7328
J . Phys. Chem. 1989, 93, 7328-7333
Molecular Structure and Vibrational Analysis of Distannane from ab Initio Second-Order Perturbation Calculations. A Theoretical Approach to the Tin-X Bond (X = C, Si, Ge, Sn) Javier Fernlndez Sam* and Antonio Miirquez Department of Physical Chemistry, Faculty of Chemistry, University of Seville, 41 01 2 Seville, Spain (Received: January 17, 1989; In Final Form: April 21, 1989)
The molecular structure and vibrational spectrum of distannane (SnzH6)have been investigated via ab initio quantum mechanical methods. Harmonic force field, frequencies, and infrared intensities have been calculated by using effective core potentials and double-{ basis set for the valence electrons. Effects of electron correlation, incorporated through second-orderMoller-Plesset perturbation approach, were carefully analyzed. Distannane was found to be a minimum in D3dsymmetry with a tin-tin bond distance of 2.80 A. The force constant associated with the tin-tin stretch is rather small (1.282 mdyn/A) revealing the weakness of this metal-metal bond. Calculated values lead to a reassignment of the experimental bands at 690 and 880 cm-'. A comparative analysis of rotational barriers, symmetric force constants, and vibrational frequencies of distannane with SnH3-XH3 molecules has been carried out.
Introduction In the past few years we have witnessed extensive application of ab initio calculations to vibrational analysis.I4 Most ab initio theoretical work has been carried out on small- and medium-size molecules containing first- and second-row atomsS4For obvious reasons, in spite of the high quality of force fields furnished by correlated wave functions, only a few calculations go beyond the Hartree-Fock leveL5 Most of these were performed from the Molier-Plesset perturbation a p p r ~ a c h ~and , ~ *some from C149*v9 or MCSCF*'Oql'calculations. Recently, considerable effort has been devoted to describe atomic and molecular systems including heavier main-group elements by using effective core potentials (ECP).12-14 Indeed, efficient routines capable of estimating the electron correlation of valence shell electrons have been developed. Simple organostannic compounds may be considered as hydrocarbons in which the carbon atoms have been replaced by tin. Investigations of the structure and properties of molecules containing tin atoms are of great interest because of the unique organometallic chemistry of tin.15 From an experimental viewpoint, only a few papers concerning spectroscopic properties of compounds containing two tin atoms have been reported. Experimental work on the infrared spectrum of distannane16 and infrared and Raman spectra of some simple (1) Pulay, P. In Modern Theoretical Chemistry; Schaefer, H. F., Ed.; Plenum: New York, 1977; Vol. 4. (2) Pulay, P.; Fogarasi, G.;Pang, F.; Boggs, J. E. J . Am. Chem. Soc. 1979, 101, 2550 and references therein. (3) Fogarasi, G.;Pulay, P. Vibrational Spectra and Structure; Durig, J. P., Ed.; Elsevier: Amsterdam, 1985; Vol. 14. (4) Hess, B. A., Jr.; Schaad, L. J.; Carsky, P.; Zahradnik, R. Chem. Reu. 1986, 86, 709 and references therein. (5) For an overview see: Jorgensen, P.; Simmons, J. J. Chem. Phys. 1983, 79, 334, 3599. (6) Ste: Hehre, W. J.; Radom, L.; Schleyer, R. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley: New York, 1986. (7) Hout, R. F., Jr.; Levi, B. A,; Hehre, W. H. J. Comput. Chem. 1982, 3, 234. (8) Simandiras, E. D.; Amos, R. D.; Handy, N. C.;Lee,T. J.; Rice,J. E.; Remington, R. B.; Schaefer, H. F. J. Am. Chem. SOC.1988, 110, 1388 and references therein. (9) Botschwina, P. Chem. Phys. Lett. 1984, 107, 535. (IO) Dupuis, M.; Wendolosky, J. J. J . Chem. Phys. 1984, 80, 5696. ( 1 1 ) Grev, R. S.;Schaefer, H. F. J . Am. Chem. Soc. 1986, 108, 5804. (12) Durand, Ph.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. Barthelat, J. C.; Durand, Ph.; Serafini, A. Mol. Phys. 1977, 33, 159. Barthelat, J. C.; Pelissier, M.; Durand, Ph. Phys. Reu. A 1981, 21, 1773. (13) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270, 284, 299. (14) Dolg, M.; Wedig, U. Preuss, H. J. Chem. Phys. 1987, 82, 866. (15) Poller, R. C. The Chemistry of Organotin Compounds; Academic Press: New York, 1970. (16) Jolly, W. L. Angew. Chem. 1960, 72, 268; J. Chem Soc. 1961, 83, 335.
