Unusual properties of novel Li₃F₃ ring: (LiF₂–Li₂F) superatomic cluster or lithium fluoride trimer, (LiF)₃?

Abstract

LiF₂ and Li₂F are typical examples of molecular species showing superhalogen and superalkali behavior, respectively. HF, DFT (B3LYP, B3PW91), MP2, CCSD and CCSD(T) calculations are performed to study the interaction between LiF₂ and Li₂F which forms a ring shaped Li₃F₃ superatomic cluster. It is well known that Li₃F₃ can be formed by trimerization of LiF. However, these two isostructures can be distinguished by considering the effect of extra electrons on Li₃F₃. Our MP2 calculations have shown that extra electrons are delocalized on Li's of the Li₂F moiety in the case of LiF₂–Li₂F but delocalized over all Li's in the case of (LiF)₃. Finally, we have discussed the formation of one dimensional assemblies of Li₃F₃ superatomic rings which may mimic the bulk behavior and can be realized by inserting Li₃F₃ rings in one dimensional nano templates such as carbon nanotubes.

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1. Introduction

In the periodic table, alkali metal (such as Li) atoms are distinguished by their low ionization potentials (IPs) and halogens (such as F) are identified as atoms with the highest electron affinities (EAs). Traditional ionic salts (Li⁺F⁻) are formed whenever Li interacts with F, satisfying the octet rule. During 1980s, Gutsev and Boldyrev suggested the design of molecular species which may possess lower IPs than alkalies and higher EAs than halogens, classifying them as superalkalies and superhalogens, respectively.^1,2

Superhalogens are initially thought of as central metallic atom (M) with excess electronegative ligands (L) belonging to the general formula of ML_k+1, where k is the formal valence of M. Typical examples of these sp superhalogens include LiF₂, BeF₃, NaCl₂ etc.^3–7 However, superhalogens based on transition metals have been studied extensively, due to variable oxidation states of d group elements.^8–15 It has also been emphasized that superhalogen anions could form complexes by interacting with appropriate metal cations.^13–15 Some of these complexes were synthesized much before the concept of superhalogen was formulated.¹⁶ For instance, KMnO₄, a popular oxidizing agent can be formed by interaction of MnO₄⁻ with K⁺, in which MnO₄⁻ has been established as a superhalogen anion.¹⁷ Furthermore, some investigations have shown that central atoms in such species need not be a metal¹⁸ and purely p group elements based superhalogens such as BF₄, PF₆ (ref. 19) etc. have also been reported.

Analogously, superalkalies were given a general formula of M_k+1L, where k = 1 for F, Cl and 2 for O. Li₂F and Li₃O (ref. 20 and 21) can be considered as typical examples in this series. These molecular 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^2,22–26 as well as experimentally.^27–29 Like alkali metal cations, superalkali cations may interact with superhalogen anions and this interaction can be expected to be stronger than the former due to even lower IPs of superalkalies.

Few attempts have already been made in the study of such superatomic interactions and resulting superatomic compounds (clusters), named as supersalts. For instance, BF₄–NLi₄ supersalt has been reported to possess remarkable non-linear optical properties³⁰ which are even more pronounced in case of BLi₆–X supersalts for X = LiF₂, BeF₃ and BF₄.³¹ More recently, some new supersalts have been predicted by using superhalogen and superalkalies as building blocks.³² In a recent investigation, our MP2 calculations have shown that it may be possible to form Li₃X₃ by interaction of LiX₂ and Li₂X superatomic species (X = F, Cl, Br & I).³³ In present investigation, we have further explored this possibility at various levels of theory and shown the formation of a stable Li₃F₃ ring. Note that Li₃F₃ has already been realized as a trimer of LiF.^34–36 Differentiating it with the trimer of LiF, we have formed one dimensional assemblies of Li₃F₃ mimicking its bulk behavior.

