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Theoretical Investigations on the Structural, Electronic and Spectral Properties of VFn (n = 1–7) Clusters

  • Li Peng EMAIL logo , Shao-Yi Wu EMAIL logo , Jia-Xing Guo , Si-Ying Zhong and Xiao-Hong Chen
Published/Copyright: September 19, 2018
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Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 73 Issue 12

Abstract

Density functional theory (DFT) investigations on neutral and anionic VFn (n = 1–7) clusters are performed, and the geometric structures, relative stability as well as electronic and spectral [IR, Raman and ultraviolet-visible (UV-Vis)] properties of these clusters are systematically calculated with DFT calculations. The clusters for n ≥ 4 exhibit superhalogen properties with very high electron affinities. Analysis of the interactions between VF6 and Li indicates high stability of LiVF6, where VF6 acts like fluorine. The IR and Raman spectra reveal that the peaks can be largely assigned to the stretching vibration of F atoms. The highest and next highest UV-Vis absorption peaks within 200–350 nm for neutral and anionic clusters are mainly ascribed to the electronic transitions between F 2p and V 3d orbitals.

Keywords: Clusters; Density Functional Theory (DFT); Electronic structures; Geometry

1 Introduction

Mixed clusters containing transition-metal and non-metal atoms are of great significance in the preparation of new materials for optoelectronic components [1], [2], thermoelectric materials [3], [4], [5], superionic conductors, as well as electrodes and solar energy batteries [6], [7], [8], [9], [10], [11]. Meanwhile, transition-metal and non-metal mixed clusters show novel properties of molecular (e.g. O2, CO and NO) adsorption [12], superhalogen [13], [14], [15], [16], [17], magnetism [18], [19], and non-linear optics [20]. Due to the unfilled d electronic orbitals of transition-metal atoms, transition-metal mixed clusters exhibit such different properties from the conventional bulk materials as chemical adsorption, photochemical catalysis and surface catalysis. Up to now, various theoretical studies have been carried out on the geometrical configurations, electronic structures, superhalogen and relevant physical and chemical properties for mixed clusters containing transition metal [21], [22], [23], [24]. However, the researches on mixed VFn clusters containing transition-metal vanadium and common non-metallic fluorine are relatively inadequate. Vanadium has unique variable valence states, high melting point, paramagnetism and anti-corrosion properties, and is widely used as alloy additives in industries. Since (i) the studies on the structures and properties of mixed VFn clusters would help to reveal the relationships between structures, properties and performances of these clusters and their mechanisms and (ii) the neutral and anionic clusters for the same transition-metal and non-metal series may exhibit some dissimilarities and novelty, further systematic investigations on the structures and physical and chemical properties of these systems are of important theoretical and practical significance. In this article, the geometric structures, relative stability as well as electronic and spectral [infrared (IR), Raman and UV-Vis] properties are uniformly studied for the neutral and anionic of VFn (n = 1–7) clusters from DFT calculations.

2 Computational Method

Geometrical optimizations and frequency analyses of VFn0/− (n = 1–7) clusters are performed by using the Gaussian 09 program [25] with the widely used B3LYP functional [26], [27], [28]. In order to obtain the appropriate basis sets, the bond lengths (r), frequencies (f) and dissociation energies (De) for V2, F2 and VF molecules are calculated from the different functionals and basis sets [29], [30], [31], [32], [33] and compared with the available experimental and theoretical results (see Tab. 1). Based on the overall assessment, the functional B3LYP/basis set 6-311+g* for F and B3LYP/lanl2dz for V atoms, respectively, can be regarded as the most suitable for the calculations and thus adopted for all clusters. In the computation procedure, the convergence thresholds for the maximum force, the root-mean-square (RMS) force, the maximum displacement of atoms and the RMS displacement of atoms are set as 0.00045, 0.0003, 0.0018 and 0.0012 a.u., respectively.

Table 1:

Present calculated and available previous experimental and theoretical bond lengths (r), frequencies (f) and dissociation energies (De) for F2, V2 and VF dimmers based on different functionals and basis sets.

