparent relationship between the 29Siparamagnetic term and the electron-withdrawing power of the substituents on the silicon was found.
Introduction Because of a low gyromagnetic ratio, low sensitivity, and meager isotopic abundance, nuclear magnetic resonance (NMR) based on the 29Siisotope, although available,' was not employed by preparative chemists for the characterization and analysis of silicon-containing molecules until after commercialization of the Fourier transform technique for NMR. Now however, 29SiNMR has become a standard tool for use in both inorganic and organic silicon chemistry. Moreover, few preparative chemists today still think of silicon as merely a misbehaving carbon analogue. Hence silicon chemistry is finally beginning to be treated as a field in its own right, so that its typical features, such as (1) the rarity of substituent numbers (Le., the number of nearest-neighbor bonded atoms) other than four in stable species and ( 2 ) the omnipresence of redistribution reactions involving the scission of any bond to silicon other than the Si-C bond, are now being exploited rather than studiously ignored. As a result, silicon chemistry is flourishing, and many new chemical structures of potential practical importance are being found (essentially all with tetracoordinate silicon). 'Chemistry Department, Dartmouth University, Hanover, N H 03755.
0022-3654/89/2093-2222$0l.50/0
Concomitant with the evolution of experimental silicon chemistry, during the past 15 years there has been a rapid development of practical, nonempirical quantum-chemical techniques for computing molecular properties of interest to experimentalists. These include details of molecular geometry and those physical properties characterizable in terms of the overall electron distribution. Although the parameters that predicate N M R spectra have proven to be a challenge to compute, for both theoretical and computational reasons, advances in these areas now permit these parameters to be obtained to a useful level of accuracy by ab initio methods for several active nuclei. The work reported here represents the initial application to the 29Sinucleus of an ab initio self-consistentfield (SCF) method using "gauge-invariant" atomic orbitals2 (the GIAO method). This m e t h ~ d ,which ~ , ~ has successfully been applied to a number of (1) Holzman, G. R.; Lauterbur, P. C.; Anderson, J. H.; Koth, W. J. Chem. Phys. 1956, 25, 172. (The first published compilation of 29Sichemical shifts.) (2) Jameson, C. J. Nuclear Magnetic Resonance, Vol. 12, Royal Society of Chemistry: London, 1983; p 1. (3) Ditchfield, R. Mol. Phys. 1974, 27, 789; also described in J . Chem. Phys. 1976, 65, 3123. (4) McMichael Rohlfing, C.; Allen, L. C.; Ditchfield, R. Chem. Phys. 1981, 63, 185.
0 1989 American Chemical Society
29SiN M R Chemical Shift Computations
The Journal of Physical Chemistry, Vol. 93, No. 6,1989 2223
magnetic nuclei, treats each molecular orbital as a linear combination of the gauge-invariant atomic functions. Use of such gauge factors eliminates the dependence of calculated magnetic properties on the choice of the coordinate origin used to define the magnetic field. In addition, gauge-invariant atomic functions enable the basis set to incorporate the perturbation produced by the external magnetic field. Using such an approach, quite satisfactory results can be obtained for chemical shielding even with moderately sized split-valence basis sets (e.g., n-31G). The molecular wave functions are determined by solving the perturbed Roothaan equations with the approach described previ~usly.~-~ If gauge-invariant orbitals are not employed, a large basis set is required to minimize the dependence of the calculated magnetic properties on the coordinate origin used to specify the field and to describe the perturbation produced by the magnetic field. Five prior publication^^-^ describe the use of such an approach (the CHFPT method) for the ab initio computation of 29Simagnetic shielding in seven silicon compounds. A procedure involving use of individual gauges for localized orbitals (the IGLO method) has also recently been appliedI0 to computing the magnetic properties of some silicon compounds. In addition, the ab initio equations-of-motion method has been used” for 29SiN M R computations. In this paper we first summarize the computational method and the properties to be obtained and compare our results with those by other authors. We then report computed %i N M R parameters for a number of compounds, most of which we divide into two classes. The first class is comprised of compounds in a substitution series based on a single quadruply coordinated silicon atom. Since neighboring species in a series are closely related structurally and many series have been thoroughly studied experimentally, they provide a useful means of testing the accuracy of the calculations in determining systematic shielding or chemical-shift differences. Members of one series are also employed to compare the use of computed versus experimental molecular geometries in calculating accurate chemical shifts. The second main class of compounds treated below contain an SiH, moiety with a variety of groups (some containing Si) comprising the fourth substituent. Then the results are interpreted for each cmpound studied, in terms of the total electron-withdrawing power of all of the substituents. We further interpret our findings for selected species in terms of the individual shielding components, molecular structures, and basis sets and compare the accuracy of our computed chemical shifts with the few previous ab initio molecular-orbital r e s ~ l t s for ~-~~ which experimental shifts have been reported.
Calculational Details1* The geometrical parameters for each of the molecular structures considered in this study were optimized with the GAUSSIAN 82 program1, in the 6-31G basis set*4and for anions in a 6-31++G basis.I2 For a few compounds, such optimizaton was also done in a 6-31G(*) basis,lS for which the (*) notation indicates that d functions were added to the silicon atoms only. The N M R shielding tensors (and the mathematical analyses thereof) were computed with the Ditchfield ab initio self-consistent field pro( 5 ) Lazzeretti, p.; Zanasi, R. J . Chem. Phys. 1980, 72, 6768. (6) Lazzeretti, P. Tossell, J. A. J . Chem. Phys. 1986, 84, 369. (7) Tossell, J. A,; Lazzeretti, P. Chem. Phys. Lett. 1986, 128, 420. (8) Tossell, J. A.; Lazzeretti, P. Chem. Phys. Letf. 1986, 132, 464. (9) Tossell, J. A,; Lazzeretti, P. J . Phys. B A?. Mol. Phys. 1986,19, 3217. (10) Fleischer, U.; Schindler, M.; Kutzelnigg, W. J . Chem. Phys. 1987, 86, 6337. (1 1) Fronzoni, G.;Galasso, V. Chem. Phys. 1986, 103, 29.
(12) For an up-to-date review of several of these topics see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. A b Initio Molecular Orbital Theory; John Wiley: New York, 1986. (13) Binkley, J. S.; Whiteside, R. A,; Raghavachari, K.; Seeger, R.; DeFrees, D. J.; Schlegel, B. J.; Topiol, s.;Khan, L. R.; Frisch, M. J.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82, Carnegie-MellonUniversity, Pittsburgh, PA. (14) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257. (15) (a) Hariharan, P. C.; Pople, J. A. J . Chem. Phys. 1973, 28, 213. (b) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; De Frees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3645.
