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arXiv:1601.04860 · Physical Chemistry Chemical Physics

Pair-eigenstates and mutual alignment of coupled molecular rotors in a magnetic field

Ketan Sharma, Břetislav Friedrich

Published Jan 1, 2016• 6 citations
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Abstract

We examine the rotational states of a pair of polar (2)Σ molecules subject to a uniform magnetic field. The electric dipole-dipole interaction between the molecules creates entangled pair-eigenstates of two types. In one type, the Zeeman interaction between the inherently paramagnetic molecules and the magnetic field destroys the entanglement of the pair-eigenstates, whereas in the other type it does not. The pair-eigenstates exhibit numerous intersections, which become avoided for pair-eigenstates comprised of individual states that meet the selection rules ΔJi = 0, ± 1, ΔNi = 2n (n = 0, ±1, ±2,…), and ΔMi = 0, ± 1 imposed by the electric dipole-dipole operator. Here Ji, Ni and Mi are the total, rotational and projection angular momentum quantum numbers of molecules i = 1, 2 in the absence of the electric dipole-dipole interaction. We evaluate the mutual alignment of the pair-eigenstates and find it to be independent of the magnetic field, except for states that undergo avoided crossings, in which case the alignment of the interacting states is interchanged at the magnetic field corresponding to the crossing point. We present an analytic model which provides ready estimates of the pairwise alignment cosine that characterises the mutual alignment of the pair of coupled rotors.

DOI
10.1039/c6cp00390g

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We examine the rotational states of a pair of polar (2)Σ molecules subject to a uniform magnetic field. The electric dipole-dipole interaction between the molecules creates entangled pair-eigenstates of two types. In one type, the Zeeman interaction between the inherently paramagnetic molecules and the magnetic field destroys the entanglement of the pair-eigenstates, whereas in the other type it does not. The pair-eigenstates exhibit numerous intersections, which become avoided for pair-eigenstates comprised of individual states that meet the selection rules ΔJi = 0, ± 1, ΔNi = 2n (n = 0, ±1, ±2,…), and ΔMi = 0, ± 1 imposed by the electric dipole-dipole operator. Here Ji, Ni and Mi are the total, rotational and projection angular momentum quantum numbers of molecules i = 1, 2 in the absence of the electric dipole-dipole interaction. We evaluate the mutual alignment of the pair-eigenstates and find it to be independent of the magnetic field, except for states that undergo avoided crossings, in which case the alignment of the interacting states is interchanged at the magnetic field corresponding to the crossing point. We present an analytic model which provides ready estimates of the pairwise alignment cosine that characterises the mutual alignment of the pair of coupled rotors.
The authors present a detailed study of low-temperature collisions between CaD molecules and He atoms in superimposed electric and magnetic fields with arbitrary orientations. Electric fields do not interact with the electron spin of the molecules directly but modify their rotational structure and, consequently, the spin-rotation interactions. The authors examine molecular Stark and Zeeman energy levels as functions of the angle between the fields and show that rotating fields may induce and shift avoided crossings between the Zeeman levels of the rotationally ground and rotationally excited states of the molecule. The dynamics of molecular collisions are extremely sensitive to external fields near these avoided crossings and it is shown that molecular collisions may be controlled by varying both the strength and the relative orientation of the fields. The effects observed in this study are due to interactions of the isolated molecules with external fields so the conclusions should be relevant for collisions of molecules with other atoms or collisions of molecules with each other. This study demonstrates that electric fields may be used to enhance or suppress spin-rotation interactions in molecules. The spin-rotation interactions induce nonadiabatic couplings between states of different total spins in systems of two open-shell species and it is suggested that electric fields might be used for controlling nonadiabatic spin transitions and spin-forbidden chemical reactions of cold molecules in a magnetic trap.
We analyze the eigenproperties of the SO and 16O18O ground-state (3Σ) molecules in congruent electric and magnetic fields. The energy levels are found to exhibit avoided crossings for states with the same projection M of the total angular momentum on the common axis of the fields. The avoided crossings are due to a first-order Stark effect which connects intersecting levels of aligned Zeeman states of opposite parity and makes them strongly oriented. We exemplify the enhancement of orientation and other generic features of the combined electric and magnetic dipole interaction in polar 3Σ molecules by evaluating the expectation values of the orientation and alignment cosines as a function of field-strength parameters for a selection of states with |M|⩽5. The molecular states created by the congruent fields can be used to state-select and focus molecules, to orient the molecular axis in studies of collision stereodynamics, to facilitate assignments of spectral transitions, and in molecular trapping. In particular, we found that mixed-isotope O2 and 17O2 are the only chalcogen molecules which are suitable for spatial trapping in a static trap, owing to their rotational ground state which correlates with a low-field seeking Zeeman state.
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We examine the potential-energy curves and polarization of the dipole moments of two static polar molecules under the influence of an external dc electric field and their anisotropic dipole-dipole interaction. We model the molecules as quantum rigid rotors to take their rotational degrees of freedom into account and consider a selection of linear, symmetric, and asymmetric top molecules. We provide a comprehensive examination of the energy curves and polarization of the dipoles for varying intermolecular separation and direction of the electric field and find that the properties of the molecules depend strongly on the field's direction at short separations, showing the importance of accounting for molecular rotation. The latter provides insight into the possible effects of accounting for rotational degrees of freedom in molecular dipolar gases. Published by the American Physical Society 2024
Zero field splittings in molecules originate from the intrinsic spin and orbital angular momentum of unpaired electrons. Here, we close a knowledge gap on a diatomic molecule built from spin-8 ground-state dysprosium atoms, where zero-field splittings correspond to the energies of states with different alignments of the two spins. We predict a paramagnetic molecular ground state with parallel Dy spins aligned along the internuclear axis. A diamagnetic state with anti-parallel spins is the first excited state with a small energy cost of hc × 2 cm−1 predominantly due to the magnetic dipole-dipole interaction. We also determine the rotations and vibrations of the diatom and show that centrifugal forces double the splittings between these para- and dia-magnetic states. The vibrational spacings and zero-field splittings have similar magnitude. Finally, the Dy2 ground state has a magnetic moment that is twice that of the atom and, thus, arrays of ultracold Dy2 can be used to simulate strongly interacting magnets. Zero-field splittings in molecules arise from the spin and orbital angular momentum of unpaired electrons, yet their behaviour in diatomic molecules with spin-8 dysprosium atoms remains underexplored. Here, the authors predict a paramagnetic ground state with parallel Dy spins and reveal implications for simulating strongly interacting magnets using ultracold Dy2 arrays.