0022-3654/89/2093-7328$01.50/0
derivatives has been carried but detailed analysis of vibrational spectroscopic data has not been performed. It is worth noting that distannane, Sn2H6, is the simplest saturated compound containing two tin atoms. Obtained first by Jolly'6 as a subproduct in the SnH4 synthesis, it appears to be very unstable and only its solid infrared spectrum has been published. Assuming an ethanelike structure for distannane, i.e., a staggered D3d structure, classical theory predicts 12 normal modes of vibration. Among all these, only five fundamentals are infrared active. So, the available experimental data are clearly insufficient for a discussion of its molecular and spectroscopic properties. Another exciting aspect is the fact that distannane provides a suitable sample of a compound containing a genuine simple metal-metal bond whose chemical interest is obvious. Unfortunately, no information regarding the nature of this bond can be extracted from the available infrared data because the normal vibration that incorporates the Sn-Sn stretching is only Raman active. Recently, Schneider and Thie120 have reported experimental and theoretical work on stannane monohalides force fields using Hartree-Fock ECP level of theory. More recently, the theoretical infrared spectra of the first and second members of the organostannane family, SnH4 and CH3SnH3, have been examined.2'v22 However, as far as we can ascertain, no theoretical work in this connection has been reported on molecules containing two tin atoms. In this paper, we report a theoretical analysis based on ab initio calculations of the vibrational spectrum and molecular force field of distannane. The goal of this work is to furnish a reliable force field for distannane; therefore, the potential function has been derived from Hartree-Fock ECP calculations including electron correlation by means of a second-order perturbation approach. This level of theory has been shown to be very suitable for computing vibrational frequencies of compounds containing the tin atom.21,22 Finally, in order to obtain some insight upon the properties of the Sn-Sn single bond, we have analyzed rotational barriers and stretching force constants of molecules XH3SnH3,X being Ge, Si, and C and compared these with those found on distannane. (17) Brown, M. P.; Cartmell, E.; Fowles, G. W. A. J . Chem. Soc. 1960, 506. (18) Carey, N. A. D.; Clark, H. C. J . Chem. Soc.,Chem. Commun. 1%7, 292. (19) Gager, H. M.; Lewis, J.; Ware, M. J. J . Chem. SOC.,Chem. Commun. 1966, 616.(20) Schneider, W.; Thiel, W. J . Chem. Phys. 1987, 86, 923. (21) Fernlndez Sanz, J.; Mirquez, A,; Pouchan, C. Chem. Phys. 1989, 130. 451. (22) Pouchan, C.; Lespes, G.; Dargelos, A. J . Phys. Chem. 1988,92, 28.
0 1989 American Chemical Societv
Molecular Structure of Distannane
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 1329
v-\\
@*
1
1.724(1.714)
1
4
Figure 1. Geometrical parameters of distannane from SCF (in parentheses) and MP2 calculations.
Theoretical Methods
Hartree-Fock SCF-MO calculations were undertaken using a nonempirical a b initio pseudopotential to describe the core electrons of heavy atoms as proposed by Durand et al.12 A classical pseudopotential was used for the core electrons of the carbon, silicon, and germanium atoms while, in order to take into account its high atomic number, a relativistic one was used for the tin atom. This latter potential take account of major relativistic corrections (mass and Darwin corrections) and gave us good results in the vibrational analysis of closely related molecules?’” For the heavy atoms a double-rquality basis set was used.12 It was augmented by a set of d-polarization orbitals on the silicon ({ = 0.45), germanium ({ = 0.25), and tin ({ = 0.20) atoms.23 For the hydrogen atom the basis set was the (2s) contraction derived by Dunning from the (4s) primitive functions.24 Calculations were performed with the PSHONDO algorithm25a implemented in the HONDO program.26 Electron correlation calculations were undertaken by using a second-order perturbation method under the Moller-Plesset formalism2’ (hereafter MP2 level of theory) as implemented in CIPSI program.28 Fully optimized geometries as well as harmonic force constants were obtained at the SCF and MP2 levels of theory. At HF-SCF level, the geometry optimizations were carried out by using analytical gradient methods.29 Force field calculations and geometry optimizations at MP2 level were performed by numerical differentiation as described elsewhere’O with residual forces being less than lo4 hartree-bohr-’. Plus and minus distortions along each symmetry coordinate were made for the diagonal force constants and appropriate crossed distortions for the off diagonal elements. The adapted symmetry coordinates, Table 11, were constructed from the standard set of internal coordinates, Table I. The set of adapted symmetry coordinates chosen3’ facilitates the assignment of the spectra of the distannane molecule and the comparison with similar molecules (X2H6,X = C, Si, Ge). Step sizes of 0.01 8,were used for bond lengths and 2-4’ for bond and dihedral angles. The vibrational analysis was carried out using Wilson et a 1 . l ~method ~ ~ using MP2 equilibrium geometry. The force field used was obtained by scaling that calculated at the MP2 (23) Fernindez Sanz, J.; Arriau, J.; Dargelos, A. Chem. Phys. 1985,94, 397. (24) Dunning, T. H.; Hay, P. J. Gaussian Basis Sets for Molecular Calculations. In Modern Theoretical Chemistry; Schaefer 111, H. F., Plenum: New York, 1977;Vol. 2. (25)Mayneau, D.; Daudey, J. P. Chem. Phys. Lett. 1981, 81, 273. Technical Report, Workshop on Pseudopotentials. Laboratoire de Physique Quantique, Universite Paul Sabatier Toulouse, 1981. (26) Dupuis, M.; Rys, J.; King, H. F. J. Chem. Phys. 1976, 65, 11. (27)Moller, C.;Plesset, M. S.Phys. Reu. 1934, 46, 618. (28)Huron, B.; Malrieu, J. P.; Rancurel, P. J. J . Chem. Phys. 1973, 58, 5745. Evangelisti, S.;Daudey, J. P.; Malrieu, J. P. Chem. Phys. 1975, 75, 91. (29)Daudey, J. P. PSGRAD Program, private communication. (30)Fernlndez Sanz, J.; Marquez, A,; Dargelos, A. PENTE Program, to be published. (31) Herzberg, G. Molecular Spectra and Molecular Structure; D. Van Nostrand: Princeton, NJ, 1945;Vol. 11. (32)Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1955.