ClustersFunctional/basic setr (Å)f (cm−1)De (eV)
Calc.Expt.Calc.Expt.Calc.Expt.
F2B3LYP/6-311+g∗1.4081.412a982.88916.64a1.3771.399a
PW91/6-311+g∗1.430923.452.086
B3LYP/6-311+g(2df)1.3961042.351.579
PW91/6-311+g(2df)1.412990.152.282
B3LYP/6-311+g(3df)1.3951039.101.572
PW91/6-311+g(3df)1.409985.042.277
V2B3LYP/LanL2DZ1.7541.783a1.9472.47a
PW91/LanL2DZ1.7112.012
B3LYP/6-311++g(2df)1.7402.835
PW91/6-311+g(2df)1.7362.881
VFB3LYP/genb1.8061.826a631.37670.4a
PW91/genb1.795633.59
B3LYP/6-311+g∗1.798641.53
PW91/6-311+g∗1.785646.11
B3LYP/6-311+g(2df)1.792658.72
PW91/6-311+g(2df)1.779662.34

  1. aRefs. [29], [30], [31], [32], [33]. bCalculations from the basis sets 6-311+g* and lanl2dz for F and V atoms, respectively.

3 Results and Discussion

3.1 Geometrical Structures

For a variety of initial geometries of VFn0,− (1 ≤ n ≤ 7) clusters, structural optimization is performed from low to high spin multiplicities in order. The stable geometries without imaginary frequencies are recorded, and the lowest energy structure is selected as the ground state. The optimised structures of neutral and anionic VFn (n = 1–7) clusters with the bond lengths, symmetries and preferred spin multiplicities are shown in Figure 1. Meanwhile, the Cartesian coordinates (in Å) for all optimized geometries, a list of all vibrational frequencies (in cm−1) and energy differences (in eV) between different multiplicities (M = 2S + 1) for neutral and anionic VFn (n = 1–7) clusters are provided in Table S1, S2 and S3 of the supplemental data, respectively. Distinct ground state structures of VFn0,− (1 ≤ n ≤ 7) clusters exhibit dissimilar symmetries, e.g. VF4−, VF5 and VF4 show higher symmetries Td, D3 and D2, respectively, while VF5− and VF6− have the lowest symmetry C1. The spin multiplicities of the clusters are in the range of 1–5. The highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) orbitals are plotted for all clusters in Figures 2 and 3. The HOMO orbitals are similar for neutral and anionic VFn clusters with the same n, while the LUMO orbitals are somewhat different.

Figure 1: The ground-state structures of neutral and anionic VFn (n = 1–7) clusters.
Figure 1:

The ground-state structures of neutral and anionic VFn (n = 1–7) clusters.

Figure 2: The HOMO orbitals (a) and LUMO orbitals (b) for neutral VFn clusters.
Figure 2:

The HOMO orbitals (a) and LUMO orbitals (b) for neutral VFn clusters.

Figure 3: The HOMO orbitals (a) and LUMO orbitals (b) for anionic VFn clusters.
Figure 3:

The HOMO orbitals (a) and LUMO orbitals (b) for anionic VFn clusters.

Figure 4 represents the variation of average bond lengths with the number n of F atoms for both neutral and anionic clusters. The average bond lengths in neutral clusters are largely smaller than anionic ones, with the exception of VF6. This point is in accordance with the general rule that the interatomic distances in a neutral molecule are usually smaller as compared to the corresponding anionic one [34], [35]. VF5 and VF6− display the shortest average bond lengths of the neutral and anionic clusters, respectively. Unlikely, VF7 and VF7− exhibit the largest average bond lengths among neutral and anionic clusters, respectively.

Figure 4: Average V–F bond lengths of neutral and anionic VFn clusters for different n.
Figure 4:

Average V–F bond lengths of neutral and anionic VFn clusters for different n.

