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Ab initio molecular orbital studies of the structure and potential energy surface of the LiAlF4 complex
Voiume
68. number 1
AB INITIO
CHEMICAL
MOLECULAR
OF THE STRUCTURE L-A. CURTISS Clreffricfit Engineering
ORBITAL
STUDIES
AND POTENTIAL
Diz ision. Argonne
1 December 1979
PHYSICS LETTERS
ENERGY
IVariotlal Laborator3;
Received 3 July 1979: in final form 12 September
SURFACE
Argonm.
OF THE LiAiF4 COMPLEX *
IIhois
60139,
USA
1979
Ab initio moIecular orbital cakulations ha\e been carried out on various structures of the LiAlF4 complex using minimal and extended basis sets. A C2v structure u ith two fluorines in the bridge was found to be more stable than structures with one and three fluorines in the bridge_ Migration of the Li* in the complex is found to be relatively easy and the AWg anion is found to be distorted from tetrahedral s: mmetry.
I. Introduction In recent years there has been considerable interest concerning the structures of gaseous halide complexes [l-3] _Among the complexes of interest are those present in vapors above equimolar mixtures of MX and AlX3 (M = Li, Ka, K, Rb. Cs, and X = F. Ci, Br). They have been studied by a number of techniques including electron diffraction [4-61 and infrared matrix isolation [7-IO]. The structures of the MAlX4 complexes are generally postulated to contain a fairly rigid tetrahedral AIX4 fragment with one. two, or three X atoms acting as a bridge between the alkali atom (hl) and the ah.u-ninumatom_ The experimental studies have resulted in conflicting conclusions as to the actual moIecuIsr shapes of these complexes_ In the study detaiied here, ab initio molecular orbital calculations have been carried out on the complex between JJF and AIF, to determine its structure_ This complex was chosen because it should be a representative model for the MA& complexes such as NaAIF4, KAIC14, etc_ Previous ab initio molecular orbital studies have led to reasonabIe srructures for a number of metal halidedimersincludingAl,F6 [11,12],A12C16 [11,12]. Li2F2 [Il,13,14],andNa7F, [i4] providinganadequate basis set is used. Besides investigatingthe struc* Workperformedundertheauspices of theMiaterid Science Office of the Divisionof Basic Energy Science of the Department of Energy-
ture of LiAlF4 we have also looked at (1) the rigidity of the AIF group; (2) the mobility of the Li atom about the AIFj group; (3) the electron distribution in the complex by the use of Mull&en populations; and (4) the binding energy of the complex.
2. Method of calcuIation Standard LCAO SCF methods were used in this study of LiAlF4. Calculations were carried out using two basis sets. The first is the minimal STO-3G basis set (basis A) [ 15]_ Dill et al. [ 161 have optimized the geometry of LiF using the STO-3G basis set_ The STO3G optimized geometries of AIF and LiF are given in table I _The AIF geometry is in good agreement with experiment. In the case of LiF, the STO-3G basis underestimates the bond length by a considerable amount (0_155 A). presumably because of the large ionic character of LiF. The second basis set, referred to as B, is composed of the 6-31G basis on Li [IY] and F [20] and Huzinaga’s [21] (11~7~) primitive set reduced to [Ss4p] according to Dunning’s [22] contraction on Al_ The optimized geometries of both A1F3 and LiF given in table 1 using basis set B are in good agreement with experiment_ Hence, it is reasonable to assume that this basis set will do welI for the structure of LiAlF,. Three structures subject only to Imposed symmetries were investigated for LiAIF4 _ The various geometrical 225
I December 1979
CHEMICAL PHYSICS LETTERS
Volume 68. number 1
Table I Cptimized geometries and total energ& of AIFs and LIF using basis sets A and B (described in text) --_---_-_________-_-_______ --__ MolecuIe -______
B&.5 __ ___~____
LiF
MF3
-~
Energ,>-(au)
A B A B __--___-.____
X31X bond ~ngIe*~)
MX bond Iergth n*b) theory
exp.=)
theory
- 105.37309 - 1069109 1
1.109 1573
1564
-
-533.24983 -540.35466 -___
1.600 1.659
1.63+0.01
120.0 120.0
___--
.__
exp.=)
120.0
‘) Bond Ien$hs in A and bond sr&s in degrw; Y = Li. A! and X = F; AIFx is assumed to have C sv symmetry in the geometry optimization b)The LiF basis set A result is from ref- [ 161. AU other resuhs are from ref. [ 1 I ] and this work_ C)LiF:ref_ fl7~1AiF~rreL [IS]_ parameters were optimized
with respect to the total
energy_ The resulting bondlengths and bond angles are believed to have computational uncertainties of 0.01 i\ and I”. respectively_
3. Results and discussion
slightly (to 1.69 A) in the compiex from their value in the AIF monomer (1.66 A) while the F at lm in the bridge is at a distance of 1.77 a from the Al atom. The assumption of CgV symmetry for structure I was tested by rotating the Li about an axis passing through the Al and perpendicular to one of the symmetry planes (descnied by B = LLiAIF’ in fig_ la)_ It was found that moving the Li off the C3 axis in either direction by small
3. I. Opritnikedgeomertfes F The three structures investigated for LiAIF4.
illustrated in fig_ 1 have been The Li atom is bridged
to the
\
AI atom by one, two or three F atoms- In each structure
the Al atom has four F atoms surrounding it_ The structures Iooked at here can be considered as a LiF molecule approaching an AiF moIecuIe or as a Li atom approaching a tetrahedral AIF, group. In the discussion of the geometry optimizations of the three structures to folIow, we refer to the results only in terms of the latter picture for the sake of simplicity_ All of the bond lengths. bond a&es, and binding energies discussed in this section are from basis set B calculatio_ns. unIess otherwise specifiedStructure 1 consists of a Li atom approaching one of the F atoms of a tetrahedral AIF group_ In the geometry optimization procedure C3v symmetry is assumed initialIy with the Al, L.i and bridge F all lying on the C3 axis. The parameters optimized are listed in table 2 aIong VGXI their resuIting values. The tetrahedral symmetry of the AIF group is distorted by the Li atom so that the terminal Al-F bonds make an angle of 103.1” with the C, axis (compared to the tetrahedral angle of 109_!?). The terminal AI-F bond lengths increase only 226
F 7
Q-j
AI
)e
_____-c-----Li
I F
& f x,
F;
\
_J/
\
\
\
-----+_
I\
F”
/
/
/
/ II
Fig_ l_ Three possible structures for Li.AIF4_
Volume 68. number 1 Table 2 Optimizedgeometries ___Structure b,
---I
II
III
CHEMICAL
ofLiAIF4
PHYSICS LETTERS
---
Parameter
Basis set A
Basis set B
r(Al-Li) r(AI-F’j r(AI-F) L F’AlF
3.196 1.723 1.616 100.0
3.397 1.769 1.686 103.1
2.440 1.683 1.606
2.647 1.764 1.673
r(AI-LI) r(Al-F’; -r(AI-F) L F’AIF
L FAIF
84.2 1215
845 IiS_8
r(Al-Li) &Xl-F’) r(Al-F) L F’AIF
1.133 1.651 1.606 125.3
2.361 I-736 1.662 124.6
a> Bond Iengtbs in A. XI&S in desee. b, IUustrated in fg. I. Structures I and III resrricred to C3v symmetry: structure II restricted to G., symmetry.
