Vibrational frequencies of AlF3

18 November 1994

ELSEVIER

CHEMICAL PHYSICS LETTERS

Chemical Physics Letters 230 ( 1994) 196-202

Vibrational frequencies of AlF3. An ab initio MO study evaluating different methods on a tricky case Gudrun Scholz ‘, Klaus Schiiffel b, Vidar R. Jensen ‘, Oystein Bathe ‘, Martin Ystenes ’ aInstitute of Chemistry,Humboldt University ofBerlin, Hessische StraJe 1-2, D-101 15 Berlin, Germany b Norsk Hydro A/S Research Centre, N-3901 Porsgrunn, Norway ’ Institute oflnorganic Chemistry Norwegian Institute of Technology, University of Trondheim, N-7034 Trondheim, Norway

Received 26 November 1993; in final form 12 September 1994

Abstract The vibrational frequencies of AIF, have been calculated with ab initio methods at the Hartree-Fock level, at correlated levels (MP2, QCISD, MCSCF) and with the LDF method including local (LSD) and non-local spin density (NLSD) functions. The basis set sensitivity was examined with a large number of basis sets including polarization and diffuse functions. The calculations do not confirm the assignment of u4 to 263 cm-‘, but suggest a frequency of -240 cm-’ for this mode. The u, mode most

probably is close to 670-675 cm-‘. The lowest recommendable level for vibrational analysis of AlF,, and probably also for related species, seems to be HF/6-3 1 + G*.

1. Introduction The most important industrial use of aluminium fluorides is in A1F3/Na3AlF6 cryolite melts as solvents for aluminium oxide in the electrolytic aluminium production [ 11. However, the high melting point of these melts has made it difficult to study their properties. Although attempts have been made to model their thermodynamic behaviour [ 2 1, there are several phenomena that are difficult to explain [ 3 1. Some infrared and Raman spectra are known from such melts [ 41, but their interpretation is disputed [ 51. For the oxide containing systems only a few studies are known [ 6,7] and these results are not easily interpreted. Ab initio quantum mechanical calculations may be helpful for studying the structure of the melt. Such studies are known for A1F3 [ 8,9], the anions AlF; [ lo], AIF:- and AIF%- [ 111, as well as for neutral molecular (XF).-A1F3 complexes (X: H, Li, Na)

[ 12- 15 1, and these studies reveal a large basis set sensitivity in the calculation of frequencies for these species. The frequencies are partly inaccurate and may lead to unreliable assignments of the often imperfect experimental vibrational spectra. The same sensitivity is found for other fluorides [ lo], and is much different from what is found for the chlorides [ 16 1, especially the aluminium chlorides [ 17,18 1. The AlF3 molecule is a good candidate for studying the effect of basis sets and calculation methods, both because it is a neutral species ’ and because several spectral investigations of this molecule are known (see e.g. Refs. [ 19-23 ] ) . Another aim of this work is ’ Anionic species in lattices or melts cannot be described exactly quantum mechanically by assuming that they are free ions. Some authors therefore regard these ions merely as fictions (e.g. see last comments in Ref. [ 241). On the other hand, several works have dealt successfully with quantum mechanical predictions of vibrational frequencies of such anions, although the deviations normally become larger with increasing charges (see Ref. [ 2 5 ] )

0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIOOO9-2614(94)01101-X

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to facilitate a more reliable assignment of the vibrational spectrum of AlF3. The assignment of the E’ inplane deformation mode is not unequivocally supported by calculations, and a direct observation of the A’ mode is lacking as no-one has performed Raman studies of this compound. Although some ab initio calculations on the vibrational frequencies of A1F3 have been reported [ 9,12-l 41, they do not give any conclusive verification of the assignment of v4 or the frequency of the unobserved vi. Therefore, the present work was performed to help determine the vi and v4 frequencies and to evaluate method sensitivity.