The validity of present optimised geometric structures of these clusters can be further illustrated by the available theoretical findings. For example, present average V–F bond lengths (≈1.7594 and 1.7299 Å) of the ground state structures for VF3 and VF5 are comparable with the previously calculated result (≈1.755 and 1.7152 Å [36], [37], respectively). Thus, present geometric optimization for VFn0,− (1 ≤ n ≤ 7) clusters can be regarded as suitable. Of course, the ground state structures of the other clusters remain to be further verified with experimental and theoretical investigations. In addition, existence of neutral VF6 and VF7 clusters has not been experimentally proved, which seem to occur merely as intermediates during some chemical reactions. So, the present calculations and analysis for the structures and properties of both “imaginary” clusters should be regarded as tentative ones for the sake of completeness and feasibility of overall variation tendencies for the whole VFn systems.

3.2 Relative Stability

In order to comprehensively analyse the relative stability of the clusters, HOMO–LUMO energy gaps and the fragment energies of VFn0,− (1 ≤ n ≤ 7) are calculated from the ground state structures. According to the relationship between Pearson’s maximum hardness η (half of the HOMO–LUMO energy gap) and stability, the greater the maximum hardness, the higher the chemical stability [38], [39]. The frontier orbital energies εHOMO and εLUMO of HOMO and LUMO are usually represented as the ionization potential IP and EA [39], respectively:

(1)−εHOMO=IP,−εLUMO=EA.

The absolute hardness η of a molecule can be written as [40]

(2)η=(IP−EA)/2=(εLUMO−εHOMO)/2.

Thus, higher difference between HOMO and LUMO corresponds to higher η and hence higher stability of the systems, while smaller HOMO–LUMO gap implies smaller excitation energies to the excited manifolds. Figure 5 represents the HOMO–LUMO gaps of VFn clusters with respect to the number n of F atoms, which vary from 2.53 to 5.50 eV for both neutral and anionic clusters, with the minimum and maximum for anionic VF2 and neutral VF5, respectively. From the HOMO–LUMO gaps, VF3, VF5, VF4− and VF6− clusters are found to show the higher stabilities, corresponding to V atoms at the favorite +3 or +5 oxidation state. In addition, VF70,− clusters (especially VF7−) exhibit relatively lower chemical stability among the systems due to the smaller HOMO–LUMO gaps.

Figure 5: HOMO–LUMO gaps of neutral and anionic VFn clusters.
Figure 5:

HOMO–LUMO gaps of neutral and anionic VFn clusters.

The dissociation energies for neutral and anionic clusters into F atom and F2 molecule are shown in Figure 6 (a) and (b), respectively. The relative stability of these clusters against fragmentations to F atom and F2 molecule is characterised by the energy ΔE needed to dissociate these clusters into VFn−1 + F and VFn−2 + F2:

(3)ΔEn=−{E[VF]n0/−−E[VF]n−m0/−−E[Fm]}, m=1,2
Figure 6: Fragmentation energies of neutral and anionic VFn clusters for fragmentation channel VFn = VFn−1 + F (a) and fragmentation channel VFn = VFn−2 + F2 (b).
Figure 6:

Fragmentation energies of neutral and anionic VFn clusters for fragmentation channel VFn = VFn−1 + F (a) and fragmentation channel VFn = VFn−2 + F2 (b).

In general, the positive fragmentation energy indicates stability of the cluster against corresponding fragmentation channel, and the preferred fragmentation channel should have the lowest reaction barrier. Thus, one can treat the channel with the lowest fragmentation energy as the preferred channel. The neutral VFn clusters prefer to dissociating into VFn−1 and F for n = 1–6. And the anionic VFn− (n = 1–6) clusters are also stable against all the fragmentation channels with the same preferred fragmentation pathway as the neutral ones. On the other hand, ΔE of VF7 against the fragmentation channel VF7 ⟶ VF6 + F or VF7 ⟶ VF5 + F2 is calculated to be −0.082 or −0.036 eV, reflecting non-stability of this cluster against either channel. And ΔE of VF7− against the fragmentation channel VF7− ⟶ VF6− + F is calculated to be −1.297 eV, also indicating non-stability of the cluster against this channel. Thus, VF7− would prefer to dissociate into VF5− and F2 with the favorite fragmentation energy of only 0.92 eV, in accordance with the fact that the “seventh F atom” is weakly bound to VF6− and of the van der Waals nature. So, these clusters are largely more feasible for dissociation into F atom than F2 molecule, which is valuable for industrial application in acquisition of atomic F with extremely high activity.