TABLE I: Comparison with Experiment of Chemical Shifts Calculated by Various Methods 29Sichem shifts referenced to silane CHFPTb9 IGLO’O GIAO“ 139,3/95,1/8,1b 117,2/95,1/5,1b 1610,1/104/46 molecule 65,3/43,1/6,lC 76,2/43,1 /3,1c 43,l /32/2c*d exptl19 Si2H6 -2 1 -1 1 -9 -13 SiH,F +49 +74 +65 +75 SiH2F2 +23 +61 +62 +64 SiHF, -3 1 +22 +20 +15 SiF4 -76 -9e -18 -2 1 SiF2-131 -97 -95 SiO2-3 1 (-40)’ +20 From the work reported below, using Pople-type orbitals. The 631G(*) orbital (of this type) for silicon consists of a contracted description of the 1s part of the core by six Gaussian primitives, with the 2s and 2p parts each similarly consisting of six Gaussians exhibiting the same exponents for the s and the p (being the so-called sp orbitals) but with appropriately different coefficients. The valence associated with this core consists of four sp Gaussians contracted into a pair of sp Slater functions (with three of the Gaussians making up the inner one), plus a d function. For all functions, the exponents and contraction coefficients were simultaneously optimized for the atom. The (*) indicates that a d polarization function was employed only for the silicon atom. bPrimitives. The notation 139,3/95,1/8,1 refers to 13 s, 9 p and 3 d Gaussian primitives to describe the Si, 9 s, 5 p, and 1 d for the F, and 8 s with 1 p for the H. For emphasis, the polarizing functions are separated by a comma from the other primitives. cContraction. dBetter known as 6-31G(*) and referred to as “with d” in subsequent tables. ‘A value of -15 from a larger basis set, 117,3/95,2 apparently contracted to 95,2/43,1. /Value corresponding to a 6-31G (nod) basis set, with sp plus functions added to the Si and 0 atoms in the sio44anion.
gram3s4employing a “gauge-invariant” treatment of the contracted basis functions for each atom, using two basis sets, 6-31G (the “no-d” basis) and 6-31G(*) (the “with-d” basis) and molecular geometries previously optimized in the 6-3 1G basis. Similarly, the shielding tensors of anions were obtained by using the same basis sets with added appropriate sp exponents (denoted by the symbol) on all atoms to allow for the molecular enlargement due to the excess of negative charge in the structure. These basis sets are called “no-d, plus” and “with-d, plus”. To make the subsequent text clear to persons not familiar with the details of N M R theory, it is helpful to review here briefly the phenomenon of magnetic shielding (a) and the terminology employed in its description: Without affecting the distribution of the electronic charge in an atom or molecule, an applied magnetic field induces electronic currents in this distribution, thus producing local magnetic fields that oppose the applied field and hence result in shielding of the atomic nuclei from it. Because the local environment of a magnetically active nucleus in many molecules is anisotropic, this shielding will in general be described by a tensor with nine independent elements. Only the symmetric portion of the tensor is measured with standard N M R techniques, and six quantities are required to specify this part. In the work reported here we consider just the symmetric part of the shieding tensor in terms of its three principal values and the three Euler angles16 defining the orientation of the principal-axis framework with respect to the chosen molecular coordinates. For molecules for which the nuclear-site symmetry is C,, or greater, the number of independent quantities required is reduced to two or one. The ,,, and uzz) three terms of the symmetric shielding tensor (axx,a are presented here along with an isotropic value (aiso= [axx+ uyyr u z z ] / 3 ) . It is aao that corresponds to the rotationally averaged N M R chemical shift (6) as usually measured in fluids. The calculhted shielding consists of two parts: a large positive term called the diamagnetic shielding, and a widely ranging
++
+
~~~~~
~
(16) For the SiH2(CH,),, SiH2F2.SiNSO, H3SiCH2SiH3,and H3SiNH,, the SiH3 molecules, which exhibit Si nuclear-site symmetries lower than C information presented in Tables I and 111 is incomplete, since the molecular orientation and Euler angles are missing. Investigators requiring this missing data may request it by writing to the principal author.
2224
The Journal of Physical Chemistry, Vol. 93, No, 6, 1989
Van Wazer et al. TABLE 11: Computed Total Shielding Tensors“ for the Methylsilanes and Fluorosilanes (Using 6-31G Optimized Geometries) in a 6-31G Basis Set (without and with d Functions)
-125
-100
-7s
-50
-25
0
25
50
Si-29 Chemical Shift (ppm)
Figure 1. Experimental N M R chemical-shift datai6for several substitution series of silicon compounds showing the pronounced bowing of the curve to be found for the silyl and permethylsilyl fluorides.
negative term (somewhat smaller in absolute value than the diamagnetic contribution) called the paramagnetic shielding, the value of which is highly dependent on the molecule and the basis set. Each of these parts is in itself a shielding tensor with an associated isotropic value. They add together to give the total shielding, which of course may also be expressed in terms of a tensor and its isotropic value. All of these contributions are obtained in an ab initio fashion from the computer program3s4we employed. Comparison of Methods
The reported comparisons4 of 13C shielding computations with gas-phase experimental chemical shifts as well as our preliminary studies dealing with 31P N M R computations (a part of which is presentedI7 in a book chapter) led us to believe that meaningful computed values of N M R chemical shifts should be obtainable from a 6-31G(*) basis set. For those compounds for which intercomparisons can be made, our results by the GIAO method in this with-d basis are compared in Table I with those reported for larger basis sets by Tossell and Lazzaretti- using the CHFPT method and by Kutzelnigg et al.1° employing the IGLO method. It is clear that our GIAO computations and the IGLO ones generally agree better with the experimental chemical shifts (corresponding to concentrated liquids) than do the CHFPT computations, although the latter work involves the largest basis sets, which still seem to be insufficient for the CHFPT method. However, it is gratifying to see how similar are the results from the three different theoretical approaches. For the SiH4 molecule, for which the energy is dominated by the silicon contribution, the S C F energy obtained with the basis set used in the IGLO computations is only 0.008 hartree lower than we obtained using the with-d basis, while the energy obtained with the basis set used with the CHFPT procedure is 0.036 hartree lower. For SiF4 these differences are greater, being 0.22 and 0.27 hartree, respectively, due to the use of a d function on each fluorine in both the IGLO and CHFPT computations. Kutzelnigg et al. have also reported the effect of omitting d functions, and their reported changes in chemical shift due to this omission are about the same as we observe. From this table it appears that our choice of basis set is not the main contributor to the occasional poor agreement between the experimental chemical shift obtained on concentrated liquids and our theoretical computation of it, as reported in the following sections. Interactions with neighboring molecules in the liquids causing a significant difference between t h e c h e m i c a l shift for t h e liquid and gas phases are thought to be considerably more significant. (More is said in the Conclusion of this paper about the comparison between the GIAO, IGLO, and CHFPT results reported in Table I.)