amounts ied to increases in enero,_ Rotation of Li by 0 = 10” towards the single F atom led to an increase in energy of 0.48 kcal mol-1 (the AIF group is kept fixed at its optimized geometry in the complex) while rotation of the J_i by 0 = - 10” towards the pair of F atoms led to an increase in energy of 055 kcal mol-l_ These results indicate that for structure I the C3v symmetry is a definite minimum in the potential energy surface and that it takes little energy to move the Li about the AIF group_ Structure II has a Li atom approaching the tetrahedra1 AIF group to form a planar ring with two F atoms as a bridge. In the geometry optimization of this complex Czv symmetry was assumed initially and the parameters optimized are given in table 2 along with the resulting values- The tetrahedral symmetry of the _41F4 group is again distorted by the Li atom so that the bridge F’Al-F’ bond angle decreases to 84_5O and the terminal F-Al-F bond angle increases to 1 l&S”_ The terminal AI-F bond lengths again increase only slightly from their value in the _AlF, monomer while the F atoms in the bridge are 1_76A from the AI_ Distortions of structure II away from the C,, symmetry were considered by rotating the Li about the x1 axis and the terminal fluorines about the x2 axis (see fig_ 1). Rotation of the Li about x1 by 5” adb IO”.
1 December 1979
keeping its distance from the Al constant, led to increases in energy of 0.46 kcal mol-l and I.88 kcal mol- t , respectively_ Rotation of the terminal F atoms about the x- axis by 5” and IO” led to increases in energy of 034 kcaI molW1 and 135 kcal mol-1 , respectively_ Hence, the Cav structure is a definite minimum in the potential energy surface. The third structure (III) considered for LiAlF4 had the Li coordinated with three F atoms of a tetrahedral AIF as ilIustrated in fig. 1. The structure was assumed to have C3v symmetry initially in the geometry optimization procedure. The optimized parameters and their values are listed in table 2. The F ‘AIF angle increases from its tetrahedral value of iO9.5” to 124.6” in the complex. The bridge &’ bond distance increases to 1.736A in the complex while the terminal AlF bond is 1.662 A which is close to its value of 1.66i% in the monomer. The assumption was tested
of C,,
by rotating
symmetry
for structure
III
the Li off the C3 axis in he same
way as was done for structure 1. It was found that moving Li off the C, axis in either direction by small amounts (SO or lOa) led to increases in energy- Hence;the structure with C,, symmetry appears to be a definite minimum in the potential energy surface_
Table 3 gives the total energies for the three structures of LiAIF4 calcuIated with the two basis sets. The minimal STO-3G basis set (A) predicts that structure III is 16.7 kcal mol-l more stable than structure II. The extended basis set (B) predicts that structure II is more stable than structure III by 8.8 kcal mol-I_ The extended basis set results are probably more reliable since it gives a more fIexiiIe description of the molecular orbitals and it does a better job on the LiF monomer than does the ST03G basis set_ ResuIts from both basis sets indicate th& structure I is the least stable. However, more sophisticated calculations are required to substantiate these conclusions_ The inclusion of d-functions and electron correlation could change the ordering of the stability of the I_iAlF4 structures. especially II and III since only 8-S kcaI mol-l separates the two structures. Table 3 also gives the complexation energies for the I.iAIF4 structures (i.e. the difference between the energg of the complex and the sum of the energies of 227
CHEMICAL
Volume 6s. number I Table 3 Total energies of LiAlF4 ______-.__--
StrustureJ)
Basis set A __--_.. cne~y
_______-_ I II ul
opGmixd
(ml)
__ _._- - --638.71647 -638.80930 -638.83584 __~--_.-__-__-
_-
s~ruc~cxs ---_ - .._...--- ----
rrhtivr
--.---.-------
(kcal mol-t ) _ --__.. 65.6 16.7 0
is sometimes
--
-----__---
energy (au)
relative eneqy (kcal mol-‘)
Complexa:ion energy (kc;\1mol-‘)
-65.0 -1 if.0 -1336 __--
-647.39550 -647_41115 -647_40720
16.1 c S-8
-753 -91-4 -82-6
-_--
--__---
TabIe 4 Atomic popuhtions of LiAIF+ a)- AIF F LiALF4 (I) LiAlI=J (II) LiAlF4
g -___~
(III)
9.7077 9.6812 9 6677 9.6668 9.7417
A1
____--1L-0034 10.9949 10.9379 109996 _---_-
and LiF (b.Gs B results) rb) 9.7539 9.7185 9.6996 -
Li 2-l I97 2.105 7 2.2955 2.2573
a) See fg. 1 and rabbb 2 for structures_ b)Tbe bridged fluorines
presented in table 5, the highest occupied orbital is lower in energy than the highest occupied orbitai in structure II.
referred to as a
Iithium cation attached to an AIF; anion. The results in tabIe 4 indicate that this is a fairly accurate picture as the lithium center has a +-O-79e- charge in structure IL Migration of the lithium about the AIF fragment resuIts in changes in the elec?ron distribution in the two fmgments: in structure I the lithium has a charge of +0.88 e- and in structure III it has a charge of +0_70e-_ AIso the eIectron distributions are polarized differently depending on where the lithium is located (see table 4) The calcuIated orbital energies for LiF_ AlF3 and structure II of LiAlF4 at the basis B Ievel are presented in table 5_ Most of the orbital energies of AlF3 are shifted slightly upward in energy in the complex while most of the L.iF orbital energies are shifted slightly downward_ These shifts indicate the stabilizing effect of the AlF3 on LiF in the complex and the destabilizing effect of LiF on AIF _ For structure III, which is not + The vibrationd fkequencies for AlF3 and LiF were taken from ref_ [33] and those for LiAlF4 from ref_ [9]_ 228
-.