3.3 Spectral Analysis

3.3.1 IR and Raman Spectra

Belonging to the molecular vibrational spectroscopies, IR and Raman spectra are powerful tools to study molecular structures. IR and Raman spectra are associated with variations of dipole moment and polarizability of a molecule in certain vibration modes, respectively, and show some complementarity. The units of abscissa for IR and Raman spectra are wavenumber, and the units of IR intensity and Raman activity are km/mol and A4/amu, respectively [41], [42].

Based on the optimised structures, the IR and Raman spectra of VFn clusters are plotted in Figure 7. The vibration peaks appear roughly in the range of 64–842 cm−1, mainly attributable to the stretching vibration modes of F atoms serving as the main negative charge carrier. In these vibration modes, the dipole moments and polarizability of the molecular systems show the largest changes with the normal coordinates and result in the strongest vibration peaks.

Figure 7: The IR spectra and Raman spectra of neutral and anionic VFn (n = 1–7) clusters.
Figure 7: The IR spectra and Raman spectra of neutral and anionic VFn (n = 1–7) clusters.
Figure 7: The IR spectra and Raman spectra of neutral and anionic VFn (n = 1–7) clusters.
Figure 7: The IR spectra and Raman spectra of neutral and anionic VFn (n = 1–7) clusters.
Figure 7:

The IR spectra and Raman spectra of neutral and anionic VFn (n = 1–7) clusters.

From Figure 7, more IR and Raman peaks are found for VFn clusters with n = 5–7. For VF5, the highest IR peaks at 725.08 and 586.35 cm−1 for neutral and anionic clusters, respectively, are associated with the stretching vibration of two F atoms. The highest Raman peaks of neutral and anionic VF5 clusters locate at 723.96 and 577.14 cm−1, respectively, correspond to the symmetrical stretching vibration of F atoms. The highest IR peaks of VF6 locate at 767.01 and 629.07 cm−1 for neutral and anionic clusters, associated with the stretching vibration of two F atoms and the swing vibration of V atom, respectively. The highest Raman peaks for VF6 at 684.57 and 649.33 cm−1 for neutral and anionic clusters are related to the stretching vibration and asymmetric swing vibration (with V atom fixed), respectively. The larger energies of the highest IR and Raman peaks for all neutral clusters except VF7 than the corresponding anionic ones are ascribed to the shorter average bond lengths and hence larger force constants of the bonds in the former systems.

3.3.2 UV-Vis spectra

The UV-Vis spectra due to the electronic transitions are plotted for VFn clusters in Figure 8, by using the Gaussian module time dependent density function theory (TDDFT) with the software Multiwfn [43]. The numbers of excited states for present systems with merely a few atoms are within the range of 18–165 by optimizing the spectra for the distinct clusters. On the whole, the profiles, numbers and positions of the absorption peaks are dissimilar for neutral and anionic VFn clusters with the same n and different for the same neutral or anionic series with distinct n. VF, VF2−, VF3−, VF4 and VFn0,− (n = 5–7) exhibit the largest and next largest molar absorption coefficients within 200–350 nm, which may be largely ascribed to the electronic transitions between F 2p and V 3d orbitals. And the various sub-peaks can be assigned to the energy splittings of V 3d orbitals under low symmetries [44], [45], [46], [47], [48]. The above dominant absorption region would reveal that VFn clusters could act as potential UV absorption materials. For neutral VFn clusters, the width of UV absorption region first decreases from n = 1–3 and then increases for n ≥ 4, revealing the narrowest UV absorption region for VF3. As regards anionic clusters, the width of UV absorption region first decreases from n = 1–3, then dramatically declines for n = 4 (with the narrowest and weakest UV absorption), and roughly remains unchanged for n = 5–7. The position of the highest UV peak of neutral clusters largely shows blue shifts with increasing n from 1 to 4 and then exhibits slight red shifts for n = 5–7. Whereas the position of the highest UV peak of anionic clusters exhibits slight red shifts from n = 1–2, then blue shift for n = 3, and again red shift for n = 4, then blue shift for n = 5, and finally red shifts for n = 6 and 7. On the other hand, the obvious absorption in visible region (500–800 nm) is found for both neutral and anionic VFn (n = 1, 3, 4) and VF2− clusters, suggesting that these systems could demonstrate potential visible light photocatalystic properties. Neutral clusters exhibits the most intense visible light absorption at about 520 nm for n = 3, weak absorption for n = 1 and 4 and absence of absorption for n = 2 and 5–7. Nevertheless, anionic clusters show the strong visible light absorption for n = 1–3, weak absorption for n = 4 and absence of absorption for n = 5–7. And the position of the visible light absorption peaks for anionic clusters displays red shifts with the increases of n from 1 to 3.

