DALTON FULL PAPER J. Chem. Soc., Dalton Trans., 1998, Pages 2787–2791 2787 Molecular structure of monomeric scandium trichloride by gas electron diVraction and density functional theory calculations on ScCl3 and Sc2Cl6† Arne Haaland,*,a Kjell-Gunnar Martinsen,a Dmitry J. Shorokhov,a Georgiy V. Girichev *,b and Vasili I. Sokolov b a Department of Chemistry, University of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway b Department of Physics, State Academy of Chemistry and Technology, Engels 7, 153460 Ivanovo, Russia The molecular structures of monomeric and dimeric scandium trichloride were optimised by DFT calculations with basis sets of valence shell TZ 1 P quality, and the molecular force fields and normal vibrational modes calculated.Optimisation of ScCl3 yielded an equilibrium geometry of D3h symmetry and bond distance Sc]Cl 228.5 pm. Optimisation of a model of the dimer with double Cl bridges indicated an equilibrium geometry of D2h symmetry, the terminal and bridging bond distances Sc]Clt 226.0 and Sc]Clb 247.5 pm, and the valence angles Clt]Sc]Clt 114.9 and Clb]Sc]Clb 86.68.Synchronous gas electron diVraction (GED) and mass spectrometric (MS) data were recorded with the eVusion cell kept at 900 ± 10 K. The gas was found to consist of 92 ± 2% monomer and 8 ± 2% dimer. Least-squares refinement of a trigonal pyramidal (C3v) model of the monomer yielded the bond distance rg(Sc]Cl) = 229.1(3) pm and a valence angle a Cl]Sc]Cl 119.8(5)8.The concentration of the dimer was too low for the GED data to give accurate structure parameters for this species. Bond energies for both monomer and dimer were calculated from thermochemical data in the literature and compared to corresponding energies in MCl3 and M2Cl6, M = Al, Ga or In. The monomeric scandium trihalides, ScX3, have been the subject of several studies aiming towards the establishment of the molecular structure, i.e. the determination of the Sc]X bond distance and the molecular shape; is the equilibrium geometry trigonal pyramidal, symmetry C3v, or planar, symmetry D3h? The first investigation of ScF3 by gas electron diVraction (GED) dates back to 1961.1 DiVraction data recorded at an unspecified temperature were found to be consistent with a monomer concentration of 100% and D3h symmetry.This, of course, is the symmetry indicated by a spherical ion model, by the VSEPR model. It is also consistent with a hybridisation model since sd2 hybrid orbitals formed from the 4s, 3dxy and 3dx2 2 y2 atomic orbitals on Sc have major lobes pointing in the appropriate directions.(Hybridisation of the 4s, 3dxz and 3dyz orbitals would, however, yield hybrids favorable for a trigonal pyramidal co-ordination geometry.) Three reports on the IR absorption spectra of ScF3 in rare gas matrices were published in the 60s or early 70s.2–4 Since the symmetric Sc]F stretching frequency (n1) could not be found, it was concluded that the molecule must be planar or near-planar.The electric deflection of molecular beams, on the other hand, indicated a polar, i.e. non-planar structure,5 and a second investigation by GED yielded a F]Sc]F valence angle of 110(2.5)8.6 Finally a third, careful analysis of GED data recorded with a nozzle temperature of 1750 K yielded a Sc]F bond distance of rg = 184.7(2) pm and a non-bonded F ? ? ? F distance which, after correction for thermal vibration, diVered from that calculated for a planar model by 0.0(15) pm;7 the molecule is clearly planar or very nearly so.Equilibrium geometries of D3h † Supplementary data available: experimental conditions for the synchronous GED/MS. For direct electronic access see http://www.rsc.org/ suppdata/dt/1998/2787/, otherwise available from BLDSC (No. SUP 57406, 2 pp.) or the RSC Library. See Instructions for Authors, 1998, Issue 1 (http://www.rsc.org/dalton). symmetry