The electric quadrupole moment of O2
Introduction
The molecular quadrupole moment Θ of O2 has recently been calculated by Bartolomei et al. using high-level multiconfigurational ab initio methods [1]. The attainment of high accuracy in ab initio computations of molecular properties such as Θ is a non-trivial task, requiring the use of large basis sets and the inclusion of electron correlation [1], [2]. Accurate experimental values for these molecular properties can serve as useful benchmarks against which to assess the effects arising from the application of higher levels of ab initio theory. Unfortunately, there is currently a paucity of experimental data of Θ for O2 against which to compare calculated values.
For non-dipolar molecules like O2, Θ is the leading electric moment describing the molecular charge-distribution and its interaction with external non-uniform electric fields, and so is crucial in describing a range of physical phenomena, including aspects of atmospheric chemical physics, as described in [1], [3] and the references therein. The preferred experimental method for measuring Θ of gaseous non-dipolar species is the Buckingham effect (electric-field-gradient-induced birefringence, EFGIB) [4], [5]. Our laboratory has yielded recent EFGIB measurements of Θ for CO2, as well as for the dipolar molecules OCS, N2O and CO [6], [7], [8]. Where possible, temperature-dependent studies are preferred, since this allows for separation of the electronic distortion and molecular orientation contributions to the measured birefringence.
We present here our value of Θ for O2, which has been obtained from room-temperature EFGIB measurements using the assumption that the electronic distortion contribution to the EFGIB is negligible. Attempts to measure the EFGIB at higher temperatures were unsuccessful, the size of the measured birefringence being particularly small for this species, leading to considerable experimental challenges which we have as yet been unable to overcome.
Coriani and co-workers [9], [10] have demonstrated how recent advances in ab initio methods have allowed for high accuracy in the computation of first-order molecular properties, allowing them to compute the electronic distortion contribution to the EFGIB for N2, and thus to perform a correction on the existing room-temperature EFGIB measurements for this molecule, yielding a refined experimental quadrupole moment which was in good agreement with their ab initio calculated Θ. A subsequent temperature-dependent experimental study of the Buckingham effect for N2 essentially confirmed the validity of their analysis [11]. In principle, the measured value of Θ for O2 presented in this work could be further refined in this manner, with the ab initio computation of the electronic distortion contribution to the EFGIB allowing for a similar correction. This task is left to the quantum chemists who are equipped to undertake such a study.
Section snippets
Theory
The EFGIB is the anisotropy in the refractive index, nx − ny, which is observed when light propagates through a fluid along the z-direction, which is perpendicular to an applied electric field gradient Exx = − Eyy. The molar field-gradient birefringence constant mQ is defined in terms of macroscopic observables as [12]
where n and ϵr are the refractive index and relative permittivity of the gas in the absence of the field gradient, and Vm is the molar volume
Experiment and results
The apparatus and experimental techniques used in the measurements of the room-temperature EFGIB of O2 reported here have been described in detail elsewhere [6]. Measurements of mQ were taken using ultra-high-purity O2, with a quoted 99.998% minimum purity, supplied by Afrox. The second and third pressure virial coefficients which are required in the calculation of the molar volumes of the gas samples were obtained from the tabulations of Dymond et al. [16]. Refractive indices were calculated
Discussion
This EFGIB investigation has yielded a molecular electric quadrupole moment of Θ = (−1.033 ± 0.027) × 10−40 C m2 for O2. Since the measurements were obtained at room temperature, the extraction of the quadrupole moment Θ from the measured mQ data via Eq. (6) has been achieved by assuming the b′ contribution to be negligible, i.e. setting b′ to zero.
Only one previous EFGIB determination of Θ for O2 exists, undertaken at room temperature by Buckingham et al., and yielding Θ = (−1.33 ± 0.33) × 10−40 C m2 [26].
Acknowledgements
This work has been supported by the South African National Laser Centre (NLC). S.S.N. also gratefully acknowledges the award of a NITheP graduate bursary.
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