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Register a new userInsights into the semiclassical Wigner treatment of bimolecular collisions
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L. Bonnet
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The semiclassical Wigner treatment of bimolecular collisions, proposed by Lee and Scully on a partly intuitive basis [J. Chem. Phys. 73, 2238 (1980)], is derived here from first principles. The derivation combines E. J. Hellers ideas [J. Chem. Phys. 62, 1544 (1975); 65, 1289 (1976); 75, 186 (1981)], the backward picture of molecular collisions [L. Bonnet, J. Chem. Phys. 133, 174108 (2010)] and the microreversibility principle.
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The emph{semiclassical Wigner treatment} of Brown and Heller [J. Chem. Phys. 75, 186 (1981)] is applied to triatomic direct photodissociations with the aim of accurately predicting final state distributions at relatively low computational cost, and having available a powerful interpretative tool. For the first time, the treatment is full-dimensional. The proposed formulation closely parallels the quantum description as far as possible. An approximate version is proposed, which is still accurate while numerically much more efficient. In addition to be weighted by usual vibrational Wigner distributions, final phase space states appear to be weighted by new emph{rotational Wigner distributions}. These densities have remarkable structures clearly showing that classical trajectories most contributing to rotational state $j$ are those reaching the products with a rotational angular momentum close to $[j(j+1)]^{1/2}$ (in $hbar$ unit). The previous methods involve running trajectories from the reagent molecule onto the products. The alternative emph{backward approach} [L. Bonnet, J. Chem. Phys. 133, 174108 (2010)], in which trajectories are run in the reverse direction, is shown to strongly improve the numerical efficiency of the most rigorous method in addition to be emph{state-selective}, and thus, ideally suited to the description of state-correlated distributions measured in velocity imaging experiments. The results obtained by means of the previous methods are compared with rigorous quantum results in the case of Guos triatomic-like model of methyl iodide photodissociation [J. Chem. Phys. 96, 6629 (1992)] and an astonishing agreement is found. In comparison, the standard method of Goursaud emph{et al.} [J. Chem. Phys. 65, 5453 (1976)] is only semi-quantitative.
Whereas collisions between atoms and molecules are largely understood, collisions between two molecules have proven much harder to study. In both experiment and theory, our ability to determine quantum state-resolved bimolecular cross sections lags behind their atom-molecule counterparts by decades. For many bimolecular systems, even rules of thumb -- much less intuitive understanding -- of scattering cross sections are lacking. Here, we report the measurement of state-to-state differential cross sections on the collision of state-selected and velocity-controlled nitric oxide (NO) radicals and oxygen (O2) molecules. Using velocity map imaging of the scattered NO radicals, the full product-pair correlations of rotational excitation that occurs in both collision partners from individual encounters are revealed. The correlated cross sections show surprisingly good agreement with quantum scattering calculations using ab initio NO-O2 potential energy surfaces. The observations show that the well-known energy-gap law that governs atom-molecule collisions does not generally apply to bimolecular excitation processes, and reveal a propensity rule for the vector correlation of product angular momenta.
Whereas atom-molecule collisions have been studied with complete quantum state resolution, interactions between two state-selected molecules have proven much harder to probe. Here, we report the measurement of state-resolved inelastic scattering cross sections for collisions between two open-shell molecules that are both prepared in a single quantum state. Stark-decelerated OH radicals were scattered with hexapole-focused NO radicals in a crossed beam configuration. Rotationally and spin-orbit inelastic scattering cross sections were measured on an absolute scale for collision energies between 70 and 300 cm$^{-1}$. These cross sections show fair agreement with quantum coupled-channels calculations using a set of coupled model potential energy surfaces based on ab initio calculations for the long-range non-adiabatic interactions and a simplistic short-range interaction. This comparison reveals the crucial role of electrostatic forces in complex molecular collision processes.
We investigated the electronic and structural properties of the infinite linear carbon chain (carbyne) using density functional theory (DFT) and the random phase approximation (RPA) to the correlation energy. The studies are performed in vacuo and for carbyne inside a carbon nano tube (CNT). In the vacuum, semi-local DFT and RPA predict bond length alternations of about 0.04 {AA} and 0.13 {AA}, respectively. The frequency of the highest optical mode at the $Gamma$ point is 1219 cm$^{-1}$ and about 2000 cm$^{-1}$ for DFT and the RPA. Agreement of the RPA to previous high level quantum chemistry and diffusion Monte-Carlo results is excellent. For the RPA we calculate the phonon-dispersion in the full Brillouine zone and find marked quantitative differences to DFT calculations not only at the $Gamma$ point but also throughout the entire Brillouine zone. To model carbyne inside a carbon nanotube, we considered a (10,0) CNT. Here the DFT calculations are even qualitatively sensitive to the k-points sampling. At the limes of a very dense k-points sampling, semi-local DFT predicts no bond length alternation (BLA), whereas in the RPA a sizeable BLA of 0.09 {AA} prevails. The reduced BLA leads to a significant red shift of the vibrational frequencies of about 350 cm$^{-1}$, so that they are in good agreement with experimental estimates. Overall, the good agreement between the RPA and previously reported results from correlated wavefunction methods and experimental Raman data suggests that the RPA provides reliable results at moderate computational costs. It hence presents a useful addition to the repertoire of correlated wavefunction methods and its accuracy clearly prevails for low dimensional systems, where semi-local density functionals struggle to yield even qualitatively correct results.
The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by $lambda x^{6}$ are considered.
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