J Mol Model (2015) 21:147 DOI 10.1007/s00894-015-2693-2
ORIGINAL PAPER
Structures, stability, and electronic properties of novel superalkali-halogen clusters Ambrish Kumar Srivastava 1 & Neeraj Misra 1
Received: 19 March 2015 / Accepted: 3 May 2015 # Springer-Verlag Berlin Heidelberg 2015
Abstract We have computationally designed some novel clusters by interaction of superalkali (SA) species (FLi2, OLi3, NLi4) with halogen (X = F, Cl) atoms. The ground state electronic structures of these superalkali-halogen (SA−X) clusters are identified and their stabilities are analyzed. The electronic properties of SA−X clusters are also discussed. Like alkali halides, these clusters can also be regarded as SA+X− species. We have noticed, however, that these clusters prefer to dissociate into ionic fragments, in contrast to alkali halides. The mean polarizabilities of SA−X clusters are much larger than alkali halides, reaching to 136.28 a.u. for NLi4−Cl, which further doubles in the case of its dimer, i.e., (NLi4−Cl)2. We believe that these SA−X clusters can be used as building blocks of novel materials, analogous to traditional alkali halides. Keywords Electronic property . Polarizability . Stability . Structures . Superalkali-halogen clusters
Introduction The fundamental understanding of the building blocks of materials helps to develop novel species with tailored properties. Khanna and Jena have computationally predicted that the small clusters may mimic the properties of the atom in the periodic table which can be called superatoms [1]. For
* Neeraj Misra [email protected] 1
Department of Physics, University of Lucknow, Lucknow 226007, Uttar Pradesh, India
instance, they found that Al13K is bound by ionic interaction, just as any alkali halide [2]. One decade later, Castleman and co-workers demonstrated the superatomic characteristics of Al13 and A14 clusters in two classes of gas-phase aluminumiodine clusters and concluded that superatoms indeed possess synthetic utility and can be employed as potential building blocks for the assembly of novel nanostructured materials [3, 4]. Alkali metal atoms are well known for their low ionization potential and halogens for their high electron affinity. Gutsev and Boldyrev have proposed the design of small clusters possessing lower ionization potentials than alkalies and higher electron affinities than halogen, and named them as superalkalies [5] and superhalogens [6], respectively. These can be regarded as a subset of superatoms, which have been extensively studied [7–15]. Superalkalies and superhalogens, both are hypervalent clusters having excess electropositive and electronegative atoms, respectively. For instance, FLi2 behaves as superalkali [5, 16, 17] which has also been synthesized experimentally [18, 19] and LiF2 is a superhalogen [6], which has not been synthesized so far. Wang and co-workers have tried to perform experimental observation on LiF2 but their electron binding energies appeared to be beyond the laser photon detachment energy (6.424 eV) and no spectra was obtained [7]. Superatoms can be considered as potential building blocks of novel materials as well as many traditional species. For instance, KMnO4, a popular oxidizing agent can be realized as K + MnO 4 − where MnO 4 has been found to be a superhalogen [20]. Similarly, superhalogen properties of FeO4 and CrO4 have also been established [21] and hence, they can also be expected to form similar compounds. In the last decade, a new kind of species namely Bsupersalt^ has been designed by interaction of superhalogens and superalkalies. Li et al. have performed studies on the interactions of BLi6
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Fig. 1 Various possible orientations for interaction of F atom with NLi4 superalkali
superalkali with various superhalogens [22] and Yang et al. have studied the interaction of BF4 superhalogen with FLi2, OLi3, and NLi4 superalkalies [23]. These interactions led to the formation of some supersalts, possessing significant nonlinear optical properties. These supersalts can be distinguished from traditional salts on the basis of their preferred dissociation to the ionic superalkali and superhalogen fragments [23]. Recently, we have investigated the interaction of XLi2 and LiX2 superatoms (X = F, Cl, Br, & I) [24] and noticed that a ring shaped Li3F3 can be formed by FLi2−LiF2 interaction. Note that Li3F3 ring has so far been realized as a trimer of LiF molecule [25, 26]. In a subsequent study, we have shown that the Li3F3 rings formed by trimerization of LiF and FLi2−LiF2 interaction can be distinguished by considering the effect of excess electrons on Li3F3 [27]. In the present investigation, we have systematically studied the interaction of halogen (X) with superalkali (SA) clusters and tried to explore whether the resulting species can be regarded as supersalts or they resemble the properties of alkali halides. To investigate this, we have chosen three typical SA clusters, SA = FLi2, OLi3, and NLi4 and considered their interactions with X = F and Cl. Here, we report the structures, stability, and electronic properties of SA−X clusters and compare them with LiF and LiCl molecules. These novel clusters may be expected as building blocks of new class of materials having some unique and interesting properties.
expands the atomic orbital of first row elements (Li−Ne) by approximately 14 functions of s, p, and d valence shells. In order to study the interaction of halogens to superalkalies, we considered various possible orientations as displayed in Fig. 1 for NLi4−F. we have placed F atom at all favorable positions relative to NLi4 and modeled the initial structures by taking into account the fact whether F interacts with the one, two, three or four Li atoms of NLi4 superalkali (see Fig. 1). Vibrational wavenumbers were calculated at the same level of theory in order to ensure that the optimized geometries correspond to a true minimum in their potential energy surfaces. All calculations were performed via Gaussian 09 code [30]. Partial atomic charges were computed by natural population analysis (NPA) scheme which has been proven to be more reliable than other population schemes due to its lower basis set dependency [31]. For the validity of the present computational scheme, MP2/ aug-cc-pVDZ, we have performed some test calculations on LiF and LiCl molecules, and compared them with corresponding experimental values [32–34] in Table 1. One can see that there is good agreement between calculated and experimental values. This may advocate the reliability of the results obtained by MP2/aug-cc-pVDZ method. Furthermore, MP2/aug-ccpVDZ has already been used in some previous studies [22, 23].
