Microwave Spectroscopy and Internal Dynamics of the Ne-NO 2 Van der Waals Complex Brian J. Howard, George Economides and Lee Dyer Department of Chemistry, University of Oxford Oxford OX1 3QZ, UK

Ne-NO 2 Have observed the microwave spectrum of the open-shell complex, Ne-NO 2 Formed in a supersonic expansion of 0.5% NO 2 in Ne and studied by microwave Fourier transform spectroscopy Whole apparatus placed within Helmholtz coils to reduce Zeeman splittings Will require accurate quantum dynamical calculations to fully interpret the spectrum

Rg-NO 2 Complexes The open-shell complexes of NO 2 with Ar, Kr and Xe have been previously studied It has been shown that they can be treated as semi-rigid asymmetric tops, but with one large amplitude motion. The A-rotational constant of the NO 2 and the barrier to rotation about the a-axis is sufficiently low that quantum mechanical tunnelling can occur between two equivalent structure; this frequency estimated at 5 cm -1 Nuclear spin statistics for O demand that only the excited tunnelling state is allowed for odd K a (not populated at the low T of supersonic expansion) Spectra, containing just K a = 0 or 2 have been analysed

Energy levels with tunnelling

Spectroscopic Constants However the Ne-NO 2 fit does not include the K a = 2 data. Problems with floppy nature of complex.

Interpretation of constants The fine and hyperfine structure due to the electron spin and the N nuclear spin can be interpreted in terms of normal fine and hyperfine constants (spin-rotation, electron-nuclear spin-spin, nuclear quadrupole ) These are related to the monomer constants via tensor transformations. That is except for the Fermi contact interaction which is a scalar and is the same in all axis systems (virtually the same value (~147.5 MHz) is obtained in all species) If the monomer constants are unaffected by complex formation, the transformation contains angular information and provides an effective angular structure of the complex

Structural coordinates

Structural Information Ne-NO 2 Ar-NO 2 Kr-NO 2 Xe-NO 2 R/ÅR/Å θ/° (52.4)(49.3)(46.1)(41.1) χ/° From the previous constants can derive effective structures for the complexes The χ information for Ne-NO 2 is clearly out-of-line, as is the K a = 2 data

Solution The interaction between Ne and NO 2 is sufficiently weak that Ne-NO 2 is a very floppy complex. Consequently it cannot be treated as a semi-rigid complex and there are significant dynamical corrections to the spectrum. In order to reproduce the spectrum, we have performed accurate quantum dynamical calculations on an accurate ab initio potential energy surface. Potential energy surface calculated with CCSD(T) method using a Dunning aug-cc-pVnZ functions extrapolated to infinite basis limit.

Potential Energy Surface Ab initio potential calculated on a grid with steps in θ of 20°, 30° in χ and 0.1 Å in R between 2.9 and 3.8 Å and 0.4 Å up to 5.0 Å. The potential was fitted globally to an atom-atom potential with an anisotropic exponential repulsion and a damped anisotropic Van der Waals dispersion, using 19 parameters. Dynamics were performed using a free rotor basis and an optimised set of Hermite functions for the radial motion. All potential matrix elements were calculated using Gauss quadrature All spectroscopic transitions converged to 2 MHz.

Potential Energy Surface θ χ Cut of angular potential at R fixed at the radial minimum

Rotational Transitions Predicted transition frequencies were systematically high by ~1%, indicating a slight error in the radial minimum of the potential. After correcting for this factor, the spectrum could be accurately reproduced

Comparison with Experiment Simple semi-rigid molecules theory (fitting to just rotational constants, etc.) gives equal spacing between the J = 2 – 3 transition for K a = 0 and the two transitions involving K a = 2 Observed splittings are 87.0 MHz and MHz, i.e. significantly different. Calculated splittings are: 51MHz and 145 MHz, but showing the same trends (but now too floppy!) Requires a slightly higher barrier to tunnelling Also gives good predictions for the hyperfine parameters (using monomer values) Still some problems with the spin-rotation interactions

Conclusions The spectrum of the Ne-NO 2 complex can be accurately modelled by performing detailed quantum dynamics on an accurate potential energy surface. To get full agreement, needs a slightly higher barrier to NO 2 rotation It demonstrates the inadequacies of the conventional semi-rigid molecule approach in a floppy complex like Ne-NO 2 Accurate ab initio spectroscopic constants have been derived, but require very accurate potentials

Acknowledgements This work was supported by the EPSRC (UK) GE thanks the Onassis foundation for a Research Studentship