are also indicated by ab initio calculations at the CISD(Q) level 8 and by DFT calculations at the same level as those described below for ScCl3.9 It would seem that the question about the equilibrium structure of ScF3 has been settled for the time being! The gas-phase IR spectra of monomeric ScCl3, ScBr3 and ScI3 have been recorded by Selivanov.10 No symmetric Sc]X stretching frequencies (n1) could be assigned.The IR spectrum of matrix-isolated ScBr3 has also been reported; n2, n3 and n4 could be assigned, but n1 was not found.11 Neither the trichloride nor the tribromide appears to have been studied by GED up to the present, but Ezhov et al.12 have recently published the results of a GED study of gaseous ScI3 at 1050 K.The molecular beam was found to contain both monomeric and dimeric species with mole fractions of 21(3) and 79(3)% respectively. Least-squares refinement of the molecular structures of both monomer and dimer yielded a monomer bond distance of 262(1) pm and a monomer valence angle of 117(2)8: the concentration of the monomer is obviously too small to allow a distinction to be made between planar and pyramidal models.In this article we report the results of density functional theory (DFT) calculations on both monomeric and dimeric scandium trichloride and a GED investigation which shows that monomeric ScCl3 is trigonal planar or very nearly so. Density Functional Theory Calculations The original plan was to optimise the molecular structures of both ScCl3 and Sc2Cl6 by DFT calculations using the program system GAUSSIAN 9413 with the Becke exchange14 and the Perdew–Wang correlation functional 15 (BPW 91).Optimisation of a trigonal planar (D3h) model of ScCl3 with the standard eVective core potential (ECP) basis LanL2DZ 13 converged to a bond distance of 229.1 pm. The dimer was assumed to have a diborane-like structure with two bridging chlorine atoms (see2788 J. Chem. Soc., Dalton Trans., 1998, Pages 2787–2791 Table 1 Structure parameters of ScCl3 and Sc2Cl6 obtained by density functional theory calculations or gas electron diVraction.Interatomic distances (r), root-mean-square vibrational amplitudes (l), perpendicular amplitude correction coeYcients (K) and shrinkages (d) in pm, angles in 8 a DFTb GED re l K rg l ScCl3 Mole fraction 93(3)% Interatomic distances Sc]Cl Cl ? ? ? Cl 228.5 395.7 7.8 23.6 3.6 0.6 229.1(3) 390.8(11) 7.6(2) d 23.3(10) d Shrinkage d(Cl ? ? ? Cl) c Valence angle Cl]Sc]Cl 6.1 e 120.0 6.0(16) a 119.8(5) Sc2Cl6 Mole fraction 7(3)% Interatomic distances Sc]Clt Sc]Clb Clb ? ? ? Clb Sc ? ? ? Sc Clb ? ? ? Clt Clt ? ? ? Clt Sc ? ? ? Clt Clt ? ? ? Clt Clt ? ? ? Clt Valence angles Clt]Sc]Clt Clb]Sc]Clb Sc]Clb]Sc R factor e 226.0 247.5 339.5 360.1 394.9 380.4 517.8 603.0 713.1 e 114.9 86.6 93.4 7.7 11.7 15.5 14.0 37.2 25.5 64.4 165.2 39.0 27.6 8.8 3.5 2.1 26.0 42.4 8.3 4.3 1.1 227.5(10) d 246(2) 325(6) 349(4) 404(2) 412(2) 501(3) 543(3) 691(3) a [114.9] 86(2) 94(2) 0.053 7.6(2) d [11] [15.5] [14.0] 37.6(10) d [25.5] [45.0] d [51.0] d [39] a Estimated standard deviations in parentheses in units of the last digit.Non-refined parameters in square brackets. b The calculations on ScCl3 have been carried out with the ADF program and the TZ 1 P basis set IV, that on Sc2Cl6 with GAUSSIAN 94 and a 6-311G* basis set. See comment in Density Functional Theory Calculations. c The shrinkage is defined as d(Cl ? ? ? Cl) = ÷3 rg(Sc]Cl) 2 rg(Cl ? ? ? Cl).d See comment in Structure refinements. e ÷[Sw(Iobs 2 Icalc)2/Sw(Iobs)2]. sketch in Contents). Optimisation of a model of D2h symmetry with the LanL2DZ basis yielded the terminal and bridging bond distances Sc]Ct 227.5 and Sc]Clb 251.2 pm. Optimisation of a C2v model of the dimer (i.e. a model in which the central Sc2Cl2 ring is non-planar) with the standard all-electron (AE) basis set 6-311G*13 