@article{Bouakline2021, author = {Bouakline, Foudhil}, title = {Umbrella inversion of ammonia redux}, series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies}, volume = {23}, journal = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies}, number = {36}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/d1cp01991k}, pages = {20509 -- 20523}, year = {2021}, abstract = {Umbrella inversion of ammonia is a prototypical example of large-amplitude vibrational motion, described with a symmetric double-well potential. The transition state of the latter corresponds to a planar (D-3h) molecular geometry, whereas the two equilibrium configurations are equivalent (C-3v) pyramidal structures, with the nitrogen atom being either 'above' or 'below' the plane of the hydrogen atoms. As commonly understood, inversion motion of ammonia corresponds to the coherent, anharmonic, vibrational motion of the molecule, which shuttles back and forth between the two potential wells; that is, oscillation of the nitrogen atom from one side of the H-3 plane to the other, via coherent tunneling. However, this intuitively appealing view of umbrella inversion results from a reduced description of the dynamics, which includes only the inversion vibrational coordinate and fully neglects all the other molecular degrees of freedom. As such, this textbook picture of inversion motion ignores the fact that the two equilibrium structures of ammonia are superimposable, and can only be distinguished by labelling the identical hydrogen nuclei. A correct description of umbrella inversion, which incorporates nuclear permutations, requires the inclusion of other molecular modes. Indeed, it is well known that the quantum symmetrization postulate engenders entanglement between ammonia's nuclear-spin, inversion, and rotation. Using the explicit expressions of the corresponding zeroth-order eigenstates, we clearly show that the inversion density of any multilevel wavepacket of ammonia, including the case of perfectly aligned molecules, is symmetrically distributed between the two potential wells, at all times. This follows from a rigorous demonstration based on the evaluation of the expectation values of the inversion coordinate or equivalent projection operators. However, provided that these wavepackets involve inversion-rotation levels with opposite parity, the inversion density may exhibit dynamical spatial localization. In the latter case, the space-fixed inversion density or, equivalently, the expectation values of the projections of the inversion coordinate on the space-fixed axes, may oscillate between opposite directions in the space-fixed frame. Nevertheless, in all cases, localization of ammonia in a single potential well is impossible, even partially or transiently. This is equivalent to saying that the nitrogen atom has the same probability (one-half) to be on either side of the H-3 plane, for any wavepacket of the molecule and at all times-a conclusion which is in perfect accord with the principle of the indistinguishability of identical particles (nuclei).}, language = {en} } @article{WitzorkyParamonovBouaklineetal.2021, author = {Witzorky, Christoph and Paramonov, Guennaddi and Bouakline, Foudhil and Jaquet, Ralph and Saalfrank, Peter and Klamroth, Tillmann}, title = {Gaussian-type orbital calculations for high harmonic generation in vibrating molecules}, series = {Journal of chemical theory and computation}, volume = {17}, journal = {Journal of chemical theory and computation}, number = {12}, publisher = {American Chemical Society}, address = {Washington}, issn = {1549-9618}, doi = {10.1021/acs.jctc.1c00837}, pages = {7353 -- 7365}, year = {2021}, abstract = {The response of the hydrogen molecular ion, H-2(+), to few-cycle laser pulses of different intensities is simulated. To treat the coupled electron-nuclear motion, we use adiabatic potentials computed with Gaussian-type basis sets together with a heuristic ionization model for the electron and a grid representation for the nuclei. Using this mixed-basis approach, the time-dependent Schrodinger equation is solved, either within the Born-Oppenheimer approximation or with nonadiabatic couplings included. The dipole response spectra are compared to all-grid-based solutions for the three-body problem, which we take as a reference to benchmark the Gaussian-type basis set approaches. Also, calculations employing the fixed-nuclei approximation are performed, to quantify effects due to nuclear motion. For low intensities and small ionization probabilities, we get excellent agreement of the dynamics using Gaussian-type basis sets with the all-grid solutions. Our investigations suggest that high harmonic generation (HHG) and high-frequency response, in general, can be reliably modeled using Gaussian-type basis sets for the electrons for not too high harmonics. Further, nuclear motion destroys electronic coherences in the response spectra even on the time scale of about 30 fs and affects HHG intensities, which reflect the electron dynamics occurring on the attosecond time scale. For the present system, non-Born-Oppenheimer effects are small. The Gaussian-based, nonadiabatically coupled, time-dependent multisurface approach to treat quantum electron-nuclear motion beyond the non-Born-Oppenheimer approximation can be easily extended to approximate wavefunction methods, such as time-dependent configuration interaction singles (TD-CIS), for systems where no benchmarks are available.}, language = {en} } @article{BouaklineSaalfrank2021, author = {Bouakline, Foudhil and Saalfrank, Peter}, title = {Seemingly asymmetric atom-localized electronic densities following laser-dissociation of homonuclear diatomics}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistry}, volume = {154}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistry}, number = {23}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/5.0049710}, pages = {10}, year = {2021}, abstract = {Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward-backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei-a result that is in perfect accordance with the principle of the indistinguishability of identical particles. Published under an exclusive license by AIP Publishing.}, language = {en} }