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Can Li2F2 cluster be formed by LiF2/Li2F–Li/F interactions? An ab initio investigation a
Ambrish Kumar Srivastava & Neeraj Misra
Department of Physics, University of Lucknow, Lucknow, Uttar Pradesh 226007, India Published online: 11 Nov 2014.
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Molecular Simulation, 2014 http://dx.doi.org/10.1080/08927022.2014.978314
Can Li2F2 cluster be formed by LiF2/Li2F – Li/F interactions? An ab initio investigation Ambrish Kumar Srivastava and Neeraj Misra* Department of Physics, University of Lucknow, Lucknow, Uttar Pradesh 226007, India (Received 11 June 2014; final version received 15 October 2014)
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Superatoms can be considered as potential building blocks not only of non-traditional species but also of many traditional species. This idea is demonstrated by considering Li2F2, traditionally a dimer of LiF which can be formed either by LiF2 – Li interaction or by Li2F– F interaction using MP2/aug-cc-pVDZ method. The existence of superatomic motifs is discussed in the resulting linear as well as square conformers of Li2F2 which are compared on the basis of the highest occupied molecular orbitals and vibrational properties. Finally, we have established that formation of Li2F2 by these interactions is exothermic at CCSD(T)//MP2/aug-cc-pVDZ level. This study is expected to provide further insights into superatomic interactions and formations of traditional salts. Keywords: superhalogen; superalkali; lithium-fluoride cluster; stability; ab initio method
1. Introduction Superhalogen and superalkali species, introduced by Gutsev and Boldyrev [1,2], have been the focus of much attention for more than three decades. These superatomic species possess higher electron affinity (EA) than halogen and lower ionisation potential (IP) than alkalis, respectively which enables them to be considered as potential building blocks of novel materials with unique properties. Actually, superhalogens and superalkalis are hypervalent clusters possessing excess electrons which can be formed by suitable combination of electropositive central atom and electronegative ligands. Typical examples of conventional superhalogens include LiF2, BeF3, NaCl2, etc.[3 –7] However, superhalogens based on transition metals have been extensively studied due to variable oxidation states of d-group elements.[8 – 17] It has also been emphasised that the superhalogen anions could form complexes by interacting with appropriate metal cations. [13 – 16] Similarly, Li2F and Li3O [18,19] can be considered as typical examples of superalkalis. The superalkali species possess potential reducing capability and can be used in the synthesis of a variety of charge transfer salts. Li2F has been extensively studied theoretically [2,20 – 24] as well as experimentally.[25 –27] Some recent investigations have proposed the formation of non-traditional species by superatomic interactions, named as supersalts with distinguished physical and chemical characteristics. For instance, BF4 2 NLi4 supersalt has been reported to possess remarkable non-linear optical properties  which are even more pronounced in the case of BLi6 2 X supersalts for X ¼ LiF2, BeF3 and BF4. More recently, some new supersalts have been predicted by using superhalogen and
*Corresponding author. Email: [email protected]
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superalkalis as building blocks.[30,31] Unlike traditional salts, supersalts prefer to dissociate into ionic fragments rather than their neutral counterparts. For the first time, we studied the interaction of Li2F with F and that of LiF2 with Li atom which lead to the formation Li2F2, a well-known dimer of LiF molecule. [33,34] We have discussed their molecular orbitals, vibrational characteristics and energetics using ab initio quantum chemical method.
All geometries considered in this study are fully optimised without any symmetry constraints using second-order Mo¨ller – Plesset perturbation theory (MP2). A correlation-consistent double-z type basis set, aug-cc-pVDZ,  is employed throughout these calculations. This basis set expands the atomic orbital of first row elements (Li – Ne) by approximately 14 functions of s, p and d valence shells. Vibrational frequencies are calculated at the same level of theory in order to ensure that the optimised geometries correspond to a true minimum in their potential energy surfaces. All calculations are performed via Gaussian 09 set of programs  and GaussView 5.0 package. Partial atomic charges are computed by natural population analysis (NPA) scheme which have been proven to be more reliable due to less dependency on their basis set. The present computational scheme, MP2/aug-ccpVDZ, has already been used in a previous study dealing with the interaction of superhalogens with alkali and superalkalis. Single-point energy calculations are carried out with the coupled cluster method including
A.K. Srivastava and N. Misra
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Figure 1. (Colour online) Equilibrium geometries of Li2F (left) ˚ ), and LiF2 (right) at MP2/aug-cc-pVDZ level. Bond lengths (in A bond angles (in 8, bold) and NPA charges (in e, italicised) are also shown.