converged to D2h symmetry (planar Sc2Cl2 ring).Interatomic distances and valence angles are listed in Table 1. The normal vibrational modes are listed in Table 2. The molecular force field was transferred to the program ASYM 40 for calculation of root-mean-square vibrational amplitudes, l, and perpendicular amplitude correction coeYcients K16 (see Table 1). After several attempts to optimise the structure of the monomer at the BPW91/6-311G* level had failed to converge, we turned to the Amsterdam Density Functional (ADF) program.17 Calculations were carried out with the Vosko–Wilk– Nusair parametrisation,18 the gradient correction of Becke 14 for exchange and of Perdew19 for correlation.A standard basis set of TZ 1 P quality (IV) was used,17 with the atomic cores of Sc and Cl up to and including the 2p AOs frozen in their atomic shape. Structure optimisation of a C3v model of ScCl3 now converged nicely to yield a structure of D3h symmetry. The vibrational modes are listed in Table 2, the bond distance, root mean square (r.m.s.) vibrational amplitudes and perpendicular amplitude correction coeYcients are listed in Table 1.Experimental A sample of ScCl3?xH2O with a stated purity of 99.99% was purchased from Aldrich Chemical Company. The anhydrous trichloride was obtained by heating the sample under reflux with thionyl chloride as described in ref. 20. Gas electron diVraction and mass spectrometry Synchronous MS and GED experiments were carried out on the modified EMR-100/ApdM-1 unit in Ivanovo.The nickel oven containing the sample was kept at the lowest possible temperature at which suYcient vaporisation took place, about 900 K, corresponding to a vapour pressure of about 0.025 Torr (Torr ª 133 Pa).21 The ratio of evaporation surface to the nozzle orifice was approximately 400. The length to diameter ratio of the diVusion nozzle was optimised to keep equilibrium concentrations of the monomer and dimer in the vapor and a negligibly small scattering volume.22 Other experimental Table 2 Normal mode frequencies (cm21) of ScCl3 and Sc2Cl6 obtained by DFT calculations Symmetry Mode w Symmetry Mode w ScCl3 (D3h) A1 E 13 341 86 E A2 24 468 79 Sc2Cl6 (D2h) Ag Ag B1g B2g B3g B1u B1u B2u B3u 13579 11 13 15 17 438 151 237 465 73 474 12 56 273 Ag Ag B1g B2g Au B1u B2u B3u B3u 2468 10 12 14 16 18 287 71 81 58 36 109 319 412 94J.Chem. Soc., Dalton Trans., 1998, Pages 2787–2791 2789 conditions are summarised in SUP 57406.A portion of the mass spectrum is given in Fig. 1. For analysis of the gas composition we assumed that the ions ScCln 1, n = 1 to 3, are formed from the monomer, that the ions Sc2Cln 1, n = 1 to 5, are formed from the dimer, and that the ratio of the ionisation cross-sections of dimer to monomer is equal to 2. Atomic electron scattering factors were taken from ref. 23 and backgrounds were drawn as smooth least-squares adjusted polynomials to the diVerence between experimental and calculated molecular intensities.Structure refinements Structure refinement of the monomer was based on a geometrically consistent ra model of C3v symmetry. The mole fraction of monomer in the molecular beam, the Sc]Cl bond distance, the non-bonded Cl ? ? ? Cl distance and the Sc]Cl and Cl ? ? ? Cl r.m.s. vibrational amplitudes were refined as independent parameters. The asymmetry constant of the Sc]Cl bond distance (and of the terminal Sc]Cl distance in the dimer) was estimated from k = (1/6)l4÷[8p2cwexem/h].Molecular constants taken from the scandium monochloride molecule24 yielded k = 7.24 × 1026 pm3. Structure refinement of the dimer was based on a geometrically consistent ra model of D2h symmetry. Such a model is characterised by four independent structure parameters, e.g. the terminal and bridging Sc]Clt and Sc]Clb bond distances and the valence angles a Clt]Sc]Clt and Clb]Sc]Clb. Since