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The vapour phase complex HFAlF3. A new ab initio molecular orbital study
Volume205,number 6
CHEMICALPHYSICSLETTERS
23 April 1993
The vapour phase complex HF-AlF3. A new ab initio molecular orbital study * L.A. Curtiss Argonne National Laboratory, 9700 South Cam Avenue, Argonne, IL 60439, USA
G.
Scholz
centre of Inorganic Polymers, Rudower Chamee 5, O-1199 Berlin, Germany
Received 23 November 1992;in final form 9 February 1993
The HF-AlF, complex is found to have a C, structure with an F-Al bond distance of about I .99 A and the hydrogen interacting with one of the fluorines of AlFs in a cyclic arrangement based on ab initio molecular orbital calculations at the MP2 level. The HF subunit has a low barrier to rotation (5 kJ/mol) about the AIFl subunit and the dissociation energy (&(HF-AIF,)) is 67.0 kJ/mol from G2(MP2) theory.
1. Introduction Vapour phase complexes between the HF and AlF3 molecules have been detected by dynamic thermal gas analysis coupled with mass spectrometry [ 1,21. In order to investigate possible structures and the
bonding situation of the complexes, theoretical calculations have been performed on HAIF, [ 3,4] and HzAIFS [ 5,6] as well as the larger molecules HAl*F,, HIAlzFs and H2A12Fs [ 71. Analogous to the known alkali fluoride complexes only the three structures depicted in fig. 1 were considered in the first paper on HAIF, [ 31. Geometry optimizations at the HF/ 6-3 lG** level showed that structure I( C,,) (cf. fig. 1) was the most stable among the three structures considered. The dissociation energy (0,) for the reaction HAlF, + AlF, + HF
(1)
ICS,)
IIlC,,)
III(CJ,)
Fig. 1. Comer(I)-, edge(II)- and face(U)-bridged structures of the HF-AlF3 complex.
basis set superposition error (BSSE). However, structure I( C,,) is not a minimum on the potential energy surface. The goal of this work was the determination of the equilibrium structure of the HF-AlFs complex. The results of Hartree-Fock (HF) and Mcdler-Plesset second-order (MP2) calculations for the HF-AlF3 complex, using several extended basis sets, are presented. In addition, the dissociation energy is determined using G2 (MP2) theory [ 8 1.
was found to be 53.5 kJ/mol after corrections for the * Work supported by the US Department of Energy, Offliceof Basic Energy Sciences, Division of Materials Sciences, under Contract No. W-31-l09-ENG-38. 550
2. Method of calculation Four basis sets were employed
in this ab initio mo-
0009-2614/93/S06.000 1993 ElsevierSciencePublishers
B.V. All rightsreserved.
CHEMICALPHYSICS LETTERS
Volume 205, number 6
23 April 1993
Table 1 Total energies, optimized geometries, and vibrational frequencies of A& and HF ‘1 Species HF
HF/6-31G* RWF) &%¶I CiF
AIF3
RWF) &Ud VI@‘)
0.911 - 100.00309 4357 1.620 -540.45045 271
~2tAl;)
316
~364'1)
745 1034
v.(E’ )
HF/DZP
HF/TZLP
0.902 -99.99790
0.898 - 100.05190
4458 1.628 - 540.39893 263
1.614 -540.57530
MP2(FULL)/6-31G’
MPZ(FULL)/6-31+G* 0.941
0.934 -100.18416 4092
- 100.205415 3942
1.645 -541.03973 261
1.657 -541.08196 245(40.0)
Exp. ‘) 0.917 4138 1.630 263
316
302
302( 155.6)
291
145 1.038
709 993
684(0.0) 953(208.1)
650 935
-
‘) Energies in atomic units, bond lengths in A, bond angles in deg, and frequencies in cm-‘. Infrared intensities are given in parentheses
for the MP2 (FULL)6-3 1t G* calculation (in units of km/mol). v1(E’ ) is asymmetric deformation, vI(A(;) is the umbrella mode, vj (A\ ) is symmetric stretch, v, (E’ ) is asymmetric stretch. b1Ref. [ZO]. The HF vibrational frequency is the observed harmonic value, while the AIF:, vibrational frequencies are observed fundamentals.