2. Method of calculation The equilibrium structure of the AlF, molecule was examined at the Hartree-Fock (HF) and at correlated levels using second-order Moller-Plesset perturbation calculations (MP2), quadratic CI (configuration interaction) calculations with single and double substitutions (QCISD) and multiconfigurational SCF (MCSCF) methods. The structures were determined by complete gradient optimizations. The following basis sets have been included. s-pbasissets: STO-3G [26], 3-21G [27,28], 6-31G HONDO [ 29 ] ; Table 1 Contraction

schemes of various

s-p basis sets+poIarization functions: STO-3G* [30],6-31G* [31],DH* [32];DZP,DZ2P [32,33], TZP, TZ2P [ 34 ] - full double and triple zeta basis sets with one or two polarization functions as used in the TURBOMOLE program system; MC* and MC(2d) [ 351 - McLean/Chandler basis set on Al and 6-3 1 lG* for F, which is standard in GAMESS; s-p basis sets+ diffuse functions: 6-3 1Gpoll , 63 lGpol2 [ 361 - which means 6-3 1G HONDO with diffuse d functions for F( poll ) and diffuse d and s functions for F(pol2); s-p basis sets + dijiise functions +polarization functions: 6-31+G* [30], 6-311+G* [37]; D95+* [ 38 ] - Dunning/Huzinaga full double zeta basis set with diffuse and polarization functions, implemented in GAUSSIAN 90. For a better distinction between the basis sets some of the contraction schemes are listed in Table 1. For the numeric Hessian calculation symmetry equivalent atoms were normally displaced 0.0 1 8, in three Cartesian directions (numerical differentiation of the first derivatives). For the studies of the effects of larger displacements the reference atoms were displaced the given distance in all six Cartesian directions. The vibrational frequencies were obtained analytically with the HF method using the GAUSSIAN 90 program and by numerical differentiation of the

basis sets used in this work F

Basis set

Al

DH’ DZP a

(1 ls7p/6s4p) (1 ls7p/6s4p)

+ ld(O.325) + ld(0.3)

(9s5p/3s2p) (8s4p/4s2p)

+ ld(0.9) + ld( 1.4)

DZZP =

(1 ls7p/6s4p)

+2d(0.17,0.52)

(Ss4p/4s2p)

+2d(0.81,2.42)

DZVP *

(12sSp/4s3p)

+ Id

(9s5p/3s2p)

+ Id

DZVP2 d

( 13s9p/4s3p)

+ Id

TZVP d TZP a TZP b TZ2P a TZZP b MC* MC(2d) MC(2d)’

( 13s9p/5s4p) + Id (12s9p/6s5p)+ld(0.311) (12s9p/6s5p) + ld(0.311) (12s9p/7s5p) +2d(0.17,0.52) (12s9p/6s5p) +24(0.1555,0.622) (12s9p/6s5p) + ld(0.325) (12s9p/6s5p) +2d(0.1625,0.65) (12s9p/6s5p) +2d(0.1625,0.325)

( lOs6p/3s2p)

+ Id

( lOs6p/4s3p) + Id (9s5p/5s3p) + ld( 1.4) ( 1 ls6p/5s3p) + ld( 1.62) (9s5p/5s3p) +2d(0.81, 2.42) (lls6p/5~3p)+2d(0.81,3.24) ( 1 ls5p/4s3p)+ ld( 1.75) = (1 lsSp/4s3p) +2d(0.875,3.5) (1 ls5p/4s3p) +2d(0.875,1.75)

Polarization functions are independent, not contracted. b Used in the GAMESS program system. a Used in the TURBOMOLE program system. d Used in the DGAUSS program; polarization c F: ( 1 ls5p/4s3p) is the 6-311G contraction.

functions:

Al: ld(0.30),

F: ld( 1.0).