the amount of dimer in the molecular beam was less than 10% we were unable to refine these four parameters without divergence, and the valence angle a Clt]Sc]Clt was fixed at the value obtained by the DFT calculations.The diVerence between the Fig. 1 A portion of the mass spectrum of scandium trichloride under the conditions of the gas electron diVraction experiment. The ionising potential is 50 V Fig. 2 Calculated (full lines) and experimental (squares) modified molecular intensity curves of ScCl3 with diVerence curves shown below Sc]Cl bond distance in the monomer and the terminal distance in the dimer, rg(Sc]Cl) 2 rg(Sc]Clt), was fixed at the value obtained by DFT calculations with LanL2DZ basis (1.6 pm).(The estimated standard deviation obtained for the Sc]Ct bond distance was expanded from 0.3 to 1.0 pm to include the uncertainty due to this constraint.) The vibrational amplitudes of the two bond distances were refined with a constant diVerence, as were the amplitudes of the Cl ? ? ? Cl distance in the monomer and of the Clb ? ? ? Clt distance in the dimer which turned out to be very similar. The calculated vibrational amplitudes of the non-bonded Sc ? ? ? Clt distance at about 500 pm and the non-bonded Clt ? ? ? Clt distance at about 540 pm were 64 and 165 pm respectively.These amplitudes were varied stepwise to minimise the square-error sum. The best fit was obtained for the values 45 and 51 pm respectively. Other amplitudes were fixed at their calculated values.The structures were refined by a modified version of the program KCED 25 originally written by H. M. Seip. The refinements converged to yield the best values listed in Table 1. Since the refinements were carried out with diagonal weight matrices the listed estimated standard deviations have been multiplied by a factor of 2.0 to include the uncertainty due to data correlation and expanded to include an estimated scale uncertainty of 0.1%. Experimental and calculated molecular intensity curves are compared in Fig. 2, radial distribution curves in Fig. 3. Results and Discussion The composition of the molecular beam The mass spectra recorded simultaneously with the GED diagrams indicated that the mole fractions of monomers and dimers in the molecular beam were 92 ± 2 and 8 ± 2% respectively, while the amount of trimer or higher species was negligible. These mole fractions are in good agreement with the less accurate values obtained by analysis of the electron diVraction data, 93(3) and 7(3)% respectively.The high concentration of the monomer allows an accurate determination of its molecular structure, while the concentration of the dimer was too low for the GED diagrams to contain much information about the molecular structure of Sc2Cl6. The molecular structure of ScCl3 Least-squares structure refinement of a molecular model of C3v symmetry to the GED data yielded a Cl]Sc]Cl valence angle Fig. 3 Calculated (full line) and experimental (squares) radial distribution curves of a mixture of ScCl3 (92%) and Sc2Cl6 (8%).Artificial damping constant k = 25 pm2. The two peaks at about 230 and 390 pm represent the Sc]Cl bond distance and the non-bonded Cl ? ? ? Cl distance in the monomer. Below: diVerence curve2790 J. Chem. Soc., Dalton Trans., 1998, Pages 2787–2791 of 119.8(5)8 while structure optimisation by DFT calculations with an all-electron basis of TZ 1 P quality yielded an equilibrium structure of D3h symmetry; calculations and experiment agree that the molecule is planar or very nearly so.A planar equilibrium structure is also indicated by the gas phase IR spectra since the symmetric Sc]Cl stretching mode (n1) could not be detected.10 The calculated Sc]Cl bond distance is 228.5 pm in good agreement with experimental (rg) distance of 229.1(3) pm. Before going on to discuss the molecular structures of