Al: 12s/7s(5211111)9p/5p(51111)+2d, F:
9s/5s(51111)5p/3p(311)+2d,
I-k 5s/3s(311) t2p. Cs(l>
A
h-’ Fb
C,(2)
Fig. 2. C,( 1) and C. (2) structures of the HF-AlFS complex.
lecular orbital study of the HF-AIF complex: ( 1) 6-31G*: split valence basis set plus polarization functions on Al and F [ 9,101. (2) 6-3 1+G*: split valence plus polarization functions and diffuse sp functions on Al and F [ 911]. (3) DZP: double-zeta basis set augmented by one polarization function on all atoms [ 12,131. (4) TZ2P: triplet-zeta basis set with two sets of polarization functions on all atoms [ 141,
Geometry optimizations at the Hartree-Fock (HF) level were done using the 6-31G*, DZP, and TZZP basis sets. Effects of electron correlation were incorporated by second-order Mraller-Plessetperturbation theory (MP2). Optimizations at the MP2 level were performed using the 6-3lG* and 6-31t G* basis sets with all electrons included in the evaluation of correlation effects, i.e. MP2(FlJLL). The dissociation energy of the HF-AlF3 complex was evaluated by G2 (MP2) theory [ 81. This is a modification of G2 theory [ 15] in which the MP4 calculations are replaced by MP2 calculations. G2(MP2) theory should be accurate to 2 12 kJ/mol. The calculations were performed on IBM RS/6000 workstation computers using the TURBOMOLE system of programs [161 and using the GAUSSIAN 90 [ 171 program.
3. Results and discussion The calculated total energies, geometries, and vibrational frequencies of the isolated species are summarized in table 1. The Hartree-Fock calculations yield bond distances which are smaller than the ex551
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CHEMICALPHYSICS LETTERS
23 April 1993
Table 2 Relative energies (in kJ/mol) of optimized structures of HF-AlFs at different levels of theory ‘)
I (C,) II (CZ”) II1 (C,) C‘ (2) C‘ (1)
HF/6-31G’
HF/DZP
MP2(FULL)/6-31G’
MPZ(FULL)/6-3I+G*
27.0(2) 41.5(l) 274.1(2) 6.7(l) 0.0(O)
17.8 19.1
39.2(2) 13.0(l)
43.4(2) 25.0( 1)
12.9(l) 0.0(O)
5.3(l) 0.0(O)
4.1 0.0(O)
al Number of imaginary frequencies in parentheses.
perimental values, whereas the results obtained at the MP2 level are larger than the experimental ones. The five structures shown in figs. 1 and 2 were optimized for HF-AlFs. These include a comer-bridged structure (I(&)), an edge-bridged structure (II (C,, ) ) , and face-bridged structure (III (C,, ) ) as illustrated in fig. 1. In addition, the two C, structures, C,( 1) and C,( 2), illustrated in fig. 2 were optimized. The relative energies of all five stmctures and the number of negative frequencies are listed in table 2. The results indicate that structures I, II, III, and C,(2) are saddle points in the potential energy surface. The equilibrium structure is the C,( 1) structure in fig. 2. Table 3 contains the optimized geometries, total energies, and dissociation energy of the complex for the C,( 1) structure at different levels of theory. The vibrational frequencies of this structure are listed in table 4.