Results and discussion Computational details All structures considered in this study were fully optimized without any symmetry constraints using second order MøllerPlesset perturbation theory (MP2) [28]. A correlation consistent double zeta type basis set, aug-cc-pVDZ [29], was employed throughout these calculations. This basis-set Table 1 Calculated and experimental parameters for LiF and LiCl molecules
Parameter
Bond-length (Å) Bond-dissociation energy (eV) Dipole moment (Debye) a
The geometry optimization carried out on initial structures leads to two potential conformers for each SA−X cluster (SA = FLi2, OLi3, NLi4; X = F, Cl) which are displayed in Fig. 2. The relative energies (ΔE) for different conformers of SA−X clusters are listed in Table 2. One can note that the ground state of SA−X clusters corresponds to the geometries
LiF
LiCl
Calculated
Experimental
Calculated
Experimental
1.61 5.94 6.72
1.56 a 5.98b 6.33c
2.08 4.66 7.57
2.02a 4.86b 7.13d
Ref. [32]; b Ref. [33]; c Ref. [34]; d Ref. [35].
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Fig. 2 Equilibrium geometries of superalkali-halogen clusters obtained at MP2/aug-cc-pVDZ method
in which X interacts with two Li atoms of SA, except for NLi4−Cl in which Cl interacts with three Li atoms. For instance, the rhombic (D2h) structure of FLi2−F and C2v structures of OLi3−F, and NLi4−F are found to be 1.25, 0.76, and 0.89 eV lower in energies than their corresponding linear (C∞v) and C3v conformers. Similarly, in the ground state, FLi2−Cl and NLi4−Cl assume distorted rhombus (C2v) and C3v structures which are 0.88 and 0.37 eV lower than corresponding potential conformers. Vibrational harmonic wavenumbers are calculated for all the optimized structures in order to ensure that they belong to true minima in the potential energy surfaces. Table 2 lists the bond-distance (d) connecting X to Li of SA, the lowest harmonic wavenumber (νmin) and atomic charge (q) on X for SA−X clusters. For comparison, the corresponding values for LiF and LiCl are also listed. The geometries of SA−X clusters indeed correspond to minima as all νmin values are positive expect for a
conformer of NLi4 − Cl. The bond-distance, Li−X for the ground state SA−X clusters 1.76−1.78 Å for X = F and 2.28−2.46 Å for X = Cl. These distances are slightly larger than those obtained for LiF and LiCl molecules. This is consistent with the charge transfer to X atoms. Note that the charge transfer from SA to F is 0.89−0.92 e and 0.77−0.83 e to Cl for the ground state of SA−X clusters (see Table 2). This may also suggest that SA−X clusters can typically be regarded as SA+X− just as traditional ionic alkali halides. In order to discuss the stability of SA−X clusters, we have analyzed their binding energies against dissociation to neutral (SA + X) and ionic (SA+ + X−) fragments. The corresponding binding energies, BEn and BEi are calculated by total electronic energies including zero point energy corrections. The calculated BEn and BEi values for SA−X clusters along with those for LiX molecules are collected in Table 3. All SA−X clusters are found to be more stable than the corresponding
Table 2 Relative energy (ΔE, in eV), bond-distance (d, in Å), lowest harmonic frequency (νmin, in cm-1) and atomic charge (q, in e) for possible equilibrium conformers of superalkali-halogen clusters
Table 3 Binding energy (BE) and dissociation energy (D e ) of superalkali-halogen clusters. All parameters are given in eV. The superscripts n and i represent neutral and ionic constituents of the clusters
Clusters Conformer ΔE
Clusters
d(Li − X)
νmin
q(X)
X=
F
Cl
F
Cl
F
Cl
F
Cl
X=
FLi2−X A B OLi3−X A B NLi4−X A B
1.25 0.0 0.0 0.76 0.89 0.0
0.88 0.0 0.0 0.52 0.37 0.0
1.66 1.76 1.78 1.94 1.67 1.78
2.14 2.28 2.30 2.48 2.16 2.46
20 287 101 255 25 109
35 231 90 171 -22 106
-0.94 -0.92 -0.90 -0.89 -0.91 -0.89
-0.87 -0.83 -0.81 -0.81 -0.83 -0.77
FLi2−X OLi3−X NLi4−X
Conformer
A B A B A B
BEi
BEn
De[LiX]
F
Cl
F
Cl
F
Cl
5.94 7.19 6.93 6.17 5.99 6.88
4.83 5.71 5.59 5.06 4.99 5.36
6.29 7.54 6.86 6.11 5.62 6.51
5.18 6.05 5.52 4.99 4.60 4.98
1.45 2.70 2.82 2.07 1.83 2.71
1.62 2.50 2.76 2.24 2.10 2.47
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Table 4 AIM calculated bond order (BO) of Li−X bonds between superalkali and halogen (X)
Clusters
Conformer
BO[Li−X]
X= FLi2−X OLi3−X NLi4−X
F
Cl
A
0.14
0.13
B A B A B
0.10 0.09 0.07 0.14 0.10 0.16
0.09 0.09 0.06 0.13 0.06 0.15
LiX