complex&on energ> (kcal mol-‘)
LiF and AIFs). The enthalpy of association for LiAlFa (from LiF and AIF3) is -7 I _I3kcal mol-t at 0 K [23]. Correction for differences in zero point \lbrationai energies’ between the comples and the LiF and AiF molecuks gives a complexation energy of -738 kcaI mol- t _ This is in fair agreement with the extended hasis set result for LiAIF4 of -9 1A kcal moI-t. but in very poor agreement with the STO-3G result of -133.6 kca1 mol-t _ Simihr types of discrepancies have been noted in the cases of otlter metal haiide comp&es such as Li7 F1, AIzF6 and A12C16 [ Ill_ An extended basis set with d-functions is probably required to get good greementThe atomic populations [r?4] calculated using basis B for the three structures of LiAIF4 are given in table 4_ The J_iAlF4 complex
---._ Basis set B --~
_-.___._mrqgy
1 Eecember 1979
PHYSICS LEITERS
3.3. Comparisons with experinrenr Esperimentaily, the structure of LiAIF, has not been determined conclusively yet. The C,,, structure has been generally adopted for LiAIF4 = as well as the related complexes such as NaAIF4 and K.AIF4) based on infrared and electron diffraction studies. However, some interpretations indicate +&at the experimental evidence does not distinguish clearly between this structure and alternatives inciuding the two C,, structures (I and III) and a C, structure in which the bridged ring of structure II is nonplanarSeveral infrared spectroscopic studies have been carried out on LiAIF4. In the most recent studies Cyvin et al- [S,9] and Huglen [lo] both found that a C,, model fits their data the best. In an eiectron diffraction study of NaAlF4 Spiridonov and Erokhin [4] found a C,, structure with some possible puckering of the bridge ring to form a C, structure- Vajda et al. [6] reported similar conclusions for KAlF, _
Volume68, number I
CHEMICAL
Table 5 >foIecuInr orbital ener@es n) of the geometry optimized sr~ctures of LiF, AIFs end LiAIF4 __-___- _I-._____---_---LiAlF4 (structure II)
1 December I979
PHYSICS LETTERS
Lrf
AS3
energy
orbiml type b)
energy
orbitei type c)
energy
orbits1 type d)
-58.55281 -26.28182 -2638183 -26.22875 -26.22875 -4.96537 -3.28147 -3.28 145 -3.28027 -250841 - 1.58048 -X55558 -151796 --1.51079 -0.72818 -0.68620 -0.67629 -0.66864 -0.63668 -0.63596 -0.61857 -0.60821 -0.59544 -059528 -0.58479 -0.57868
Al 1s F’ Is F’ Is F Is F Is Al 2s Ai2p XI 2p
-58.61553 --1628418 --3?6.25417 -2618424 -5-0297s -3.34503 -3.34503 -3.34472 -157950 -156657 -156657 -012 197 -0.67732 -0.67732 -0.66387 -0.64101 -0.64101 -0 63889 -0.63889 -0.62650
Al Is F Is F Is F Is Al 2s Al 2p AI 2p AI 2p
-26.09278 -2.44937 -135648 -0.47167 -0-45156 -0.45 156
F Is Li Is a 0 a n
*2P Li Is ns bt 31 bz 31 e1 bt bz 32 =1 bt bz bt 91 =z! bz
& e’ e* ei e’ e’ a; e’ e’ e” e” 5
3 In atomic unirs (I ati = 372 1 eV = 627.5 liea mol-r ). b) LiAIFG: Vaience orbital nota:ion is for C av symmetry ns in ret [25], nuoriues in 1heyz pkne. ‘) AIFs: Valence orbital notstion is for D,h symmetry_ d, LIF: Valence orbitel notation is for C,,, symmetry.
The basic assumption in the LiAIF4 models used in analyzing the infrared data is that the A1F4 group nearly retains its tetrahedral symmetry, based for the most part on the NaA1F4 electron diffraction results Hence, the bridge and external FaIF bond angles are both assumed to be approximately tetrahedral (I09S”) and the bridge and external AIF bond lengths are both taken to be X-68 a. Also the F’LiF’ bond angle is taken to be 107O on the basis of the LiF dirner experimental structure_ In the basis B geometry optimization of structure II the bridge F’AlF’ bond vlgle was found to decrease considerably from its tetrahedral value of 84_?, similar to what was found in calculations on A12FG and A12CIG [ 11) _ The external FAlF bond angle increases to 118.8 _
n~th the bridge fluorines in these phme and the terminai
Also, the bridge AIF bond lengths were 0.09A longer than the extema1 AlF bond lengths and the F’LiF’ bond angle is 83.0° which is slightly smaller than the 9~5~ found for the same angle in Li2F2 [I I] using the same basis. These results indicate that in structure II the AlF4 group is somewhat distorted from its tetrahedral symmetry in disagreement with the models used for LiAIFa which assume a fairly rigid tetrahedraf AlF4 arrangement_ It shotrId also be pointed out that the distortion of the AIFG group from tetrahedral symmetry in structure II is somewhat different from the distortions in I and III. Some of the experimental results on the MAlX4 type complexes 1461 have indicated that the bridged 229
Vofume
68. nitmher
I
CHEMICAL
PIiYSiCS LETXERS
I December 1979