Figure 8: The UV-Vis spectra of neutral (left) and anionic (right) VFn (n = 1–7) clusters.
Figure 8: The UV-Vis spectra of neutral (left) and anionic (right) VFn (n = 1–7) clusters.
Figure 8:

The UV-Vis spectra of neutral (left) and anionic (right) VFn (n = 1–7) clusters.

3.4 EA of VFn Clusters and Prediction of Novel Salt Li-(VF6)

3.4.1 EA of VFn Clusters

Figure 9 shows the relationship between EA and the number n of F atoms. EA is calculated from the energy difference between the neutral and corresponding anionic forms of the cluster, both in their ground state configurations. EA increases from 0.984 to 7.187 eV as the number of F atoms increases from 1 to 6. Particularly, EA of VF6 (≈7.187 eV) is much higher than halogen (e.g. 3.399, 3.617 and 3.365 eV for F, Cl and Br, respectively [49], [50]). Thus, VFn (n = 4– 7) clusters may be likely to show superhalogen property.

Figure 9: Electron affinities of VFn clusters as a function of n.
Figure 9:

Electron affinities of VFn clusters as a function of n.

3.4.2 Prediction of Novel Salt Li-(VF6)

Now we discuss the interaction of the typical VF6 superhalogen with an alkali atom Li. A structure in which a Li atom is placed on the top of V atom is chosen and then the geometry is optimised by adopting 6-311+G(d) basis set for Li. Binding to two F atoms, V atom in the optimised structure is found to shift slightly in the molecular plane [Figure 10 (a)]. The stability of this complex is confirmed by frequency and binding energy calculations. All the real frequencies imply the stability of the complex. Since the calculated binding energy (about 7.67 eV) of Li-(VF6) is higher than that (≈5.89 eV) for a Li atom and an F atom, the former is expected to show higher thermodynamic stability. This point is consistent with the fact that halogens tend to bond with an alkali metal atom and form a more stable compound. Figure 10 (b) and (c) shows the HOMO and LUMO pictures of LiVF6 salt, in which both HOMO and LUMO situate in the whole molecule except Li atom. This is somewhat different from conventional LiF where Li does not contribute to HOMO but contributes to LUMO. To the best of our knowledge, the related experimental data for the structure and physical and chemical properties have not been reported for LiVF6 up to now, and the feasibility and properties of present predicted LiVF6 need to be checked with further theoretical and experimental verification.

Figure 10: (a) Optimised structure of LiVF6 complex; (b) HOMO and (c) LUMO pictures for LiVF6.
Figure 10:

(a) Optimised structure of LiVF6 complex; (b) HOMO and (c) LUMO pictures for LiVF6.

4 Conclusions

From DFT calculations, the geometrical structures, stabilities, electronic properties and spectral properties are studied for neutral and anionic VFn (n = 1–7) clusters and the conclusions are summarised as follows:

  1. Based on geometry optimization, a V atom is found to bind with up to six F atoms in VFn clusters, and the corresponding VFn complexes in both neutral and anionic forms are stable against all dissociation channels, ensuring that V can exist in hexavalent state. However, neutral and anion VF7 are unstable instead. The calculated larger HOMO–LUMO gaps of VF3, VF5, VF4− and VF6− clusters reflect the higher stability, corresponding to V atom at the favorite +3 or +5 oxidation state.