LiX molecule due to higher BEn values. Thus, the interaction between SA and X is stronger than that in LiX which is due to lower ionization potentials of SA than Li. It is well known that lithium halide (LiX) dissociate into Li and X atoms but not into Li+ and X− ions, because the ionization potential of lithium is larger than the electron affinities of halogen atoms. Therefore, the calculated BEi values (7.74 eV for LiF and 6.45 eV for LiCl) are greater than BEn for LiX molecules (see BDE values given in Table 1). However, in the case of SA−X clusters, we note an interesting feature, i.e., BEi values for OLi3−X and NLi4−X are smaller than their corresponding BEn values. To put it another way, SA−X clusters prefer ionic dissociation channels to the covalent dissociation paths. This is in contrast to traditional ionic alkali halides. Thus, OLi3−X and NLi4−X clusters indeed possess supersalt characteristics. On the contrary, FLi2−X clusters follow the same dissociation trend as that of LiX. We will show later that this is due to their molecular orbital composition which is similar to that of LiX molecules. To investigate whether the SA−X clusters can be realized experimentally, we have considered their dissociation into stable molecules viz. LiF, LiCl, OLi2, and NLi3. All dissociation energy (De) values are found to be positive
which range 2.70−2.82 eV for X = F and 2.50−2.76 eV for X = Cl in the ground state SA−X clusters. Although the exact route of syntheses is not known, it is energetically possible to obtain these novel species at least in gas phase reactions if LiF, LiCl, OLi2, and NLi3 molecules are used in their syntheses. The negative of energy eigenvalues of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) can be used to estimate the ionization potential (I) and electron affinity (A), respectively within the framework of Koopmans’ approximation. However, this approximation considers neither electron-correlation nor orbital relaxation which result in the overestimation and underestimation of the calculated I and A values, respectively. For instance, one can compare the calculated I and A of LiCl with corresponding experimental values of 9.57 eV [36] and 0.59 eV [37]. The calculated I and A values of SA−X clusters are listed in Table 5. One can see that the A values of SA−X clusters are smaller than LiX molecules. This suggests that SA−X clusters are relatively more stable against addition of extra electron which can be expected due to charge transfer from SA moieties. The bond orders (BOs) of Li−X bonds between SA to X in SA−X clusters are listed in Table 4, which provide a measure for the strength of bonds in clusters and complexes [38]. These are calculated by using atoms in molecules (AIM) approach introduced by Richard Bader [39]. The BOs of LiF and LiCl, 0.16 and 0.15, are consistent with their BDEs (see Table 1). Similarly, the BOs of SA−F clusters are larger than SA−Cl by 0.01 which is in accordance with their BE values (see Table 3). In the case of FLi2−X cluster (conformer A), there is one Li−X bond with the BO of 0.14 (X = F) and 0.13 (X = Cl) which is less than that of LiF and LiCl by 0.02. This may suggest that Li−X bond in FLi2−X cluster (conformer A) is weaker than those in free LiX molecule. This fact is also reflected in their BE values listed in Table 3. On the contrary, the more
Table 5 Ionization potential (I), electron affinity (A), HOMO-LUMO gap (Egap), total static dipole moment (μ), and mean polarizability (αo) of superalkali-halogen clusters Clusters
Conformer
X= FLi2−X OLi3−X NLi4−X LiX
A B A B A B
I (eV)
μ (Debye)
Egap (eV)
A (eV)
αo (a.u.)
F
Cl
F
Cl
F
Cl
F
Cl
F
Cl
11.37 14.02 8.41 8.44 6.88 5.77 12.77
9.09 10.95 8.89 8.76 7.21 6.07 10.24
0.96 -0.18 0.13 -0.08 0.28 0.07 0.32
1.06 -0.14 0.26 -0.09 0.37 -0.01 0.47
10.40 14.20 8.28 8.52 6.60 5.70 12.45
8.02 11.09 8.63 8.85 6.84 6.07 9.77
14.57 0.00 6.73 3.54 12.17 6.61 6.72
15.89 2.03 8.97 0.22 13.95 4.87 7.57
17.13 15.70 41.51 41.29 109.39 127.62 9.19
32.99 30.86 54.60 53.38 120.20 136.28 25.20
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Fig. 3 Highest occupied molecular orbitals (HOMOs) of superalkali-halogen clusters in the ground state configuration
stable B conformer of FLi2−X possess two Li−X bonds each with the BO of 0.10 (X = F) and 0.09 (X = Cl). The energy separation between the HOMO and the LUMO is a useful quantity for examining the stability of clusters and nanostructures. The HOMO-LUMO gap (Egap) of SA−X clusters are listed in Table 5. It has been noticed that the systems with higher Egap values are less reactive. The Egap values of FLi2−F cluster are 10.4 eV (conformer A) and 14.2 eV (conformer B) which is smaller and larger than that of LiF molecule, respectively. Therefore, the conformer B of FLi2−F cluster is relatively more stable than LiF. A similar trend is observed in the case of FLi2−Cl cluster. The Egap values of other SA−X clusters are in the range of 5.70 − 8.85 eV for SA = OLi3, NLi4, and X = F, Cl, which are significantly larger than that