the actual symmetry is C,_ The basis B results show that the structure with Czv symmetry is the most StabIe and is 5 defiite minimum in the porentir.il ene"Dy surface. However, the theoretical resuits do indicate that it takes little energy to move the lithium about the AIF4 fragment. As mentioned eartier rotation of lithium about xl in fig. t by 5’ takes 0.46 kcal mol-1 _Since this is less than kTat 500 K (099 kcjl mol’l), it is possible that distortions of this type ~vnld be easily pi&xc% up by the electron diffmction or infkued studies Also, the fact that structures 11and III are close in energy (823 ken! mui- 1 at the basis B tevei) indkxteo that it would be r&at&&y ensy for fithium ta move about the AIF, fragment making it difficult for the experimental studies to distinguish defmitely between the various structures_ The stretching force constants for structure II of ti41Fa have been determined at the basis B level for comparison with experiment_ The force constants were calculated by quadratic fits j26] to points about the potential encrgg surface minimum using a grid size of 0_02A_ The calcuhted srerching force txxtstnnts for Alp3 and LiF nref,(Al-F) = S-46 mdynfA andfr(Li--F) = 338 mdynf& respectiveIy_ The experimental values for the Al-F and Li-F stretches are 4.9 I mdyr$& [X7] and 287, mdyn[A [tS f , respectivefy. The overestimation of force constants by the theoretical calcuhttions are typical ofab initio tx&xdations at this revel j291_ For the LiAlF+ comple.~ ulculation of the stretching force constants gz~e the following results: &(Al-I+) = 524,f,(Al--F’) = 3-83, and&(Li--F’) = f-07; all in mdyn/A with the prime referring to the bridge Ruorine_The ratio of the terminal ta bridge AI-F stretching force ~.xx~stanfis 137_ Thii is in agreement with the two infrared studies in which ratios of I2X [8,9] and 192 tICl] for the C2v structure were found. Aho, the decrense in the LiF bond stretching force constant in the comPkx is in agreement with infrared studies f8-ltl$ where values of about 0.6 rndyn!A in the complex were reported.. Bnldyrev et nL [30] have reported ab initio cakulations on the compLxes LiI3% and LiBeH3 in which they considered structures which were similar to those optimized in this study of LiAIFa. Their results for these complexes are similar to what has been reported here,
The following conchsions can be drawn from this SCF study of LiAlF4 zrt the extended basis set level: (I) The LiAIFLs structum with two fluorines fomling a planar bridge between the Al and Li and haying C&v symmetry is found to be most stable. The addition of d-functions and electron correlation could change this cxxtctusion_ (2) Migntion of the Li about the AIF fragment: is found to be relatively easy and could account for the experimentat studies not being able to distinguish definitively between the various possible structures for MAlF4 compfexer (3) The structure of the AIF fragment is found ta be distorted in the complex This distortion is found to be dependent on the position of the Li. The eIectron distribution in the complex is aho found to be dependent on the position of the Li in relation to the AIF fragment _ LCAO
Achnowiedgement The author wishes to thank Dr. Milton Blander and for heIpfui discussions_
Dr. George ~apatil~o~u
Ref&-eiWeS 1i 1 ,\f_Haqittai and I- H;~~_i:tai-The moka.&r gcomctries of ccaordimttbn ~ampoands ia the vapcmr ph;ue (E&v&r. Amsterdam. 1977). 12j S-H. Bauerand R-F. Porter, ix Molten nit ehcmistrly,cd.
Y- Blander(Interscience,New York, 1964) Pp. 607-680.
I3j H- Sc&%er, Anger-C&em.. Intern- Ed. I5 f1976) 113. f4 j V-P_ S#ridonov and E-V. Erokhin. Russian 1..Inorg_ Chem. 14 (1969) 33x
Struct. Chem, USSR I2 ci9il) 9961. f6f B Vi&la, I. ilargittai and J. TremmeZ, Inorg. Chim. Acta 25 (1977) Li43. f71 L-D- NcCnry, RX- Paule and J-L_ Margrae, J. Phys. C&an. 67 (1963) 1086. 181 S-J- QMn, B.N. Cyvin. D. Bhogeswara Rae and A. S&son, 2. Anor& Al.& Chem 380 (1971) 312. 191SJ- CWin, B&- Cyvin and A. Snelsen,J. Phya Chem, 75
(197112609. [Ii% R Hu&W PhD- Theah Txondheim, Norway (X976).
Volume 68. number I
CHEMICAL
[ II]
L A Cuttiss, Intern. J. Quantum Chem. 14 (1978) 709. [12! L.A. Curt&. in: Proceedings of the 10th Materials Research Symposium, National Bureau of Standards, 1978. to be published.
[I31 C.P. B&in.
I December
PHYSICS LETTERS [21]
[22]
C.F. Bender and P-A. Kolhnan. J. Am. Chem.
Sot- 95 (1973) 5868. _ [14] Y_ Rupp and R Ahlrichs. Theoret. Chhn. Acta 46 (1977) 117. [ 151 W-J. Hehre. R-F. Stesart and J-A. Pople, J. Chem. Phys. 51 (1969) 2657. [ 161 J-D_ DilI. P. \on R_ Schky er. J-S. Binkley and J.A. Popk, J. Am. Chem. Sot. 99 (1977) 6159_ [17] SE_ Venzy and W_Gordy. Phys. Rev_ 138 (1965) 1303_ [IS] P-A- Akishin, N-G_ Rambidi and EZ_ Zarosin. Kristsllogratiya 4 (1959) 186 [En@ish transi. Russian J. Cry%. 4 (1959) 167][I91 J-D. Drlland J.A. Pople, J. Chem. Phys. 62 (1975) 2921. [ZO] W-l_ H&m. R_ Ditch&Id and J-A_ Pople, J_ Chem- Phys56 (1972) 2257s
!23] [24] [25 ] [26] 1271 [28] [29]
1979
S. HuzinaSa, Approximate Atomic Wave Functions. II, Department of Chemistry Technical Report, University of Alberta, Edmonton, Alberta, Canada (1971) T-H. Dunning Jr. and P.J. Hay, in: Modern theoretical chemistry, Vol. 3, ed. H F. Schaefer III (Plenum Press, New York, 1977) ch. 1. D-R. Stull and H_ Prophet. eds.. JANAF Thermochemical Tables, 2nd Ed.. NSRDS-NBS37 (1971). RS- hlulbken, J. Chem. Phys. 23 (1955) 1833. F.A. Cotton, Chemical applications of group theory (Interscience, New York, 1963). L.A. Curtiss and J-A. Pople, J. hlol. Spectry- 48 (1973) 41:. A_ Snelson, J_ Phyr Chem. 71 (1967) 3202_ G-L. Vidale, J. Phys. Chem. 64 (1960) 314. &f-D_Newton. WA. Lathan, W-H_ Hehre end J_A_ Pople,
J. Chem. Phys. 52 (1970) 4064. [x0] A-1. Boldyrev, 0-P. Charkin, N-G_ Rambidi and V.I. Avdeev, Chem- Phyr
Letters 44 (1976)
20; 50 (1977)
239_
231
68. number 1
AB INITIO
CHEMICAL
MOLECULAR
OF THE STRUCTURE L-A. CURTISS Clreffricfit Engineering
ORBITAL
STUDIES
AND POTENTIAL
Diz ision. Argonne
1 December 1979
PHYSICS LETTERS
ENERGY
IVariotlal Laborator3;
Received 3 July 1979: in final form 12 September
SURFACE
Argonm.