the monomeric trichlorides of the heavier Group 3 metals, yttrium and lanthanum, we pause to note that while the bond distances in the Group 13 trichlorides MCl3, M = Al, Ga or In, are 6 to 11 pm shorter than the bond distance in the monochlorides MCl,25 the bond distance in ScCl3 is 6 pm longer than in ScCl, 222.9 pm.26 An early GED investigation of YCl3 indicated that the equilibrium structure is planar.27 More recently, Konings and Booij 28 have recorded the infrared spectrum of gaseous YCl3 and assigned the four normal modes under the assumption that the structure is pyramidal.This assignment has been challenged by Marsden and Smart29 who optimised the structure at the MP2 level with a ECP basis of DZ quality and obtained an equilibrium structure of D3h symmetry. Finally, a reinvestigation by a combination of GED and DFT calculations has shown that the structure is indeed planar or very nearly so.30 The equilibrium structure of monomeric LaCl3 is still not definitely established.Two relatively recent investigations of LaCl3 by GED led to the conclusion that the equilibrium geometry is pyramidal,31,32 while quantum chemical calculations at various levels indicate that it is planar.33–36 The molecular structure of Sc2Cl6 Density functional theory calculations on the dimer with a 6-311G* basis converged to a model of D2h symmetry. Bond distances and valence angles are listed in Table 1. Attempts to refine the four independent structure parameters characterising a D2h model, viz.the terminal and bridging Sc]Clt and Sc]Clb bond distances and the valence angles a Clt]Sc]Clt and Clb]Sc]Clb, to the GED data failed to converge. The diVerence between the Sc]Cl bond distance in the monomer and the terminal distance in the dimer, rg(Sc]Cl) 2 rg- (Sc]Clt), was therefore fixed at the value obtained by DFT calculations with LanL2DZ basis (1.6 pm), and Clt]Sc]Clt at the value obtained by the all-electron calculations on the dimer. The best values obtained for the two structure parameters that could be refined without constraints rb(Sc]Clb) = 246(2) pm and a Clb]Sc]Clb 86(2)8 are not significantly diVerent from their calculated values.In the following we base our discussion of the dimer on the calculated structure parameters. The compound Sc2Cl6 appears to be similar to the Group 13 analogues M2Cl6, M = Al,37 Ga37,38 or In,38 insofar as the bridging M]Cl distance is about 20 pm longer than the terminal and the Clb]Sc]Clb angle is close to 908, but to diVer from the Group 13 analogues by having a Clt]Sc]Clt less than 1208: Clt]Al]Clt 123.6(16),37 Clt]Ga]Clt 124.7(18) 37 and Clt]In]Clt ª 1308.38 The crystal structure of ScCl3 is constructed from ScCl6 octahedra, each Cl atom bridges two Sc atoms at a distance, 252 pm, about 5 pm longer than the Sc]Clb distance in the gaseous dimer.39 Bond energies The mean bond energy of monomeric ScCl3 at 298 K may be calculated from the standard enthalpy of formation:24 MBE(ScCl3) = {DH8f[Sc(g)]13DH8f[Cl(g)]2DH8f[ScCl3(g)]}/3 = 478(3) kJ mol21.Similarly the mean bond energy of gaseous LaCl3 calculated from the standard enthalpy of formation 40 is found to be 509 kJ mol21. Both the Sc]Cl and La]Cl MBEs are larger than those of the Group 13 analogues, MCl3, M = B, Al, Ga or In, which range from 456 to 327 kJ mol21.25 While the MBEs of the Group 13 trichlorides decrease as the group is descended, those of the Group 3 trichlorides appear to increase. Since the terminal Sc]Cl bond distance in Sc2Cl6 is very close to the bond distance of the monomer, we assume the bond energies to be equal; BE(Sc]Clt) = MBE(ScCl3).The mean energy of the bridge bonds may then be estimated from the dimerisation enthalpy,41 DH8d = 2199 kJ mol21 where DH8d = 2 BE(Sc]Clt) 2 4 BE(Sc]Clb) or BE(Sc]Clb) = 289 kJ mol21. 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