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arXiv:1202.0597 · The Journal of Chemical Physics

Efficient method for quantum calculations of molecule-molecule scattering properties in a magnetic field

Yu. V. Suleimanov, Timur V. Tscherbul, Roman V. Krems

Published Jul 10, 2012• 28 citations
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Abstract

We show that the cross sections for molecule-molecule collisions in the presence of an external field can be computed efficiently using a total angular momentum basis, defined either in the body-fixed frame or in the space-fixed coordinate system. This method allows for computations with much larger basis sets than previously possible. We present calculations for (15)NH-(15)NH collisions in a magnetic field. Our results support the conclusion of the previous study that the evaporative cooling of rotationally ground (15)NH molecules in a magnetic trap has a prospect of success.

DOI
10.1063/1.4733288

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Cold NH–NH collisions in a magnetic field: Basis set convergence versus sensitivity to the interaction potential

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Abstract We explore the combined effect of the uncertainties due to the interaction potential and basis set convergence on low-temperature collisional properties of spin-polarized NH molecules in a magnetic field. We show that quantum scattering calculations with different rotational basis sets and λ -scaled interaction potentials produce qualitatively different ratios of elastic to inelastic cross sections for collision energies above 10 −3 cm −1 , leading to favorable (unfavorable) prospects for sympathetic cooling of NH molecules depending on the basis set cutoff parameter N max . The physical reason behind this effect is that the resonance widths, which determine the maximum variation of the scattering cross sections with λ , tend to depend strongly on N max . At ultralow collision energies, all basis sets produce highly uncertain (and statistically indistinguishable) elastic and inelastic cross sections; however, their ratio γ is much less sensitive to small variations of the interaction potential. Our results highlight the importance of basis set convergence in quantum scattering calculations and establish the existence of parameter regimes where unconverged calculations can still be used to make qualitatively accurate predictions of scattering observables.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 4, 2016•10 citations
We show that the cross sections for molecule-molecule collisions in the presence of an external field can be computed efficiently using a total angular momentum basis, defined either in the body-fixed frame or in the space-fixed coordinate system. This method allows for computations with much larger basis sets than previously possible. We present calculations for (15)NH-(15)NH collisions in a magnetic field. Our results support the conclusion of the previous study that the evaporative cooling of rotationally ground (15)NH molecules in a magnetic trap has a prospect of success.
We show that the integral cross sections for state-to-state quantum scattering of cold molecules in a magnetic field can be efficiently computed using the total angular momentum representation despite the presence of unphysical Zeeman states in the eigenspectrum of the asymptotic Hamiltonian. We demonstrate that the unphysical states arise due to the incompleteness of the space-fixed total angular momentum basis caused by using a fixed cutoff value Jmax for the total angular momentum of the collision complex J. As a result, certain orbital angular momentum (l) basis states lack the full range of J values required by the angular momentum addition rules, resulting in the appearance of unphysical states. We find that by augmenting the basis with a full range of J-states for every l, it is possible to completely eliminate the unphysical states from quantum scattering calculations on molecular collisions in external magnetic fields. To illustrate the procedure, we use the augmented basis sets to calculate the state-to-state cross sections for rotational and spin relaxation in cold collisions of 40CaH(X2Σ+, v = 0, N = 1, MN = 1, MS = 1/2) molecules with 4He atoms in a magnetic field. We find excellent agreement with benchmark calculations, validating our proposed procedure. We find that N-conserving spin relaxation from the highest-energy to the lowest-energy Zeeman state of the N = 1 manifold, |1112〉→|1−1−12〉 is nearly completely suppressed due to the lack of spin–rotation coupling between the fully spin-stretched Zeeman states. Our results demonstrate the possibility of rigorous, computationally efficient, and unphysical state-free quantum calculations on cold molecular collisions and on near-threshold energy levels of strongly anisotropic atom-molecule collision complexes in an external magnetic field.
Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta J of the collision complex. We show that by restricting the total angular momentum basis to include only the states with helicities K ≤ Kmax, it is possible to obtain accurate elastic and inelastic cross sections for low-temperature He + CaH, Li + CaH, and Li + SrOH collisions in the presence of an external magnetic field at a small fraction of the computational cost of the full coupled-channel calculations (where K is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field, with the minimal basis set (Kmax = 0) producing quantitatively accurate results for, e.g., ultracold Li + CaH and Li + SrOH scattering at low magnetic fields, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in the magnetic field dependence of Li + CaH and Li + SrOH inelastic cross sections in the few partial wave-regime as well as indirect spin relaxation in He + CaH collisions. Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different K and the couplings between the rotational states of the same K induced by the anisotropy of the interaction potential.
Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We specifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that 15N^{15}\mathrm{N}15NH is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar coupling term. At higher energies and fields, intramolecular spin-spin coupling becomes increasingly important. Our qualitative results and conclusions are fairly independent of the exact form of the potential and of the size of the channel basis set.
Cold collisions of polyatomic molecular radicals with S-state atoms in a magnetic field: An ab initio study of He + CH2(X~){\rm CH}_2(\tilde{X})CH2​(X~) CH 2(X) collisions
We develop a rigorous quantum mechanical theory for collisions of polyatomic molecular radicals with S-state atoms in the presence of an external magnetic field. The theory is based on a fully uncoupled space-fixed basis set representation of the multichannel scattering wave function. Explicit expressions are presented for the matrix elements of the scattering Hamiltonian for spin-1/2 and spin-1 polyatomic molecular radicals interacting with structureless targets. The theory is applied to calculate the cross sections and thermal rate constants for spin relaxation in low-temperature collisions of the prototypical organic molecule methylene [CH(2)(X(3)B(1))] with He atoms. To this end, two accurate three-dimensional potential energy surfaces (PESs) of the He-CH(2)(X(3)B(1)) complex are developed using the state-of-the-art coupled-cluster method including single and double excitations along with a perturbative correction for triple excitations and large basis sets. Both PESs exhibit shallow minima and are weakly anisotropic. Our calculations show that spin relaxation in collisions of CH(2), CHD, and CD(2) molecules with He atoms occurs at a much slower rate than elastic scattering over a large range of temperatures (1 μK-1 K) and magnetic fields (0.01-1 T), suggesting excellent prospects for cryogenic helium buffer-gas cooling of ground-state ortho-CH(2)(X(3)B(1)) molecules in a magnetic trap. Furthermore, we find that ortho-CH(2) undergoes collision-induced spin relaxation much more slowly than para-CH(2), which indicates that magnetic trapping can be used to separate nuclear spin isomers of open-shell polyatomic molecules.
Abstract We explore the combined effect of the uncertainties due to the interaction potential and basis set convergence on low-temperature collisional properties of spin-polarized NH molecules in a magnetic field. We show that quantum scattering calculations with different rotational basis sets and λ -scaled interaction potentials produce qualitatively different ratios of elastic to inelastic cross sections for collision energies above 10 −3 cm −1 , leading to favorable (unfavorable) prospects for sympathetic cooling of NH molecules depending on the basis set cutoff parameter N max . The physical reason behind this effect is that the resonance widths, which determine the maximum variation of the scattering cross sections with λ , tend to depend strongly on N max . At ultralow collision energies, all basis sets produce highly uncertain (and statistically indistinguishable) elastic and inelastic cross sections; however, their ratio γ is much less sensitive to small variations of the interaction potential. Our results highlight the importance of basis set convergence in quantum scattering calculations and establish the existence of parameter regimes where unconverged calculations can still be used to make qualitatively accurate predictions of scattering observables.