2. Methodology

Quantum chemical calculations are carried out without any symmetry constraint by self consistent field iterations using all atom basis set of Stuttgart–Dresden–Dunning (SDD). We have employed various levels of ab initio (HF, MP2 and CCSD) and density functional theory (DFT) such as B3LYP and B3PW91. The hybrid DFT functionals, B3LYP and B3PW91 mix Becke's 3 parameter exchange term³⁷ (20% HF exchange) with correlation terms of Lee–Yang–Parr³⁸ and Perdew–Wang,³⁹ respectively.

All geometries are fully optimized by HF, B3LYP, B3PW91, second order perturbative approach of Moller and Plesset (MP2)⁴⁰ and coupled cluster calculations with single and double excitations (CCSD). In addition, triply substituted CCSD(T) method has also been employed for single point energy calculations at CCSD optimized geometries. Vibrational IR frequencies are calculated within same computational schemes in order to ensure that optimized geometries correspond to at least a local minimum in the potential energy surface (PES). All computations are performed with Gaussian 09 package.⁴¹

3. Results and discussion

First we concentrate on our building blocks viz. LiF₂ and Li₂F. Both LiF₂ and Li₂F take planar C_2v structure. Tables 1 and 2 list the bond-length, bond-angle and partial charges on Li of LiF₂ and Li₂F, respectively calculated at various levels of theory. Partial charges are obtained by natural population analysis (NPA) scheme.⁴² Both LiF₂ and Li₂F violate the octet rule, becoming hypervalent clusters. The excess electrons in both clusters are delocalized such that F atoms possess nearly maximum anionic charges (F⁻). The adiabatic EA (vertical IP) is calculated by difference of energies of neutral species (cations) and corresponding anions (neutrals) at their ground state configuration.

Table 1 Geometrical parameters, NPA charge (q) on Li and adiabatic electron affinity (EA) of LiF₂ superhalogen

LiF2	HF	B3LYP	B3PW91	MP2	CCSD	CCSD(T)^a
a Single point calculation@CCSD optimized geometry.
Li–F (Å)	1.75	1.74	1.75	1.77	1.77
F–Li–F (°)	67.2	72.3	71.5	68.0	68.3
q(Li) (e)	+0.92	+0.87	+0.88	+0.92	+0.86
EA (eV)	4.44	4.60	4.54	5.06	4.85	4.85

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Table 2 Geometrical parameters, NPA charge (q) on Li and vertical ionization potential (IP) of Li₂F superalkali

Li2F	HF	B3LYP	B3PW91	MP2	CCSD	CCSD(T)^a
a Single point calculation@CCSD optimized geometry.
Li–F (Å)	1.69	1.67	1.70	1.72	1.71
Li–F–Li (°)	111.2	179.9	116.0	108.6	109.8
q(Li) (e)	+0.46	+0.44	+0.44	+0.46	+0.44
IP (eV)	3.64	4.17	4.08	3.70	3.71	3.71

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Tables 1 and 2 also list the EA of LiF₂ and IP of Li₂F, respectively calculated at various levels. Our calculated EA values of LiF₂ slightly underestimate its previously estimated value of 5.45 eV.² On the other hand, calculated IPs of Li₂F at MP2 and CCSD levels fairly agree with experimental values of 3.78 eV (ref. 27) and 3.8 ± 0.2 eV (ref. 28) by photo-ionization mass spectrometry and thermal-ionization mass spectrometry, respectively. Higher EA of LiF₂ as compared to Cl, which is 3.62 eV (ref. 43) and lower IP of Li₂F as compared to Li, which is 5.39 eV,⁴⁴ re-establish their superhalogen and superalkali behavior, respectively.

3.1. Formation of Li₃F₃

In order to study the interaction of LiF₂ superhalogen with Li₂F superalkali, we place these two units parallel to each other. After optimization, we find a ring shaped planar C_2v structure of Li₃F₃ as shown in Fig. 1. Table 3 lists various geometric parameters of Li₃F₃ ring calculated at different level of theories. It is worthwhile to mention that all Li–F bond-lengths are equalized to 1.73–1.75 Å. Furthermore in Li₃F₃, the bond-angle in LiF₂ moiety is significantly increased by about 50% whereas, change in the bond-angle of Li₂F is only marginally. The binding energy of Li₃F₃ are calculated as.