Substitution Series of Molecules In silicon chemistry, much of which is under thermodynamic control and hence is often dominated by scrambling reactions,I* (17) Van Wazer, J. R.; Ditchfield, R. In Phosphorus N M R in Biology; Burt, C . T., Ed.; CRC Press: Boca Raton, FL, 1987; Chapter 1, pp 1-23. (18) Van Wazer, J. R. In Homoatomic Rings, Chains, and Macromolecules of The Main-Group Elements; Reingold, A L., Ed.; Elsevier: Amsterdam, 1977; Chapter 1, pp 1-24. Also see: Van Wazer, J. R. Ann. N.Y. Acad. Sci. 1969, 159, 5 .
Si(CHd4 (with 6 d’s on Si) Si(CH3), rotamer (with 6 d’s on Si) SiH(CH,), (with 6 d’s on Si) SiH(CH,), rotamer (with 6 d’s on Si) SiHdCHd, (with 6 d’s on Si) SiH2(CH3)2rotamer (with 6 d’s on Si) SiH,(CH3) (with 6 d’s on Si) SiH, (with 6 d’s on Si) SiH,F (with 6 d’s on Si) SiH2F2 (with 6 d’s on Si) SiHF, (with 6 d’s on Si) SiF, (with 6 d’s on Si)
484.5 447.9 495.2 457.1 509.7 470.3 518.5 419.6 518.7 476.4 520.1 477.9 524.9 480.4 565.5 518.0 441.9 421.2 437.8 427.5 494.2 482.4 540.2 536.2
484.5 447.9 495.2 457.7 509.7 470.3 518.5 479.6 490.1 449.2 493.1 452.1 524.9 480.4 565.5 518.0 441.9 421.2 479.7 443.8 494.2 482.4 540.2 536.2
484.5 447.9 495.2 457.7 478.5 441.5 483.2 444.2 545.2 504.2 547.7 507.1 571.3 527.4 565.5 518.0 559.4 508.3 498.8 495.3 528.4 529.5 540.2 536.2
484.5 447.9 495.2 457.7 499.3 460.7 506.8 457.8 518.0 476.6 520.3 479.0 540.4 496.1 565.5 518.0 481.1 450.2 472.1 455.6 505.6 498.1 540.2 536.2
” T h e above shielding tensors may be referenced to TMS by subtracting them from 484.5 ppm for the data calculated without d functions or from 447.9 ppm for the data with 6 d functions on each silicon.
the series of molecules resulting from stepwise scrambling of one kind of substituent (or nearest-neighbor atom) with another are of considerable practical importance. Moreover, as illustrated by Figure 1, experimental 29SiNMR chemical shift^'^,^^ commonly show considerable deviation from linearity across such a substitution series, particularly for the substitution of either hydrogen or an alkyl group by a halogen. In contradistinction to experimental chemical shifts, which are usualy determined as differences in isotropic shielding values between species, quantum calculations give the chemical-shielding tensor for each nucleus directly, as referenced to the bare nucleus (29Si14+ in this case). As an initial example the calculated principal elements of the 29Sishielding tensors as well as uisofor the methylsilanes and fluorosilanes are presented in Table 11. In addition, data on rotational isomers are compared here for Si(CH3)4, SiH(CH&, and SiH2(CHJ2. Comparison ofSi(CH3),,H+,, Rotamers. For tetramethylsilane (the usual 29Sichemical-shift reference standard) the stable form exhibits Td symmetry in which all of the methyl hydrogens are positioned over the faces of the tetrahedron of carbon atoms; whereas the other rotamer of Td symmetry, which we compute in the no-d basis set to be less stable by 6.3 kcal, corresponds to the hydrogens sitting above the edges of this tetrahedron. Our computations, with or without d functions, show an increase in shielding of 10.8 ppm of the magnetic field upon going from the stable symmetrical rotamer to the less stable one. For trimethyisilane both rotamers studied exhibit C,, symmetry, with the less stable one (by 4.1 kcal) corresponding to one hydrogen of each methyl group pointed inward toward the C3 axis, while one of the hydrogens of each methyl group points outward away from the C3 axis for the stable conformer. Values of 7.5 ppm (no d) and 7.1 ppm (with d) were found for the increase in isotropic shielding upon going from the more stable to the less stable rotamer. The more stable isomer of dimethylsilane that was treated corresponds to a hydrogen on each methyl group pointing away from the other group, while the less stable one (by 1.2 kcal) has (19) Marsmann, H. In N M R Basic Principles and Progress; SpringerVerlag: Berlin, 1981; Vol. 1, p 65, gives a good review of 29Sichemical shifts. Also see ref 16. (20) Williams, E. A . Annu. Rep. N M R Spectrosc. 1983, 15, 235-89.
The Journal of Physical Chemistry, Vol. 93, No. 6,1989 2225
29SiN M R Chemical Shift Computations
,n
0-
.
v
0
2 3 Number of Methyl Groups 1
0
4
Figure 2. Calculated and experimental total isotropic chemical shifts for the methylsilanes, the H / C H 3 substitution series of molecules. The calculated chemical shifts were obtained by subtracting the average shielding constant of the compound from that of tetramethylsilane in the same basis set.
these two hydrogens pointing toward each other. Again for this molecule, adding Si d functions has little effect on the computed increase in the shielding of 2.4 ppm upon going from the more to the less stable rotamer. Note that for all three of these molecules the sign and magnitude of the difference in shielding between rotamers may be empirically correlated to their relative thermodynamic stabilities, corresponding to ca. 1.8 ppm/kcal of destabilization. Comparison with Experimental Shifts. Although most of the available experimental 29Sichemical-shift data19-20 correspond to neat liquids or very concentrated solutions, the wide range of shifts and the reported relatively small19 solvent effects indicate a reasonable probability for the computed shielding values (corresponding to infinitely dilute gases with no nuclear motion) to correlate to a useful degree with such data. A good way to test this hypothesis is to compare the experimental and calculated shifts for several of the substitution series of compounds. Let us start with the methylsilanes, since tetramethylsilane (TMS) is the usual shift reference standard. The isotropic shielding constants (qSJof Table 11, which conceptually are referenced to the hypothetical bare silicon nucleus, can be converted to chemical shifts referenced to gaseous T M S by subtracting2I the isotropic shielding of the chosen compound from that shown for TMS, all calculated in the same basis set. This means that the chemical shift (6) is given by 6 2 uTMS - u, where for the no-d computations uTMS= 484.5 ppm and for the with-d uTMS= 447.9 ppm. The computed chemical shifts obtained in this manner are plotted along with experimental data corresponding to a concentrated liquid phase in Figure 2. From this it can be seen that the shifts from Si(CH3)4to SiH4 are systematically larger for the experimental data than for the 6-31G computations, which in turn are larger than for the 6-31G(*) computations. This fact is shown in quantitative form for any value of n between 0 and 4 in Si(CH3),H4-, by the following equations obtained by curve fitting of the data of Figure 2: exptl
6 = -93.4
6-31G calcd
6 = -81.4
6-31G(*)calcd
6 = -70.2
+ 31.0n - 1.94n2 + 27.3n - 1.74n2 + 23.8n - 1.56n2
(1) (2)
(3)
The differences between the d and no-d values may indicate that the main problem for this molecular series is that neither basis set is sufficiently large to give precise results (although the calculated values are satisfactory for many practical purposes); but it could also be due to a systematic change across the series due t o either the as-yet-unknown difference between the gaseous and (21) Originally chemical shifts were reasonably defined so as to increase with the magnetic shielding. However, this meant that the 'H shifts of common organic compounds were all negative with respect to the experimentally desirable reference compound TMS. Since this abundance of negative signs was offensive to many organic chemists, it was finally resolved to reverse the sign of the chemical shifts of all nuclei. Thus the conversion from shielding ( u ) to shift (6) is now obtained from the relationship 6 = urtd - u rather than from 6 = u - usld.
