Density functional study on the evolution of superhalogen properties in VO n (n = 1

Abstract

We perform density functional calculations on the ground state geometries of VO_n (n = 1–5) complexes and analyze their stability against dissociation to O atom and O₂ molecule in neutral as well as anionic forms. It is shown that a V binds with four O atoms stably such that the maximum possible oxidation state of V can be as high as +7. The electron affinity of VO_n suggests that these species behave as superhalogen for n≥3, which become as large as 4.52 eV for n = 5. The interaction of VO_n superhalogen with appropriate alkali metal is stronger than traditional alkali halides. This is exemplified by formation of stable NaVO₃ complex compound by interacting alkali Na atom with VO₃ superhalogen. This finding demonstrates that VO_n superhalogens form a new class of salt,which is relatively more stable than NaCl molecule.

Keywords

Superhalogen stability electron affinity complex compounds DFT

1 Introduction

Seventh group elements in the periodic table have the highest electron affinity (EA) than the rest of elements. The term “superhalogen” refers to molecular species having higher EA than halogens (3.40 eV for F, 3.61 eV for Cl, 3.36 eV for Br etc [1, 2]. Superhalogen consists of a metal which may be surrounded peripherally by halogen, oxygen, pseudohalogen or halogenoid etc. such that the last electron is delocalized over peripherally attached atoms, hence, EA increases [3 –7]. The concept of superhalogen was introduced in 1981 by Gutsev and Boldyrev [8] by using sp elements. First superhalogen came in light was LiF₂ with EA 5.45 eV 9]. Due to the fixed valence of s block element, they were able to bind with fixed number of atoms. To overcome this difficulty, transition metal element came to play the central role. The transition metal elements possess variable coordination number and hence, their binding property is enhanced. The study of superhalogen has been continuously expanding due to their interesting applications [10 –16]. For instance, gold (Au) having electronic configuration 5d¹⁰6s¹ should be monovalent but its oxidation state varies from 5 to 7 [17, 18]. The oxidation state of any metal element is number of electron removed from its outer orbit to participate in chemical bonding. Another example might be Mn with electronic configuration 3d⁵4s², which interacts with oxygen and makes MnO₄ having EA 5 eV [19]. Likewise, FeO₄ and CrO₄ complex show super halogen properties with EA 3.8 and 4.96 eV, respectively [20 –22]. There are a number of studies on transition metal oxide clusters [23 –27] including 3d elements such as Sc [25], Ni [26], Co [27] etc.

Vanadium is 3d transition metal element having outer shell electronic configuration of 3d³4s², its oxidation state may be as high as +5. This is exemplified by V₂O₅, an important compound of industrial use. Vanadium oxides are widely known as cathode materials in lithium batteries [28], ferromagnetic nanotubes [29], in bolometric detectors [30], and their use as supported catalysts [31]. Vanadium catalysts are widely used in production of sulphuric acid; the reduction of nitrogen oxides with ammonia and the selective oxidation of hydrocarbons utilize industrially important bulk and fine chemicals [32]. In this paper, we have studied VO_n species for n = 1–5. We discuss the structures of neutral and anionic state of these species in different spin states and their stability against decomposition in O and O₂. The evolution of superhalogen properties of VO_n species have been analyzed with high oxygen content.

2 Computational methodology

The geometry and total energy were calculated by hybrid exchange correlation functional B3LYP [33, 34] method and aug-cc-pVTZ basis set [35] using Gaussian 09 [36]. The geometry optimization was followed by frequency calculations to ensure that optimized structures correspond to at least some local minima in the potential energy surface. All calculations were repeated for higher spin states to obtain preferred spin state of neutral as well as anionic species. B3LYP functional has been employed to study the superhalogen properties of a variety of transition metal oxides [26, 37]. Furthermore, B3LYP calculated values match well with experimental data. For instance, the bond length, binding energy of Cl₂ 1.98 A°, 2.34 eV, respectively and EA of (Cl) 3.70 eV agree well with corresponding experimental values [38].