level of theory. The procedure used in the scaling is outlined here. As is well-known, scaling of a force field is a suitable manner for reducing the basis set and electron correlation effects as well as discrepancies due to mechanical anharmonicity. Among all the schemes suggested in the literature we have used, as proposed by Pulay et al.,33separate scaling factors for qualitatively different distortions. This scheme introduces a scaling factor ci for each diagonal force constant Fii associated with symmetry coordinate Si. The scaled off-diagonal force constants Fijs are then defined in terms of unscaled Fij as
FiF = Fij(c,ej)’I2 Unfortunately, the experimental available data on distannane are clearly insufficient and prevent us from deducing a homogeneous set of scaling factors. Therefore, we have used the relative transferability of scaling factors between closely related structural groups to deduce two parameters to scale the stretching and bending force constants. In this way, by minimizing the rootmeanquare deviation between the scaled frequencies of stannane, calculated at the same level of theory, and its harmonic experimental, we have estimated a scale factor of 0.95 for the Sn-H stretch and 0.94 for the SnH, bend. This latter will be used also for the deformation and rocking of SnH3 group. In order to complete the vibrational analysis, the set of theoretical frequencies has been complemented by computational estimation of infrared intensities. Assuming electrical and mechanical harmonicity, the integrated infrared intensity can be obtained by using the relationship Ak
=
(N0.gk/3C2)
(acln/aQk)2 n-xy,z
The derivatives of the dipole moment with respect to normal coordinates are calculated from the derivatives with respect to symmetry adapted coordinates set by multiplying by the L matrix obtained from the G F matrix method i
The numerical differentiation technique using a two-point approximation was employed in the present work. The derivatives of the dipole moment with respect to the symmetry coordinates were calculated in such a manner that the variations of the Cartesian coordinates used to calculate &/asi satisfy the Eckart conditions34 which cancel the rotational contribution^.^^ Results and Discussion
The optimized geometries obtained in this study are shown in Figure 1 for both the HF-SCF (in parentheses) and MP2 levels of theory. Distannane was found to be a minimum in Djd symmetry with a Sn-Sn bond of 2.802 A. Electron correlation does not affect significantly this value, the bond length being 2.804 (33) Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J . Am. Chem. SOC.1983, 105, 7037. (34) Eckart, C. Phys. Rev. 1935, 45, 552. (35) Pulay, P.;Fogarasi, G.; Pang, F.; Boggs, J. E. J . Am. Chem. SOC. 1979,101,2550 and references therein. Lakdar, T. B.; Suard, M.; Taillandier, E.; Berthier, G.Mol. Phys. 1978, 36, 509.
7330 The Journal of Physical Chemistry, Vol. 93, No. 21, 1989
Sanz and MBrquez
SnH3 rock
8,at MP2 level. As expected, the bond distance becomes longer but only by 0.002 A. No experimental data for the distannane structure is known, but this bond length is reasonably close to the crystallographic data obtained for hexaphenyldistannane (2.79 It seems, also, to be consistent with data that can be extrapolated from other ethanelike compounds: ethane itself (rC4 = 1.53 1 A”), disilane (rsc-si= 2.327 A’”), and digermane (rotGe = 2.41 AJ9). The calculated Sn-H bond distance agrees with ex rimental value found on the stannane molecule SnH, (1.71 1 Ag). This structural parameter seems to be more sensitive to the electron correlation effects being a t MP2 level longer than at SCF level by 0.01 A. The H-Sn-Sn bond angle was found to be close to the tetrahedral value whatever the level of calculation used. 1. Force Constants. The harmonic force constants of distannane estimated from HF-SCF and MP2 calculations are reported in Table 111. As can be seen, there are four essentially different kinds of diagonal force constants corresponding to the four main types of motions depicted by the internal symmetry coordinates. They are the Sn-H stretch ( F l l ,FS5,F77,Flolo), the Sn-Sn stretch (F33),and the variation of the plane (FZ2,Fu, Fss, F,, F l l l l F1212) , and torsion (F4) angles. As expected, their values are significantly close. At SCF level, the Sn-H stretch force constant is found to be ca. 2.5 mdyn/A whatever the block of symmetry considered. This value is very close to that calculated in SnH, molecule.21 Electron correlation effects decrease these constants by about 4%. Since the goal of this research is to furnish a more reliable force field, we have reported also in Table I11 the “adjusted” set of force constants obtained by scaling the MP2 values. Using a scale factor of 0.95 we are able to predict a mean Sn-H stretch harmonic force constant of 2.3 mdyn/A. As indicated above, since no experimental value for this force field is known, no direct comparison can be made. Therefore, to have a referencing viewpoint we have also reported in Table I11 the well-known experimental harmonic force constants of ethane.4’ If we compare the mean Sn-H and C-H force constants, it turns out that the former value is half of the latter. This fact is undoubtedly related to the lower strength of the Sn-H bond. The internal coordinate describing the Sn-Sn stretch does not mix and is al symmetry. The force constant associated with this coordinate is 1.322 mdyn/A at SCF level and decreases only to 1.282 mdyn/A at MP2 level. As in the case of the Sn-Sn bond (36) Preut, H.; Haupt, H. J.; Huber, F. 2.Anorg. Allg. Chem. 1973,396, 81.