The equilibrium C, ( 1) structure of HF-AlF, consists of a slightly pyramidal AlFs and a nearly undistorted HF molecule which is bonded to AUF3 through both the fluorine and hydrogen (see fig, 2) in a cyclic arrangement. The subunits are connected via a long F,-Al bond of 1.99 A and an H...Al,bond of 2.23 8, (MP2(FULL)/6-31 +G* results). In agreement with previous results (ref. [ 3 ] ) there is no indication for the existence of an AIF; anion and the results are analogous to those for the AlFr(HF)2 molecule (see ref. [ 51). The bond distances correlate well with the shared electron numbers (SEN) obtained from Roby-Ahlrichs population analysis [ l&l9 ] (SEN: AlF, bond: 0.03, F,H bond: 1.20,calculated for the SCF/DZP optimized geometries). The C,(2) structure is 5 kJ/mol (MP2(FULL)/63 1+G*) higher in energy than the C,( 1) structure and has one imaginary frequency. This suggestsa low
Table 3 Total enemies, dissociation energies, and optimized geometries for the C.( 1) structure of HF-AIFaal
&.I Deb) D.(BSSE) U) L AlF,H L FtiFb L FtiF, L FAF, r(HF.) r(MF.) r(AlF,) r(AlF,) r(HFtJ
HF/6-31G*
HF/DZP
HF/TZ2P
MP2(FULL)/6-31G”
MP2(FULL)/6-31+G*
-640.48898
-640.43072 88.9 67.0 109.0 87.3 101.4 119.8 0.918 1.979 1.657 1.637 2.333
-640.65452 71.7 64.1 110.9 89.2 100.9 119.3 0.912 1.962 1.639 1.624 2.398
-641.26790 115.5
-641.31726 79.1
88.2 80.6 105.3 120.4 0.971 1.959 1.694 1.651 1.796
103.0 86.5 101.9 119.9 0.960 1.987 1.686 1.665 2.230
93.0 102.7 85.7 102.6 119.6 0.930 1.966 1.649 1.629 2.176
‘) Distances in A,bond angles in deg. See fg. 2 for atom labeling. Total energies in au and dissociation enemies in kJ/mol. w Dissociation energy for HF-AlFj+HF+AlF3 ClCorrected for basis set superposition error. ‘) The HF/6-31 +G* dipole moment ofthis structure is 3.68 D.
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Table 4 Vibrational frequencies in (cm-‘) of the C,( 1) optimized structure of HF-AlFs ‘)
a” a’ a” a’ a’ a’ a” a’ a’ a’ a” a’
HF/6-3 lG*
HF/DZP
HF/TZZP
MP2(FULL)/6-31G*
MP2(FULL)/6_31+G*
152 170 250 267 293 397 445 728 731 984 1011 4088
150 160 232 251 288 386 390 669 731 989 1014 4203
152 163 224 263 282 353 374 686 724 970 992 4258
150 183 246 252 301 412 637 689 197 976 985 3525
142( 1.7) 153( 12.3) 220(0.0) 237(46.5) 274(71.3) 381(155.7) 400(212.5) 671t26.4) 699(240.0) 909(213.6) 934(227.0) 3697(295.3)
Mode ‘)
AlF, AlF3 AW HF
al Infrared intensities are @en in parentheses for the MP2 (FULL)/6-31 +G* calculation (in units of km/mol). b, Vibrational modes which arise predominantly from one subunit are indicated. The others arise from mixture of subunit modes and intermolecular degrees of freedom. Table 5 G2 (MP2 ) energies ‘)
HF AlF, HAlF, C,( 1) l)
J&(au)
Do (kJ/mol)
0. (kJ/mol)
-100.34704 -541.48824 -641.85784
59.2
67.1
Scaled (0.893) HF/6-31G* frequencies used for zero-point energies.
Table 6 Thermodynamic functions for complex formation A&+HF+ HF-AlF, ‘) T(K)
MT
273 498 598 648 698 748 1148
-61.8 -60.4 -59.4 -58.9 -58.4 -57.9 -53.2
l)
(kJ/mOl)
-TAS
32.7 57.8 68.4 73.6 78.7 83.8 122.9
(kJ/mol)
is 67.1 kJ/mol without zero-point energies (0,) and 59.2 kT/mol with zero-point energies (Do). The G2( MP2) value of De is in agreement with the HF/ DZP and HF/TZZP values for 0, (67.0 and 64.1 kJ/ mol, respectively) that were corrected for basis set superposition error (BSSE). The thermodynamic functions of complex formation of HF-AlF3 were calculated within the standard rigid-rotor harmonicoscillator ideal-gas approximation [ lo]. They were calculated using the G2(MP2) dissociation energy D,, the MP2 (FULL) /6-3 1 + G* equilibrium geometry and MP2( FULL) /6-3 1+G* vibrational frequencies. Values from 298 to 1148 K are listed in table 6.