1 2 3 4 No. of Fluorines in the Fluorosilane Molecule
Figure 3. Calculated and experimental total isotropic chemical shifts of the fluorosilanes, as referenced to tetramethylsilane.
TABLE 111: Comparisons of Computed and Experimental Geometries' for Three Molecules in the Fluorosilane Substitution Series (A) Data
SiH4 parameter Si-H Si-F LHSiH calcd uIso,no d calcd uIso,with d exptl tii,,
exptl calcd 1.481b 1.4917 567.3 565.5 519.2 518.0 -92.5
SiH3F
SiF4
exptl calcd exptl calcd 1.485b 1.4837 1.593 1.6822 1.555' 1.6253 110.5 111.03 486.7 481.1 548.1 540.2 457.1 450.2 540.4 536.2 -17.4 -113.0
(€3) Shift Differences
source exptl AL3im Auiso,no d Auisarwith d
SiH4 to SiH3F exptl calcdC +75.1 +84.4 +80.6 +62.1 +67.8
SiH, to SiF, exptl
calcdc -20.5
+19.2 -21.2
+25.3 -18.2
'Distances in angstroms, angles in degrees, and shielding in ppm, while *uiso,no d" refers to the 29Siisotropic total shielding as computed in the 6-31G basis, "qs0, with d" to the same value as computed in the 6-31G(*) basis, and "exptl 6i," to the reportedI9 chemical shift for the liquid phase. *References 22 and 23. CGeometryoptimized only in the 6-3 1G basis set but employed for NMR shielding computations in both the 6-31G and 6-31G(*) bases.
liquid chemical shifts or the disregardance of certain electroncorrelation effects. A similar set of curves is presented for the fluorosilanes in Figure 3 with the experimental datal9 again corresponding to a concentrated liquid phase. It is readily seen that part of the poorness of fit is due to the choice of the reference standard. If H3SiF had been chosen as the reference compound, or SiH4 as was done in Table I, the experimental and the computed with-d curves would have matched better (see Table I), although there would still be a discrepancy between the no-d and the with-d data points for the other fluorosilanes. For this series it would appear that the with-d basis gives the more acceptable representation. Some work was also done on the fluoromethylsilanes (CH3 groups scrambled with F on Si) as well as on the chlorosilanes and the chloromethylsilanes. The results on the fluoromethylsilanes were very similar to those on the fluorosilanes, as would be expected from the experimental data shown in Figure 1. Similarly, this figure indicates the general shape of the computed curves for the chloro compounds. For all three systems the fit between the computed and experimental values was about the same as for the fluorosilanes (see Figure 3). Choice of Molecular Geometry. The reason that computed rather than experimental geometries were employed above is that the computed values can be obtained for those molecules for which geometries based on experimental data for the gases are poor or have not been reported. Moreover, the computed geometries are consistent with each other (to about seven significant figures); whereas the experimental datal9vZ0for gas-phase polyatomic
2226 The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 TABLE IV: Computed Total Shielding Tensors‘ for Some Silyl Compounds Not Listed in Table I (Using 6-31G Optimized Geometries) in a 6-31G Basis Set (without and with d Functions)
molecule SiH3C1 (with 6 d’s on Si)
SiNSO (with 6 d’s on Si)
SiH3CF3 (with 6 d’s on Si)
uxx
UYY
g*z
‘Jim
464.8 438.0 481.0 475.0 510.6 476.8
464.8 438.0 488.4 463.3 510.6 476.8
556.1 500.7 559.2 501.8 556.9 497.3
495.3 458.9 509.5 480.0 526.1 483.7 574.0 526.5 533.7 49 1.9 521.3 485.6 508.2 479.9
Bridged Disilanes H,SiSiH3 (with 6 d’s on Si’s) H3SiCH2SiH3 (with 6 d’s on Si’s) H,SiNHSiH, (with 6 d’s on Si’s) H,SiOSiH, (with 6 d’s on Si’s)
573.3 524.7 522.0
573.3 524.7 508.9
575.3 530.1 570.2
491.1
498.6
574.2
474.6
474.6
575.4
Van Wazer et al. TABLE V Comparison of Calculated and Experimental 29Si Chemical Shifts (in ppm Referenced to TMS) of Some Bridged Disilyl Compounds
calcd’ compd H,SiSiH3 H3SiOSiH3 H3SiNHSiH3 H3SiCH2SiH3
exptl
no d
with d
-104.8 -37.8
-89.5 -23.7 -36.8 -49.2
-78.6 -32.0 -37.7 -44.0
“From the equation 6 = K ( f f T M S - u), with 484.5 for %o d” and 447.9 for “with d”.
K = 1.0 and
(with 6 d’s on Si)
626.7 611.5
molecule SiCl4 SiLi,
626.7 611.5
609.0 587.2
620.8 603.4
”The above shielding tensors may be referenced to TMS by subtracting them from 484.5 ppm for the data calculated without d functions or from 447.9 ppm for the data with 6 d functions on each silicon. /
1001
7
OS8H3
CHZSiH3
uTMS
=
TABLE VI: Shielding for Some Silicon Compounds, with All Substituents Identical, Computed in Various Basis Sets (Geometry Optimized in No-d Basis‘ unless Otherwise Noted)
Silyl Anion SiH,-
-60.9
SiO,4SiF62-
basis
%O
no d with d no d with d no d, p l ~ s “ ~ ~ no d with d no d, plus‘*‘
522.6 512.4 755.3 756.5 605.6 611.7 611.1 615.6
““Nod” stands for the 6-31G, “with d” for the 6-31G(*) basis, corresponding to 6 d’s on Si, and “no d plus” for the 6-31++G basis, where the ++ indicates an additional sp function on Si and an s on the H to allow for the larger molecular diameter caused by the anionic charge. With a +1 countercharge placed 1 8, out from each oxygen on its 0-Si axis, with the geometry optimized in the 6-3 1 ++G basis using these countercharges. CGeometryoptimized in the “no d, plus” basis set.