(37) Shaw, D. E.; Lepard, D. W.; Welsh, H. L. J . Chem. Phys. 1965,42, 3736. (38) (a) Shotton, K. C.; Lee, A. G . ;Jones, W. J. J . Raman Specfrosc. 1973, I , 243. (b) Durig, J. R.; Church, J. S. J . Chem. Phys. 1980, 73,4784. Bethke, G.; Wilson, M. K. J . Chem. Phys. 1957, 26, 1107. (39) Pauling, L.; Laubengayer, A. W.; Hoard, J. L. J . Am. Chem. SOC. - . 1938,150. 1605 (40) (a) Kattenberg, H. W.; Oskam, A. J . Mol. Spectrosc. 1974, 51, 377. )!$ i?;mstrong, R. S.; Clark, R. J. H. J. Chem. SOC.,Faraday Trans. 2 1976, / I ,1 1 .
(41) (a) Duncan, J. L. Specfrochim.Acta 1964, 20, 1197. (b) Hilderbrandt, R. L. J . Mol. Specfrosc. 1972, 44, 599. (c) Nyquist, I. M.; Mills, I . M.; Person, W. B.; Crawford, B. J . Chem. Phys. 1957, 26, 552. (d) Warshel, A. J . Chem. Phys. 1971, 55, 3327.
TABLE III: Harmonic Force Field for Distannand description SCF MP2 adjusted ethaneb A,, F,, SnH, str 2.539 2.403 2.283 4.893 F2, SnH, bend 0.554 0.474 0.445 0.683 Sn-Sn str 1.322 1.282 1.282 4.450 F,, F12 -0.046 -0.041 -0.040 -0.050 F13 0.012 -0.004 -0.004 0 F23 0.085 0.080 0.079 0.489 A,,
Fa
torsion
0.012
0.012
0.077
A,,
F,, F&
SnH, str SnH, bend
2.505 2.384 0.442 0.380 -0.113 -0.102
2.380 0.357 -0.094
4.907 0.573 -0.050
SnH, str SnH, def SnH, rock
F89
2.493 2.331 0.474 0.415 0.278 0.211 -0.068 0.060 0.033 0.046 -0.021 -0.014
2.214 0.390 0.198 0.057 0.043 -0.013
4.815 0.565 0.543 -0.076 0.076 0.003
F,o,,o SnH, str F l l , l l SnH, def F,,,,, SnH, rock FIOJI F10,12 F11,12
2.482 2.297 0.466 0.406 0.558 0.456 -0.084 -0.070 0.077 0.025 -0.050 -0.041
2.182 0.382 0.429 -0.066 0.024 -0.039
4.714 0.554 0.820 -0.076 0.076 0.012
F56
E,
F77 Fa, F9, F78
F79 E,
0.013
Stretching, bending, and stretch-bend force constants are in mdyn/A, mdyn-A, and mdyn, respectively. Reference 41a.
length, the effect of the correlation is small. Since no experimental reference is known for this force constant, no scaling has been carried out. We can compare our value with that obtained by Riter using a diatomic approximation. Extrapolating the known values of X2Hs molecules (X = C, Si, Ge), estimated a Sn-Sn stretch harmonic force constant in distannane of 1.40 mdyn/A. This value is only 10%higher than that which we predict, demonstrating the usefulness of the diatomic approximation applied to medium-sized molecules (presumably, taking into account the general trend of theoretical calculations to give overestimated force fields, our value is still higher than the true one). On the other hand, the comparison of the tin-tin stretch force constant with that for the carbon-carbon bond in the ethane molecule reveals the weakness of this metal-metal bond. As far as the distortions of bond angles are concerned, the higher force constant obtained is the symmetric SnH3 bend (F22 = 0.554 mdyn/A). This value, together with the antisymmetric ah bending force constant F,, is considerably decreased by electron correlation (17% and 16%). Finally, the scaling of these MP2 values by 0.94 yields 0.445 and 0.357 mdyn.A. These adjusted values are close to the experimental harmonic symmetric and antisymmetric bends of stannane (0.345 and 0.418 mdyn.A, respectively). In addition t o the bending we have, for the degenerate e8 and e, modes, the rocking and deformation coordinates of stannyl groups. At SCF level, the SnH3 e, deformation force constant (0.474 m d y d ) is higher than the SnH3 rocking (0.278 m d y d ) . The opposite (42) Riter, J. R., Jr. Spectrochim. Acta 1971, 27A, 635.
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 7331
Molecular Structure of Distannane TABLE IV: Calculated Harmonic Frequencies (cm-') and Potential Energy Distribution for Distannane calcd w , cm-l
AI,
WI
~1
wj
Alu Alu
w4
w5 wg
E,
w,
us wg
E,
wIO
w I ~ ~ 1 2
1964 730 189 72 1957 653 1944 742 315 1928 736 471
exptl :v cm-l
1840 1840 690b
PED SnH, str (100) SnH, bend (100) Sn-Sn str (100) SnH, tors (100) SnH,str (100) SnH, bend (100) SnH, str (100) SnH, def (100) SnH, rock (100) SnH, str (100) SnH, def (93) + SnH, rock (7) SnH, def (4) SnH, rock (96)
+
Measured from a solid sample of distannane. bOriginal assignment: v6 = 690 cm-' and vs = 880 cm-I. See ref 16.
