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arXiv:1209.3071 · The Journal of Chemical Physics

Cold collisions of polyatomic molecular radicals with S-state atoms in a magnetic field: An ab initio study of He + ${\rm CH}_2(\tilde{X})$ CH 2(X) collisions

Timur V. Tscherbul, Timur A. Grinev, Hua‐Gen Yu, A. Dalgarno, Jacek A. Kłos, Lifang Ma, Millard H. Alexander

Published Sep 10, 2012• 10 citations
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Abstract

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.

DOI
10.1063/1.4748258

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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.
We present a rigorous theoretical study of low-temperature collisions of polyatomic molecular radicals with (1)S(0) atoms in the presence of an external magnetic field. Accurate quantum scattering calculations based on ab initio and scaled interaction potentials show that collision-induced spin relaxation of the prototypical organic molecule CH(2)(X(3)B(1)) (methylene) and nine other triatomic radicals in cold (3)He gas occurs at a slow rate, demonstrating that cryogenic buffer-gas cooling and magnetic trapping of these molecules is feasible with current technology. Our calculations further suggest that it may be possible to create ultracold gases of polyatomic molecules by sympathetic cooling with alkaline-earth atoms in a magnetic trap.
Ab initio calculations of cross sections and rate constants for elastic scattering and Zeeman relaxation in collisions of $\mathrm{NH}(X{}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}})$ molecules with 3He{}^{3}\mathrm{He}3He atoms in a magnetic field are presented and the mechanism for Zeeman transitions in ground-state ${}^{3}\ensuremath{\Sigma}$ molecules is established. The potential surface for He-NH interaction is obtained using all-electron coupled-cluster calculations with single, double, and noniterative triple excitations in a basis set augmented by bond functions. The ratio of the rates for elastic energy transfer and Zeeman relaxation in NH-3He{}^{3}\mathrm{He}3He collisions exceeds 105{10}^{5}105 at temperatures between 0.50.50.5 and 1 K.
We use accurate ab initio and quantum scattering calculations to explore the prospects for sympathetic cooling of the heavy molecular radical $\mathrm{SrOH}{(}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+})$ by ultracold Li atoms in a magnetic trap. Our ab initio calculations show that the chemical reaction between spin-polarized Li and SrOH, which occurs on the triplet Li-SrOH potential energy surface (PES), is strongly endothermic and hence energetically forbidden at ultralow temperatures. The chemical reaction $\mathrm{Li}(^{2}S)+\mathrm{SrOH}{(}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+})\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}\mathrm{Sr}(^{1}S)+\mathrm{LiOH}{(}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+})$ occurs barrierlessly on the singlet PES and is exothermic by 2505 ${\mathrm{cm}}^{\ensuremath{-}1}$. A two-dimensional PES for the triplet electronic state of Li-SrOH is calculated ab initio using the partially spin-restricted coupled cluster method with single, double, and perturbative triple excitations and a large correlation-consistent basis set. The highly anisotropic PES has a deep global minimum in the skewed Li-HOSr geometry with ${D}_{e}=4932\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and saddle points in collinear configurations. Our quantum scattering calculations predict low spin-relaxation rates in fully spin-polarized Li + SrOH collisions with the ratios of elastic to inelastic collision rates well in excess of 100 over a wide range of magnetic fields (1--1000 G) and collision energies (${10}^{\ensuremath{-}5}$ to 0.1 K), suggesting favorable prospects for sympathetic cooling of SrOH molecules with spin-polarized Li atoms in a magnetic trap. We find that spin relaxation in Li + SrOH collisions occurs via a direct mechanism mediated by the magnetic dipole-dipole interaction between the electron spins of Li and SrOH, and that the indirect (spin-rotation) mechanism is strongly suppressed. The upper limit to the Li + SrOH reaction rate coefficient calculated for the singlet PES using adiabatic capture theory is found to decrease from $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{3}$/s to a limiting value of $3.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{3}$/s with decreasing temperature from 0.1 K to 1 $\ensuremath{\mu}\mathrm{K}$.