Y
-100 -100
0 Si-29 Experimental Chem. Shill (ppin)
lIN
Figure 4. Calculated with-d 29Sitotal isotropic chemical shifts for some silyl derivatives vs their experimental chemical shifts in concentrated liquids. The shift calculated for the disilyl anion is compared with the experimental shift for KSiH,.
molecules are variously reported with respect to (1) the equilibrium nuclear positions, (2) the average of these positions, (3) the positions adjusted to give the best fit to effective ground-state rotational constants, (4) “substitution” positions, determined by Kraitchman’s equations, and (5) various other procedures.20 We believe that these differences, albeit small, along with imprecisions in the raw data and their interpretation may lead in some cases to noticeable differences in the computed N M R shielding values. An intercomparison of the use of SCF-optimized vs good experimental geometries is presented in Table I11 to show the kind of differences to be expected. Table 111 is divided into two sections, A and B. The first gives pertinent geometrical and N M R parameters for the three molecules silane, difluorosilane, and tetrafluorosilane, while the second shows the changes in experimental chemical shift (6) and average total shielding upon going from SiH4 to either SiH,F or SiF4-changes that allow a direct comparison between the various treatments.
Other Families of Molecules S l y 1 Compounds. In the preceding substitution series of silicon compounds, the sequential replacement of one kind of substituent with another was studied. Now we shall look at the substitution of a single hydrogen of silane, SiH4, with a variety of substituents to obtain a group of silyl compounds. For this work the replacement substituents were selected to be F, C1, CH,, CF,, NSO, and an electron pair (in the silyl anion), as well as SiH,, NHSiH,, OSiH,, and CH2SiH3. The shielding tensors for these molecules are reported in Tables I1 and IV (although the anisotropy has not been measured for any of these compounds), and we are unaware
of 29Siexperimental data for the CF, and NHSiH, substituents. Referencing to silane, we obtain Figure 4, which presents the theoretical with-d chemical shifts vs the experimental values for these compounds as concentrated liquids. The angled line in this figure corresponds to perfect agreement between theory and experiment. Silane, which has often been reported as a 29Sishift reference, is labeled H and lies in the center of the figure at the 0,O coordinate. It was chosen as the reference because it is chemically similar to all of the silyl derivatives. The point labeled K corresponds to the experimental value reported for KSiH, and to computations on the SiH,- anion. Since we did not find experimental data for the CF, and the NHSiH, substituents, we report their computed chemical shifts referenced to silane as +39.1 (no d), +34.2 (with d) and +44.2 (no d), 67.8 ppm (with d), respectively. A plot like Figure 4 but showing the no-d computed values is quite similar to this figure with respect to the average deviations from the equivalence line, but with positive deviations for the K, OSiH, and the F entries and somewhat larger positive ones for NSO and C1. Referencing to TMS gives poorer agreement for both the with-d and no-d points in a graph similar to Figure 4. Bridged Disilyl Molecules. As shown in Table V, the agreement between the calculated and experimental chemical shifts with respect to TMS is not impressive for the bridged disilyl structures. However, when these substances are referenced to compounds having more closely related environments around the silicon than is afforded by TMS, the agreement between the calculated and experimental values becomes very good, as shown by the following examples: Using silane as the shift reference, the shift for disilane is -12.3 (experimental) and -8.5 (calculated with or without d). Referencing the H3SiCH2SiH3molecule to H3SiCH3gives the shift of the former as +4.3 (experimental), +6.7 (calculated, no d), and +4.2 (calculated, with d). Silicon with All Substituents Identical. In addition to the SiH4, SiF,, and Si(CH3)4 (including rotational isomers) molecules discussed above, four other molecular structures with a set of identical substituents-SiCI4, SiLi4, SO4’, and SiF,”-have been investigated. Their isotropic total shielding values are reported in Table VI. Using the relationship 6 = UTMS - u,with u T M ~equal
+
The Journal of Physical Chemistry, Vol. 93, No. 6,1989 2227
29SiN M R Chemical Shift Computations Diamag. Paramag.
-
.-
a
-0.1
0.0
0.1
0.2
0.3
0.5
0.4
0.6
Change in Si-C Distance (A)
Figure 5. Plot of the changes in the various 29Si magnetic-shielding contributions with variation in the Si-C internuclear distance of Si(CH3)4 from its optimized value of 1.9178 A, which corresponds to zero on the horizontal coordinate. The underlying computations were all done in the no-d basis set.
to the appropriate computed shielding for the Si(CH3)4molecule, we obtain d for (the hypothetically gaseous) SiF62-equal to -56 (no d) and -88 ppm (with d), values that do not agree well with the reported concentrated-solution measurements of -1 88 ppm for (NH4)2SiF6and -186 ppm for ZnSiF6. However, when referenced to SiF4 rather than to Si(CH3),, the calculated values of -7 1 (no d) and -85 ppm (with d) are close to the experimental one of ca. -74 ppm. The computed shift of -1 8.5 ppm from TMS for SiC14 may be compared with the theoretical values of -38.1 (no d) and -64.5 ppm (with d). The computed shift with respect to T M S for the SO4" anion (optimized Si-0 = 1.6131 A) is -121.1 ppm (no d, with plus functions) as compared to the reported values of -70 to -74 ppm for concentrated orthosilicate solutions. Note in Table I that Tossell and Lazzeretti6 with their CHFPT compution using a very large basis set found the shift of the SO4"- anion to be 5 1 ppm lower than the silane experimental value, similar to our no-d finding of a 60 ppm lowering. However, referencing to SiF4 reduces the absolute difference between our computed and the experimental shift to 25 ppm. Among the various possible factors contributing to these large differences between experimental and theoretical shifts for the orthosilicate ion are (1) poor comparability of the theoretical value due to the addition of plus functions to the basis set used for this highly charged anion and (2) such strong intermolecular interactions in alkaline orthosilicate solutions that the model no longer holds. It seems likely that the latter may be dominant. There are no experimental data available for the SiLi4structure, but its very negative calculated shift with respect to TMS of -271 (no d) and -309 ppm (with d) is not inconsistent with the following estimation assuming additive shift contributions due to each substituent: Using the relationship '/4d~1Llr 3/46siHl = ~ L ~ s ~ H , , with the experimental shift for SiH4 = -97 ppm and for LiSiH3 = -165 ppm, gives a rough estimate for the shift of SiLi4of -272 PPm.
