Dynamical Quantum Filtering via Enhanced Scattering of para-H2 on the Orientationally Anisotropic Potential of SrTiO3(001)

Quantum dynamics calculation, performed on top of density functional theory (DFT)-based total energy calculations, show dynamical quantum filtering via enhanced scattering of para-H2 on SrTiO3(001). We attribute this to the strongly orientation-dependent (electrostatic) interaction potential between the H2 (induced) quadrupole moment and the surface electric field gradient of ionic SrTiO3(001). These results suggest that ionic surfaces could function as a scattering/filtering media to realize rotationally state-resolved H2. This could find significant applications not only in H2 storage and transport, but also in realizing materials with pre-determined characteristic properties.

www.nature.com/scientificreports www.nature.com/scientificreports/ adsorption atop the Ti-site, with H-H bond oriented parallel to the surface, and an adsorption energy E ads = − 191 meV 24 . Atop the O-site, H 2 preferentially adsorbs with the H-H bond oriented perpendicular to the surface, with E ads = − 72.5 meV 24 . As a result, in Fig. 4(a), we find a corresponding spectra dominated by off-specularly scattered H 2 , with dominant components coming from backscattering. Most of the H 2 (J i = 0, m i = 0) would be www.nature.com/scientificreports www.nature.com/scientificreports/ molecularly adsorbed (due to reorientation/steering 31,32 ), and only a small fraction would be elastically scattered (due to shadow effect 9 ). Considering the angle of incidence, the inelastically scattered H 2 would come from those hitting the repulsive part of the potential well near the O-site (shadow effect, cf., solid curve in Fig. 4(d)), resulting in a change in surface lateral momentum and off-specular scattering angles. Energy transfer from the   www.nature.com/scientificreports www.nature.com/scientificreports/ translational degree-of-freedom (DOF) to the rotational DOF allows the molecule more time to sample the anisotropic surface through reorientation/steering. Those that succeed would molecularly adsorb. Those that fail, would be rotationally de-excited on the way back to the gas phase, because of the smaller anisotropic potential further (out in the vacuum) from the surface. Thus, the scattering spectra shows negligible rotationally excited H 2 , i.e., H 2 (J f = 2, m i = 0). H 2 (J i = 1, m i = ±1) also encounters a strongly anisotropic PES (cf., dash-dot curve in Fig. 4(d)). Thus, we see the same trend in Fig. 4(c), i.e., a corresponding spectra dominated by off-specularly scattered H 2 , with dominant components coming from backscattering. On the other hand, H 2 (J i = 1, m i = 0) encounters an almost flat PES (cf., dotted curve in Fig. 4(b)). As a result, we see strong (dominant) specular scattering of H 2 (J i = 1, m i = 0) ( Fig. 4(b)). Finally, we could observe a p-H 2 to o-H 2 ratio as large as ca. 4.96 (cf., Table 1) compared to that of normal-H 2 (n-H 2 ) (i.e., >1/3 at 300 K) at scattering angle Θ f = 5.26° (Fig. 4).  www.nature.com/scientificreports www.nature.com/scientificreports/ potential encountered by the impinging  24 . As a result, in Fig. 5(a), we find a corresponding spectra dominated by off-specularly scattered H 2 , with dominant components coming from backscattering. Again, most of the H 2 (J i = 0, m i = 0) would be molecularly adsorbed (due to reorientation/steering 31,32 ), and only a small fraction would be elastically scattered (possibly due to shadow effect 9 ). Considering the angle of incidence, the inelastically scattered H 2 would come from those hitting the repulsive part of the potential well near the Sr-site (shadowing effect, cf., solid curve in Fig. 4(d)), resulting in a change in surface lateral momentum and off-specular scattering angles. Note that the impinging H 2 has a larger surface lateral momentum as compared to the corresponding surface perpendicular component. This allows the impinging H 2 more time to explore the anisotropic surface. Those that succeed would molecularly adsorb via reorientation/steering. Those that fail, would be rotationally de-excited on the way back to the gas phase, because of the smaller anisotropic potential further (out in the vacuum) from the surface. Thus, the scattering spectra shows negligible rotationally excited H 2 , i.e., H 2 (J f = 2, m i = 0). H 2 (J i = 1, m i = ± 1) also encounters a strongly anisotropic PES (cf., dash-dot curve in Fig. 5(d)). But now recall that the preferred adsorption site is at the O-site, with the H-H bond oriented perpendicular to the surface. Thus, we see strong specular scattering in Fig. 5(c). H 2 (J i = 1, m i = 0) shows higher backscattering probabilities (cf., Fig. 5(b)) due to the larger surface anisotropy along X, making it more susceptible to reorientation/steering. Finally, we could observe a p-H 2 to o-H 2 ratio as large as ca. 16.1 (cf., Table 2) compared to that of n-H 2 (i.e., >1/3 at 300 K) at scattering angle Θ f = − 76.5° (Fig. 5). . For reference, normal-H 2 (n-H 2 ) have a p-H 2 to o-H 2 ratio of 1/3, at room temperature (T = 300 K). We attribute this to the strongly orientation-dependent (electrostatic) interaction potential between the H 2 (induced) quadrupole moment and the surface electric field of ionic SrTiO 3 (001). These results suggest that ionic surfaces (with tunable surface terminations) could function as a scattering/filtering media to realize rotationally state-resolved H 2 . This could find significant applications not only in H 2 storage and transport, but also in realizing materials with pre-determined characteristic properties.
We can compare the present results to previous reports for the inelastic scattering of H 2 on LiF(001), at normal incidence (Θ i = 0°) and incident energy of E i = 100 meV 33 . From the scattering probability data 33  www.nature.com/scientificreports www.nature.com/scientificreports/ surface temperature of 100 K and incidence angle Θ i : [0°, 66°]. For TiO 2 -terminated SrTiO 3 (001), we estimated Debye-Waller factor values (cf., e.g., ref. 12 for more details) ranging from ca. 0.3 to 0.6, increasing with increasing incidence angle Θ i . In comparison, for SrO-terminated SrTiO 3 (001), we estimated 12 Debye-Waller factor values ranging from ca. 0.6 to 0.8, increasing in value with increasing incidence angle Θ i . The modulation/attenuation would become more pronounced with increased temperature. However, regardless of the degree of modulation/ attenuation, the maximum p-H 2 to o-H 2 ratio for each surface termination remained almost the same (viz., ca.