3 Results and discussions

3.1 Structures and stability

We have considered structures of VO_n clusters in which O atoms bind associatively as well as dissociatively to V core. The possible initial geometries of VO_n clusters are shown in Supplementary Figure S1. The optimized structures of neutral VO_n (n = 1–5) clusters and their anions for various spin states are shown in Figs. 1 and 2, respectively. Table 1 lists the relative energies of VO_n and ${VO}_{n}^{-}$ for different spin multiplicities. All neutral VO_n species favour lower spin state, i.e., doublet except VO and VO₅. On the contrary, the ground states of ${VO}_{n}^{-}$ are triplet except ${VO}_{3}^{-}$ and ${VO}_{4}^{-}$ , which are singlet. The ground state structures of VO_n clusters are approximately similar in neutral and anions. The structure VO₂ is more bent than that of ${VO}_{2}^{-}$ . This is due to the fact that additional charge given to VO₂ goes to nonbonding orbitals of oxygen, which creates repulsion between O atoms. VO₃ is a trigonal planar in which one of the bond lengths is increased while ${VO}_{3}^{-}$ shows equilateral structure. The structures of neutral VO₄ and its anion are distorted tetrahedral shape. VO₄ exists in the form of (VO₂)O₂ complex in which V binds with one molecular oxygen (O₂) and two oxygen atoms (O). In anionic form, however, all O atoms bind dissociatively to V due to excess electron on O atoms. In VO₅, both anionic and neutral structures form (VO₃)O₂ complexes. Vibrational analysis reveals all frequencies are real for optimised structures. Therefore, they belong to at least a local minimum in the potential energy surface. The stability of VO_n clusters has been analyzed by calculating dissociation energy (De) against O atom and O₂ molecule:

$\begin{matrix} De ({VO}_{n}^{-} \to {VO}_{n - 1}^{-} + O) = E [{VO}_{n - 1}^{-}] + E [O] - E [{VO}_{n}^{-}] \\ De ({VO}_{n}^{-} \to {VO}_{n - 2}^{-} + O_{2}) = E [{VO}_{n - 2}^{-}] + E [O_{2}] - E [{VO}_{n}^{-}] \end{matrix}$ where E […] represents the total energy of respective species including zero-point energy correction for n = 1–5.

Fig.1

Equilibrium geometries of VO_n (n = 1–5) neutral. Central gray sphere represent (V) atoms and peripheral red spheres represent oxygen (O) atoms. Bond lengths (in A°) are also shown.

Fig.2

Equilibrium geometries of VO_n (n = 1–5) anion. Central gray sphere represent (V) atoms and peripheral red spheres represent oxygen (O) atoms. Bond lengths (in A°) are also shown.

Table 1

Relative energies are (in kcal/mol) for different spin multiplicities (2S+1) of neutral and anionic VO_n species. The expectation values <S²>are given in parenthesis

n	VO_n			VO_n^-
(2S+1)	2	4	6	1	3	5
1	30.7 (0.79)	0 (3.79)	66.5 (8.75)	23.2	0 (2.14)	13.2 (6.04)
2	0 (0.76)	40.8 (3.76)	96.0 (8.76)	15.7	0 (2.02)	50.8 (6.01)
3	0 (0.77)	39.5 (3.76)	94.7 (8.76)	0	35.1 (2.01)	97.9 (6.02)
4	0 (0.76)	38.9 (3.76)	105.4(8.77)	0	11.3 (2.08)	80.3 (6.10)
5	0.6 (1.77)	0 (3.78)	48.9 (8.77)	25.7	0 (2.05)	53.3 (6.04)

The calculated dissociation energies (De) for neutral and anionic VO_n species are listed in Tables 2 and 3, respectively. All VO_n species are found to be stable as all dissociation energy values are positive. The dissociation energy decreases as the successive O atoms are attached to V. The dissociation energy of VO_n against O removal is higher than O₂ in neutral and anionic forms. VO_n anions are more stable than their neutral form due to high energy values for dissociation to O₂.