We explore the quantum dynamics of nuclear spin relaxation in cold collisions of 1 Σ + molecules with structureless atoms in an external magnetic field. To this end, we develop a rigorous coupled-channel methodology, which accounts for rotational and nuclear spin degrees of freedom of 1 Σ + molecules and their interaction with an external magnetic field as well as anisotropic atom–molecule interactions. We apply the methodology to study the collisional relaxation of the nuclear spin sublevels of 13 CO molecules immersed in a cold buffer gas of 4 He atoms. We find that nuclear spin relaxation in the ground rotational manifold ( N = 0) of 13 CO occurs extremely slowly due to the absence of direct couplings between the nuclear spin sublevels. The rates of collisional transitions between the rotationally excited ( N = 1) nuclear spin states of 13 CO are generally much higher due to the direct nuclear spin–rotation coupling between the states. These transitions obey selection rules, which depend on the values of space-fixed projections of rotational and nuclear spin angular momenta ( M N and M I ) for the initial and final molecular states. For some initial states, we also observe a strong magnetic field dependence, which can be understood by using the first Born approximation. We use our calculated nuclear spin relaxation rates to investigate the thermalization of a single nuclear spin state of 13 CO( N = 0) immersed in a cold buffer gas of 4 He. The calculated nuclear spin relaxation times ( T 1 ≃ 1 s at T = 1 K at a He density of 10 –14 cm –3 ) display a steep temperature dependence decreasing rapidly at elevated temperatures due to the increased population of rotationally excited states, which undergo nuclear spin relaxation at a much faster rate. Thus, long relaxation times of N = 0 nuclear spin states in cold collisions with buffer gas atoms can be maintained only at sufficiently low temperatures ( k B T ≪ 2 B e ), where B e is the rotational constant.
In this dissertation, I present ab initio theoretical results on cold and ultra-cold collision of atomic and molecular systems with magnetic and electric dipole moments. The collisions of different isotopes of maximally spin-polarized chromium atoms (52Cr and 53Cr), alkali-metal atom (Rb) - chromium atom, and magnetically trapped hydroxide (OH) with cold supersonic helium beam are considered in this thesis. Spin-changing cross sections and rate constants in Cr-Cr isotopic collision in the presence of a magnetic field are calculated by propagating a set of multichannel equations in the field. The coupling between dipole-dipole allowed and hyperfine channels are included. The short range electrostatic interactions between atoms and atom-molecule are represented with highly-accurate Born-Oppenheimer (BO) potential energy curves. Due to the large spin multiplicity in Cr-Cr and Rb-Cr interactions, more than the usual singlet and triplet channels are obtained. The long-range van der Waals (vdW) interactions between atoms are calculated, for Cr, by including accurate transition frequencies, discrete dipole matrix elements, and photoionization continuum oscillator strengths, and for Rb, using published dynamic polarizabilities. The vdW coefficients for Cr-Cr and Rb-Cr are obtained. In the cold collision regime, I investigate the influence of angular momentum shape resonances on the elastic and inelastic (loss channel) rate coefficients, and when the Zeeman relaxation, resulting in the loss of atoms from the trap, dominates elastic collision. Dipolar collisions are crucial to achieving quantum degeneracy. Magnetically tuned Fano-Feshbach closed-channel resonances are used to obtain zero-energy scattering lengths in comparison with observation of trap loss. In bosonic chromium collisions, resonances appear due only to dipolar interaction. The interplay between hyperfine and dipolar resonances in mixed-species Cr-Cr and Rb-Cr collisions is studied. In Rb-Cr, it is found that the molecule has broken symmetry and therefore contains a large permanent electric dipole moment in the ground state. A recent collisional experiment at JILA of a supersonic helium beam with a magnetically trapped OH radical found the onset of a quantum threshold in the total OH loss rate. Using ab initio BO energy surfaces, I calculated the spin-changing collisions which removed OH from the trap. Only after including the effect of the trapping potential on the collision dynamics, some agreement with observation was found. ^
We present quantum-theoretical studies of collisions between an open-shell S-state atom and a (2)Π-state molecule in the presence of a magnetic field. We analyze the collisional Hamiltonian and discuss possible mechanisms for inelastic collisions in such systems. The theory is applied to the collisions of the nitrogen atom ((4)S) with the OH molecule, with both collision partners initially in fully spin-stretched (magnetically trappable) states, assuming that the interaction takes place exclusively on the two high-spin (quintet) potential energy surfaces. The surfaces for the quintet states are obtained from spin-unrestricted coupled-cluster calculations with single, double, and noniterative triple excitations. We find substantial inelasticity, arising from strong couplings due to the anisotropy of the interaction potential and the anisotropic spin-spin dipolar interaction. The mechanism involving the dipolar interaction dominates for small magnetic field strengths and ultralow collision energies, while the mechanism involving the potential anisotropy prevails when the field strength is larger (above 100 G) or the collision energy is higher (above 1 mK). The numerical results suggest that sympathetic cooling of magnetically trapped OH by collisions with ultracold N atoms will not be successful at higher temperatures.