and 16.7 along the SrTiO 3 (001)[100] and SrTiO 3 (001)[110] of the TiO 2 -and SrO-terminated SrTiO 3 (001), respectively, at 100 K).
Finally, because of the wide spread of the scattering angle, we could expect small scattering probabilities at each particular scattering angle. Furthermore, the larger the (surface lateral) incident energy, the more number of (surface lateral) diffraction channels (would be) involved (excited). As a result, the normalized p-H 2 to o-H 2 ratio R J J 0/ 1 = = shows small values (cf. , Tables 1 and 2). Thus, so far, we can collect only a small amount of H 2 through any given scattering event. (But with high purity!) For engineering applications, scattering at optimum surface angles should resolve this problem.

Model Hamiltonian.
To study the dynamics of H 2 scattering on STO(001) (Fig. 1), we performed quantum dynamical calculations (cf., e.g., refs. [1][2][3][4][5]8,9,24,31,32 ) by solving the corresponding time-independent Schrödinger equation for H 2 , in the vibrational ground state (ν = 0), under the influence of an orientationally anisotropic potential energy (hyper-) surface (PES), using the coupled-channel method [36][37][38][39][40][41][42] . The dynamical variables we considered include the H 2 center-of-mass (CM) distance Z from the surface, the H 2 bond-length r, the polar and azimuthal angular orientations of the H-H bond with respect to the surface, θ and φ, respectively, and the position of the H 2 CM X, along STO(001)[100] and STO(001)[110] of the TiO 2 -and SrO-terminated STO(001), respectively. Considering that the energy scale of the H 2 molecular vibration (ℏω = 516 meV) exceeds the energy range relevant to our current study (i.e., E i : [10,80] meV), we can neglect the molecular vibrational excitations, and fix the H 2 interatomic distance at r = 0.74 Å. The small variation of the potential energy with respect to φ allows us to further neglect the φ-dependence 24 . Thus, we can reduce the original 6-Dimensional (6-D) Hamiltonian (for the diatomic molecule-surface system) to the following simplified 3-D form :  24 . We fitted the potential energy curves for each configuration using Morse potentials: give the corresponding potential depth, potential width, and equilibrium (normal/perpendicular) distance of H 2 from the surface cation sites (A:[Ti, Sr]) and oxygen site (B), at H-H bond angle θ, respectively. The reciprocal lattice constant g X (= π/a X ), with corresponding direct lattice constants = .  46 . Table 3 shows the fitted parameters for each configuration. We used spherical harmonics and plane waves as basis sets for the rotational motion and the translational motion (perpendicular to the surface and along the surface direction X), respectively.
To extract the contribution of the electrostatic interaction between the H 2 quadrupole moment and the surface local electric field, as discussed above, we used the charge density distribution obtained from previous DFT-based total energy calculations 24 . We calculated the induced dipole ΔD i (i = x, y, z) and quadrupole moments ΔQ i,j (i, j = x, y, z) from the charge density difference ( ρ ) as a function of Z for the Ti and O sites (TiO 2 -termination) and Sr and O sites (SrO-termination) with θ = 0 and π/2. We also calculated the H 2 quadrupole moment Q i,j from the charge density distribution of the isolated system. We used the pristine STO(001) to calculate the surface electric field and its gradient.
Scattering probability. Consider a H 2 impinging with an initial rotational state (J i , m i ), incident energy E i , and angle of incidence with respect to the surface normal Θ i (cf., e.g., Fig. 1(c,d), and Table 4). Using the coupled-channel method 36 Table 3. Fitted values of the potential depth D, potential width α, and equilibrium distance from the surface Z eq , at each surface site, in Eq. (3).