single, double and triple excitations (CCSD(T)) at MP2 optimised geometries. This procedure yields the IP of Li and EA of F, 5.34 eV and 3.13 eV, which are consistent with corresponding experimental values of 5.39 eV  and 3.40 eV, respectively. Furthermore, the bond ˚ , which is very close to length of LiF is calculated as 1.60 A ˚ . the experimental value of 1.56 A
Results and discussion
We begin our discussion by considering the superatomic species Li2F and LiF2. The equilibrium geometries of Li2F and LiF2 at MP2/aug-cc-pVDZ level are displayed in Figure 1. Both species assume bent C2v geometries but the ˚ ) is slightly higher than bond length Li 2 F in LiF2 (1.74 A ˚ that in Li2F (1.71 A). Furthermore, both species are hypervalent possessing excess electrons which delocalise over peripheral atoms as reflected by NPA charges given in Figure 1. For instance, in Li2F, an excess electron delocalises over Li atoms forming a cage of positive charge (Liþ 2 ) such that F possesses its maximum anionic charge (F2). The stability of Li2F is governed by the attractive electrostatic interactions between Liþ 2 cage and the F2 as well as the covalent interactions between the lithium atoms in the cage. In contrast, the stability of LiF2 is only due to ionic interactions between Li and F. The IP
of Li2F and EA of LiF2 is calculated as the energy difference between neutral and ionic counterparts at the ground-state geometries. CCSD(T) calculated single-point energies at MP2-optimised geometries provide the IP of Li2F and EA of LiF2, 3.91 eV and 5.34 eV, respectively. These values re-establish the superalkali and superhalogen nature of Li2F and LiF2, respectively. The dipole moments of Li2F and LiF2 are found to be 1.2 D and 5.75 D, respectively. We now discuss the equilibrium geometries of Li2F2 cluster, which is apparently a dimer of LiF, i.e. (LiF)2. We place two LiF molecules linearly as well as perpendicularly. After optimisation, we obtain linear (C/v) and square-shaped (C2v) geometries of Li2F2 as shown in Figure 2. The ground state of Li2F2 corresponds to the square planar geometry and linear structure is 1.25 eV higher in energy. Note that this difference has been estimated to be 1.30 eV by a previous study in the case of LiF dimer. In order to explore the possibility whether Li2F2 cluster can be formed by LiF2 – Li and Li2F – F interactions, we place Li (F) atom on the side as well as top of LiF2 (Li2F) species. Geometry optimisation leads to linear as well as square-shaped structures for Li2F – F and LiF2 –Li as obtained in the case of (LiF)2. Furthermore, the groundstate structure in both cases corresponds to square Li2F2. The bond length in linear Li2F2 ranges between 1.64 and ˚ , whereas equalised to 1.76 A ˚ in square Li2F2. The 1.80 A NPA charges on each atom in Li2F2 cluster are also given in Figure 2. Let us justify the existence of superatomic moieties in Li2F2. The NPA charge contained on Li is þ 0.97 e which suggests a charge transfer of 2 0.97 e to LiF2 moiety in linear Li2F2. This charge is distributed in such a way that F atoms possess maximum anionic charge (– 0.94 e). Note that the same calculation on LiF provides a charge of þ 0.95 e on Li. This is not only consistent with the higher EA of LiF2 as compared with F but also supports the existence of LiF2 in linear Li2F2. Similarly, in square Li2F2, the Li2F – F interaction results in the increase
Figure 2. (Colour online) Equilibrium geometries of linear and square Li2F2 (dimer of LiF) at MP2/aug-cc-pVDZ level formed by ˚ ), bond angles (in 8, bold) and NPA charges (in e, italicised) are also shown. LiF2/Li2F– Li/F interactions. Bond lengths (in A