of BLi6−F (4.56 eV) calculated by Li et al. [22]. It is also interesting to note that the order of Egap values is FLi2−X > OLi3−X > NLi4−X for X = F or Cl. This may suggest that SA −X clusters become more reactive or conducting with the increase in the size of SA cluster. In order to further evaluate the electronic properties of these novel clusters, we have calculated the total static dipole moment (μ) and mean polarizability (αo) using the finite-field approach [40]. The total energy of a molecular system in the presence of a homogeneous electric field can be expressed as [41], 1 E ¼ E o −μi F i − αi j F i F j −::::: 2 Where Eo is the total energy in the absence of the electric field, and F i , μ i , and α i j represent the
Fig. 4 Equilibrium geometry of (NLi4−Cl)2 dimer. Interaction between two units is shown by dotted line
components of the electric field, dipole moment and polarizability, respectively along the directions specified by subscripts, i and j = x, y and z. The μ and αo can be obtained accordingly as: 1=2 μ ¼ μ2x þ μ2y þ μ2z 1 αxx þ αyy þ αzz αo ¼ 3 The μ and αo values calculated by numerical differentiation with an electric field magnitude of 0.001 a.u. are listed in Table 5. One can note that the dipole moments of the ground state structures of OLi3−F and NLi4−F clusters are comparable to LiF, whereas that of OLi3−Cl and NLi4−Cl are slightly higher and smaller than LiCl, respectively. The dipole moment of FLi2−Cl, however, is reduced to 2.03 D and vanishes in case of FLi2−F due to its symmetry. More interestingly, the linear conformers of FLi2−X possess very high dipole moments which are greater than twice of LiX due to relatively higher charge transfer to X (see Table 5). The αo values of SA−F clusters range from 15.70 to 127.62 a.u., which are remarkably high as compared to LiF (9.19 a.u.). This range further spans in the case of SA−Cl and reaches to 136.28 a.u. for NLi4−Cl. This can be explained by analyzing the HOMOs of SA−X clusters, displayed in Fig. 3. One can note that the HOMOs of LiX molecules consist of atomic orbital of X. Thus in alkali halide, alkali atoms do not contribute to the HOMO. This is in contrast to SA−X clusters in which the HOMOs are delocalized over SA moieties. The larger polarizability of NLi4−Cl can be explained on the basis
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of more delocalized electron cloud due to the larger size of NLi4 moiety. It is also interesting to note that in the case of FLi2−X, the HOMOs closely resemble that of LiX. This may explain the reason behind their preferred dissociation into neutral fragments and relatively lower polarizability values. Khanna and Jena have already proposed some superatomic clusters mimicking the behavior of elements in the periodic table and consequential possibility of using them as building blocks of novel salts. According to them, the basic criterion that ensures the identity of clusters in their bulk analogs is the uniformity in their HOMO-LUMO gaps. Therefore, in order to form a bulk analog, the cluster units should be assembled in such a way that leaves the HOMO-LUMO gap unaltered. To demonstrate this idea, we have considered NLi4−Cl cluster and studied the formation of its dimer at MP2/augcc-pVDZ level. In equilibrium configuration, two NLi4−Cl cluster units interact via Li⋯Cl to form (NLi4−Cl)2, as depicted in Fig. 4. Vibrational frequency calculations characterize this dimeric complex as a local minimum in the potential energy surface. The Li⋯Cl bond-distance in (NLi4−Cl)2 is 2.37 Å and the binding energy is 0.32 eV per NLi4−Cl unit. Therefore, the dissociation of (NLi4−Cl)2 dimer into two NLi4−Cl monomer is endothermic and requires an energy amount of 0.64 eV. The HOMO-LUMO gap of (NLi4−Cl)2 is found to be 5.98 eV which is slightly smaller than that of NLi4−Cl (see Table 5). However, the dipole moment and polarizability of (NLi4−Cl)2 dimer are found be to 12.81 Debye and 267.99 a.u., respectively which are three and two times that of NLi4−Cl cluster. Thus, one can form the bulk assemblies of SA−X clusters in which aforementioned electronic properties will be further enhanced, suggesting their potential applications in the development of novel materials with unique and tailored properties.
parameters. It is established that the polarizabilities of SA−X clusters are much larger than alkali halides, which are expected to further increase in their bulk assemblies. Therefore, these novel SA−X clusters might be employed in the future to design a new class of materials. Acknowledgement A. K. Srivastava acknowledges Council of Scientific and Industrial Research, New Delhi, India for providing a research fellowship [grant number 09/107(0359)/2012-EMR-I].