is found for the eg symmetry force constants, although the differences are lower. The same general trends are observed in the ethane force field. On the other hand, as for the bending, these force constants are rather sensitive to the correlation effects, being smaller at this level of calculation by about 17%. The last diagonal force constant to be discussed here is also the smallest. It is related to the torsional motion around the Sn-Sn bond. Its very small value of 0.013 m d y d at SCF level and 0.012 m d y d at correlated level is indicative of the near free rotation about this bond. As for the Sn-Sn stretch force constant, no experimental reference is available, so no scaling has been carried out. If we turn our attention to the interaction force constants, we find that in general they are small, revealing slight coupling between internal symmetry coordinates. A comparison of these off-diagonal force constants with that of ethane shows, however, a surprising difference in the F23 force constant coupling the tin-tin stretch to the SnH, bend. Effectively, we predict for this constant a value of 0.079 mdyn while a value of 0.489 mdyn has been found for ethane. The same fact was noted by K ~ m o r n i c k comparing i~~ analogous methylsilane and ethane interaction terms involving the silicon-carbon stretch and the deformation of the SiH, and the methyl groups. As was pointed by Komornicki, we could try to rationalize the reduced magnitude of these interaction force constant as a consequence of the lower values found for the diagonal. 2. Vibrational Analysis. Using the scaled force field listed in Table I11 and the MP2 equilibrium geometry, calculations of the harmonic frequencies ( a i )have been carried out. They are reported in Table IV together with the experimental ones ( v i ) obtained by Jolly from a frozen sample. In order to gain some insight about the normal modes of vibration and facilitate the assignments, we have also reported in Table IV the results obtained from an analysis of the potential energy distribution. Our calculations show that all the modes are practically pure and the concept of characteristic group frequencies can be applied to the Sn2H6species. Finally, in order to complete the vibrational analysis, we have calculated the dipole moment derivatives respect to the azuand e,, symmetry coordinates. Using the L matrix obtained by solving the vibrational equations we have estimated the integrated absorption intensities for the modes of such symmetry. These are all reported in Table V. The theoretical sequence of band positioning agrees with the pattern found by Griffiths and Walrafen for the closely related molecule digermane Ge2H6.44a The symmetric, wl(alg),and antisymmetric, w5(a2J, w7(eu),and wlo(eg)Sn-H stretch bands appear at 1964, 1957, 1944, and 1928 cm-l, respectively. These frequencies are close to those harmonic (43) Komornicki, A. J . Am. Chem. SOC.1984, 106, 3114. (44) (a) Griffiths, J. E.; Walrafen, G. E. J . Chem. Phys. 1964, 40, 321. (b) Dows, D. A.; Hexter, R. M. J . Chem. Phys. 1956,24, 1029. Crawford, V. A.; Rhee, K. H.; Wilson, M. K. J. Chem. Phys. 1962, 37, 2377. (45) Grev, R. S.; Shaefer, H. F. 111 J . Am. Chem. SOC.1987, 109,6571.
TABLE V: Dipole Moment Derivatives ap/dSi and Integrated Intensities for Distannane assimnent description aulas? A,. kmmol-' obsb Azu
E"
Qs Q6
SnH,str SnH, bend
-2.754 -3.304
143.1 423.7
vs
Q7 Qs
SnH,str SnH, def
SnH,rock
374.1 129.3 31.0
vs
Q9
-3.015 -1.473 0.844
a In D k I or Darad-l for stretch or bend coordinates. sample of distannane. See ref 16.
S
From a solid
found in stannane SnH4 (1990 and 1962 cm-', respectively, for the symmetric a l and antisymmetric tz modes). The u5 and u7 fundamentals are infrared-active modes and, therefore, experimental information is available. The infrared nonharmonic band at 1840 cm-' was assigned by Jolly to the overlap of the v5 and v, fundamentals. This assignment is coherent with our calculated mean value of 1950 cm-' for these two fundamentals (in stannane v 1 fundamental, anharmonicity takes about 70-80 cm-I). Concerning the intensity of these bands, Jolly observed a strong character for the band at 1840 cm-'. Our calculated dipole moment derivatives lead to an integrated absorption intensities for the v5 and u7 fundamentals of 143.1 and 374.1 kmemol-I, respectively. Both together appear clearly as the most intense band of the infrared spectrum. The next region of spectrum to be considered now takes account of the frequencies associated to the bending and deformation of the stannyl group. The symmetric w2 and antisymmetric bends has been calculated to be 730 and 653 cm-I. The SnH3 deformations are estimated to appear at close wavenumbers: 742 cm-' for w8(eu) and 736 cm-l for wll(eg). All of them are also close to those found in stannane for harmonic symmetric (v2 = 772 cm-') and antisymmetric (v4 = 698 cm-') values.21 Among infraredactive modes, our theoretical frequencies (4 and w8 are in agreement with that measured experimentally at 690 cm-' for However, they are considerably lower than that found at 880 cm-' which was assigned to the v8 fundamental. Such a deviation seems to be too high (us - 0 8 = 138 cm-I) and it cannot be attributed to a hypothetical overestimation of electron correlation a t MP2 level, suggesting a reexamination of the assignment of this band. In this sense, it is very interesting to compare the frequencies of the modes concerning of the bond angle deformation of the CH3 group in methane (v2 = 1567, v4 = 1357 cm-l) and ethane (u2 = 1449, V6 = 1437, v8 = 1551, v l l = 1525 cm-I); it turns out that ethane frequencies are always smaller than the highest of methane. The same rule works in the silane-disilane (SiH4:40bu2 = 972, V4 = 913; U 2 = 920, v6 = 844, v8 = 940, Vi1 = 941 cm-') and germane-digermane couples (GeH4:40b v2 = 930, v4 = 821; Ge2H6:44a V 2 = 832, Ug = 756, V 8 = 879, VI1 = 880 Cm-'). For stannane, the experimental frequencies40bv2 and u4 are 753 and 681 cm-I. Therefore, the experimental value of 880 cm-' assigned by Jolly to the V 8 fundamental seems to be too high. This suspect assignment can be verified in the following way: assuming the Jolly frequencies of 1840 and 880 cm-' to be true, taken from ug our value of 3 15 cm-' (this is reasonable since for methylstannane the experimental frequency associated for SnH, rock is 430 cm-' and a detailed PED shows mixing (30%) with CH3 rock) and using our adjusted off-diagonal terms F,,, we can fit a set of diagonal terms Fll: F77 = 1.983 mdyn/A, F88 = 0.550 m d y d , and Fgg = 0.204 mdyn-A. As we can see, F77 and Fgg are close to the estimated values but Fs8 is clearly higher. In fact, this SnH3 deformation force constant is higher than those calculated (harmonic) for d i g e r m a t ~ e(0.239 ~ ~ mdyn.A), d i ~ i l a n e(0.47 ~~ 1 mdyn.A), and close to the experimental value found for ethane (0.565 m d y d ) . These arguments lead us to conclude that the assignment of the band at 880 cm-I carried out by Jolly in his (46) Marquez, A.; Fernlndez Sanz,J.; Pouchan, C.; Dargelos, A. To be published. In our opinion, the value derived by Griffiths and Walrafen'. is too high (u4 = 140 cm-I).