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Molecular Simulation of Li – F bond length and corresponding decrease in Li –Li in the cage due to electron transfer from Li2F to F. Note ˚ that Li –Li bond length in a free Li2 dimer is 2.71 A calculated at the same level of theory. The existence of Li2 cage supports the presence of Li2F superatomic moiety in Li2F2 which is more stabilised by covalent Li – Li interaction in Li2F2 which forms a Li2þ 2 cage. Note that the NPA charges on both Li atoms add to þ 1.84 e which is very close to þ 2 e. The above-mentioned discussion reveals that both conformers of (LiF)2 can be realised by interactions of superatomic species LiF2 or Li2F with Li or F atom. We compare the highest occupied molecular orbital (HOMO) of Li2F2 in both cases. The HOMO plots of linear and square-shaped Li2F2 cluster are shown in Figure 3. One can see that the HOMO of linear Li2F2 is formed by 2p atomic orbital of an F atom, whereas the HOMO of square Li2F2 is contributed by both F atoms. This may be explained on the basis of overall charge transfer to the last F in linear Li2F2 but to both F atoms in the case of square Li2F2 (due to symmetry). The relative stability of both conformers can also be analysed with the help of the energy gap between HOMO and lowest unoccupied molecular orbital. This energy gap has been proven to be an important index for the stability of molecular species.  The energy gaps of linear and square Li2F2 are found to be 10.4 eV and 14.2 eV, respectively, which further suggest the relative stability of the square geometry over linear Li2F2. The energy gaps of Li2F, LiF2 and LiF are calculated as 4.7 eV, 15.9 eV and 12.5 eV, respectively. Thus, Li2F moiety is significantly stabilised but LiF2 is destabilised by the interaction of F and Li, respectively. Likewise, LiF is stabilised in the case of square Li2F2 but destabilised for its linear counterpart. Vibrational analysis performed at the same level of theory reveals all real frequencies corresponding to the optimised linear and square geometries of Li2F2. Thus, they belong to at least a minimum in the potential energy surface, implying vibrational stability of the clusters. In order to compare the vibrational properties of linear and square Li2F2, we have plotted vibrational IR spectra in Figure 4. In linear Li2F2, there are five distinguished
Figure 3. (Colour online) HOMO surfaces of linear Li2F2 (left) and square Li2F2 (right) generated at MP2/aug-cc-pVDZ level with an isovalue of 0.02.
modes at 881, 804, 302, 198 and 19 cm – 1 which are all IR active. The most intense mode corresponding to Li – F stretching is found at 881 cm – 1, whereas modes at 198 and 19 cm – 1 are doubly degenerate. On the contrary, square Li2F2 possesses six vibrational modes out of which only three are IR active which can be found at 654, 559 and 286 cm – 1 (see Figure 4). There are no IR active degenerate modes. The most intense mode of vibration of square Li2F2 is calculated at 654 cm – 1 which corresponds to distortion of square to a prism-shaped structure. Our calculated frequencies are in good agreement with the experimentally observed values of 641, 553 and 287 cm – 1 by Snelson . Up to this point, we have discussed that Li2F2 cluster which is a dimer of LiF can also be formed by interaction of superatomic Li2F or LiF2 with F or Li atom. In order to explore whether the formation of Li2F2 by these interactions is exothermic, we have calculated dissociation energies of Li2F2 against fragmentation to neutral and ionic LiF2 þ Li and Li2F þ F. The corresponding dissociation energies are calculated as follows: D1e ¼ E½Li þ E½LiF2 2 E½Li2 F2 ; for LiF2 þ Li fragments; 2 ¼ E½Liþ þ E½LiF2 2 2 E½Li2 F2 ; for LiF2
þ Liþ fragments
D2e ¼ E½F þ E½Li2 F 2 E½Li2 F2 ; for Li2 F þ F fragments; ¼ E½F2 þ E½Li2 Fþ 2 E½Li2 F2 ; for Li2 Fþ þ F2 fragments; where E[..] represents total electronic energy of respective species including zero point energy calculated at CCSD (T)//MP2/aug-cc-pVDZ level.