+
Analyses and Interpretations Geometrical and Electronic Applied Deformations. By calculating the changes in magnetic shielding due to deforming molecules by small amounts, a measure is obtained of the effect on the shielding of molecular perturbations such as substituent substitutions, solvent changes, etc., that might be rationalized in terms of changes in the molecular geometry or in the electronwithdrawing power of the substituents. To this end a few such deformations were made on tetra- and monomethylsilane (which might be considered as models for the alkylsilanes in general). The variations in the magnetic shielding of the 29Sinucleus due t o simultaneous shortening or lengthening of the four Si-C internuclear distances in tetramethylsilane, while keeping all other geometrical parameters unchanged, are plotted in Figure 5 . Note in this figure that for small changes in the Si-C bonds (CO.05 A) all of the shielding components contribute appreciably to the change in the total shielding. Thus for a change in the Si-C distance from 1.9178 to 1.8678 A, Aa,, = +3.0 ppm, based on Padla= +1.4, Aupara = +1.6 ppm. However, for large changes in Si-C, Aa,,, becomes dominated by Aupara. The increase in total
-50 -I -1
I
0
1
Change in Nuclear Charge of Carbon
Figure 6. Variations in the various calculated 29Si magnetic-shielding parameters and in the total-SCF and nuclear-repulsion energies upon changing the normal nuclear charge of the carbon atom in the SiH3CH, molecule by plus or minus one unit (1 proton), keeping all other adjustable parameters constant. The curves to the three calculated points were artibrarily chosen to be second-degree polynomials. All of the underlying computations were done in the no-d basis set. The vertical coordinates correspond to shielding changes in ppm of the magnetic field and energy changes in megacalories. The zero position on the vertical axis, corresponding to the unperturbed SiH,CH, molecule (bond distances optimized in no-d basis), is 0 for the shielding terms and -20 for the energy values.
SCF energy with an increase or decrease in the four Si-C distances to give a change in the total shielding corresponds to values of Au,,,~/AEsc~ ranging from near 2 ppm/kcal for small Si-C deformations to ca. 0.5 for the larger ones (say, 0.6 %.). The main lesson to be learned from Figure 5 is that an increase in the interatomic distance for this molecule leads to a drop in the total shielding whereas a decrease causes it to rise. To study the effect of changing the electron-withdrawing power of a substituent, it is necessary to simulate such a change mathematicaly by a suitable procedure. One possibility would be to unbalance the basis by affording a considerably larger (or smaller) basis set to the substituent atom in question; but this would be difficult to calibrate in terms of electron-withdrawing power or a related parameter. The method that we chose was, while leaving all other parameters unchanged, to increase (or decrease) the charge on the nucleus of the subject substituent in order to increase (or decrease) its electron-withdrawing power by the amount of the nuclear charge added (or subtracted). The results of applying this idea to the carbon of monomethylsilane is shown in Figure 6, in which the plotted curves were obtained from fitting a second-order polynomial to the three points on which each curve is based. As a result the curves are only indicative, and the maxima in the curves showing the changes in the paramagnetic shielding contribution and the total shielding must be considered to be wholly speculative. Note that increasing the positive charge on the carbon nucleus results in deshielding of the 29Sinucleus. As shown by the figure, the reverse process occurs with a considerably less prominent effect. Note that when the molecular geometry is reoptimized with the different charge, the angles between the hydrogens on both the carbon and the silicon are increased by about 8 O by a unit increase in the positive charge on the carbon. Contributions to the Computed Shielding. An apportionment of the computed 29Simagnetic shielding of two typical silicon molecules (one with strongly and the other with weakly electron-withdrawing substituents) is presented in Table VII, from which it can be seen that the diamagnetic contribution to the shielding is a large positive number to which is added the somewhat smaller paramagnetic deshielding (a negative contribution) to give the total shielding. The diamagnetic shielding depends only on the distribution of the electrons in the unperturbed occupied orbitals and, as formulated here, it describes the shielding of the nucleus due to the electronic currents induced by the magnetic field in the electron cloud unimpeded by the other atoms in the molecule. The paramagnetic deshielding, which accounts for the restrictions in the electronic currents due to the other atoms, requires knowledge of the perturbed occupied molecular orbitals, which are represented by a combination of the occupied and vacant unperturbed orbitals.
2228
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989
Van Wazer et al.
TABLE VII: Computed 29Si NMR Shielding Contributions (in ppm) for Silane and Silicon Tetrafluoride (with Geometry Optimized in a 6-31G Basis Set)
SiH4 contribution
6-31G
SiF,
6-31G(*)
6-31G
6-31G(*)
850.7 2.9 8.8 862.4
851.4 4.6 10.4 863.4
-1 26.1 6.3
-115.6 8.2
-1 15.5 0.0
-118.9 0.0
-19.1 -73.2 5.9 -322.2
-34.0 -70.5 0.6 -330.2
540.2
536.2
Diamagnetic one-center (Si) one-center (other atoms) two-center subtotal
858.9 1.2 13.7 873.8
859.0
1 .o
13.7 873.7
Paramagnetic one-center (Si) occ/vac -296.1 -303.9 one-center (others) occ/vac 0.0 0.0 two-center occ/vac 0.0 0.0 occ/occ 0.0 0.0 three-center occ/vac -12.9 -35.1 occ/occ -4.9 -15.4 interatomic terms 5.2 -1.4 subtotal -308.3 -355.7 total shielding 565.5 518.0
As has been widely reported (e.g., ref 5), the use of different basis sets in the computation of the magnetic shielding of the 29Si nucleus has much less effect on the diamagnetic than on the paramagnetic term. For example, our preliminary study of silicon tetrafluoride, using an experimental geometry, showed only about a 1% drop in the diamagnetic term upon going from a 6-31G {or a 6-31G(*)) to a 3-21G for a 3-21G(*)) basis, while the paramagnetic term increased by 8% (no d) and 6% (with d). This caused an increase in total shielding of 45 ppm (no d) and 29 ppm (with d) upon going frm the larger to the somewhat smaller basis set. Since a similar preliminary studyZZon 31Pshielding showed that quite different and less useful results were found for STO-nG and STO-nG( *) representations than for the split-valence basis sets, we did not include minimum-Slater bases in this work. As indicated in Table VI and the other data reported here (e.g., Table I), the effect of adding a 6-fold set of d orbitals to the silicon atom is quite appreciable. The electrons treated as being centered on the chosen magnetically active nucleus (Si in this case) are consistently reponsible for much of the shielding. For the examples of Table VII, they contribute 97-98% of the diamagnetic part of the shielding as well as about 90% of the paramagnetic part of the shielding of SiH4 and about 35% of that of SiF4. The other important contribution consists of the two-center terms involving the silicon and its nearest-neighbor atoms. For the paramagnetic term, the interactions between the occupied and the vacant orbitals usually account for roughly 4 times more of the paramagnetic deshielding of the 29Sinucleus than do those interactions involving only the occupied orbitals. This comes about in good part because of the large one-center occupied/vacant contribution of the silicon. Diamagnetic Shielding and Electron- Withdrawing Power. To a first approximation the 29Sidiamagnetic-shielding contribution may be considered to be a constant (say, ca.875 ppm, for the basis sets employed) to which the negative paramagnetic shielding is added to obtain the total shielding, so that otot= K + apra,where K = udia. However, the diamagnetic-shielding ontribution does vary and in an interesting manner. We investigated this variation first by computing the diamagnetic shielding of the silicon ions having inert-gas electron configurations, Le., the Si4+cation and the Si" anion. The diamagnetic shielding for the former was found to be 836.9 ppm for the no-d or with-d basis and 837.4 ppm for (22) Callomon, J. H.; Hirota, E.; Kuchitsu, K.; Lafferty, W. J.; Maki, A. G.; Pote, C. S . In Landolr-B6rnsfein (New Seriese; Helwege, K. H., Ed.; Springer-Verlag: Berlin, 1976; Group I1 Vol. 7. For another careful compilation of experimental molecular structures see ref 23. (23) Harmony, M. D.; Laurie, V. W.; Kuczkowski, R. L.; Schwendeman, R. H.; Ramsay, D.A.; Lovas, F. J.; Lafferty, W. J.; Maki, A. G. J . Phys. Chem. ReJ Data 1979, 8, 619. (24) Bagley, B.; et al. J . Mol. Srruct. 1973, 18, 337.