  2. IR and Raman spectra reveal that the highest vibration peaks can be largely assigned to the stretching vibration of F atoms. The larger energies of the highest IR and Raman peak for all neutral clusters except VF7 than the corresponding anionic ones are ascribed to the shorter average bond lengths and hence larger force constants of the bonds in the former systems. The highest and next highest UV-Vis absorption peaks within 200–350 nm for neutral and anionic clusters are mainly ascribed to the electronic transitions between F 2p and V 3d orbitals, suggesting that VFn clusters could act as potential UV absorption materials. The obvious absorption in visible region (500–800 nm) for both neutral and anionic VFn (n = 1, 3, 4) and VF2− clusters indicate that these systems could be adopted as potential visible light photocatalysts.

  3. The electronic properties of VFn clusters are related to the geometrical structures and the value of n. Particularly, the clusters for n ≥ 4 exhibit superhalogen properties with very high EA, with the maximum of 7.19 eV for VF6. The analysis of the interactions between VF6 and Li atom indicates the high stability of LiVF6 complex, where VF6 unit may act like fluorine atom.

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11764028

Funding statement: This work was financially supported by the Sichuan Province Academic and Technical Leaders Support Fund [Y02028023601041] and the National Natural Science Foundation of China Granted No. 11764028.

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Supplementary Material

The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/zna-2018-0102).

Received: 2018-03-01
Accepted: 2018-08-02
Published Online: 2018-09-19
Published in Print: 2018-11-27

©2018 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Investigation of Gamma-Ray’s Transmission Geometries for the Measurement of Attenuation Coefficients
  4. Atomic, Molecular & Chemical Physics
  5. Theoretical Investigations on the Structural, Electronic and Spectral Properties of VFn (n = 1–7) Clusters
  6. Dynamical Systems & Nonlinear Phenomena
  7. Parametric Instability of a Rotating Axially Loaded FG Cylindrical Thin Shell Under Both Axial Disturbances and Thermal Effects
  8. Generalised Sasa–Satsuma Equation: Densities Approach to New Infinite Hierarchy of Integrable Evolution Equations
  9. Quantum Theory
  10. The Schrödinger Equation and Negative Energies
  11. Gravitational Drift Instability in Quantum Dusty Plasmas
  12. Hydrodynamics
  13. Unsteady Peristaltic Transport of a Particle-Fluid Suspension: Application to Oesophageal Swallowing
  14. Solid State Physics & Materials Science
  15. First-Principles Investigation of Structural Stability, Mechanical, Anisotropic, and Thermodynamic Properties of CeT2Al20 Intermetallics
https://doi.org/10.1515/zna-2018-0102
Keywords for this article
Clusters; Density Functional Theory (DFT); Electronic structures; Geometry

Articles in the same Issue

  1. Frontmatter
  2. General
  3. Investigation of Gamma-Ray’s Transmission Geometries for the Measurement of Attenuation Coefficients
  4. Atomic, Molecular & Chemical Physics
  5. Theoretical Investigations on the Structural, Electronic and Spectral Properties of VFn (n = 1–7) Clusters
  6. Dynamical Systems & Nonlinear Phenomena
  7. Parametric Instability of a Rotating Axially Loaded FG Cylindrical Thin Shell Under Both Axial Disturbances and Thermal Effects
  8. Generalised Sasa–Satsuma Equation: Densities Approach to New Infinite Hierarchy of Integrable Evolution Equations
  9. Quantum Theory
  10. The Schrödinger Equation and Negative Energies
  11. Gravitational Drift Instability in Quantum Dusty Plasmas
  12. Hydrodynamics
  13. Unsteady Peristaltic Transport of a Particle-Fluid Suspension: Application to Oesophageal Swallowing
  14. Solid State Physics & Materials Science
  15. First-Principles Investigation of Structural Stability, Mechanical, Anisotropic, and Thermodynamic Properties of CeT2Al20 Intermetallics
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