Theoretical and Experimental EPR Study of VO²⁺-Doped Ammonium Hydrogen Tartrate

1 Introduction

The electron paramagnetic resonance (EPR) spectroscopic technique is a useful tool to study the magnetic behaviour, site symmetry, bonding nature, and dynamics of paramagnetic centres. There are many methods to have such centres in the host crystal lattices. One of the methods is doping transition metal ions to the crystal centres [1–4].

Vanadium has an electronic configuration [Ar]3d³4s² and is a stable cation existing in di-, tri-, and tetravalent states in complexes [5–7]. The tetravalent state of the vanadium ion has only one unpaired electron in the ground-state configuration. Usually, in solids or in solutions, vanadium coordinates to five or six oxygens [8]. One of the oxygens is bound to vanadium ion by a strong double covalent bond and forms vanadyl (VO²⁺) ion. Therefore, most of the complexes having VO²⁺ ions possess C_4v symmetry and show axial symmetry in paramagnetic centres [9].

Some researchers have studied tartrate-containing complexes such as di-sodium tartrate [10] and diammonium d-tartrate [5] doped with VO²⁺ by EPR spectroscopy in recent years. The title complex in our study, ammonium hydrogen tartrate (AHT) or ammonium bitartrate, is used as baking powder [11]. Some other researchers have studied different physical properties of the AHT such as Fourier transform infrared (FT-IR) and Raman spectra [12]; magnetic susceptibility [13]; electrical conductivity [14]; and thermal, optical, and dielectric properties [15]. However, there is no EPR spectroscopic report for the AHT complex in the literature.

One can study the bonding nature and magnetic behaviour of the complex by the EPR method after doping with VO²⁺ ions. In this study, we tried to identify the dynamics of the paramagnetic centre in AHT complex by using EPR technique. We calculated the spin Hamiltonian parameters and the molecular bonding coefficients of the complex both in theoretical and experimental ways.

2 Experimental

AHT single crystals were grown from a saturated solution of ammonia with tartaric acid in stoichiometric proportion. An aqueous solution of 1 wt% of vanadyl(IV) sulphate was added as dopant to the saturated solution of AHT. After about 3 weeks, colourless single crystals were obtained by using slow evaporation method. The crystal system of AHT is orthorhombic and belongs to the space group P2₁2₁2₁ having four molecules per unit cell with the following parameters: a=7.648, b=11.066, and c=7.843 Å [16]. EPR spectra of the AHT:VO²⁺ single crystal were recorded on a Varian E109 Century series X-band EPR spectrometer. We used a diphenylpicrylhydrazyl (dpph) sample (g=2.0036) to make corrections to the g values.

3 Results and Discussion

We recorded the EPR spectra of the AHT:VO²⁺ single crystal at room temperature. The nuclear spin of the vanadium is 7/2, and vanadyl ion has a single electron of spin 1/2 in its d orbitals. The interaction between these spins results hyperfine splitting giving an octet in an EPR spectrum [17]. Since there are four molecules in the unit cell of the AHT:VO²⁺ complex, we can expect 32 peaks in the EPR spectrum. However, the positions of the sites in the complex depending on the crystal planes cause the complex to feel different external magnetic fields. If two of the sites feel the same magnetic field, there will be an octet instead of 16 peaks in the EPR spectrum as if there was a single site. But this time, the intensity of the lines increases twice. Both of the sites have the same g values and same hyperfine splitting constants (A). If two of the sites feel different magnetic fields, there will be 16 peaks having nearly the same g but different A values in the EPR spectrum. In this case, still some of the lines overlap and increase the intensity of the peaks [10].