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G. Scholz et al. / Chemical Physics Letters 230 (1994) 196-202

first derivatives with QCISD and MP2 methods. In all cases the vibrational frequencies were calculated using the harmonic approximation. Additionally, calculations with local density functionals (LDF) were performed using the DMOL [ 39 ] program for LSD (local spin density) calculations and the DGAUSS [40] program for NLSD (non-local spin density) calculations. DMOL geometry optimizations were carried out with a double numerical basis set (DNP) (comparable to 6-31G**) [ 411 and the grid mesh size for the numerical integration set to FINE was used with analytical gradients and the frequencies by a 2-point numerical differentiation of the analytical gradients and using the HedinLundquist/Janak-Morruzi-Williams [ 42 ] local correlation functionals. In the DGAUSS program the Vosko-Wilk-Nusair exchange-correlation treatment [ 43 1, and the grid size FINE for the exchangecorrelation was used and non-local corrections were added via the Becke-Perdew scheme [ 441. The DGAUSS vibrational frequencies are obtained by two 2-point numerical differentiations of the analytical gradients. The DGAUSS-UNICHEM implementation 1.1.1 /UC-l. 1.1 was used on a Cray Y-MP264. Furthermore, calculations were performed using the TURBOMOLE system of programs [ 451, the GAUSSIAN 90 program [ 461 and the GAMESS program [ 471 on IBM RS6000-, Vax-, Silicon Graphics-, Dee-workstations and a Sun Sparkstation.

3. Results and discussion 3.1. Geometry The molecular dimensions of aluminium trifluoride have been repeatedly investigated, e.g. Ref. [ 191. In 1989 the geometry of gaseous aluminium trifluoride was reinvestigated by Hargittai et al. at 1300 K [ 201. The electron diffraction results are compatible with a planar bond configuration (D,, symmetry) and an Al-F bond length of 163 -t 0.3 pm. Three infrared active frequencies are available in the literature (Table 2) from IR measurements in rare gas matrices such as Ne, Ar, Kr [22,23] and gas phase frequencies [ 2 11. As Table 2 shows they are surprisingly dependent on the experimental conditions. The value of the A’, symmetric stretching frequency has

not yet been determined experimentally. In Refs. [ 19,201, for example, it has been predicted from other available frequencies and the mean amplitudes of the vibration determined by electron diffraction. In Table 2 the optimized bond lengths, total energies and vibrational frequencies are summarized for all methods and basis sets used in this work. 3.2. Vibrationalfrequencies The vibrational frequencies for u2 and v3 calculated at the MP2/D95 + * level are in excellent agreement with the experimental values from Ref. [ 2 11. For u1 no direct observation is reported, but the calculated value corresponds well to the estimates in Refs. [ 19,201. The MP2 results with extended basis sets seem to converge towards the experimental values from Ref. [21] with the MP2/D95+* in best agreement. For the HF calculations there is no definite trend or convergence of the values, and the results are scattered. However, by scaling to give the best fit to v2 and v3 (the most reliably observed frequencies) the scaled quantum mechanical (SQM) frequencies for basis sets such as 6-3 lG* or higher are 237-248 cm-’ for vq and 677-693 cm-’ for vl. The D95+*, TZP, TZP + and MC + * basis sets (which give SQM frequencies within t 1% for both v2 and v3, indicating that these are the most balanced basis sets) give SQM values for v4 at 237-240 and 678-681 cm-’ for vl. The results of the HF calculations are theiefore consistent with the MP2/D95 +* values. The QCISD and LDF (LSD or NLSD) calculations are in agreement with the MP2 calculations. We find no explanation for the deviation between the calculated and experimental values for v4. Calculation with larger displacements show that the deviation cannot be attributed to anharmonicity. We suggest a reinvestigation of the vibrational spectrum of AlF3 to verify or correct this assignment. The vibrational frequency for Y, has not been observed directly, and the estimated frequencies given in the literature range from x 650-685 cm-’ [ 19,201. The MP2/D95+* calculation underestimates slightly the frequency of v3, and a similar deviation may occur for Y,. On the other hand, the harmonic approximation should lead to a slight overestimation of the

Table 2 Optimized bond lengths R (pm), and correlated levels Basis set

total energies E”’ (&)

and vibrational

frequencies

v, (cm-‘)

of the AlFS molecule,

calculated

at HF

R (Al-F)

vq E 6 in plane

IQ A; 6 umbrella

81 A; v symm.

vj E’ v asymm.