7332 The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 TABLE VI: Calculated Geometries (A and deg) and Rotational Barriers (in kcal-mol-') for SnH3-XH3 Molecules''
RSn-X
?Sn-H
rX-HC
(YXSnH
%nXH
barrier
2.140 2.140 2.146
1.718 1.708 1.718
1.085 1.083 1.085
110.43 109.36 110.84
110.24 110.36 110.17
0.572d 0.650
S 2.589 e 2.592 SnH3GeH3 S 2.649 e 2.655 SnH3SnH3 S 2.802 e 2.801
1.717 1.715
1.481 1.481
110.60 110.70
110.45 110.51
0.505
1.714 1.714
1.560 1.560
110.46 110.54
110.53 110.59
0.462
1.714 1.714
1.714 1.714
110.63 110.62
110.63 110.62
0.387
SnH3CH3 S
expt' e SnH3SiH,
Sanz and Mgrquez TABLE VII: Harmonic Force Field for the Symmetric Modes H$SFXHB'' H,SnCH, description calcd exptlb H3SnSiH3 H3SnGeH3 F,, SnH3 str 2.496 2.241 2.523 2.526 FZ2 SnH3 bend 0.531 0.431 0.494 0.493 F3, Sn-X str 2.629 2.214 1.529 1.466 FM XH3 str 5.897 5.391 3.189 2.803 F5, XH3 bend 0.587 0.453 0.547 0.525 F12 0.061 0.054 0.075 0.076 0.054 0.010 -0.023 -0.101 -0.023 0.024 0.021 -0.223 0.190
F13 F14
Fi5
F2 3 F14
Fz 5
0.011 -0.046
0.017 0.017 -0.037 -0.067 -0.030 0.001 0.016 -0.063 0.081
of
Sn2H6 2.522c 0.498d 1.322 2.522c 0.498d
0.015 0.018 -0.037 -0.063 -0.031 0.055 0.007 -0.068 0.090
"s and e refer to staggered and eclipsed conformations. 'Reference 48. CExperimentalvalues of rX-Hfound in X H 4 molecules: rc- = 1.094,49s r ~ i = - ~1.4741,49b rG,H = 1.527,4'' and ?Sn-H = 1.711
F34
d o t h e r calculated values reported in literature are (kcal/mol): (ECP, SCF),500.690 (ECP, SCF),51and 0.500 (SCF + CI).50
" Stretching, bending, and stretch-bend force constant are in mdyn/A, m d y d , and mdyn, respectively. bReference 48b. CMean value of a18(Fll)and aZ"(F55) stretch force constants. dMean value of alg(F22)and a2u(F66)bend force constants.