K (atm-‘) 3.67x 10’ 1.84 0.16 0.06 0.03 0.02 6.7x IO-’
Reaction energy at 0 K is - 67.1 kJ/mol; reaction enthalpy at 0 K is - 58.8 kJ/mol.
barrier to rotation of the HF subunit about AlF3. The dissociation energy for the HF-AlF, complex (eq. ( 1) ) was derived from G2 (MP2) theory. The results are listed in table 5. The dissociation energy
4. Conclusions The following conclusions can be drawn from this ab initio molecular orbital study of the HF-AlF3 complex: ( 1) The equilibrium structure has C, symmetry with HF attached to AlF3 by a long F-Al bond ( e 1.99 A) and the hydrogen interacting with one of the fluorines of AlF, in a cyclic arrangement. There is a low barrier (5 kJ/mol) for rotation of the HF subunit about the F-AI bond. (2) The C, structure is the only local minimum that was located. The face-bridged, comer-bridged and edge-bridgedstructures that have been found for 553
Volume 205, number 6
CHEMICALPHYSICSLETTERS
other alkali fluoride complexes are saddle points in the potential energy surface of the HF-AlF3 complexes. (3 ) The dissociation energy 0, of the HF-AIF complex is 67.1 kJ/mol from G2( MP2) theory.
References [ 1 ] D. Menz, L. Kolditz, K. Heide, C. Schmidt, Ch. Kunert, Ch. Mensing, H.G. von Schnering and W. Hiinle, 2. Anorg. Allg.Chem. 551 (1987) 231. [2] D.-H. Menz, Ch. Mensing, W. Hlinle, H.G. von Schnering, Z. Anorg. Allg. Chem. 611 (1992) 107. [ 31 G. Scholz, J. Sauer and D.-H. Menz, Chem. Phys. Letters 156 (1989) 125. [4] G. Scholz and L.A. Cur&, J. Mol. Struct. THEOCHEM 258 (1992) 251. [ 5] A. Burkhardt, U. Wedig, G. Scholz and D. Menz, Chem. Phys. Letters 182 (1991) 556. [6] G. Scbolz, C. Nieke, D.-H. Menz and L. Kolditz, J. Mol. Struct. THEOCHEM 231 (1991) 95. [7] C. Nieke, G. Scholz and D.-H. Menz, .I. Fluor. Chem., in press. (81 L.A. Curt& K. Raghavachari and J.A. Pople, J. Chem. Phys., in press. [9] P.C. Hariharan and J.A. Pople, Theoret. Chim. Acta 28 (1973) 213.
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[lo] W.J. Hehre, L. Radom, P. von R. Schleyer and J.A. Pople, Ab initio molecularorbital theory (Wiley,New York, 1986). [ 111T. Clark, J. Chandrashekar, G.W. Spitznagel and P. von R. Scbleyer,J. Comput. Chem. 4 ( 1983) 294. [ 121T.H. Dunning Jr., J. Chem. Phys. 53 (1970) 2823. [ 131T.H. Dunning Jr. and P.J. Hay, in: Methods of electronic structure theory, Gaussian basis sets for molecular calculations,ed. H.F. SchaeferIIl (Plenum Press, New York, 1977). [ 141S. Huzinaga, J. Andzelm, M. Klobukowski, E. RadzioA&elm, Y. Sakai and H. Tatewaki, Physical sciencesdata, Vol. 16. Gaussian basis sets for molecular calculations (Elsevier, Amsterdam, 1984). [ 151L.A. Curt& K. Raghavachari,G.W. Trucks and J.A. Pople, J. Chem. Phys. 94 ( 1991) 7221. [ 161R. Ahhichs, R. B&r,M. H&xx, H. Horn and C. Kiilmel, Chem. Phys. Letters 162 (1989) 165. [ 171M.J. Frisch, M. Head-Gordon, G.W. Trucks,J.B. Foresman, H.B. Schlegel, K. Raghavachari, MA. Robb, J.S. Binkley, C. Gonzalez, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger,CF. Melius,J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart,S. Topiol and J.A. Pople, GAUSSIAN90 (Gaussian Inc., Pittsburgh, PA, 1990). [ 181K.R. Roby, Mol. Phys. 27 (1974) 81. [ 191C. Ehrhardt and R. Ahlrichs,Theoret. Chim. Acta 68 (1985) 231. [20] M.W. Chase Jr., CA. Davis, J.R. Downey Jr., D.J. F~rip, R.A. McDonald and A.N. Syvemd, J. Phys. Chem. Data 14 Suppl. 1 (1985).
