Photoabsorbance of supported metal clusters: ab initio density matrix and model studies of large Ag clusters on Si surfaces.

Metal clusters with 10 to 100 atoms supported by a solid surface show electronic structure typical of molecules and require ab initio treatments starting from their atomic structure, and they also can display collective electronic phenomena similar to plasmons in metal solids. We have employed ab initio electronic structure results from two different density functionals (PBE and the hybrid HSE06) and a reduced density matrix treatment of the dissipative photodynamics to calculate light absorbance by the large Ag clusters AgN, N = 33, 37(open shell) and N = 32, 34 (closed shell), adsorbed at the Si(111) surface of a slab, and forming nanostructured surfaces. Results on light absorption are quite different for the two functionals, and are presented here for light absorbances using orbitals and energies from the hybrid functional giving correct energy band gaps. Absorption of Ag clusters on Si increases light absorbance versus photon energy by large percentages, with peak increases found in regions of photon energies corresponding to localized plasmons. The present metal clusters are large enough to allow for modelling with continuum dielectric treatments of their medium. A mesoscopic Drude-Lorentz model is presented in a version suitable for the present structures, and provides an interpretation of our results. The calculated range of plasmon energies overlaps with the range of solar photon energies, making the present structures and properties relevant to applications to solar photoabsorption and photocatalysis.

Electronic relaxation of photoexcited open and closed shell adsorbates on semiconductors: Ag and Ag2 on TiO2.

A theoretical treatment based on the equations of motion of an electronic reduced density matrix, and related computational modeling, is used to describe and calculate relaxation times for nanostructured TiO2(110) surfaces, here for Ag and Ag2 adsorbates. The theoretical treatment deals with the preparation of a photoexcited system under two different conditions, by steady light absorption with a cutoff and by a light pulse, and describes the following relaxation of electronic densities. On the computational modeling, results are presented for electronic density of states, light absorbance, and relaxation dynamics, comparing results for Ag and Ag2 adsorbates. The aim of this work is to provide insight on the dynamics and magnitude of relaxation rates for a surface with adsorbed open- and closed-shell Ag species to determine whether the advantages in using them to enhance light absorbance remain valid in the presence of charge density relaxation. Different behaviors can be expected depending on whether the adsorbate particles (Ag metal clusters in our present choice) have electronic open-shell or closed-shell structures. Calculated electron and hole lifetimes are given for pure TiO2(110), Ag/TiO2(110), and Ag2/TiO2(110). The present results, while limited to chosen structures and photon wavelengths, show that relaxation rates are noticeably different for electrons and holes, but comparable in magnitude for pure and adsorbate surfaces. Overall, the introduction of the adsorbates does not lead to rapid loss of charge carriers, while they give large increases in light absorption. This appears to be advantageous for applications to photocatalysis.

Ab initio design of light absorption through silver atomic cluster decoration of TiO2.

A first-principles study of the stability and optical response of subnanometer silver clusters Agn (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 DLPNO-CCSD(T) calculations along with the Symmetry-Adapted Perturbation Theory [SAPT(DFT)] applied to 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 in the near-infrared and the visible regions 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 3d Ti band states of the supporting material.

Implementation of analytical gradients and of a mixed real and momentum space DVR method for excess electron systems described by a self-consistent polarization model.

This work presents two extensions of our self-consistent polarization model for treating non-valence excess electron systems. The first extension is the implementation of analytical gradients, and the second extension is the implementation of a mixed real space plus momentum space approach combined with fast Fourier transforms to reduce the computational time compared to a purely real space discrete variable representation approach. The performance of the new algorithms is assessed in calculations of the excess electron states of various size water clusters and of the non-valence correlation-bound anion of the C240 fullerene.

Quantum confinement effects on electronic photomobilities at nanostructured semiconductor surfaces: Si(111) without and with adsorbed Ag clusters.