'0.568 !i
pioneering work is incorrect. Taking into account the observed experimental features we are inclined to assign the band at 690 cm-l, for which a strong character has been reported, to the v8 fundamental in agreement with our calculated frequency (us = 742 cm-I) and integrated intensity (129.3 km-mol-I). In its turn, it is reasonable to suppose that our harmonic value of 653 cm-' is an upper bound of the expected solid nonharmonic frequency of v6 fundamental and so to assume that in the range studied by Jolly (4000-600 cm-') it has not been detected (for this band, the solid shift in digermane is about 40 cm-I 44b). On the other hand, with respect to the weak band at 880 cm-', we prefer its assignment to a combination band for which there are several Dossibilities. In fact. such a band has also been observed in the solid infrared spectrum of d i g e r m a r ~ e . ~ ~ ~ With regard to stannyl rocking, we find two frequencies at 315 cm-l (eU3w9) and 471 cm-' (eg,w12)' The integrated intensity Of the ' 9 mode is found to be 31'0 k"ol-'' Therefore* if this value is reliable, a very weak band will appear in the low region of the infrared spectrum. The harmonic frequency associated with the tin-tin stretch is predicted to lie at 189 cm-I. This value agrees well with those obtained by Carey and Clark'* from the infrared spectra of some distannane derivatives: 194 cm-l in Ph3SnSnMe,, 199 cm-' in Et3SnSnBu3, and 208 cm-l in Et3SnSnPh3' There is agreement also with the results obtained by Gager, Lewis, and from the Raman spectrum Of hexamethyl and hexaphenyldistannane 'pecies (' 90 and 208 cm-l, Finally, the lowest vibrational frequency of the molecular spectrum is the torsional mode vq. Our MP2 calculations indicate that this stannyl torsion should appear at 72 cm-'. This vibration is infrared and Raman inactive. As expected, this torsional frequency decreases On going from ethane (289 Cm-1)41dt' disilane (132 C ~ - I ) ,digermane ~$ (104 ~ m - ' ) and , ~ ~distannane. As indicated above, we can relate this evolution to the relative increment of the X-X internuclear distance. Indeed, additional insight can be obtained from rotational barriers of stannyl groups around the Sn-Sn bond. On going from the staggered to the eclipsed form, changes in bonds distances or angles are negligible and the energy gain is calculated to be only 0.39 kcal-mol-'. Comparing this value with the experimental barriers found in ethane (2.92 kcal-m~l-')~' or methylstannane (0.6 kcal.mol-l)a much more free rotation can be predicted. 3. Comparison of Distannane with SnH&H3 Compounds. In order to understand further the nature of the tin-tin bond, the properties of the SnH,XH, compounds have been examined. Table VI provides structural parameters obtained from molecular energy optimization at S C F level under C,,, constraint both for (47) Weiss, S.;Leroi, G. E. J. Chem. Phys. 1968, 48, 962. (48) (a) Durig, J. R.; Whang, C. M.; Attia, G. M. J . Mol. Specfrosc.1984, 108, 240. (b) Kimmel, H.; Dillard, C. R. Specfrochim. Acta 1968,244 909.
F3 5 F45
-0.282 0.101
TABLE VIII: SCF Harmonic Frequencies (cm-') for the Symmetric Modes of H8n-XHq H3Sn-CH3 description calcd exptl" H,SnSiH, H,SnGeH, Sn,H6 u1
u2
XH3str SnH3str
u3 X H 3 bend
SnH, bend us Sn-X str u4
" Reference
3193 2054 1420 798 576
3058 1935 1242 716 527
2336 2065 972 773 330
2'79 2066 895 152 23 1
(2072'
( 820' 192
48b. 'Calculated from S C F mean values of Table VII.
staggered and eclipsed molecular conformations. Methylstannane excepted, no experimental data on the SnH3XH3 are available. However, the g& reliability of our ECP Hartree-Fock calculations can be predicted by cornparing our theoretical results with those deduced by Durig et a1,48 from microwave analysis of methylstannane. Comparing bond lengths and bond angles it turns out that (i) as expected, the X-H bond length increases regularly from X = C to X = Sn and agrees reasonably with the experimental value found in the XH4 compounds;49 (ii) the Sn-X-H and X-Sn-H about 1100; (iii) the structure of the SnH3 angles are in all group seems to be unaffected by the nature of the XH3 group; a similar behavior was found by Pople et al. on the SiH,-XH, and CH,-XH, series;52 (iv) the Sn-X bond length increases regularly from = (rsrrc = 2.140 A) to = Sn (rSRSn = 2.802 A); (v) the structural parameters of the eclipsed and staggered conformations are markedly identical, Internal rotation barriers, calculated as the difference between eclipsed and staggered energies, are also reported in Table VI, Their value decrease from X = C to X = Sn,and, as noted by Nicolas et a1.53on other related ethane-like molecules, an correlation between the central bond length and the rotation barrier can be found, Data concerning force constants and vibrational frequencies of modes are reported in Tables vII and vIII. As found on distannane, the potential energy distribution (PED) shows no significant mixing of symmetry internal coordinates and the modes are practically pure. Among the five modes of al symmetry, two (49) (a) Tarrago, G.; Dang-Nhu, M.; Poussigue, G. J . Mol. Specfrosc. 1974, 49, 322. (b) Kattemberg, H. W.; Oskam, A. J . Mol. Specfrosc. 1974, 49, 52. (e) Eades, R. A.; Dixon, D. A. J. Chem. Phys. 1980, 72, 3309. (50) Lespes, G.; Fernindez Sanz, J.; Dargelos, A. Chem. Phys. 1987,115, 453. ( 5 1 ) Ewig, C. S.;Van Wazer, J. R. J . Chem. Phys. 1976.65, 2035. (52) Luke, B. T.; Pople, J. A.; Krogh-Jespersen, M.; Apeloig, Y.; Chandrasekhar, J.; Schleyer, P.v. R. J . Am. Chem. SOC.1986, 108, 260. (53) Nicolas, G.; Barthelat, J. C.; Durand, Ph. J . Am. Chem. Soc. 1976, 98, 1346.