CHEMICALPHYSICSLETTERS
23 April 1993
The vapour phase complex HF-AlF3. A new ab initio molecular orbital study * L.A. Curtiss Argonne National Laboratory, 9700 South Cam Avenue, Argonne, IL 60439, USA
G.
Scholz
centre of Inorganic Polymers, Rudower Chamee 5, O-1199 Berlin, Germany
Received 23 November 1992;in final form 9 February 1993
The HF-AlF, complex is found to have a C, structure with an F-Al bond distance of about I .99 A and the hydrogen interacting with one of the fluorines of AlFs in a cyclic arrangement based on ab initio molecular orbital calculations at the MP2 level. The HF subunit has a low barrier to rotation (5 kJ/mol) about the AIFl subunit and the dissociation energy (&(HF-AIF,)) is 67.0 kJ/mol from G2(MP2) theory.
1. Introduction Vapour phase complexes between the HF and AlF3 molecules have been detected by dynamic thermal gas analysis coupled with mass spectrometry [ 1,21. In order to investigate possible structures and the
bonding situation of the complexes, theoretical calculations have been performed on HAIF, [ 3,4] and HzAIFS [ 5,6] as well as the larger molecules HAl*F,, HIAlzFs and H2A12Fs [ 71. Analogous to the known alkali fluoride complexes only the three structures depicted in fig. 1 were considered in the first paper on HAIF, [ 31. Geometry optimizations at the HF/ 6-3 lG** level showed that structure I( C,,) (cf. fig. 1) was the most stable among the three structures considered. The dissociation energy (0,) for the reaction HAlF, + AlF, + HF
(1)
ICS,)
IIlC,,)
III(CJ,)
Fig. 1. Comer(I)-, edge(II)- and face(U)-bridged structures of the HF-AlF3 complex.
basis set superposition error (BSSE). However, structure I( C,,) is not a minimum on the potential energy surface. The goal of this work was the determination of the equilibrium structure of the HF-AlFs complex. The results of Hartree-Fock (HF) and Mcdler-Plesset second-order (MP2) calculations for the HF-AlF3 complex, using several extended basis sets, are presented. In addition, the dissociation energy is determined using G2 (MP2) theory [ 8 1.
was found to be 53.5 kJ/mol after corrections for the * Work supported by the US Department of Energy, Offliceof Basic Energy Sciences, Division of Materials Sciences, under Contract No. W-31-l09-ENG-38. 550
2. Method of calculation Four basis sets were employed
in this ab initio mo-
0009-2614/93/S06.000 1993 ElsevierSciencePublishers
B.V. All rightsreserved.
CHEMICALPHYSICS LETTERS
Volume 205, number 6
23 April 1993
Table 1 Total energies, optimized geometries, and vibrational frequencies of A& and HF ‘1 Species HF
HF/6-31G* RWF) &%¶I CiF
AIF3
RWF) &Ud VI@‘)
0.911 - 100.00309 4357 1.620 -540.45045 271
~2tAl;)
316
~364'1)
745 1034
v.(E’ )
HF/DZP
HF/TZLP
0.902 -99.99790
0.898 - 100.05190
4458 1.628 - 540.39893 263
1.614 -540.57530
MP2(FULL)/6-31G’
MPZ(FULL)/6-31+G* 0.941
0.934 -100.18416 4092
- 100.205415 3942
1.645 -541.03973 261
1.657 -541.08196 245(40.0)
Exp. ‘) 0.917 4138 1.630 263
316
302
302( 155.6)
291
145 1.038
709 993
684(0.0) 953(208.1)
650 935
-
‘) Energies in atomic units, bond lengths in A, bond angles in deg, and frequencies in cm-‘. Infrared intensities are given in parentheses
for the MP2 (FULL)6-3 1t G* calculation (in units of km/mol). v1(E’ ) is asymmetric deformation, vI(A(;) is the umbrella mode, vj (A\ ) is symmetric stretch, v, (E’ ) is asymmetric stretch. b1Ref. [ZO]. The HF vibrational frequency is the observed harmonic value, while the AIF:, vibrational frequencies are observed fundamentals.