163.0

263 270 277

291 300 286

665f 15 [20] 672kl3 [19]

935 965 909

163.6 156.2 162.7 165.9 165.0 165.0 162.0

239 350 295 297 298 305 316 317 320 314 311 32014.6 315 316

612 825 755 694 721 720 745 749 762 730 722 732 721 745

923 1165 1073 984 1006 1003 1034 1039 1054 1007 1000 1015/5.5 993 1038

-533.18814 -533.49504 -537.52326 - 540.35466 - 540.38 185 - 540.38950 - 540.45045

162.7 163.2 162.1 163.1 162.8

233 268 287 268 252 255 271 271 271 260 251 26611.1 255 263

162.2 161.4 162.7 161.4 162.4 162.4 161.1 162.7 162.3 161.2 163.1 161.4

268 268 258 265 25411.2 25511.2 261 25811.1 26311.0 264/1.0 25211.1 26311.1

320 315 317 312 31714.8 31514.6 311 31314.8 31214.2 31114.3 31 l/4.8 30814.5

748 749 728 739 729 728 740 725 732/O 739/o 718/O 731/o

1036 1040 1008 1020 1008/5.8 1006/5.8 1017 1016/5.3 1016/5.1 102215.9 1000/5.9 1008/5.6

-540.41185 - 540.42833 -540.55152 - 540.57530 - 540.58450 -540.58732 -540.60914 - 540.54335 - 540.56859 - 540.57707 - 540.55422 - 540.58079

MP2 6-3lG* 6-31 +G’ 6-31l+G* D95+*

164.5 165.7 165.5 166.2

261 245 237 238

302 302 300 297

709 684 683 672

993 953 952 932

-541.03973 -541.08196 -541.42205 -541.28782

OCISD 6-3lG’ 6-31 +G*

164.2 165.3

261 245

302 303

712 691

997 961

-541.04435 -541.08514

LDF LSD(DMOL) DNP

164.7

225

268

641

943

-539.41524

165.3

252 250 233 232 230 231 232 234

282

677

- 542.17960

276

646

273

640

287

658

953 954 906 906 898 899 917 916

experimental Vll v31 1221 HF STO-3G STO-3G’ 3-21G 6-31G 6-31G poll 6-3 1G ~012 6-3 1G* displacement displacement 6-31 +G* 6-3ll+G* DH* D95+* DZP = DZP(AI), DZ2P(F) DZ2P a TZP a TZZP = TZP b TZP+ b TZZP+ b MC’ MC(2d) ’ MC(2d) d MC+* MC+ (2d)

0.1 B 0.2B

’

’

NLSD (DGAUSS) 6-3lG*

- 540.46875 -540.55333 - 540.54703 -540.54302 -540.39893

=

DZVP

167.2

DZVPZ

167.2

TZVP

165.8

= TURBOMOLE. bGAMESS. cSplitting factors, polarization functions: 1.0 and 0.5. d Splitting factors, polarization ’ The splitting of the degenerates with DGAUSS is an artefact of the calculations.

functions:

2.0 and 0.5.

- 542.24706 - 542.30847 - 542.32881

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G. Scholz et al. / ChemicalPhysicsLetters 230 (1994) 196-202

frequency. Hence, we conclude that this frequency in or near the range 670-675 cm- *.

is

3.3. Basis set sensitivity The bond distance results in Table 2 indicate that only extended basis sets with polarization functions (e.g. 6-3 1 +G*, 6-311 +G*, D95 +*, DZP, TZP, MC*, MC+*) reflect the experimental bond distance in a satisfying manner at the HF level. Increasing the number of polarization functions (cf. the sequence DZP; DZP(Al), DZ2P(F); DZ2P or TZP; TZZP) causes a shortening of the Al-F distance. Higher levels of theory (MP2, QCISD) yield in all cases too large Al-F distances. The calculated geometries and frequencies show that polarization functions are imperative for these calculations and the influence on the vibrational frequencies are all linked to the changes in the bonding distances. There is a stronger influence of including polarization functions on Al than on F. The lack of influence of these functions on the A; out-of-plane bend frequency indicates that backdonation from p(F) to d(A1) is of minor importance. This conclusion is supported by the fact that introducing split polarization functions significantly increases (and improves) the frequencies of this mode in the related species A1C13 [ 18 1. The basis set sensitivity for the calculations of the vibrational frequencies of AlF3 is much larger than for e.g. AlC13, where basis set saturation seems to be reached already at the 6-3 1G* level [ 18 ] (although split polarization functions influence the A$’ mode). For A1F3 the calculated frequencies, using the 6-3 lG* basis set or higher, the variation ranges are 16, 12,24 and 46 cm-’ for the four modes, respectively, and the variations are not parallel for the different basis sets. Diffuse orbitals seem to be crucial, whereas double, split polarizations seem to have a smaller influence, although the latter significantly influences the bond length. There also seems to be a correlation between the effects of extended basis functions and diffuse orbitals, which indicates that we still have not reached basis set saturation. Also for the MP2 calculations a basis set sensitivity is seen, partly a reflection of the sensitivity of the HF/ SCF calculations. The effect of the MP2 correction depends to a great extent on the basis functions. For