7333
J. Phys. Chem. 1989, 93, 7333-7335 modes correspond to distortions of the separated XH3 and SnH3 groups. Values of force constants and vibrational frequencies of XH3 groups are similar to that found on the XzH6 compounds. With regard to the Sn-X stretch force constants and associated frequencies, it can be seen that they decrease monotonically on going from X = C cfsnx = 2.269 mdyn/A, w5 = 576 cm-’) to X = Sn CfSn-Sn = 1.322 mdyn/A, o5= 192 cm-I). It is obvious that this evolution of force constants is responsible of the progressive destabilization of the Sn-X bond and of the higher instability of distannane with respect to the methylstannane. Conclusions
In this work we have carried out ab initio calculations on a series of molecules SnH3XH3 (X = C, Si, Ge, Sn). With regard to distannane, we have shown that is an ethane-like compound with D3dsymmetry. Our predicted tin-tin bond distance (2.804 A) is in reasonably good agreement with experimental value found in hexaphenyldistannane (2.79 A). The force constant associated with the tin-tin stretch (1.282 mdyn/A) is quite small, indicating a weak metal-metal bond. These results together with the small
torsional force constant (0.012 m d y d ) and the very low rotational barrier (0.39 kcal-mol-’) seem to suggest that molecular structure of distannane can be understood as two weakly COMected stannyl groups with near free rotation around the tin-tin bond and poor interaction. Calculated harmonic frequencies and infrared intensities agree qualitatively with available experimental data (solid sample) and we have argued for an alternative assignment of the bands at 690 and 880 cm-’, although further experimental work (mainly Raman) is encouraged. Comparing distannane with SnH3XH3molecules, we have shown that on going from X = C to X = Sn, the Sn-X bond distance increases whereas fsn-x stretch force constants and rotational barriers decrease, all together revealing a progressive loss of bond strength. Acknowledgment. This work was supported by the Direccion General de Investigacion Cientifica y Tecnica (PB86-0140). We are grateful to Dr. C. Pouchan for helpful discussions and a referee for valuable comments. Registry No. SnH,SnH,, 32745-15-6; GeH,SnH,, 151 18-47-5; SiH,SnH,, 14450-86-3; CH3SnH3,1631-78-3; Sn, 7440-31-5.
A New Electronegativity Scale. 8. Correlatlon of the Ionization Potentials of the Main-Group Atoms (I-VI I) Yu-Ran Luo* and Sidney W. Benson Donald P. and Katherine B. Loker Hydrocarbon Research Institute, Department of Chemistry, University of Southern California, University Park, Los Angeles, California 90089-1 661 (Received: February 6, 1989; In Final Form: May 22, 1989)
Linear correlations are found to exist between the ionization potentials of the seven main-group elements (I-VII) and four different measures of their electronegativity. The electronegativity scales tested are the Pauling scale, xp, a modification xp2,the Allred-Rochow scale, xA, and our recently proposed scale Vx. The latter gives a fit for all main-group elements with an average deviation of 0.14 eV and a root-mean-square deviation of 0.16 eV. The other three scales give fits that show larger deviations by factors of about 2. The maximum deviation with Vx are 0.45 and 0.35 eV for Bi and Pb, respectively. These along with T1 may show anomalies relative to the lighter elements. By use of the correlations, estimates are made of the covalent radii of Ra and Po and the IP of Fr and At.
Introduction
Over 20 years ago, the unshielded core potential of atom X, Vx = nx/rx, where nx is the number of valence electrons in the bonding atom X and rx (A) is its covalent radius, was proposed as the basis for a new electronegativity scale by Yuan.’ However, no one including Yuan has since attempted to use Vx for the estimation or correlation of physical properties. Recently we have found that Vx can be quantitatively correlated with heats of formation, bond dissociation energies, and the group parameters of polyatomic molecules in homologous series?+ These properties correlate only qualitativelyg with the more traditional electro(1) Yuan, H. C. Acta Chim. Sin. 1964, 30, 341. (2) Luo, Y. R.; Benson, S.W. J . Phys. Chem. 1988, 92, 5255. (3) Luo, Y. R.; Benson, S.W. J . Am. Chem. SOC.1989, 1 1 1 , 2480. (4) Luo, Y. R.; Benson, S. W. J . Phys. Chem. 1989, 93, 3304. (5) Luo, Y. R.; Benson, S. W. J . Phys. Chem. 1989, 93, 3306. (6) Luo, Y. R.; Benson, S.W. J . Phys. Chem. 1989, 93, 1674. (7) Luo, Y. R.; Benson, S.W. J . Phys. Chem. 1989, 93, 4643. (8) Luo, Y. R.; Benson, S.W. J . Phys. Chem. 1989, 93, 3791. (9) Luo, Y.R.; Benson, S. W. J. Phys. Chem. Submitted for publication 1989.
0022-365418912093-7333$01.50/0
TABLE I: Slopes and Intercepts for the Linear Corrclations of V x with IP for Main Grouas I-VI1 (See Ea 1)
group I I1 111
IV V
VI VI1
slope“
intercept/eV
4.83 f 0.29 3.70 f 0.19 1.62 f 0.14 1.57 f 0.10 2.05 f 0.10 1.26 f 0.05 1.62 f 0.05
1.86 f 0.18 1.74 f 0.27 2.29 f 0.39 2.97 f 0.35 1.0 f 0.45 3.34 f 0.32 1.85 f 0.32
“If we put V, in units of energy, then the slopes are dimensionless. negativity scales, such as Pauling’s,Io Mulliken’s,’ l * I 2 AllredRochow’s,13 and others. The unshielded core potential, Vx,is a very simply calculated property of atom X. Vx although derived for atoms has been also ~~
(10) Pauling, L. The Nature of the Chemical Bond, 3rd ed.: Cornell University Press: Ithaca, New York, 1960. (1 1) Mulliken, R. S. J . Chem. Phys. 1934, 2, 782. (12) Mulliken, R. S. J. Chem. Phys. 1935, 3, 573. (13) (a) Allred, A. L.;Rochow, E. G. J. Inorg. Nucl. Chem. 1958,5,264, 269. (b) Ibid. 1961, 17, 215.
0 . 1989 American Chemical Societv