0
20
40
60
SO
100
'70 Shared Electrons on Si [with dl
Figure 7. Comparison of the computations with-d functions on the silicon (horizontal axis) and without-d functions (vertical axis) of the calculated percentage of its shared electrons held by the silicon atom, estimated from the diamagnetic shielding of the compounds as described in this work. TABLE VIII: Estimation' of Valence-Electron Attraction by Silicon, Obtained from the 29Si Diamagnetic Shielding 3'% valence electrons on Si' udia Audia molecule nod d-nod nod with d Si4+cation 836.9 0.0 0.0 0.0 Si4+(222-316) 837.4 0.0 (1 .O) (0.9) 854.2 si0:- anionb 36.0 SiF,*- anionb 859.4 2.3 46.8 46.2 SiF2- anion 860.1 1.6 48.2 46.3 862.4 SiF4 55.0 1.o 52.8 Si(CH3)F3 864.4 2.9 57.2 56.7 SiHF, 864.7 57.1 2.8 57.8 SiH2F2 867.2 59.5 1.6 63.0 868.9 Si(CH3)4rot. 61.6 1.o 66.5 869.1 62.1 1.1 66.9 Si(CH,), 870.0 Si(CH3)2C12 68.8 870.1 SiH3F 0.7 69.0 63.2 870.3 SiH(CH,) 0.7 69.4 63.6 H,SiOSiH, 870.4 1.2 69.6 64.7 870.5 SiCI4 0.6 69.9 63.8 SiHMe3 rot. 870.5 0.6 69.9 63.8 871.3 SiH3CF3 0.5 71.5 65.1 871.8 SiH3NS0 0.2 72.5 65.5 SiH2Me, rot. 871.8 0.4 72.6 65.9 87 1.8 SiH2Me2 0.5 72.6 66.0 H,SiNHSiH, 871.8 0.6 72.6 66.2 872.4 SiH,CI -0.5 73.8 65.3 872.9 SiH3CH3 0.2 74.8 67.5 H,SiCH2SiH3 872.9 0.2 74.8 67.5 SiH, 68.8 873.8 4.1 76.7 H,SiSiH, 874.1 -0.3 77.3 68.8 876.0 SiH3- anionb 73.5 0.3 81.3 SiLi, 879.1 -0.4 87.7 78.0 Si4-anionb 885.0 5.5 100.0 100.0
"Obtained from the equation A , = K(udia - C), where A , is the percentage of its shared electrons assigned to silicon, udiais the total diamagnetic shielding, and C = udiafor the Si4+ion. K = 2.079 with C = 836.9 corresponds to the shielding computations in the 6-31G basis set, while K = 1.866 with C = 836.9 corresponds to the 6-31G(*) computations. The geometrical-optimizationand magnetic-shielding computations were carried out by using a 6-31++G basis set for this structure.
a 222-316 basis (having the same orbital exponents as the no-d basis, but employed to allow for core shrinkage due to the +4 charge on this all-core electronic arrangement); whereas for the latter it was 885.0 ppm for 6-31++G (no-d, plus basis) and 890.5 ppm for 6-31++G(*) (with-d, plus basis). According to Table VII, these values lie on either side of the observed range 850-880 ppm calculated in these basis sets for the various compounds studied. Furthermore, as shown in this table, the presence of substituents generally accepted to be highly electron withdrawing led to the lower values of gdia, whereas the higher ones were associated with the more electron-donating substituents. This observation indicates that the physical feature determining the value of the 29Sidiamagnetic shielding is the effective charge on the silicon and that this shielding component might be employed to estimate an electron-withdrawing power for the silicon atom
29SiNMR Chemical Shift Computations
The Journal of Physical Chemistry, Vol. 93, No. 6,1989 2229
/ 40
50
60
70
80
% Shared Electrons on Si (from Diamag. Shielding)
Figure 8. Plot of the 29Siparamagnetic shielding vs the percentage of its shared electrons residing on the silicon atom of various compounds, as computed in the with-d basis using no-d optimized geometries. The value for the "5% shared electrons on Si", A,, was calculated from the empirical relationship A, = 2.079(udiaE 836.9), where udisis the total diamagnetic shielding. The labeled points in the figure correspond to the following compounds: A, SiC14; B, SiF,; C , H3SiOSiH3; D, SiHF3.
with respect to its substituents. This was achieved by ass'uming that the percentage of its shared electrons associated with the silicon atom, A,, varies linearly with the isotropic diamagnetic shielding, ndia, and ranges from 100% for the si4-anion to zero for the Si4+cation. This gave the equation A, = K(Q* - C),where K = 2.079 with C = 836.9 for the shielding computations in the no-d basis and K = 1.866 with C = 836.9 for the with-d computations. Both the no-d and with-d values are presented in the last two columns of Table VU, and they are plotted against each other in Figure 7. It is apparent from the third column of Table VIII, entitled Andia,that the computed diamagnetic shielding in the 6-31G(*) basis differs from that in the 6-31G more markedly for some structures than for others (note in particular that Andla is negative for only three compounds and that its value for the Si' anion is about 10 times larger than that for any other entry). In general, the ordering of the compounds according to the numbers in either of the last two columns of the table (A, for the no-d and with-d bases, respectively) is the same, with two exceptions attributable to unusual values of Andia. In addition, the large value of Andiafor the Si4- anion causes the larger values for the with-d computation of the valence-electron attraction of the silicon to be smaller than those for the no-d. We believe that the approach to estimating electron attraction (or electronegativity, etc.) presented here may be a valuable one; but the question of how large and what kind of a basis set is needed t achieve an accurate representation of this type for any molecule still needs to be answered in detail. In several papers25published about 20 years ago by our group, we showed (using theoretical approximations of that period) that the isotropic paramagnetic shielding of the nucleus of an atom such as silicon should vary parabolically with the electron-withdrawing power of its substituents, giving a minimum26 when the electron-withdrawing power equals that of the silicon. In Figure 8, the paramagnetic shielding is plotted against the percentage of its shared electrons held by the silicon (calculated from the diamagnetic shielding, from the same 6-3 1G(*) computation) and, as predicted by the prior work, the resulting curve is a parabola facing in the expected directionz6 but with the minimum at 60% rather than at the 50% expected for all four substituents having the same electron-withdrawing power as the silicon. The data of Figure 8 suggest that a simple approximate method for estimating NMR chemical shifts might be developed on the basis of an ab initio or semiempirical calculation of the paramagnetic shielding followed by an estimation of the diamagnetic shielding from a carefully and thoughtfully constructed curve similar to that of Figure 8. Indeed this kind of approach could be employed in a fully parameterized form (using a computer program with gauge invariance to set up the parameters) to convert forward (25) Letcher, J. H.; Van Wazer, J. R. J . Chem. Phys. 1966, 44, 815; Ibid. 1966, 45, 2916. (26) In ref 25 the paramagnetic-shielding term was handled as a positive
number so that the parabolic curve similar to that of Figure 8 of this paper exhibited a maximum rather than the minimum of Figure 8.