all basis sets used at the MP2 level the correction compared to the HF results - can within roundoff errors be modelled by a constant scaling factor (6-3 lG*: 0.958, 6-31 +G*: 0.948, 6-311 +G*: 0.951, D95+*: 0.936). It is also seen that D95 +* is more suited for MP2 calculations than 6-3 11+ G*, although these basis sets are hardly distinguishable at the HF/SCF level. The QCISD results resemble the MP2 data, both for the calculated energies, geometries and frequencies as well as the influence of the basis sets. For the stretching mode the QCISD calculated frequencies are slightly higher, and therefore less correct than with MP2, but this should not be overemphasized. Nevertheless, it seems that QCISD is not significantly better than MP2 for AlF3, probably not for other related systems, either. MCSCF (CAS) calculations were carried out for 6-3 lG*, 6-3 1+ G* and MC* (3-7 active orbitals, 26 electrons) giving bond lengths of 1.665-l .67 A. The energies were improved by less than 0.1 Eh, and the coefficients for excited configuration state functions were always well below 0.1. Unfortunately, it was not possible to obtain a reliable vibrational analysis at this level of theory, because of convergence problems for distorted A1F3. The LSD and NLSD calculations generally gave too low vibrational frequencies, but they support our general conclusions. By scaling the NLSD/TZVP values with a factor of 1.027 (derived from vz and v3), the SQM frequencies of v, and vq become 676 and 239 cm-‘, in excellent agreement with the MP2/ D95 +* and SQM/HF values.

4. Conclusions Accurate modelling of the frequencies of v2 and v3 with MP2/D95 + * indicate that an estimate of v1 at x 672 cm-’ is reliable and reasonably accurate. The significant and inexplicable deviation for vq, a deviation confirmed by all calculations given here, indicate that a revision of the assignment may be needed. The best results are obtained at the MP2 level, notably with the D95 +* basis set. But as the MP2 corrections can be modelled by a constant scaling, also HF calculations with the same basis set should lead to reliable predictions of the vibrational frequencies. In

G. Scholz et al. / Chemical Physics Letters 230 (1994) 196-202

this context one should keep in mind that in AlF, all bonds are equal, and in compounds with mixed types of bonds (e.g. AlzF6 ( Dzh dimer), MA1F4 and Al,F,O,) this may not hold true. The lowest level calculations that can be recommended for vibrational analysis of aluminium fluorides is HF/6-31 +G*, which after scaling (0.925) closely reproduces the MP2/D95 + * values. The most pronounced deviation here is for the umbrella mode, and it is therefore possible that such calculations will work even better for species with only tetrahedral aluminium atoms. The other methods used here, QCISD and LDF, verify our main conclusions, but do not give any additional information or improved accuracy.

Acknowledgement Anders Jahres Fond, Statoil and RNF, Norway, are acknowledged for the financing of computer resources. The Deutsche Forschungsgemeinschaft is acknowledged for financial support. We wish to express sincere thanks to Professor L.A. Curtiss (Argonne, USA) for performing the 6-31G* and 631 +G* calculations at the HF-, MP2- and QCISD level and for helpful discussions and, furthermore, to Professor J. Sauer for giving us access to the TURBOMOLE program system.

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