OF THE LiAiF4 COMPLEX *
IIhois
60139,
USA
1979
Ab initio moIecular orbital cakulations ha\e been carried out on various structures of the LiAlF4 complex using minimal and extended basis sets. A C2v structure u ith two fluorines in the bridge was found to be more stable than structures with one and three fluorines in the bridge_ Migration of the Li* in the complex is found to be relatively easy and the AWg anion is found to be distorted from tetrahedral s: mmetry.
I. Introduction In recent years there has been considerable interest concerning the structures of gaseous halide complexes [l-3] _Among the complexes of interest are those present in vapors above equimolar mixtures of MX and AlX3 (M = Li, Ka, K, Rb. Cs, and X = F. Ci, Br). They have been studied by a number of techniques including electron diffraction [4-61 and infrared matrix isolation [7-IO]. The structures of the MAlX4 complexes are generally postulated to contain a fairly rigid tetrahedral AIX4 fragment with one. two, or three X atoms acting as a bridge between the alkali atom (hl) and the ah.u-ninumatom_ The experimental studies have resulted in conflicting conclusions as to the actual moIecuIsr shapes of these complexes_ In the study detaiied here, ab initio molecular orbital calculations have been carried out on the complex between JJF and AIF, to determine its structure_ This complex was chosen because it should be a representative model for the MA& complexes such as NaAIF4, KAIC14, etc_ Previous ab initio molecular orbital studies have led to reasonabIe srructures for a number of metal halidedimersincludingAl,F6 [11,12],A12C16 [11,12]. Li2F2 [Il,13,14],andNa7F, [i4] providinganadequate basis set is used. Besides investigatingthe struc* Workperformedundertheauspices of theMiaterid Science Office of the Divisionof Basic Energy Science of the Department of Energy-
ture of LiAlF4 we have also looked at (1) the rigidity of the AIF group; (2) the mobility of the Li atom about the AIFj group; (3) the electron distribution in the complex by the use of Mull&en populations; and (4) the binding energy of the complex.
2. Method of calcuIation Standard LCAO SCF methods were used in this study of LiAlF4. Calculations were carried out using two basis sets. The first is the minimal STO-3G basis set (basis A) [ 15]_ Dill et al. [ 161 have optimized the geometry of LiF using the STO-3G basis set_ The STO3G optimized geometries of AIF and LiF are given in table I _The AIF geometry is in good agreement with experiment. In the case of LiF, the STO-3G basis underestimates the bond length by a considerable amount (0_155 A). presumably because of the large ionic character of LiF. The second basis set, referred to as B, is composed of the 6-31G basis on Li [IY] and F [20] and Huzinaga’s [21] (11~7~) primitive set reduced to [Ss4p] according to Dunning’s [22] contraction on Al_ The optimized geometries of both A1F3 and LiF given in table 1 using basis set B are in good agreement with experiment_ Hence, it is reasonable to assume that this basis set will do welI for the structure of LiAlF,. Three structures subject only to Imposed symmetries were investigated for LiAIF4 _ The various geometrical 225
I December 1979
CHEMICAL PHYSICS LETTERS
Volume 68. number 1
Table I Cptimized geometries and total energ& of AIFs and LIF using basis sets A and B (described in text) --_---_-_________-_-_______ --__ MolecuIe -______
B&.5 __ ___~____
LiF
MF3
-~
Energ,>-(au)
A B A B __--___-.____
X31X bond ~ngIe*~)
MX bond Iergth n*b) theory
exp.=)
theory
- 105.37309 - 1069109 1
1.109 1573
1564
-
-533.24983 -540.35466 -___
1.600 1.659
1.63+0.01
120.0 120.0
___--
.__
exp.=)
120.0
‘) Bond Ien$hs in A and bond sr&s in degrw; Y = Li. A! and X = F; AIFx is assumed to have C sv symmetry in the geometry optimization b)The LiF basis set A result is from ref- [ 161. AU other resuhs are from ref. [ 1 I ] and this work_ C)LiF:ref_ fl7~1AiF~rreL [IS]_ parameters were optimized
with respect to the total
energy_ The resulting bondlengths and bond angles are believed to have computational uncertainties of 0.01 i\ and I”. respectively_
3. Results and discussion
slightly (to 1.69 A) in the compiex from their value in the AIF monomer (1.66 A) while the F at lm in the bridge is at a distance of 1.77 a from the Al atom. The assumption of CgV symmetry for structure I was tested by rotating the Li about an axis passing through the Al and perpendicular to one of the symmetry planes (descnied by B = LLiAIF’ in fig_ la)_ It was found that moving the Li off the C3 axis in either direction by small
3. I. Opritnikedgeomertfes F The three structures investigated for LiAIF4.
illustrated in fig_ 1 have been The Li atom is bridged
to the
\
AI atom by one, two or three F atoms- In each structure
the Al atom has four F atoms surrounding it_ The structures Iooked at here can be considered as a LiF molecule approaching an AiF moIecuIe or as a Li atom approaching a tetrahedral AIF, group. In the discussion of the geometry optimizations of the three structures to folIow, we refer to the results only in terms of the latter picture for the sake of simplicity_ All of the bond lengths. bond a&es, and binding energies discussed in this section are from basis set B calculatio_ns. unIess otherwise specifiedStructure 1 consists of a Li atom approaching one of the F atoms of a tetrahedral AIF group_ In the geometry optimization procedure C3v symmetry is assumed initialIy with the Al, L.i and bridge F all lying on the C3 axis. The parameters optimized are listed in table 2 aIong VGXI their resuIting values. The tetrahedral symmetry of the AIF group is distorted by the Li atom so that the terminal Al-F bonds make an angle of 103.1” with the C, axis (compared to the tetrahedral angle of 109_!?). The terminal AI-F bond lengths increase only 226
F 7
Q-j
AI
)e
_____-c-----Li
I F
& f x,
F;
\
_J/
\
\
\
-----+_
I\
F”
/
/
/
/ II
Fig_ l_ Three possible structures for Li.AIF4_
Volume 68. number 1 Table 2 Optimizedgeometries ___Structure b,
---I
II
III
CHEMICAL
ofLiAIF4
PHYSICS LETTERS
---
Parameter
Basis set A
Basis set B
r(Al-Li) r(AI-F’j r(AI-F) L F’AlF
3.196 1.723 1.616 100.0
3.397 1.769 1.686 103.1
2.440 1.683 1.606
2.647 1.764 1.673
r(AI-LI) r(Al-F’; -r(AI-F) L F’AIF
L FAIF
84.2 1215
845 IiS_8
r(Al-Li) &Xl-F’) r(Al-F) L F’AIF
1.133 1.651 1.606 125.3
2.361 I-736 1.662 124.6
a> Bond Iengtbs in A. XI&S in desee. b, IUustrated in fg. I. Structures I and III resrricred to C3v symmetry: structure II restricted to G., symmetry.