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Conclusions Using second order Møller-Plesset perturbation theory based calculations; we have shown that a new class of clusters, superalkali-halogen clusters, can be formed by interaction of superalkali (SA) clusters with halogen (X) atoms. The equilibrium structures of SA−X clusters are obtained and the ground state geometries are identified. It has been noticed that due to the charge transfer from SA unit to X, SA−X clusters can be realized as SA+X− species similar to alkali halides. Their bond strengths are discussed by calculating bond orders and stabilities are analyzed by fragmentation to neutral and ionic parts as well as some stable molecules. The analyses reveal that SA−X clusters can be synthesized experimentally at least in gas phases. Furthermore, these clusters are found to prefer their dissociations into ionic fragments, in contrast to alkali halides. The electronic properties of SA−X clusters are explored and discussed by calculating a number of
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ORIGINAL PAPER
Structures, stability, and electronic properties of novel superalkali-halogen clusters Ambrish Kumar Srivastava 1 & Neeraj Misra 1
Received: 19 March 2015 / Accepted: 3 May 2015 # Springer-Verlag Berlin Heidelberg 2015
Abstract We have computationally designed some novel clusters by interaction of superalkali (SA) species (FLi2, OLi3, NLi4) with halogen (X = F, Cl) atoms. The ground state electronic structures of these superalkali-halogen (SA−X) clusters are identified and their stabilities are analyzed. The electronic properties of SA−X clusters are also discussed. Like alkali halides, these clusters can also be regarded as SA+X− species. We have noticed, however, that these clusters prefer to dissociate into ionic fragments, in contrast to alkali halides. The mean polarizabilities of SA−X clusters are much larger than alkali halides, reaching to 136.28 a.u. for NLi4−Cl, which further doubles in the case of its dimer, i.e., (NLi4−Cl)2. We believe that these SA−X clusters can be used as building blocks of novel materials, analogous to traditional alkali halides. Keywords Electronic property . Polarizability . Stability . Structures . Superalkali-halogen clusters
Introduction The fundamental understanding of the building blocks of materials helps to develop novel species with tailored properties. Khanna and Jena have computationally predicted that the small clusters may mimic the properties of the atom in the periodic table which can be called superatoms [1]. For
* Neeraj Misra [email protected] 1
Department of Physics, University of Lucknow, Lucknow 226007, Uttar Pradesh, India
instance, they found that Al13K is bound by ionic interaction, just as any alkali halide [2]. One decade later, Castleman and co-workers demonstrated the superatomic characteristics of Al13 and A14 clusters in two classes of gas-phase aluminumiodine clusters and concluded that superatoms indeed possess synthetic utility and can be employed as potential building blocks for the assembly of novel nanostructured materials [3, 4]. Alkali metal atoms are well known for their low ionization potential and halogens for their high electron affinity. Gutsev and Boldyrev have proposed the design of small clusters possessing lower ionization potentials than alkalies and higher electron affinities than halogen, and named them as superalkalies [5] and superhalogens [6], respectively. These can be regarded as a subset of superatoms, which have been extensively studied [7–15]. Superalkalies and superhalogens, both are hypervalent clusters having excess electropositive and electronegative atoms, respectively. For instance, FLi2 behaves as superalkali [5, 16, 17] which has also been synthesized experimentally [18, 19] and LiF2 is a superhalogen [6], which has not been synthesized so far. Wang and co-workers have tried to perform experimental observation on LiF2 but their electron binding energies appeared to be beyond the laser photon detachment energy (6.424 eV) and no spectra was obtained [7]. Superatoms can be considered as potential building blocks of novel materials as well as many traditional species. For instance, KMnO4, a popular oxidizing agent can be realized as K + MnO 4 − where MnO 4 has been found to be a superhalogen [20]. Similarly, superhalogen properties of FeO4 and CrO4 have also been established [21] and hence, they can also be expected to form similar compounds. In the last decade, a new kind of species namely Bsupersalt^ has been designed by interaction of superhalogens and superalkalies. Li et al. have performed studies on the interactions of BLi6
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Fig. 1 Various possible orientations for interaction of F atom with NLi4 superalkali
superalkali with various superhalogens [22] and Yang et al. have studied the interaction of BF4 superhalogen with FLi2, OLi3, and NLi4 superalkalies [23]. These interactions led to the formation of some supersalts, possessing significant nonlinear optical properties. These supersalts can be distinguished from traditional salts on the basis of their preferred dissociation to the ionic superalkali and superhalogen fragments [23]. Recently, we have investigated the interaction of XLi2 and LiX2 superatoms (X = F, Cl, Br, & I) [24] and noticed that a ring shaped Li3F3 can be formed by FLi2−LiF2 interaction. Note that Li3F3 ring has so far been realized as a trimer of LiF molecule [25, 26]. In a subsequent study, we have shown that the Li3F3 rings formed by trimerization of LiF and FLi2−LiF2 interaction can be distinguished by considering the effect of excess electrons on Li3F3 [27]. In the present investigation, we have systematically studied the interaction of halogen (X) with superalkali (SA) clusters and tried to explore whether the resulting species can be regarded as supersalts or they resemble the properties of alkali halides. To investigate this, we have chosen three typical SA clusters, SA = FLi2, OLi3, and NLi4 and considered their interactions with X = F and Cl. Here, we report the structures, stability, and electronic properties of SA−X clusters and compare them with LiF and LiCl molecules. These novel clusters may be expected as building blocks of new class of materials having some unique and interesting properties.
expands the atomic orbital of first row elements (Li−Ne) by approximately 14 functions of s, p, and d valence shells. In order to study the interaction of halogens to superalkalies, we considered various possible orientations as displayed in Fig. 1 for NLi4−F. we have placed F atom at all favorable positions relative to NLi4 and modeled the initial structures by taking into account the fact whether F interacts with the one, two, three or four Li atoms of NLi4 superalkali (see Fig. 1). Vibrational wavenumbers were calculated at the same level of theory in order to ensure that the optimized geometries correspond to a true minimum in their potential energy surfaces. All calculations were performed via Gaussian 09 code [30]. Partial atomic charges were computed by natural population analysis (NPA) scheme which has been proven to be more reliable than other population schemes due to its lower basis set dependency [31]. For the validity of the present computational scheme, MP2/ aug-cc-pVDZ, we have performed some test calculations on LiF and LiCl molecules, and compared them with corresponding experimental values [32–34] in Table 1. One can see that there is good agreement between calculated and experimental values. This may advocate the reliability of the results obtained by MP2/aug-cc-pVDZ method. Furthermore, MP2/aug-ccpVDZ has already been used in some previous studies [22, 23].