Al: 12s/7s(5211111)9p/5p(51111)+2d, F:
9s/5s(51111)5p/3p(311)+2d,
I-k 5s/3s(311) t2p. Cs(l>
A
h-’ Fb
C,(2)
Fig. 2. C,( 1) and C. (2) structures of the HF-AlFS complex.
lecular orbital study of the HF-AIF complex: ( 1) 6-31G*: split valence basis set plus polarization functions on Al and F [ 9,101. (2) 6-3 1+G*: split valence plus polarization functions and diffuse sp functions on Al and F [ 911]. (3) DZP: double-zeta basis set augmented by one polarization function on all atoms [ 12,131. (4) TZ2P: triplet-zeta basis set with two sets of polarization functions on all atoms [ 141,
Geometry optimizations at the Hartree-Fock (HF) level were done using the 6-31G*, DZP, and TZZP basis sets. Effects of electron correlation were incorporated by second-order Mraller-Plessetperturbation theory (MP2). Optimizations at the MP2 level were performed using the 6-3lG* and 6-31t G* basis sets with all electrons included in the evaluation of correlation effects, i.e. MP2(FlJLL). The dissociation energy of the HF-AlF3 complex was evaluated by G2 (MP2) theory [ 81. This is a modification of G2 theory [ 15] in which the MP4 calculations are replaced by MP2 calculations. G2(MP2) theory should be accurate to 2 12 kJ/mol. The calculations were performed on IBM RS/6000 workstation computers using the TURBOMOLE system of programs [161 and using the GAUSSIAN 90 [ 171 program.
3. Results and discussion The calculated total energies, geometries, and vibrational frequencies of the isolated species are summarized in table 1. The Hartree-Fock calculations yield bond distances which are smaller than the ex551
Volume 205, number 6
CHEMICALPHYSICS LETTERS
23 April 1993
Table 2 Relative energies (in kJ/mol) of optimized structures of HF-AlFs at different levels of theory ‘)
I (C,) II (CZ”) II1 (C,) C‘ (2) C‘ (1)
HF/6-31G’
HF/DZP
MP2(FULL)/6-31G’
MPZ(FULL)/6-3I+G*
27.0(2) 41.5(l) 274.1(2) 6.7(l) 0.0(O)
17.8 19.1
39.2(2) 13.0(l)
43.4(2) 25.0( 1)
12.9(l) 0.0(O)
5.3(l) 0.0(O)
4.1 0.0(O)
al Number of imaginary frequencies in parentheses.
perimental values, whereas the results obtained at the MP2 level are larger than the experimental ones. The five structures shown in figs. 1 and 2 were optimized for HF-AlFs. These include a comer-bridged structure (I(&)), an edge-bridged structure (II (C,, ) ) , and face-bridged structure (III (C,, ) ) as illustrated in fig. 1. In addition, the two C, structures, C,( 1) and C,( 2), illustrated in fig. 2 were optimized. The relative energies of all five stmctures and the number of negative frequencies are listed in table 2. The results indicate that structures I, II, III, and C,(2) are saddle points in the potential energy surface. The equilibrium structure is the C,( 1) structure in fig. 2. Table 3 contains the optimized geometries, total energies, and dissociation energy of the complex for the C,( 1) structure at different levels of theory. The vibrational frequencies of this structure are listed in table 4.