Figure 4. Vibrational IR spectra of linear Li2F2 (left) and square Li2F2 (right) calculated at MP2/aug-cc-pVDZ level.
A.K. Srivastava and N. Misra of a conformer follows the Boltzmann distribution as e2DE=kT N f ¼ P 2DE =kT ; n ne
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Figure 5. Possible dissociations of linear Li2F2 (left) and square Li2F2 (right). Corresponding dissociation energies (in eV) are calculated at CCSD(T)//MP2/aug-cc-pVDZ level.
The dissociation energies for linear and square Li2F2 cluster are depicted in Figure 5. All values are positive implying that Li2F2 is stable against all dissociation paths. One can notice that:
where DE is relative energy of a conformer with respect to its minimum energy conformation and summation runs over the number of possible conformers (n). For Li2F2, two possible conformers, linear and square, possess energies 2 214.4256 a.u. and 2 214.4723 a.u., respectively at CCSD (T)//MP2/aug-cc-pVDZ level. The fractions of linear and square conformers are obtained approximately as 0.8928 £ 10 – 8 and 0.9999, respectively (at T ¼ 298.15 K, kT < 0.0009 a.u.). Thus, the probability of getting linear conformer is quite small, 0.89 out of 108.
is higher than for dissociation into neutral fragments. This may suggest that LiF2 – Li interaction is stronger than Li2F – F interaction. (2) D2e is higher than D1e for dissociation into ionic fragments. This may imply that Li2F2 can preferably be formed by interaction of Li2Fþ cation with F2 anion. (3) D1e for ionic fragments is same as that for neutral fragments, suggesting equal probability of disþ sociation of Li2F2 into LiF2 þ Li and LiF2 2 þ Li fragments. (4) D2e for ionic fragments is higher than that for neutral fragments, further supporting the formation of Li2F2 by interaction of Li2Fþ cation with F2 anion. The same calculations provide the binding energies of LiF dissociating to Li þ F and Liþ þ F2, 5.6 eV and 7.8 eV, respectively. Apparently, the binding energy of LiF (dissociating to Li and F) is smaller than that of Li2F2 dissociating either to LiF2 þ Li or to Li2F þ F (see Figure 5). This fact is again consistent with the higher EA of LiF2 and lower IP of Li2F as compared with F and Li, respectively. In order to explore the possibility whether Li2F2 is stable against Li2 þ F2 and 2 Li þ 2 F dissociation paths, we have calculated the corresponding dissociation energies. The square Li2F2 requires 0.98 eV for dissociation to Li2 þ F2 and 13.93 eV for 2 Li þ 2 F, hence stable against both dissociation channel. However, linear Li2F2 becomes slightly unstable for dissociation to Li2 þ F2 by 0.29 eV but stable for dissociation to 2 Li þ 2 F by 12.66 eV. This may also explain enhanced stability of square over linear Li2F2. Now, we calculate population distribution of linear and square conformers of Li2F2. The fractional population (Nf)
Using second-order perturbative approach, we have established that the dimer of LiF (Li2F2) can also be realised either by interaction of LiF2 superhalogen with Li atom or by that of Li2F superalkali with F atom. Superatomic LiF2 or Li2F moieties may exist in both linear and square conformers of Li2F2; however, global minimum corresponds to the square geometry. The HOMOs of linear and square Li2F2 consist of purely atomic orbitals of one F and two F atoms, respectively. Vibrational calculations have shown five IR active modes in the linear conformer and three modes in the square Li2F2. Considering dissociations of Li2F2 into various possible neutral and ionic fragments, we have found the formation of Li2F2 by such interactions is energetically favourable as both conformers are stable against all dissociation paths.
Funding A. K. Srivastava acknowledges the Council of Scientific and Industrial Research (CSIR), India for financial support in the form of a research fellowship.
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