amounts ied to increases in enero,_ Rotation of Li by 0 = 10” towards the single F atom led to an increase in energy of 0.48 kcal mol-1 (the AIF group is kept fixed at its optimized geometry in the complex) while rotation of the J_i by 0 = - 10” towards the pair of F atoms led to an increase in energy of 055 kcal mol-l_ These results indicate that for structure I the C3v symmetry is a definite minimum in the potential energy surface and that it takes little energy to move the Li about the AIF group_ Structure II has a Li atom approaching the tetrahedra1 AIF group to form a planar ring with two F atoms as a bridge. In the geometry optimization of this complex Czv symmetry was assumed initially and the parameters optimized are given in table 2 along with the resulting values- The tetrahedral symmetry of the _41F4 group is again distorted by the Li atom so that the bridge F’Al-F’ bond angle decreases to 84_5O and the terminal F-Al-F bond angle increases to 1 l&S”_ The terminal AI-F bond lengths again increase only slightly from their value in the _AlF, monomer while the F atoms in the bridge are 1_76A from the AI_ Distortions of structure II away from the C,, symmetry were considered by rotating the Li about the x1 axis and the terminal fluorines about the x2 axis (see fig_ 1). Rotation of the Li about x1 by 5” adb IO”.
1 December 1979
keeping its distance from the Al constant, led to increases in energy of 0.46 kcal mol-l and I.88 kcal mol- t , respectively_ Rotation of the terminal F atoms about the x- axis by 5” and IO” led to increases in energy of 034 kcaI molW1 and 135 kcal mol-1 , respectively_ Hence, the Cav structure is a definite minimum in the potential energy surface. The third structure (III) considered for LiAlF4 had the Li coordinated with three F atoms of a tetrahedral AIF as ilIustrated in fig. 1. The structure was assumed to have C3v symmetry initially in the geometry optimization procedure. The optimized parameters and their values are listed in table 2. The F ‘AIF angle increases from its tetrahedral value of iO9.5” to 124.6” in the complex. The bridge &’ bond distance increases to 1.736A in the complex while the terminal AlF bond is 1.662 A which is close to its value of 1.66i% in the monomer. The assumption was tested
of C,,
by rotating
symmetry
for structure
III
the Li off the C3 axis in he same
way as was done for structure 1. It was found that moving Li off the C, axis in either direction by small amounts (SO or lOa) led to increases in energy- Hence;the structure with C,, symmetry appears to be a definite minimum in the potential energy surface_
Table 3 gives the total energies for the three structures of LiAIF4 calcuIated with the two basis sets. The minimal STO-3G basis set (A) predicts that structure III is 16.7 kcal mol-l more stable than structure II. The extended basis set (B) predicts that structure II is more stable than structure III by 8.8 kcal mol-I_ The extended basis set results are probably more reliable since it gives a more fIexiiIe description of the molecular orbitals and it does a better job on the LiF monomer than does the ST03G basis set_ ResuIts from both basis sets indicate th& structure I is the least stable. However, more sophisticated calculations are required to substantiate these conclusions_ The inclusion of d-functions and electron correlation could change the ordering of the stability of the I_iAlF4 structures. especially II and III since only 8-S kcaI mol-l separates the two structures. Table 3 also gives the complexation energies for the I.iAIF4 structures (i.e. the difference between the energg of the complex and the sum of the energies of 227
CHEMICAL
Volume 6s. number I Table 3 Total energies of LiAlF4 ______-.__--
StrustureJ)
Basis set A __--_.. cne~y
_______-_ I II ul
opGmixd
(ml)
__ _._- - --638.71647 -638.80930 -638.83584 __~--_.-__-__-
_-
s~ruc~cxs ---_ - .._...--- ----
rrhtivr
--.---.-------
(kcal mol-t ) _ --__.. 65.6 16.7 0
is sometimes
--
-----__---
energy (au)
relative eneqy (kcal mol-‘)
Complexa:ion energy (kc;\1mol-‘)
-65.0 -1 if.0 -1336 __--
-647.39550 -647_41115 -647_40720
16.1 c S-8
-753 -91-4 -82-6
-_--
--__---
TabIe 4 Atomic popuhtions of LiAIF+ a)- AIF F LiALF4 (I) LiAlI=J (II) LiAlF4
g -___~
(III)
9.7077 9.6812 9 6677 9.6668 9.7417
A1
____--1L-0034 10.9949 10.9379 109996 _---_-
and LiF (b.Gs B results) rb) 9.7539 9.7185 9.6996 -
Li 2-l I97 2.105 7 2.2955 2.2573
a) See fg. 1 and rabbb 2 for structures_ b)Tbe bridged fluorines
presented in table 5, the highest occupied orbital is lower in energy than the highest occupied orbitai in structure II.
referred to as a
Iithium cation attached to an AIF; anion. The results in tabIe 4 indicate that this is a fairly accurate picture as the lithium center has a +-O-79e- charge in structure IL Migration of the lithium about the AIF fragment resuIts in changes in the elec?ron distribution in the two fmgments: in structure I the lithium has a charge of +0.88 e- and in structure III it has a charge of +0_70e-_ AIso the eIectron distributions are polarized differently depending on where the lithium is located (see table 4) The calcuIated orbital energies for LiF_ AlF3 and structure II of LiAlF4 at the basis B Ievel are presented in table 5_ Most of the orbital energies of AlF3 are shifted slightly upward in energy in the complex while most of the L.iF orbital energies are shifted slightly downward_ These shifts indicate the stabilizing effect of the AlF3 on LiF in the complex and the destabilizing effect of LiF on AIF _ For structure III, which is not + The vibrationd fkequencies for AlF3 and LiF were taken from ref_ [33] and those for LiAlF4 from ref_ [9]_ 228
-.
