Wavepacket Approach to the Cumulative Reaction Probability within the Flux Operator Formalism

Expressions for the singular flux operator eigenfunctions and eigenvalues are given in terms of the Dirac δ-function representable as a localized Gaussian wavepacket. This functional form enables computation of the cumulative reaction probability N(E) from the wavepacket time-correlation functions. The Gaussian based form of the flux eigenfunctions, which is not tied to a finite basis of a quantum-mechanical calculation, is particularly useful for approximate calculation of N(E) with the trajectory based wavepacket propagation techniques. Numerical illustration is given for the Eckart barrier using the conventional quantum-mechanical propagation and the quantum trajectory dynamics with the approximate quantum potential. N(E) converges with respect to the Gaussian width parameter, and the convergence is faster at low energy. The approximate trajectory calculation overestimates tunneling in the low energy regime, but gives a significant improvement over the parabolic estimate of the tunneling probability

Efficient Quantum Trajectory Representation of Wavefunctions Evolving in Imaginary Time

The Boltzmann evolution of a wavefunction can be recast as imaginary-time dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentum-dependent quantum potential – computed approximately to be practical in high-dimensional systems – influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys.132, 014112 (2010)]. For a nodelesswavefunction represented as ψ(x, t) = exp ( − S(x, t)/ℏ) with the trajectory momenta defined by ∇S(x, t), analysis of the Lagrangian and Eulerian evolution shows that for bound potentials the former is more accurate while the latter is more practical because the Lagrangian quantum trajectories diverge with time. Introduction of stationary and time-dependent components into the wavefunction representation generates new Lagrangian-type dynamics where the trajectory spreading is controlled improving efficiency of the trajectory description. As an illustration, different types of dynamics are used to compute zero-point energy of a strongly anharmonic well and low-lying eigenstates of a high-dimensional coupled harmonic system

Computational Modeling of the Dielectric Function of Silicon Slabs with Varying Thickness

The dynamical dielectric function of a silicon slab, in the region from near IR to UV light frequencies, is expected to vary with its thickness, and it is important to know whether its optical properties are similar to those of bulk silicon. Slabs of varying thickness are modeled starting from their atomic structure. Modeled Si(111) surfaces are terminated by hydrogen atoms to compensate the dangling bonds, and optical properties have been obtained for Si slabs with 4, 8, and 12 layers. Real and imaginary parts of the dielectric function are obtained from the polarization of the slab, expressed in terms of a delayed response function constructed from a reduced density matrix (RDM) which includes electronic dissipative effects due to coupling of photoexcited electrons to the substrate lattice and to electronic excitations. The related index of refraction and absorption coefficient have also been calculated from the above treatment. These optical properties are obtained using density functional theory (DFT) and plane wave basis sets to construct the equation of motion of a RDM, solved for steady light absorption. Both GGA (PBE) and hybrid (HSE) DFT exchange-correlation density functionals are employed to calculate the optical properties from the RDM. The imaginary part of the dielectric function is related to the light absorbance, and has been compared to measurements showing that better agreement is obtained with the HSE hybrid functional containing part of the exact short-range electronic exchange energy. We present a procedure by which one can reproduce the HSE results for the dielectric function from the computationally less expensive GGA PBE functional calculations, using a single photon energy shift parameter and results from PBE calculations. Our treatment shows that the onset of light absorption and strong diffraction are similar for thin slabs and bulk silicon, and that they have similar peak structure as functions of photon energy. Both properties increase with slab thickness at most photon energies. This makes silicon slabs reliable structures for photovoltaic applications

Theoretical Characterization of the Minimum-Energy Structure of (SF₆)₂

MP2 and symmetry-adapted perturbation theory calculations are used in conjunction with the aug-cc-pVQZ basis set to characterize the SF₆ dimer. Both theoretical methods predict the global minimum structure to be of <i>C</i>₂ symmetry, lying 0.07–0.16 kJ/mol below a <i>C</i>_2<i>h</i> saddle point structure, which, in turn, is predicted to lie energetically 0.4–0.5 kJ/mol below the lowest-energy <i>D</i>_2<i>d</i> structure. This is in contrast with IR spectroscopic studies that infer an equilibrium <i>D</i>_2<i>d</i> structure. It is proposed that the inclusion of vibrational zero-point motion gives an averaged structure of <i>D</i>_2<i>d</i> symmetry

Ab-initio design of light absorption through silver atomic clusters decoration of TiO 2

International audienceA first-principle study of the stability and optical response of subnanometer silver clusters Agnn (n ≤5) on a TiO2(110) surface is presented. First, the adequacy of the vdW-corrected DFT-D3 approach is assessed using the domain-based pair natural orbital correlation approach DLPNO-CCSD(T) along with the Symmetry-Adapted Perturbation Theory [SAPT(DFT)] method with a cluster model. Next, using the DFT-D3 treatment with a periodic slab model, we analyze the interaction energies of the atomic silver clusters with the TiO2(110) surface. Finally, the hybrid HSE06 functional and a reduced density matrix treatment are applied to obtain the projected electronic density of states and photo-absorption spectra of the TiO2(110) surface, with and without adsorbed silver clusters. Our results show the stability of the supported clusters, the enhanced light absorbance intensity of the material upon their deposition, and the appearance of intense secondary broad peaks at the near-infrared and the visible region of the spectrum, with positions depending on the size and shape of the supported clusters. The secondary peaks arise from the photo-induced transfer of electrons from intra-band valence 5s orbitals of the noble-metal cluster to conduction 3d Ti band states of the supporting material