Results and discussion Computational details All structures considered in this study were fully optimized without any symmetry constraints using second order MøllerPlesset perturbation theory (MP2) [28]. A correlation consistent double zeta type basis set, aug-cc-pVDZ [29], was employed throughout these calculations. This basis-set Table 1 Calculated and experimental parameters for LiF and LiCl molecules
Parameter
Bond-length (Å) Bond-dissociation energy (eV) Dipole moment (Debye) a
The geometry optimization carried out on initial structures leads to two potential conformers for each SA−X cluster (SA = FLi2, OLi3, NLi4; X = F, Cl) which are displayed in Fig. 2. The relative energies (ΔE) for different conformers of SA−X clusters are listed in Table 2. One can note that the ground state of SA−X clusters corresponds to the geometries
LiF
LiCl
Calculated
Experimental
Calculated
Experimental
1.61 5.94 6.72
1.56 a 5.98b 6.33c
2.08 4.66 7.57
2.02a 4.86b 7.13d
Ref. [32]; b Ref. [33]; c Ref. [34]; d Ref. [35].
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Fig. 2 Equilibrium geometries of superalkali-halogen clusters obtained at MP2/aug-cc-pVDZ method
in which X interacts with two Li atoms of SA, except for NLi4−Cl in which Cl interacts with three Li atoms. For instance, the rhombic (D2h) structure of FLi2−F and C2v structures of OLi3−F, and NLi4−F are found to be 1.25, 0.76, and 0.89 eV lower in energies than their corresponding linear (C∞v) and C3v conformers. Similarly, in the ground state, FLi2−Cl and NLi4−Cl assume distorted rhombus (C2v) and C3v structures which are 0.88 and 0.37 eV lower than corresponding potential conformers. Vibrational harmonic wavenumbers are calculated for all the optimized structures in order to ensure that they belong to true minima in the potential energy surfaces. Table 2 lists the bond-distance (d) connecting X to Li of SA, the lowest harmonic wavenumber (νmin) and atomic charge (q) on X for SA−X clusters. For comparison, the corresponding values for LiF and LiCl are also listed. The geometries of SA−X clusters indeed correspond to minima as all νmin values are positive expect for a
conformer of NLi4 − Cl. The bond-distance, Li−X for the ground state SA−X clusters 1.76−1.78 Å for X = F and 2.28−2.46 Å for X = Cl. These distances are slightly larger than those obtained for LiF and LiCl molecules. This is consistent with the charge transfer to X atoms. Note that the charge transfer from SA to F is 0.89−0.92 e and 0.77−0.83 e to Cl for the ground state of SA−X clusters (see Table 2). This may also suggest that SA−X clusters can typically be regarded as SA+X− just as traditional ionic alkali halides. In order to discuss the stability of SA−X clusters, we have analyzed their binding energies against dissociation to neutral (SA + X) and ionic (SA+ + X−) fragments. The corresponding binding energies, BEn and BEi are calculated by total electronic energies including zero point energy corrections. The calculated BEn and BEi values for SA−X clusters along with those for LiX molecules are collected in Table 3. All SA−X clusters are found to be more stable than the corresponding
Table 2 Relative energy (ΔE, in eV), bond-distance (d, in Å), lowest harmonic frequency (νmin, in cm-1) and atomic charge (q, in e) for possible equilibrium conformers of superalkali-halogen clusters
Table 3 Binding energy (BE) and dissociation energy (D e ) of superalkali-halogen clusters. All parameters are given in eV. The superscripts n and i represent neutral and ionic constituents of the clusters
Clusters Conformer ΔE
Clusters
d(Li − X)
νmin
q(X)
X=
F
Cl
F
Cl
F
Cl
F
Cl
X=
FLi2−X A B OLi3−X A B NLi4−X A B
1.25 0.0 0.0 0.76 0.89 0.0
0.88 0.0 0.0 0.52 0.37 0.0
1.66 1.76 1.78 1.94 1.67 1.78
2.14 2.28 2.30 2.48 2.16 2.46
20 287 101 255 25 109
35 231 90 171 -22 106
-0.94 -0.92 -0.90 -0.89 -0.91 -0.89
-0.87 -0.83 -0.81 -0.81 -0.83 -0.77
FLi2−X OLi3−X NLi4−X
Conformer
A B A B A B
BEi
BEn
De[LiX]
F
Cl
F
Cl
F
Cl
5.94 7.19 6.93 6.17 5.99 6.88
4.83 5.71 5.59 5.06 4.99 5.36
6.29 7.54 6.86 6.11 5.62 6.51
5.18 6.05 5.52 4.99 4.60 4.98
1.45 2.70 2.82 2.07 1.83 2.71
1.62 2.50 2.76 2.24 2.10 2.47
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Table 4 AIM calculated bond order (BO) of Li−X bonds between superalkali and halogen (X)
Clusters
Conformer
BO[Li−X]
X= FLi2−X OLi3−X NLi4−X
F
Cl
A
0.14
0.13
B A B A B
0.10 0.09 0.07 0.14 0.10 0.16
0.09 0.09 0.06 0.13 0.06 0.15
LiX