As a general case, when there is more than one site in a paramagnetic centre, the number of lines in the EPR spectrum increases as well. The sites have nearly the same g values, while A values may change slightly. This is the case for some lines at some orientations overlapping in the spectrum for the AHT:VO²⁺ complex. Figure 1 shows one of such spectra at an orientation in the bc plane. To determine the principal g and A values of the single crystal, one must take the EPR spectra in all three mutually perpendicular axes. When taking the spectra in one axis, generally one rotates the crystal from 0° to 180° in the external applied magnetic field. It will be very difficult to follow the same line, say for the magnetic spin quantum number m=−7/2, in all spectra for a single axis in anisotropic cases. To handle the problem, we used a simple numerical technique explained in [18]. Figure 2 shows the line positions and fitted curves. One can easily find the g² values for a specific line with respect to rotation angle in each plane after the fitting process [19].

Figure 1:

EPR spectrum of AHT:VO²⁺ single crystal. The magnetic field is in the bc plane making 10° from the b-axis.

Figure 2:

Angular variation of g² values of AHT:VO²⁺ single crystal.

Including only electronic Zeeman and hyperfine interactions, one can describe the EPR spectra of the single crystal in terms of the following spin Hamiltonian:

(1)H = βH ⋅ g ⋅ S + S ⋅ A ⋅ I. (1)

After calculations described in [18], we constructed g and A tensors and diagonalised them to find the principal g and A values. One can find both the results of our work and some other tartrate containing complexes in Table 1.

If we examine Figure 2 carefully, we can see four chemically identical but magnetically not identical sites in the complex. It means that the sites align in different directions in the unit cell of the complex. All sites in the single crystal show nearly axial symmetry as is the case for paramagnetic vanadyl ions in orthorhombic crystal systems. The single-crystal EPR spectra also show that the VO²⁺ group localises interstitially and make a defection in the host lattice. It coordinates with two bidentate tartrate dianions in the equatorial plane and an aqua molecule in the axial position opposite to the oxide. The proton vacancy in tartrate dianions provides the charge compensation in the complex [10]. The value of the ratio g_||/g_⊥ is greater than unity and hence indicates the tetragonal distortion of the vanadyl ions in AHT single crystals [20]. The distortion is along V=O direction and removes the degeneracy of the ground state of vanadyl ion with its d_xy orbital lying lowest.

The g_i (i=||, ⊥) values and the molecular bonding coefficients are related to each other [21]:

(2)g|| = ge(1 − 4λβ12β22Δ||), (2)

(3)g⊥ = ge(1 − λγ2β22Δ⊥), (3)

where g_e (2.0023) is the free electron g factor, and λ is the spin-orbit coupling coefficient for the VO²⁺ ion. We take λ=170 cm⁻¹ for VO²⁺ ion [22]. β12, β22, and γ² are the molecular orbital bonding coefficients characterising in-plane σ, in-plane π, and out-of-plane π-bonding, respectively, for the central transition metal ion with the ligands. The denominators are optical absorption bands assigned to Δ_⊥=²B_2g → ²E_g, and Δ_||=²B_2g → ²B_1g transitions for the title complex [8]. Since there is no optical absorption report for the AHT:VO²⁺ complex, we used the two bands Δ_⊥=10,762 cm⁻¹, and Δ_||=16,621 cm⁻¹ reported for vanadyl-doped diammonium d-tartrate complex, which is similar to the structure under study [5].

On the other hand, the relation between A_i (i=||, ⊥) values and the molecular bonding coefficients is as follows [21, 22]:

(4)A|| = −P[κ + 47β22 + (ge − g||) + 37(ge − g⊥)], (4)

(5)A⊥ = −P[κ − 27β22 + 1114(ge − g⊥)], (5)

where κ is the Fermi contact term and indicates the 4s orbital mixing with 3d_xy orbital of the vanadium. P is the dipolar interaction term between magnetic moments of the unpaired electron and the vanadium nucleus. One can calculate the dipolar interaction term by neglecting second-order effects and using the negative values for A_i [23, 24]:

(6)P = 7(A|| − A⊥)6 + (3/2)(λ/Δ||). (6)

Using (4) and (5) and eliminating v, we have an expression for β22 as follows [20, 24]:

(7)β22 = −76((A|| − A⊥)P + (ge − g||) − 514(ge − g⊥)). (7)