The equilibrium C, ( 1) structure of HF-AlF, consists of a slightly pyramidal AlFs and a nearly undistorted HF molecule which is bonded to AUF3 through both the fluorine and hydrogen (see fig, 2) in a cyclic arrangement. The subunits are connected via a long F,-Al bond of 1.99 A and an H...Al,bond of 2.23 8, (MP2(FULL)/6-31 +G* results). In agreement with previous results (ref. [ 3 ] ) there is no indication for the existence of an AIF; anion and the results are analogous to those for the AlFr(HF)2 molecule (see ref. [ 51). The bond distances correlate well with the shared electron numbers (SEN) obtained from Roby-Ahlrichs population analysis [ l&l9 ] (SEN: AlF, bond: 0.03, F,H bond: 1.20,calculated for the SCF/DZP optimized geometries). The C,(2) structure is 5 kJ/mol (MP2(FULL)/63 1+G*) higher in energy than the C,( 1) structure and has one imaginary frequency. This suggestsa low
Table 3 Total enemies, dissociation energies, and optimized geometries for the C.( 1) structure of HF-AIFaal
&.I Deb) D.(BSSE) U) L AlF,H L FtiFb L FtiF, L FAF, r(HF.) r(MF.) r(AlF,) r(AlF,) r(HFtJ
HF/6-31G*
HF/DZP
HF/TZ2P
MP2(FULL)/6-31G”
MP2(FULL)/6-31+G*
-640.48898
-640.43072 88.9 67.0 109.0 87.3 101.4 119.8 0.918 1.979 1.657 1.637 2.333
-640.65452 71.7 64.1 110.9 89.2 100.9 119.3 0.912 1.962 1.639 1.624 2.398
-641.26790 115.5
-641.31726 79.1
88.2 80.6 105.3 120.4 0.971 1.959 1.694 1.651 1.796
103.0 86.5 101.9 119.9 0.960 1.987 1.686 1.665 2.230
93.0 102.7 85.7 102.6 119.6 0.930 1.966 1.649 1.629 2.176
‘) Distances in A,bond angles in deg. See fg. 2 for atom labeling. Total energies in au and dissociation enemies in kJ/mol. w Dissociation energy for HF-AlFj+HF+AlF3 ClCorrected for basis set superposition error. ‘) The HF/6-31 +G* dipole moment ofthis structure is 3.68 D.
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Table 4 Vibrational frequencies in (cm-‘) of the C,( 1) optimized structure of HF-AlFs ‘)
a” a’ a” a’ a’ a’ a” a’ a’ a’ a” a’
HF/6-3 lG*
HF/DZP
HF/TZZP
MP2(FULL)/6-31G*
MP2(FULL)/6_31+G*
152 170 250 267 293 397 445 728 731 984 1011 4088
150 160 232 251 288 386 390 669 731 989 1014 4203
152 163 224 263 282 353 374 686 724 970 992 4258
150 183 246 252 301 412 637 689 197 976 985 3525
142( 1.7) 153( 12.3) 220(0.0) 237(46.5) 274(71.3) 381(155.7) 400(212.5) 671t26.4) 699(240.0) 909(213.6) 934(227.0) 3697(295.3)
Mode ‘)
AlF, AlF3 AW HF
al Infrared intensities are @en in parentheses for the MP2 (FULL)/6-31 +G* calculation (in units of km/mol). b, Vibrational modes which arise predominantly from one subunit are indicated. The others arise from mixture of subunit modes and intermolecular degrees of freedom. Table 5 G2 (MP2 ) energies ‘)
HF AlF, HAlF, C,( 1) l)
J&(au)
Do (kJ/mol)
0. (kJ/mol)
-100.34704 -541.48824 -641.85784
59.2
67.1
Scaled (0.893) HF/6-31G* frequencies used for zero-point energies.
Table 6 Thermodynamic functions for complex formation A&+HF+ HF-AlF, ‘) T(K)
MT
273 498 598 648 698 748 1148
-61.8 -60.4 -59.4 -58.9 -58.4 -57.9 -53.2
l)
(kJ/mOl)
-TAS
32.7 57.8 68.4 73.6 78.7 83.8 122.9
(kJ/mol)
is 67.1 kJ/mol without zero-point energies (0,) and 59.2 kT/mol with zero-point energies (Do). The G2( MP2) value of De is in agreement with the HF/ DZP and HF/TZZP values for 0, (67.0 and 64.1 kJ/ mol, respectively) that were corrected for basis set superposition error (BSSE). The thermodynamic functions of complex formation of HF-AlF3 were calculated within the standard rigid-rotor harmonicoscillator ideal-gas approximation [ lo]. They were calculated using the G2(MP2) dissociation energy D,, the MP2 (FULL) /6-3 1 + G* equilibrium geometry and MP2( FULL) /6-3 1+G* vibrational frequencies. Values from 298 to 1148 K are listed in table 6.