or backward from isotropic chemical shifts to some electronwithdrawal parameter, such as electronegativity (as was done previously25with the "mean-excitation-energy" approximation). Conclusions In general, quantum-chemical computations are more accurate in describing rather small differences in physical properties, because in these cases there is more cancellation of terms that may not be approximated sufficiently well to account for large difference where there is less cancellation. For example, the concept of isodesmic2' reactions, which exhibit particularly small errors in the computed energy, always refers to small energy differences. A similar kind of behavior has been demonstrated throughout this paper, where the rather small chemical shifts between related molecules are calculated more accurately than are the large shifts between quite different chemical structures. In this paper we have reported 29Sichemical-shift computations for the no-d basis set even though it was to be expected that these results would on the whole be inferior to the with-d computations, as was found. We did this because many chemists still believe that d orbitals play a special role for the third-period elements by participating in the bonding framework (e.g., as in sp3d2hybrids or the multiple-bonding representation of coordinate-covalent bonds) in the same way as do atom-centered s and p functions-with the d orbitals behaving as more than just polarization functions to afford more angular freedom to the mathematical description of the electron distribution. The fact that the no-d chemical shifts did give a not-unreasonable approximation to the experimental and other computed shifts serves to depreciate the idea that d functions play a qualitatively different role for third- than for second-period elements in their compounds. Inspection of Tables 11, IV, and VI shows that the no-d values of uw (the shift referenced to the bare Si nucleus) are consistently larger than the with-d values (except for SiLi,). As would be expected, these shifts referenced to the bare 29Sinucleus are very large (450 through 760 ppm for the molecules studied here), and so they would be expected to be quite inaccurate. Therefore it is sensible to re-reference the computed values to one of their number, Le., to a chosen molecule, say tetramethylsilane (TMS) or silane. But there are problems here with respect to comparing computations from different mathematical models (Le., different basis sets or procedures to obtain gauge invariance, etc.). Using our work as an example, values of Aniso= qso(no d) - q,,(with d) for four diverse molecules are 57.5 ppm for SiH,, 36.6 ppm for Si(CH,),, and 4.0 ppm for SiF,. Furthermore, if we reference a given compound (compd) to another chosen one (ref), the value of A6 = Auw(ref) - Auw(compd) will equal the difference between the no-d and with-d computed chemical shifts. For example, the no-d minus with-d shift difference, A& for silicon tetrafluoride is 32.6 ppm as referenced to T M S and 53.5 ppm as referenced to silane. For silane referenced to TMS, A6 is -10.9 ppm, and for referencing to itself, A6 is of course zero. From extension of this kind of reasoning to all of our computed results, it appears that the values of Aui,'are greatest for substituents that exhibit electron-withdrawing powers close to that of silicon (e.g., 48 ppm for SiH4 and also for H3SiSiH3). Conversely, small values of Auiso result when the substituents have electronegativities that are much higher (4 for SiF,) or much lower (-1 for SiLi4) than silicon. Kutzelnigg et reported a few IGLO computations using a double-{, Le., DZ, basis, with and without d functions and obtained results similar to ours in giving a large value for Anisofor SiH4 (41 ppm) and H3SiSiH3(46 nd a smaller one for SiF4 (22 ppm). Employing various basis sets for the S i H 4 , Si2H6, and SiF4 molecules, Kutzelnigg et a1.,I0 found that for the IGLO method the value of nisodiminished with increasing basis size, until for the larger bases (involving an f o r more than 3 d orbitals) uisono longer varied in a systematic manner. Furthermore, our with-d values of nisolay between those corresponding to the DZ with d (27) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. J . Am. Chem. Sor. 1970, 92,
4196.
2230
J . Phys. Chem. 1989, 93. 2230-2236
and the I17,2/95,1/5,1 bases of the IGLO paper, while the qso values reported by Tossell and L a ~ z e r e t t i ~for - ~ the CHFPT method were rather close to but sometimes larger and sometimes smaller than those of the 117,2/95,1/5,1 basis favored for the IGLO method. Since Kutzelnigg et a1.I' used a large basis set for intercomparing compounds and also employed gauge-invariant orbitals, the IGLO work is the best tested and will be used here as a comparison standard. For the compounds of Table I, the values of Adim = u,(GIAO method) - u,,(IGLO method), using the favored basis set for each, are found to be 40 and 38 for Si,H2,+2 with n = 1, 2 and 41, 38, 42 and 48 for SiH,_,F, with n = I , 2, 3, 4. The average of these six Auisovalues is 41 f 4. On the other hand, Auiso = uiso(CHFPT method) - ui,(IGLO method), each with its favored basis set, equals 2, 12, 22,40, 55, and 48. The average of these six Au, values is 30 f 21. Obviously our GIAO computations are quite uniformly consistent with the IGLO computations and changing the choice of shift reference standard will not lead to large differences between the two. The opposite is true for the comparison between the CHFPT and the IGLO methods. As would be expected from this analysis, our GIAO and the IGLO computed chemical shifts both agree rather well with the experimental data for these test compounds, as shown in Table I, while the CHFPT method does not. It is interesting
to note that a theoretical paper28predicted the superiority of the gauge-invariant method in 1977. This paper has shown that the kind of with-d calculation we have employed in this paper should be useful in predicting experimental 29Sichemical shifts of new and unknown compounds, with the best results obtained when the shift is measured with respect to a related molecular structure. In referencing an unknown to a related known molecule, obtain this chemical shift from the difference in the calculated isotropic total shieldings and then convert this shift to the TMS standard by using a table16J7 that contains the shift of the related molecule with respect to the usual reference standard. Registry No. H3SiSiH3, 1590-87-0; SiH3F, 13537-33-2;SiH2F2, 13824-36-7; SiHF3, 13465-71-9;SiF4, 7783-61-1;SiFt-, 17084-08-1; SO:-, 17 18 1-37-2: Si(CH3),, 75-76-3; SiH(CH3)3,993-07-7;SiH2(CH3)*, 1 I 1 1-74-6; SiH3(CH3),992-94-9; SiH4, 7803-62-5; SiH3C1, 13465-78-6;SiH3NS0, 57251-86-2;SiH3CF3,10112-1 1-5; H3SiCH2SiH3, 1759-88-2; H3SiNHSiH3,5702-11-4; H3SiOSiH3,13597-73-4; SiH