Table 2

Preferred spin multiplicity (m), symmetry (s) and partial NPA charge on V atom (q), HOMO-LUMO energy gaps (E_gap, in eV) and dissociation energy (D_e, in eV) of neutral VO_n clusters for n = 1–5

	VO_n			De(VO_n)
n	m	s	q	E_gap	VO_n - 1 + O	VO_n-2 + O₂
1	4	C_∞v	0.650	2.55	11.05	–
2	2	C_2v	1.218	2.81	8.19	10.07
3	2	C₁	1.060	2.85	6.78	5.80
4	2	C₁	0.989	3.55	6.67	4.27
5	4	C₁	0.793	2.27	4.60	2.10

Table 3

Preferred spin multiplicity (m), symmetry (s) and partial NPA charge on V atom (q), HOMO-LUMO energy gaps (E_gap, in eV) and dissociation energy (D_e, in eV) of anion ${VO}_{n}^{-}$ clusters for n = 1–5

	${VO}_{n}^{-}$			De( ${VO}_{n}^{-}$ )
n	m	s	q	E_gap	${VO}_{n - 1}^{-} + O$	${VO}_{n - 2}^{-} + O_{2}$
1	3	C_∞v	–0.206	1.77	16.95	–
2	3	C_2v	0.644	2.23	9.14	16.92
3	1	C_2v	1.024	3.75	9.09	9.06
4	1	C₁	0.922	3.64	5.96	5.88
5	3	C₁	0.598	2.81	5.47	2.26

The highest occupied molecular orbital (HOMO) represents the ability to donate an electron and while lowest unoccupied molecular orbital (LUMO) shows ability to accept it. The HOMO-LUMO gap (E_gap) is also a parameter to explain relative stability of VO_n species. Pearson [39] gave the principle of maximum hardness, which states that the species with higher E_gap values are chemically hard, i.e., possess higher chemical hardness value (η). This value correlates with electronic stability as hard species with larger E_gap are less polarized in comparison to soft molecule having smaller E_gap. In order to compare their chemical reactivity of VO_n species, we have given E_gap values in Tables 2 and 3. The higher E_gap (3.55 eV) for VO₄ suggests that it is relatively more stable while smaller gap for VO₅ (2.27 eV) indicate that it is chemically more reactive that means it can interact easily with other species. In anionic form, E_gap value is higher for ${VO}_{3}^{-}$ (3.75 eV) and lower for VO^- (1.77 eV).

3.2 Binding and electron affinity

The stability of VO_n species clearly suggest that the oxidation state of V can easily reach to +5. From Table 2, one can note that ${VO}_{3}^{-}$ has sufficiently large De values against dissociation to O as well as O₂. Furthermore, ${VO}_{5}^{-}$ exists in the form of ( ${VO}_{3}^{-}$ ) O₂ complex. As mentioned earlier, the oxidation state of transition metals vary due to presence of d orbital electrons. In VO_n species, there is interaction between 3d orbital of V with 2p orbital of O, which perturbs both 3d and 2p orbitals. This results in bonding orbital with mixed characteristics of d and p orbitals. These 3d orbital’s electron are responsible for variable coordination number of VO_n. We have performed NBO analyses on these species to explain the participation of 3d electrons in bonding. In Fig. 3, we plot the contribution of 3d electrons as a function of number of O atoms in both anion and neutral cases. In anionic case, the participation of 3d electrons in bonding increases with the increase in the number of O atoms up to n = 5. In neutral (VO₃) from MO theory HOMO and LUMO picture does contain whole site, but in anionic case ( ${VO}_{3}^{-}$ ) HOMO picture does not contain V site while LUMO covered whole site (see Fig. 4).

Fig.3

Contribution of 3d electrons in bonding of neutral and anion of VO_n for n = 1–5.

Fig.4

HOMO (upper) and LUMO (lower) surfaces of neutral and anionic VO₃ clusters with an isovalue of 0.01 a.u.