K (atm-‘) 3.67x 10’ 1.84 0.16 0.06 0.03 0.02 6.7x IO-’
Reaction energy at 0 K is - 67.1 kJ/mol; reaction enthalpy at 0 K is - 58.8 kJ/mol.
barrier to rotation of the HF subunit about AlF3. The dissociation energy for the HF-AlF, complex (eq. ( 1) ) was derived from G2 (MP2) theory. The results are listed in table 5. The dissociation energy
4. Conclusions The following conclusions can be drawn from this ab initio molecular orbital study of the HF-AlF3 complex: ( 1) The equilibrium structure has C, symmetry with HF attached to AlF3 by a long F-Al bond ( e 1.99 A) and the hydrogen interacting with one of the fluorines of AlF, in a cyclic arrangement. There is a low barrier (5 kJ/mol) for rotation of the HF subunit about the F-AI bond. (2) The C, structure is the only local minimum that was located. The face-bridged, comer-bridged and edge-bridgedstructures that have been found for 553
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CHEMICALPHYSICSLETTERS
other alkali fluoride complexes are saddle points in the potential energy surface of the HF-AlF3 complexes. (3 ) The dissociation energy 0, of the HF-AIF complex is 67.1 kJ/mol from G2( MP2) theory.
References [ 1 ] D. Menz, L. Kolditz, K. Heide, C. Schmidt, Ch. Kunert, Ch. Mensing, H.G. von Schnering and W. Hiinle, 2. Anorg. Allg.Chem. 551 (1987) 231. [2] D.-H. Menz, Ch. Mensing, W. Hlinle, H.G. von Schnering, Z. Anorg. Allg. Chem. 611 (1992) 107. [ 31 G. Scholz, J. Sauer and D.-H. Menz, Chem. Phys. Letters 156 (1989) 125. [4] G. Scholz and L.A. Cur&, J. Mol. Struct. THEOCHEM 258 (1992) 251. [ 5] A. Burkhardt, U. Wedig, G. Scholz and D. Menz, Chem. Phys. Letters 182 (1991) 556. [6] G. Scbolz, C. Nieke, D.-H. Menz and L. Kolditz, J. Mol. Struct. THEOCHEM 231 (1991) 95. [7] C. Nieke, G. Scholz and D.-H. Menz, .I. Fluor. Chem., in press. (81 L.A. Curt& K. Raghavachari and J.A. Pople, J. Chem. Phys., in press. [9] P.C. Hariharan and J.A. Pople, Theoret. Chim. Acta 28 (1973) 213.
554
23 April 1993
[lo] W.J. Hehre, L. Radom, P. von R. Schleyer and J.A. Pople, Ab initio molecularorbital theory (Wiley,New York, 1986). [ 111T. Clark, J. Chandrashekar, G.W. Spitznagel and P. von R. Scbleyer,J. Comput. Chem. 4 ( 1983) 294. [ 121T.H. Dunning Jr., J. Chem. Phys. 53 (1970) 2823. [ 131T.H. Dunning Jr. and P.J. Hay, in: Methods of electronic structure theory, Gaussian basis sets for molecular calculations,ed. H.F. SchaeferIIl (Plenum Press, New York, 1977). [ 141S. Huzinaga, J. Andzelm, M. Klobukowski, E. RadzioA&elm, Y. Sakai and H. Tatewaki, Physical sciencesdata, Vol. 16. Gaussian basis sets for molecular calculations (Elsevier, Amsterdam, 1984). [ 151L.A. Curt& K. Raghavachari,G.W. Trucks and J.A. Pople, J. Chem. Phys. 94 ( 1991) 7221. [ 161R. Ahhichs, R. B&r,M. H&xx, H. Horn and C. Kiilmel, Chem. Phys. Letters 162 (1989) 165. [ 171M.J. Frisch, M. Head-Gordon, G.W. Trucks,J.B. Foresman, H.B. Schlegel, K. Raghavachari, MA. Robb, J.S. Binkley, C. Gonzalez, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger,CF. Melius,J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart,S. Topiol and J.A. Pople, GAUSSIAN90 (Gaussian Inc., Pittsburgh, PA, 1990). [ 181K.R. Roby, Mol. Phys. 27 (1974) 81. [ 191C. Ehrhardt and R. Ahlrichs,Theoret. Chim. Acta 68 (1985) 231. [20] M.W. Chase Jr., CA. Davis, J.R. Downey Jr., D.J. F~rip, R.A. McDonald and A.N. Syvemd, J. Phys. Chem. Data 14 Suppl. 1 (1985).