LiX molecule due to higher BEn values. Thus, the interaction between SA and X is stronger than that in LiX which is due to lower ionization potentials of SA than Li. It is well known that lithium halide (LiX) dissociate into Li and X atoms but not into Li+ and X− ions, because the ionization potential of lithium is larger than the electron affinities of halogen atoms. Therefore, the calculated BEi values (7.74 eV for LiF and 6.45 eV for LiCl) are greater than BEn for LiX molecules (see BDE values given in Table 1). However, in the case of SA−X clusters, we note an interesting feature, i.e., BEi values for OLi3−X and NLi4−X are smaller than their corresponding BEn values. To put it another way, SA−X clusters prefer ionic dissociation channels to the covalent dissociation paths. This is in contrast to traditional ionic alkali halides. Thus, OLi3−X and NLi4−X clusters indeed possess supersalt characteristics. On the contrary, FLi2−X clusters follow the same dissociation trend as that of LiX. We will show later that this is due to their molecular orbital composition which is similar to that of LiX molecules. To investigate whether the SA−X clusters can be realized experimentally, we have considered their dissociation into stable molecules viz. LiF, LiCl, OLi2, and NLi3. All dissociation energy (De) values are found to be positive
which range 2.70−2.82 eV for X = F and 2.50−2.76 eV for X = Cl in the ground state SA−X clusters. Although the exact route of syntheses is not known, it is energetically possible to obtain these novel species at least in gas phase reactions if LiF, LiCl, OLi2, and NLi3 molecules are used in their syntheses. The negative of energy eigenvalues of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) can be used to estimate the ionization potential (I) and electron affinity (A), respectively within the framework of Koopmans’ approximation. However, this approximation considers neither electron-correlation nor orbital relaxation which result in the overestimation and underestimation of the calculated I and A values, respectively. For instance, one can compare the calculated I and A of LiCl with corresponding experimental values of 9.57 eV [36] and 0.59 eV [37]. The calculated I and A values of SA−X clusters are listed in Table 5. One can see that the A values of SA−X clusters are smaller than LiX molecules. This suggests that SA−X clusters are relatively more stable against addition of extra electron which can be expected due to charge transfer from SA moieties. The bond orders (BOs) of Li−X bonds between SA to X in SA−X clusters are listed in Table 4, which provide a measure for the strength of bonds in clusters and complexes [38]. These are calculated by using atoms in molecules (AIM) approach introduced by Richard Bader [39]. The BOs of LiF and LiCl, 0.16 and 0.15, are consistent with their BDEs (see Table 1). Similarly, the BOs of SA−F clusters are larger than SA−Cl by 0.01 which is in accordance with their BE values (see Table 3). In the case of FLi2−X cluster (conformer A), there is one Li−X bond with the BO of 0.14 (X = F) and 0.13 (X = Cl) which is less than that of LiF and LiCl by 0.02. This may suggest that Li−X bond in FLi2−X cluster (conformer A) is weaker than those in free LiX molecule. This fact is also reflected in their BE values listed in Table 3. On the contrary, the more
Table 5 Ionization potential (I), electron affinity (A), HOMO-LUMO gap (Egap), total static dipole moment (μ), and mean polarizability (αo) of superalkali-halogen clusters Clusters
Conformer
X= FLi2−X OLi3−X NLi4−X LiX
A B A B A B
I (eV)
μ (Debye)
Egap (eV)
A (eV)
αo (a.u.)
F
Cl
F
Cl
F
Cl
F
Cl
F
Cl
11.37 14.02 8.41 8.44 6.88 5.77 12.77
9.09 10.95 8.89 8.76 7.21 6.07 10.24
0.96 -0.18 0.13 -0.08 0.28 0.07 0.32
1.06 -0.14 0.26 -0.09 0.37 -0.01 0.47
10.40 14.20 8.28 8.52 6.60 5.70 12.45
8.02 11.09 8.63 8.85 6.84 6.07 9.77
14.57 0.00 6.73 3.54 12.17 6.61 6.72
15.89 2.03 8.97 0.22 13.95 4.87 7.57
17.13 15.70 41.51 41.29 109.39 127.62 9.19
32.99 30.86 54.60 53.38 120.20 136.28 25.20
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Fig. 3 Highest occupied molecular orbitals (HOMOs) of superalkali-halogen clusters in the ground state configuration
stable B conformer of FLi2−X possess two Li−X bonds each with the BO of 0.10 (X = F) and 0.09 (X = Cl). The energy separation between the HOMO and the LUMO is a useful quantity for examining the stability of clusters and nanostructures. The HOMO-LUMO gap (Egap) of SA−X clusters are listed in Table 5. It has been noticed that the systems with higher Egap values are less reactive. The Egap values of FLi2−F cluster are 10.4 eV (conformer A) and 14.2 eV (conformer B) which is smaller and larger than that of LiF molecule, respectively. Therefore, the conformer B of FLi2−F cluster is relatively more stable than LiF. A similar trend is observed in the case of FLi2−Cl cluster. The Egap values of other SA−X clusters are in the range of 5.70 − 8.85 eV for SA = OLi3, NLi4, and X = F, Cl, which are significantly larger than that of BLi6−F (4.56 eV) calculated by Li et al. [22]. It is also interesting to note that the order of Egap values is FLi2−X > OLi3−X > NLi4−X for X = F or Cl. This may suggest that SA −X clusters become more reactive or conducting with the increase in the size of SA cluster. In order to further evaluate the electronic properties of these novel clusters, we have calculated the total static dipole moment (μ) and mean polarizability (αo) using the finite-field approach [40]. The total energy of a molecular system in the presence of a homogeneous electric field can be expressed as [41], 1 E ¼ E o −μi F i − αi j F i F j −::::: 2 Where Eo is the total energy in the absence of the electric field, and F i , μ i , and α i j represent the