The adiabatic electron affinity (EA) of VO_n species are calculated by the difference of energies between neutral species and corresponding anions both in their ground state configurations. The calculated EA of VO_n species are collected in Table 4. We can see that the EA increases as the successive O atoms are attached to V up to n = 5. The EA of VO₂, 2.04 eV is larger than that of O atom. Furthermore, the EA for VO₃ attains the value of 4.35 eV, which exactly reproduces the experimental value 4.36 eV [40]. Although EA of VO₄ is smaller than that of VO₃, it is still higher than that of F atom. Therefore, EA values clearly show that VO_n (for n≥3) clusters behave as superhalogen. The large EA values of VO_n superhalogens can be explained on the basis of natural bonding orbital (NBO) charge analysis [41]. In Table 4, we have also listed the NBO charge difference on V (ΔQ) in VO_n and ${VO}_{n}^{-}$ . In VO^-, more than 85% of electronic charge is contained by V atom. As the number of O atoms increase in VO_n_, the extra charge becomes delocalized over O atoms. For n = 3, extra charge is completely delocalized over O atoms such that ΔQ becomes negligibly small. This is due to the saturation of charge on V atom in VO₃ (see Table 1). Consequently, the EA of VO₃ becomes very high due to delocalization of charge over O atom. For n = 4, ΔQ tends to increase, resulting in the decrease in EA value of VO₄. The EA further increases for n = 5, however, electronic delocalization decreases due to existence of ( ${VO}_{3}^{-}$ )O₂ complex.

Table 4

Electron affinity (EA, in eV) and NBO charge difference on V (ΔQ, in e) for VO_n species

n	EA	ΔQ
1	1.09	0.856
2	2.04	0.574
3	4.35	0.036
4	3.65	0.067
5	4.52	0.195

3.3 Formation of dimer and complex salt

Having established VO_n as super halogens for n≥3, we expect it to mimic some characteristics of halogen atoms. For instance, halogen atoms have tendency to form dimer such as Cl₂ and ionic salt such as NaCl. Therefore, it is desirable that VO₃ should exhibit similar properties. We choose two different configurations for the study of possible dimeric structure of VO₃. In first configuration, both VO₃ units are placed parallel to each other. In second configuration, both units are placed perpendicular to each other. In both cases, V of one unit is close to O atom of another to promote the interaction. The optimized structure of VO₃ dimer along with their HOMO and LUMO surfaces are shown in Fig. 5. Binding energy of above dimer VO₃ (3.35 eV) is greater than the binding energy of Cl₂ (2.34 eV).

Fig.5

Equilibrium geometry of dimer VO₃ structure and all bond-lengths (in A°) and HOMO – LUMO surfaces with an isovalue of 0.01 a.u. are also given.

Now we discuss the formation of complex salt with Na. Initially we have substituted Na atom just above to the V atom. After full optimization, the Na atom binds with two O atom forming a planner structure as shown in Fig. 6 along with their HOMO-LUMO surfaces. Binding energy of above complex salt is equal to 4.52 eV. This binding energy is greater than that of calculated binding energy of NaCl (3.99 eV). In NaCl, the HOMO surface does not contain Na site but LUMO is covered whole molecule. In NaVO₃, however, both HOMO and LUMO do not contain Na site. This clearly indicates that binding nature of Na with VO₃ is covalent rather than electrovalent as in case of NaCl salt.

Fig.6

Equilibrium geometry of NaVO₃ complex and all bond-lengths (in A°) and HOMO – LUMO surfaces with an isovalue of 0.01 a.u. are also given.

4 Conclusions

The results of B3LYP calculations on VO_n clusters have been discussed. We have shown that V atom can bind with a maximum of five O atoms, expanding its oxidation state to +7. VO_n species are stable in the neutral as well as anionic states against dissociations to O atom and O₂ molecule. The superhalogen behaviour of VO_n cluster has been established due to their larger electron affinities as compared to halogen for n≥3. The interaction of VO₃ superhalogen with alkali metal Na is found to be covalent form and leads to the formation of a stable NaVO₃ complex. This opens up an opportunity for the researcher a new class of compounds by the interaction of VO₃ superhalogen with appropriate alkali atoms.

Supplementary information

Figure S1

Initial geometries of VO_n (n = 1–5) clusters considered in this study.

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Density functional study on the evolution of superhalogen properties in VO n (n = 1–5) species

Abstract

Keywords

1 Introduction

2 Computational methodology

3 Results and discussions

3.1 Structures and stability

Supplementary information

References