The conductivity of holes and electrons photoexcited in Si slabs is affected by the slab thickness and by adsorbates. The mobilities of those charged carriers depend on how many layers compose the slab, and this has important scientific and technical consequences for the understanding of photovoltaic materials. A previously developed general computational procedure combining density matrix and electronic band structure treatments has been applied to extensive calculations of mobilities of photoexcited electrons and holes at Si(111) nanostructured surfaces with varying slab thickness and for varying photon energies, to investigate the expected change in mobility magnitudes as the slab thickness is increased. Results have been obtained with and without adsorbed silver clusters for comparison of their optical and photovoltaic properties. Band states were generated using a modified ab initio density functional treatment with the PBE exchange and correlation density functionals and with periodic boundary conditions for large atomic supercells. An energy gap correction was applied to the unoccupied orbital energies of each band structure by running more accurate HSE hybrid functional calculations for a Si(111) slab. Photoexcited state populations for slabs with 6, 8, 10, and 12 layers were generated using a steady state reduced density matrix including dissipative effects due to energy exchange with excitons and phonons in the medium. Mobilities have been calculated from the derivatives of voltage-driven electronic energies with respect to electronic momentum, for each energy band and for the average over bands. Results show two clear trends: (a) adding Ag increases the hole photomobilities and (b) decreasing the slab thickness increases hole photomobilities. The increased hole populations in 6- and 8-layer systems and the large increase in hole mobility for these thinner slabs can be interpreted as a quantum confinement effect of hole orbitals. As the slab thickness increases to ten and twelve layers, the effect of silver adsorbates decreases leading to smaller relative enhancements to the conduction electron and hole mobilities, but the addition of the silver nanoclusters still increases the absorbance of light and the mobility of holes compared to their mobilities in the pure Si slabs.

Photoconductivities from band states and a dissipative electron dynamics: Si(111) without and with adsorbed Ag clusters.

A new general computational procedure is presented to obtain photoconductivities starting from atomic structures, combining ab initio electronic energy band states with populations from density matrix theory, and implemented for a specific set of materials based on Si crystalline slabs and their nanostructured surfaces without and with adsorbed Ag clusters. The procedure accounts for charge mobility in semiconductors in photoexcited states, and specifically electron and hole photomobilities at Si(111) surfaces with and without adsorbed Ag clusters using ab initio energy bands and orbitals generated from a generalized gradient functional, however with excited energy levels modified to provide correct bandgaps. Photoexcited state populations for each band and carrier type were generated using steady state solution of a reduced density matrix which includes dissipative medium effects. The present calculations provide photoexcited electronic populations and photoinduced mobilities resulting from applied electric fields and obtained from the change of driven electron energies with their electronic momentum. Extensive results for Si slabs with 8 layers, without and with adsorbed Ag clusters, show that the metal adsorbates lead to substantial increases in the photomobility and photoconductivity of electrons and holes.

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 nodeless wavefunction represented as ψ(x, t) = exp(-S(x, t)/h) 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.

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 delta-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.

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 C2 symmetry, lying 0.07-0.16 kJ/mol below a C2h saddle point structure, which, in turn, is predicted to lie energetically 0.4-0.5 kJ/mol below the lowest-energy D2d structure. This is in contrast with IR spectroscopic studies that infer an equilibrium D2d structure. It is proposed that the inclusion of vibrational zero-point motion gives an averaged structure of D2d symmetry.

Modeling the surface photovoltage of silicon slabs with varying thickness.

The variation with thickness of the energy band gap and photovoltage at the surface of a thin semiconductor film are of great interest in connection with their surface electronic structure and optical properties. In this work, the change of a surface photovoltage (SPV) with the number of layers of a crystalline silicon slab is extracted from models based on their atomic structure. Electronic properties of photoexcited slabs are investigated using generalized gradient and hybrid density functionals, and plane wave basis sets. Si(1 1 1) surfaces have been terminated by hydrogen atoms to compensate for dangling bonds and have been described by large supercells with periodic boundary conditions. Calculations of the SPV of the Si slabs have been done in terms of the reduced density matrix of the photoactive electrons including dissipative effects due to their interaction with medium phonons and excitons. Surface photovoltages have been calculated for model Si slabs with 4-12, and 16 layers, to determine convergence trends versus slab thickness. Band gaps and the inverse of the SPVs have been found to scale nearly linearly with the inverse thickness of the slab, while the electronic density of states increases quadratically with thickness. Our calculations show the same trends as experimental values indicating band gap reduction and absorption enhancement for Si films of increasing thickness. Simple arguments on confined electronic structures have been used to explain the main effects of changes with slab thickness. A procedure involving shifted electron excitation energies is described to improve results from generalized gradient functionals so they can be in better agreement with the more accurate but also more computer intensive values from screened exchange hybrid functionals.