complex&on energ> (kcal mol-‘)
LiF and AIFs). The enthalpy of association for LiAlFa (from LiF and AIF3) is -7 I _I3kcal mol-t at 0 K [23]. Correction for differences in zero point \lbrationai energies’ between the comples and the LiF and AiF molecuks gives a complexation energy of -738 kcaI mol- t _ This is in fair agreement with the extended hasis set result for LiAIF4 of -9 1A kcal moI-t. but in very poor agreement with the STO-3G result of -133.6 kca1 mol-t _ Simihr types of discrepancies have been noted in the cases of otlter metal haiide comp&es such as Li7 F1, AIzF6 and A12C16 [ Ill_ An extended basis set with d-functions is probably required to get good greementThe atomic populations [r?4] calculated using basis B for the three structures of LiAIF4 are given in table 4_ The J_iAlF4 complex
---._ Basis set B --~
_-.___._mrqgy
1 Eecember 1979
PHYSICS LEITERS
3.3. Comparisons with experinrenr Esperimentaily, the structure of LiAIF, has not been determined conclusively yet. The C,,, structure has been generally adopted for LiAIF4 = as well as the related complexes such as NaAIF4 and K.AIF4) based on infrared and electron diffraction studies. However, some interpretations indicate +&at the experimental evidence does not distinguish clearly between this structure and alternatives inciuding the two C,, structures (I and III) and a C, structure in which the bridged ring of structure II is nonplanarSeveral infrared spectroscopic studies have been carried out on LiAIF4. In the most recent studies Cyvin et al- [S,9] and Huglen [lo] both found that a C,, model fits their data the best. In an eiectron diffraction study of NaAlF4 Spiridonov and Erokhin [4] found a C,, structure with some possible puckering of the bridge ring to form a C, structure- Vajda et al. [6] reported similar conclusions for KAlF, _
Volume68, number I
CHEMICAL
Table 5 >foIecuInr orbital ener@es n) of the geometry optimized sr~ctures of LiF, AIFs end LiAIF4 __-___- _I-._____---_---LiAlF4 (structure II)
1 December I979
PHYSICS LETTERS
Lrf
AS3
energy
orbiml type b)
energy
orbitei type c)
energy
orbits1 type d)
-58.55281 -26.28182 -2638183 -26.22875 -26.22875 -4.96537 -3.28147 -3.28 145 -3.28027 -250841 - 1.58048 -X55558 -151796 --1.51079 -0.72818 -0.68620 -0.67629 -0.66864 -0.63668 -0.63596 -0.61857 -0.60821 -0.59544 -059528 -0.58479 -0.57868
Al 1s F’ Is F’ Is F Is F Is Al 2s Ai2p XI 2p
-58.61553 --1628418 --3?6.25417 -2618424 -5-0297s -3.34503 -3.34503 -3.34472 -157950 -156657 -156657 -012 197 -0.67732 -0.67732 -0.66387 -0.64101 -0.64101 -0 63889 -0.63889 -0.62650
Al Is F Is F Is F Is Al 2s Al 2p AI 2p AI 2p
-26.09278 -2.44937 -135648 -0.47167 -0-45156 -0.45 156
F Is Li Is a 0 a n
*2P Li Is ns bt 31 bz 31 e1 bt bz 32 =1 bt bz bt 91 =z! bz
& e’ e* ei e’ e’ a; e’ e’ e” e” 5
3 In atomic unirs (I ati = 372 1 eV = 627.5 liea mol-r ). b) LiAIFG: Vaience orbital nota:ion is for C av symmetry ns in ret [25], nuoriues in 1heyz pkne. ‘) AIFs: Valence orbital notstion is for D,h symmetry_ d, LIF: Valence orbitel notation is for C,,, symmetry.
The basic assumption in the LiAIF4 models used in analyzing the infrared data is that the A1F4 group nearly retains its tetrahedral symmetry, based for the most part on the NaA1F4 electron diffraction results Hence, the bridge and external FaIF bond angles are both assumed to be approximately tetrahedral (I09S”) and the bridge and external AIF bond lengths are both taken to be X-68 a. Also the F’LiF’ bond angle is taken to be 107O on the basis of the LiF dirner experimental structure_ In the basis B geometry optimization of structure II the bridge F’AlF’ bond vlgle was found to decrease considerably from its tetrahedral value of 84_?, similar to what was found in calculations on A12FG and A12CIG [ 11) _ The external FAlF bond angle increases to 118.8 _
n~th the bridge fluorines in these phme and the terminai
Also, the bridge AIF bond lengths were 0.09A longer than the extema1 AlF bond lengths and the F’LiF’ bond angle is 83.0° which is slightly smaller than the 9~5~ found for the same angle in Li2F2 [I I] using the same basis. These results indicate that in structure II the AlF4 group is somewhat distorted from its tetrahedral symmetry in disagreement with the models used for LiAIFa which assume a fairly rigid tetrahedraf AlF4 arrangement_ It shotrId also be pointed out that the distortion of the AIFG group from tetrahedral symmetry in structure II is somewhat different from the distortions in I and III. Some of the experimental results on the MAlX4 type complexes 1461 have indicated that the bridged 229
Vofume
68. nitmher
I
CHEMICAL
PIiYSiCS LETXERS
I December 1979