Fig. 4 Equilibrium geometry of (NLi4−Cl)2 dimer. Interaction between two units is shown by dotted line
components of the electric field, dipole moment and polarizability, respectively along the directions specified by subscripts, i and j = x, y and z. The μ and αo can be obtained accordingly as: 1=2 μ ¼ μ2x þ μ2y þ μ2z 1 αxx þ αyy þ αzz αo ¼ 3 The μ and αo values calculated by numerical differentiation with an electric field magnitude of 0.001 a.u. are listed in Table 5. One can note that the dipole moments of the ground state structures of OLi3−F and NLi4−F clusters are comparable to LiF, whereas that of OLi3−Cl and NLi4−Cl are slightly higher and smaller than LiCl, respectively. The dipole moment of FLi2−Cl, however, is reduced to 2.03 D and vanishes in case of FLi2−F due to its symmetry. More interestingly, the linear conformers of FLi2−X possess very high dipole moments which are greater than twice of LiX due to relatively higher charge transfer to X (see Table 5). The αo values of SA−F clusters range from 15.70 to 127.62 a.u., which are remarkably high as compared to LiF (9.19 a.u.). This range further spans in the case of SA−Cl and reaches to 136.28 a.u. for NLi4−Cl. This can be explained by analyzing the HOMOs of SA−X clusters, displayed in Fig. 3. One can note that the HOMOs of LiX molecules consist of atomic orbital of X. Thus in alkali halide, alkali atoms do not contribute to the HOMO. This is in contrast to SA−X clusters in which the HOMOs are delocalized over SA moieties. The larger polarizability of NLi4−Cl can be explained on the basis
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of more delocalized electron cloud due to the larger size of NLi4 moiety. It is also interesting to note that in the case of FLi2−X, the HOMOs closely resemble that of LiX. This may explain the reason behind their preferred dissociation into neutral fragments and relatively lower polarizability values. Khanna and Jena have already proposed some superatomic clusters mimicking the behavior of elements in the periodic table and consequential possibility of using them as building blocks of novel salts. According to them, the basic criterion that ensures the identity of clusters in their bulk analogs is the uniformity in their HOMO-LUMO gaps. Therefore, in order to form a bulk analog, the cluster units should be assembled in such a way that leaves the HOMO-LUMO gap unaltered. To demonstrate this idea, we have considered NLi4−Cl cluster and studied the formation of its dimer at MP2/augcc-pVDZ level. In equilibrium configuration, two NLi4−Cl cluster units interact via Li⋯Cl to form (NLi4−Cl)2, as depicted in Fig. 4. Vibrational frequency calculations characterize this dimeric complex as a local minimum in the potential energy surface. The Li⋯Cl bond-distance in (NLi4−Cl)2 is 2.37 Å and the binding energy is 0.32 eV per NLi4−Cl unit. Therefore, the dissociation of (NLi4−Cl)2 dimer into two NLi4−Cl monomer is endothermic and requires an energy amount of 0.64 eV. The HOMO-LUMO gap of (NLi4−Cl)2 is found to be 5.98 eV which is slightly smaller than that of NLi4−Cl (see Table 5). However, the dipole moment and polarizability of (NLi4−Cl)2 dimer are found be to 12.81 Debye and 267.99 a.u., respectively which are three and two times that of NLi4−Cl cluster. Thus, one can form the bulk assemblies of SA−X clusters in which aforementioned electronic properties will be further enhanced, suggesting their potential applications in the development of novel materials with unique and tailored properties.
parameters. It is established that the polarizabilities of SA−X clusters are much larger than alkali halides, which are expected to further increase in their bulk assemblies. Therefore, these novel SA−X clusters might be employed in the future to design a new class of materials. Acknowledgement A. K. Srivastava acknowledges Council of Scientific and Industrial Research, New Delhi, India for providing a research fellowship [grant number 09/107(0359)/2012-EMR-I].
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Conclusions Using second order Møller-Plesset perturbation theory based calculations; we have shown that a new class of clusters, superalkali-halogen clusters, can be formed by interaction of superalkali (SA) clusters with halogen (X) atoms. The equilibrium structures of SA−X clusters are obtained and the ground state geometries are identified. It has been noticed that due to the charge transfer from SA unit to X, SA−X clusters can be realized as SA+X− species similar to alkali halides. Their bond strengths are discussed by calculating bond orders and stabilities are analyzed by fragmentation to neutral and ionic parts as well as some stable molecules. The analyses reveal that SA−X clusters can be synthesized experimentally at least in gas phases. Furthermore, these clusters are found to prefer their dissociations into ionic fragments, in contrast to alkali halides. The electronic properties of SA−X clusters are explored and discussed by calculating a number of
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