ΔE₁ = E[LiF₂] + E[Li₂F] − E[Li₃F₃]

where E[ ] represents electronic energy of respective species including zero point correction. The calculated ΔE₁ values lie between 180.5 and 199.3 kcal mol⁻¹ at various levels of theory, except MP2 which gives it 239.5 kcal mol⁻¹. Note that the binding energy of LiF dissociating to Li and F is 115.2 kcal mol⁻¹ at CCSD level which is lower than ΔE₁ as expected due to higher EA of LiF₂ and lower IP of Li₂F as compared to F and Li, respectively. We have also calculated the binding energy of Li₃F₃ for its ionic fragments viz. LiF₂⁻ and Li₂F⁺ as follows,

ΔE₂ = E[LiF₂⁻] + E[Li₂F⁺] − E[Li₃F₃]

Fig. 1 Equilibrium geometry of Li₃F₃ ring which can be formed by interaction of LiF₂ and Li₂F as well as trimerization of LiF.

Table 3 Geometrical parameters and binding energies for various dissociations of Li₃F₃ superatomic ring formed by interaction of LiF₂ and Li₂F

Parameter	HF	B3LYP	B3PW91	MP2	CCSD	CCSD(T)^a
a Single point calculation@CCSD optimized geometry.
Li–F (Å)	1.72	1.73	1.73	1.75	1.75
Li–F–Li (°)	116.0	114.0	114.4	114.2	114.5
F–Li–F (°)	124.0	126.0	125.6	125.8	125.5
ΔE1 (kcal mol^−1)	187.9	183.7	180.5	239.5	196.6	196.5
ΔE2 (kcal mol^−1)	169.7	173.8	169.9	208.2	170.2	170.1
De (kcal mol^−1)	138.0	135.2	131.5	172.3	135.4	135.3

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The calculated ΔE₂ values, 169.7–173.8 kcal mol⁻¹ (208.2 kcal mol⁻¹ at MP2 level) are lower than ΔE₁, suggesting that Li₃F₃ favors dissociation into ionic fragments rather than neutral parts. This is one of the features already seen in the case of superatomic compounds³⁰ but not a case for traditional salts. For instance, the binding energy of Li⁺ and F⁻ in LiF calculated by CCSD method, 197.3 kcal mol⁻¹ is higher than that of Li and F in LiF. Thus Li₃F₃ can indeed be regarded as a supersalt, unlike LiF. However, Li₃F₃ ring formed by interaction of LiF₂ and Li₂F superatoms is a structural isomer of highly symmetric D_3h geometry of trimer of LiF i.e. (LiF)₃. To further establish this fact, we calculated dissociation energy of Li₃F₃ against fragmentation to LiF molecules,

D_e = 3E[LiF] − E[Li₃F₃]

The calculated D_e values are found to be 131.5–138.0 kcal mol⁻¹ (172.3 kcal at MP2) which is even lower than both ΔE₁ and ΔE₂. This suggests that Li₃F₃ ring may be formed preferably by trimerization of LiF. We have shown the dissociation energetics of Li₃F₃ for a qualitative comparison in Scheme 1. Naturally, one can ask whether Li₃F₃ should be regarded as LiF₂–Li₂F superatomic cluster or lithium fluoride trimer, (LiF)₃. We address this issue in the next section.

Scheme 1 Systematic representation of possible dissociations of Li₃F₃. Refer to Table 3 for dissociation energy values calculated by various levels of theory.