One can find the calculated molecular bonding coefficients in Table 2. β22 is the covalency ratio of V=O bonds [3, 20, 24]. The value of β12 is 0.5 or 1.0 indicating whether the bond is covalent or ionic in nature, respectively. However, if the value is neither of them, the bonding is moderately ionic and covalent. The parameters (1 − β12) and (1 − γ²) show the covalency rates of the vanadium atom. The first parameter gives the effect of the σ-bonding with the equatorial ligands, while the second gives the effect of π-bonding with the vanadyl oxygen [3, 20]. In this work, γ² is less than β12 for all sites in AHT:VO²⁺ complex indicating that in-plane σ-bonding is more ionic and out-of-plane π-bonding is moderately ionic in nature.

Figure 3 shows the powder EPR spectrum of the AHT:VO²⁺ single crystals and its computer simulation. We measured the g and A values of the powder spectrum. The results are as follows: g_||=1.941, g_⊥=1.986, A_||=192.1×10⁻⁴ cm⁻¹, and A_⊥=72.86×10⁻⁴ cm⁻¹. These results are reasonable and compatible with the single-crystal data.

Figure 3:

Experimental and simulated EPR spectrum of AHT:VO²⁺ powder sample at room temperature.

One can calculate the octahedral field parameter (Dq) and the tetragonal field parameters (Ds and Dt) by fitting the theoretical results of optical absorption and EPR spectra to the experimental results [8]:

(8)Δ⊥ = ²B2g→²Eg = −3Ds + 5Dt, (8)

(9)Δ|| = ²B2g → ²B1g = 10Dq, (9)

(10)Δ = ²B1g→²A1g = 10Dq − 4Ds − 5Dt. (10)

We used the theoretical formulas to calculate the tetragonal field parameters as described in [25, 26]. The calculated values for the parameters are Dq=1662, Ds=−1974.5, and Dt=977.6 cm⁻¹. Hence, the theoretical optical absorption energies are Δ_⊥=10 811, Δ_||=16 620, and Δ=19 630 cm⁻¹.

From perturbation theory, one can derive the equations for the theoretical values of the spin Hamiltonian parameters for 3d¹ ions in tetragonal symmetry as [27, 28]:

(11)g|| = ge − 8kζΔ|| − (k + ge)ζ2Δ⊥2 − 4kζ2Δ⊥Δ||, (11)

(12)g⊥ = ge − 2kζΔ⊥ + (k − ge)ζ2Δ⊥2 − 2geζ2Δ||2, (12)

where k is the orbital reduction factor, and ζ is the spin-orbital coupling parameter. We have ζ ≈ kζ₀, where ζ₀ ≈ 248 cm⁻¹ for a free V⁴⁺ ion [1]. After calculating the g factors theoretically, one can use (4) and (5) to find theoretical A values. Here, again we have P ≈ kP₀, where P₀ ≈ 172×10⁻⁴ cm⁻¹ for a free V⁴⁺ ion [29]. Taking β22 = 1 [8] and adjusting the parameters κ ≈ 0.95 and k ≈ 0.69, we found the theoretical values for the AHT:VO²⁺ powder sample. One can find both experimental and theoretical results in Table 2.

4 Conclusion

We studied the EPR spectra of the vanadyl ions in AHT single crystal. The angular variation in g² values in the EPR spectra shows that VO²⁺ ions form four magnetically non-equivalent sites in the unit cell of AHT complex. The paramagnetic centre (VO²⁺) exhibits axial symmetry in the complex. An octahedral complex with a tetragonal compression shows the relation between the g and A values as follows [1]: g_||<g_⊥<g_e and |A_|||>|A_⊥|. Since our results suit the case, we can conclude that the paramagnetic centre in AHT single crystal is tetragonally compressed.

Molecular orbital bonding coefficients indicate the bonding nature of the paramagnetic centre with its environment. One can infer from Table 2 that the in-plane σ-bonding of the vanadium ion with the equatorial ligands is 30 % covalent and out-of-plane π-bonding of the vanadium with the oxide is 52 % covalent in the powder sample.