the actual symmetry is C,_ The basis B results show that the structure with Czv symmetry is the most StabIe and is 5 defiite minimum in the porentir.il ene"Dy surface. However, the theoretical resuits do indicate that it takes little energy to move the lithium about the AIF4 fragment. As mentioned eartier rotation of lithium about xl in fig. t by 5’ takes 0.46 kcal mol-1 _Since this is less than kTat 500 K (099 kcjl mol’l), it is possible that distortions of this type ~vnld be easily pi&xc% up by the electron diffmction or infkued studies Also, the fact that structures 11and III are close in energy (823 ken! mui- 1 at the basis B tevei) indkxteo that it would be r&at&&y ensy for fithium ta move about the AIF, fragment making it difficult for the experimental studies to distinguish defmitely between the various structures_ The stretching force constants for structure II of ti41Fa have been determined at the basis B level for comparison with experiment_ The force constants were calculated by quadratic fits j26] to points about the potential encrgg surface minimum using a grid size of 0_02A_ The calcuhted srerching force txxtstnnts for Alp3 and LiF nref,(Al-F) = S-46 mdynfA andfr(Li--F) = 338 mdynf& respectiveIy_ The experimental values for the Al-F and Li-F stretches are 4.9 I mdyr$& [X7] and 287, mdyn[A [tS f , respectivefy. The overestimation of force constants by the theoretical calcuhttions are typical ofab initio tx&xdations at this revel j291_ For the LiAlF+ comple.~ ulculation of the stretching force constants gz~e the following results: &(Al-I+) = 524,f,(Al--F’) = 3-83, and&(Li--F’) = f-07; all in mdyn/A with the prime referring to the bridge Ruorine_The ratio of the terminal ta bridge AI-F stretching force ~.xx~stanfis 137_ Thii is in agreement with the two infrared studies in which ratios of I2X [8,9] and 192 tICl] for the C2v structure were found. Aho, the decrense in the LiF bond stretching force constant in the comPkx is in agreement with infrared studies f8-ltl$ where values of about 0.6 rndyn!A in the complex were reported.. Bnldyrev et nL [30] have reported ab initio cakulations on the compLxes LiI3% and LiBeH3 in which they considered structures which were similar to those optimized in this study of LiAIFa. Their results for these complexes are similar to what has been reported here,
The following conchsions can be drawn from this SCF study of LiAlF4 zrt the extended basis set level: (I) The LiAIFLs structum with two fluorines fomling a planar bridge between the Al and Li and haying C&v symmetry is found to be most stable. The addition of d-functions and electron correlation could change this cxxtctusion_ (2) Migntion of the Li about the AIF fragment: is found to be relatively easy and could account for the experimentat studies not being able to distinguish definitively between the various possible structures for MAlF4 compfexer (3) The structure of the AIF fragment is found ta be distorted in the complex This distortion is found to be dependent on the position of the Li. The eIectron distribution in the complex is aho found to be dependent on the position of the Li in relation to the AIF fragment _ LCAO
Achnowiedgement The author wishes to thank Dr. Milton Blander and for heIpfui discussions_
Dr. George ~apatil~o~u
Ref&-eiWeS 1i 1 ,\f_Haqittai and I- H;~~_i:tai-The moka.&r gcomctries of ccaordimttbn ~ampoands ia the vapcmr ph;ue (E&v&r. Amsterdam. 1977). 12j S-H. Bauerand R-F. Porter, ix Molten nit ehcmistrly,cd.
Y- Blander(Interscience,New York, 1964) Pp. 607-680.
I3j H- Sc&%er, Anger-C&em.. Intern- Ed. I5 f1976) 113. f4 j V-P_ S#ridonov and E-V. Erokhin. Russian 1..Inorg_ Chem. 14 (1969) 33x
Struct. Chem, USSR I2 ci9il) 9961. f6f B Vi&la, I. ilargittai and J. TremmeZ, Inorg. Chim. Acta 25 (1977) Li43. f71 L-D- NcCnry, RX- Paule and J-L_ Margrae, J. Phys. C&an. 67 (1963) 1086. 181 S-J- QMn, B.N. Cyvin. D. Bhogeswara Rae and A. S&son, 2. Anor& Al.& Chem 380 (1971) 312. 191SJ- CWin, B&- Cyvin and A. Snelsen,J. Phya Chem, 75
(197112609. [Ii% R Hu&W PhD- Theah Txondheim, Norway (X976).
Volume 68. number I
CHEMICAL
[ II]
L A Cuttiss, Intern. J. Quantum Chem. 14 (1978) 709. [12! L.A. Curt&. in: Proceedings of the 10th Materials Research Symposium, National Bureau of Standards, 1978. to be published.
[I31 C.P. B&in.
I December
PHYSICS LETTERS [21]
[22]
C.F. Bender and P-A. Kolhnan. J. Am. Chem.
Sot- 95 (1973) 5868. _ [14] Y_ Rupp and R Ahlrichs. Theoret. Chhn. Acta 46 (1977) 117. [ 151 W-J. Hehre. R-F. Stesart and J-A. Pople, J. Chem. Phys. 51 (1969) 2657. [ 161 J-D_ DilI. P. \on R_ Schky er. J-S. Binkley and J.A. Popk, J. Am. Chem. Sot. 99 (1977) 6159_ [17] SE_ Venzy and W_Gordy. Phys. Rev_ 138 (1965) 1303_ [IS] P-A- Akishin, N-G_ Rambidi and EZ_ Zarosin. Kristsllogratiya 4 (1959) 186 [En@ish transi. Russian J. Cry%. 4 (1959) 167][I91 J-D. Drlland J.A. Pople, J. Chem. Phys. 62 (1975) 2921. [ZO] W-l_ H&m. R_ Ditch&Id and J-A_ Pople, J_ Chem- Phys56 (1972) 2257s
!23] [24] [25 ] [26] 1271 [28] [29]
1979
S. HuzinaSa, Approximate Atomic Wave Functions. II, Department of Chemistry Technical Report, University of Alberta, Edmonton, Alberta, Canada (1971) T-H. Dunning Jr. and P.J. Hay, in: Modern theoretical chemistry, Vol. 3, ed. H F. Schaefer III (Plenum Press, New York, 1977) ch. 1. D-R. Stull and H_ Prophet. eds.. JANAF Thermochemical Tables, 2nd Ed.. NSRDS-NBS37 (1971). RS- hlulbken, J. Chem. Phys. 23 (1955) 1833. F.A. Cotton, Chemical applications of group theory (Interscience, New York, 1963). L.A. Curtiss and J-A. Pople, J. hlol. Spectry- 48 (1973) 41:. A_ Snelson, J_ Phyr Chem. 71 (1967) 3202_ G-L. Vidale, J. Phys. Chem. 64 (1960) 314. &f-D_Newton. WA. Lathan, W-H_ Hehre end J_A_ Pople,
J. Chem. Phys. 52 (1970) 4064. [x0] A-1. Boldyrev, 0-P. Charkin, N-G_ Rambidi and V.I. Avdeev, Chem- Phyr
Letters 44 (1976)
20; 50 (1977)
239_
231