3.2. Effect of extra electrons on Li₃F₃

As mentioned earlier, the interaction LiF₂–Li₂F lowers the symmetry of Li₃F₃ to C_2v as compared to (LiF)₃ with D_3h symmetry. LiF₂–Li₂F is more stabilized by charge transfer from Li₂F superalkali moiety to LiF₂ superhalogen. This is why Li₃F₃ favors dissociation to Li₂F⁺ + LiF₂⁻ than Li₂F + LiF₂. In order to analyze the effect of extra electrons on Li₃F₃, we have optimized the geometries of Li₃F₃^q− for q = 1–3 at MP2/SDD level. The NPA charges on Li atoms in Li₃F₃^q− (q = 0–3) are listed in Table 4. One can see that atomic charges are identically distributed in Li₃F₃ for both LiF₂–Li₂F and (LiF)₃ making them indistinguishable.

Table 4 Partial NPA charges on Li's of Li₃F₃^q− (q = 0–3) for superatomic interaction (LiF₂–Li₂F) as well as trimerization of LiF, (LiF)₃ calculated at MP2 level of theory

Species	(Li2F–LiF2)			(LiF)3
	Li1	Li2	Li3	Li1	Li2	Li3
Li3F3	+0.89	+0.89	+0.89	+0.89	+0.89	+0.89
Li3F3^−	+0.80	+0.43	+0.43	+0.57	+0.57	+0.57
Li3F3^2−	+0.60	+0.03	+0.03	+0.24	+0.24	+0.24
Li3F3^3−	−0.09	−0.09	−0.09	−0.09	−0.09	−0.09

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However, addition of an electron brings a dramatic change in the story, making them clearly identifiable. For instance, in Li₃F₃⁻, more than 90% of extra electron is located on Li's of Li₂F moiety in LiF₂–Li₂F, as expected due to its electron deficient nature. This is in contrast to (LiF)₃ in which extra electron is equally shared by all Li atoms (see Table 4). The same conclusion also holds for Li₃F₃²⁻ but extra electron delocalization (85%) is slightly diminished as compared to that in Li₃F₃⁻. In case of Li₃F₃³⁻, atomic charge distribution restores itself to make LiF₂–Li₂F and (LiF)₃ identical.

Thus, the superatomic effect in Li₃F₃ is clearly reflected in its mono- and bi-anions, Li₃F₃⁻ and Li₃F₃²⁻ which not only establish Li₃F₃ as a superatomic cluster formed by interaction LiF₂ superhalogen with Li₂F superalkali species but also make it different from LiF-trimer. This fact is also supported by corresponding equilibrium geometries of Li₃F₃^q− as shown in Fig. 2. For instance, in case of LiF₂–Li₂F cluster, Li₃F₃²⁻ assumes a distorted bi-square planar C_2v structure in which LiF₂ moiety is pushed out due to excess electrons on Li's of Li₂F (see Fig. 2, upper set). The bond-lengths Li–F, in LiF₂ 1.80 Å is smaller than those in Li₂F (1.85 Å) whereas, the distances between LiF₂ and Li₂F lie in the range 1.83–1.91 Å. Note, however, that Li₃F₃²⁻ preserves its symmetry in case of (LiF)₃ (Fig. 2, lower set) in which all Li–F become 1.77 Å slightly larger than those in neutral Li₃F₃ (1.72 Å).

Fig. 2 Equilibrium geometries of Li₃F₃⁻, Li₃F₃²⁻ and Li₃F₃³⁻ formed by LiF₂–Li₂F interaction (upper set) and (LiF)₃ trimerization (lower set) at MP2 level.

3.3. One dimensional arrays of Li₃F₃

We have established that Li₃F₃ ring formed by interaction of LiF₂ and Li₂F superatoms shows distinguished property of extra electron delocalization over Li's of Li₂F unit, unlike that formed by trimerization of LiF. Li₃F₃ superatomic ring can be considered as building blocks of new salts. To explore this possibility, we consider one dimensional assemblies of Li₃F₃ by placing Li₃F₃ rings coaxially. After optimization at B3LYP/SDD level, we find tubular structures of (Li₃F₃)_n for n = 2, 3 and 4 as shown in Fig. 3. These structures correspond to true minima in the PES as all frequencies are found to be positive. To further investigate this, we have performed PES scan on (Li₃F₃)₂ at the same level of theory whose result is plotted in Fig. 4. We can see that the minimum on the PES corresponds to equilibrium distance of 1.90 Å between two rings. The Li–F, bond-length in each Li₃F₃ unit in (Li₃F₃)_n for n = 2–4 becomes 1.81 Å which is larger than those in isolated Li₃F₃, 1.72 Å. However, the equilibrium distance between two Li₃F₃ units is decreased to 1.86 Å in (Li₃F₃)₃ from 1.90 Å in (Li₃F₃)₂. Similarly, this distance lies between 1.86 and 1.90 Å in (Li₃F₃)₄.

Fig. 3 One dimensional assemblies of Li₃F₃ at B3LYP level- (a) dimer (Li₃F₃)₂, (b) trimer (Li₃F₃)₃ and (c) tetramer (Li₃F₃)₄.

Fig. 4 PES scan curve of (Li₃F₃)₂ at B3LYP level. Equilibrium separation between two Li₃F₃ units is 1.9 Å.

The binding energy per Li₃F₃ ring in (Li₃F₃)_n can be calculated as,

The calculated ΔE values of (Li₃F₃)_n at B3LYP level are 33.7, 45.5 and 51.4 kcal mol⁻¹ for n = 2, 3 and 4, respectively which are in accordance with the calculated equilibrium distances between two Li₃F₃ units in (Li₃F₃)_n for n = 2, 3 and 4. Note that the binding energy of Li₃F₃ or (LiF)₃ per LiF is 45.1 kcal mol⁻¹ at B3LYP (see Table 3) which is comparable to ΔE of (Li₃F₃)₃. This may suggest that the ring-ring interaction in (Li₃F₃)_n assembly becomes stronger as n increases.

Above discussion suggests that it can be possible to assemble Li₃F₃ superatomic clusters which mimic the salt in condensed phase. According to Khanna et al.,⁴⁵ the formation of such superatomic assemblies demand the preservation of the energy difference between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), popularly known as HOMO–LUMO gap. The uniformity in HOMO–LUMO gap ensures the existence of superatomic block, maintaining its identity. Fig. 5 plots molecular energy spectrum of (Li₃F₃)_n for n = 1–4. The HOMO–LUMO gap of Li₃F₃ calculated at B3LYP level is 8.22 eV. Apparently, assemblies of Li₃F₃ units do not change the HOMO–LUMO gap but result in increasing the molecular energy levels for occupied as well as unoccupied states. Thus, it is indeed possible to form novel salts using Li₃F₃ superatomic ring as their building blocks. These one dimensional arrays can be treated like a quantum nanowire. Experimentally, these arrays can be realized by inserting the superatomic clusters into one dimensional nanoscale templates such as carbon nanotubes.

Fig. 5 Molecular energy spectra of (Li₃F₃)_n (n = 1–4). Red lines represent occupied states and yellow correspond to unoccupied states.

4. Conclusions

Quantum chemical calculations performed at various levels of theory have established that the interaction between LiF₂ superhalogen and Li₂F superalkali leads to the formation of a planar ring shaped stable superatomic cluster Li₃F₃ which can also be realized by trimerization of LiF. With the addition of electrons to Li₃F₃, extra charges are completely delocalized on Li's of Li₂F moiety in case of LiF₂–Li₂F but distributed equally over all Li's in case of (LiF)₃. Atomic charge distribution also changes the geometry of LiF₂–Li₂F as compared to (LiF)₃ as demonstrated in case of Li₃F₃²⁻ at MP2 level of theory. We have also explored the possibility at B3LYP level that novel salts can be formed by assembling Li₃F₃ superatomic rings in such a way that its identity is maintained due to uniformity in HOMO–LUMO gaps.

Acknowledgements

A. K. Srivastava acknowledges Council of Scientific and Industrial Research, New Delhi, India for providing a research fellowship via grant number 09/107(0359)/2012-EMR-I.

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