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We develop an extension of the time-dependent equation-of-motion formulation of the polarizable continuum model (EOM-TDPCM) to introduce nonequilibrium cavity field effects in quantum mechanical calculations of solvated molecules subject to time-dependent electric fields. This method has been implemented in Octopus, a state-of-the-art code for real-space, real-time time-dependent density functional theory (RT-TDDFT) calculations. To show the potential of our methodology, we perform EOM-TDPCM/RT-TDDFT calculations of trans-azobenzene in water and in other model solvents with shorter relaxation times. Our results for the optical absorption spectrum of trans-azobenzene show (i) that cavity field effects have a clear impact in the overall spectral shape and (ii) that an accurate description of the solute shape (as the one provided within PCM) is key to correctly account for cavity field effects., published under ACS Authorchoice license

An accurate description of electron transport at a molecular level requires a precise treatment of quantum effects. These effects play a crucial role in determining the electron transport properties of single molecules, such as current-voltage curves, which can be challenging to simulate classically. Here we introduce a quantum algorithm to efficiently calculate the electronic current through single-molecule junctions in the weak-coupling regime. We show that a quantum computer programmed to simulate vibronic transitions between different charge states of a molecule can be used to compute sequential electron transfer rates and electric current. In the harmonic approximation, the algorithm can be implemented using Gaussian boson sampling devices, which are a near-term platform for photonic quantum computing. We apply the algorithm to simulate the current and conductance of a magnesium porphine molecule. The simulations demonstrate quantum effects that are manifested as discrete steps in the current and conductance, in agreement with experimental and theoretical data.

The excitation of vibrational modes in molecules affects the outcome of chemical reactions, for example by providing molecules with sufficient energy to overcome activation barriers. In this work, we introduce a quantum algorithm for simulating molecular vibrational excitations during vibronic transitions. We discuss how a special-purpose quantum computer can be programmed with molecular data to optimize a vibronic process such that desired modes get excited during the transition. We investigate the effect of such excitations on selective bond dissociation in pyrrole and butane during photochemical and mechanochemical vibronic transitions. The results are discussed with respect to experimental observations and classical simulations. We also introduce quantum-inspired classical algorithms for simulating molecular vibrational excitations in special cases where only a limited number of modes are of interest., 10 pages, 9 figures

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light–matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials)., This work was supported by the European Research Council (Grant No. ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM), Grupos Consolidados (IT1249-19), and SFB925. The Flatiron Institute is a division of the Simons Foundation. X.A., A.W., and A.C. acknowledge that part of this work was performed under the auspices of the U.S. Department of Energy at Lawrence Livermore National Laboratory under Contract No. DE-AC52-07A27344. J.J.-S. gratefully acknowledges the funding from the European Union Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie Grant Agreement No. 795246-StrongLights. J.F. acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG Forschungsstipendium FL 997/1-1). D.A.S. acknowledges University of California, Merced start-up funding.

We determine here the evolution of the bandgap energy with size in graphene quantum dots (GQDs). We find oscillatory behaviour of the bandgap and explain its origin in terms of armchair and zigzag edges. The electronic energy spectra of GQDs are computed using both the tight binding model and {\it ab-initio} density functional methods. The results of the tight binding model are analyzed by dividing zigzag graphene quantum dots into concentric rings. For each ring, the energy spectra, the wave functions and the bandgap are obtained analytically. The effect of inter-ring tunneling on the energy gap is determined. The growth of zigzag terminated GQD into armchair GQD is shown to be associated with the addition of a one-dimensional Lieb lattice of carbon atoms with a shell of energy levels in the middle of the energy gap of the inner zigzag terminated GQD. This introduces a different structure of the energy levels at the bottom of the conduction and top of the valence band in zigzag and armchair GQD which manifests itself in the oscillation of the energy gap with increasing size. The evolution of the bandgap with the number of carbon atoms is compared with the notion of confined Dirac Fermions and tested against {\it ab-initio} calculations of Kohn-Sham and TD-DFT energy gaps.

We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical methods for problems involving low-rank matrices, but with complexity bounds that exhibit a hefty polynomial overhead compared to quantum algorithms. This raised the question of whether these methods were actually useful in practice. We conduct a theoretical analysis aimed at identifying their computational bottlenecks, then implement and benchmark the algorithms on a variety of problems, including applications to portfolio optimization and movie recommendations. On the one hand, our analysis reveals that the performance of these algorithms is better than the theoretical complexity bounds would suggest. On the other hand, their performance as seen in our implementation degrades noticeably as the rank and condition number of the input matrix are increased. Overall, our results indicate that quantum-inspired algorithms can perform well in practice provided that stringent conditions are met: low rank, low condition number, and very large dimension of the input matrix. By contrast, practical datasets are often sparse and high-rank, precisely the type that can be handled by quantum algorithms., A popular summary can be found at https://medium.com/xanaduai/everything-you-always-wanted-to-know-about-quantum-inspired-algorithms-38ee1a0e30ef . Source code is available at https://github.com/XanaduAI/quantum-inspired-algorithms

We present here a theory and a computational tool, Silicon-{\sc Qnano}, to describe atomic scale quantum dots in Silicon. The methodology is applied to model dangling bond quantum dots (DBQDs) created on a passivated H:Si-(100)-(2$\times$1) surface by removal of a Hydrogen atom. The electronic properties of DBQD are computed by embedding it in a computational box of Silicon atoms. The surfaces of the computational box were constructed by using DFT as implemented in {\sc Abinit} program. The top layer was reconstructed by the formation of Si dimers passivated with H atoms while the bottom layer remained unreconstructed and fully saturated with H atoms. The computational box Hamiltonian was approximated by a tight-binding (TB) Hamiltonian by expanding the electron wave functions as a Linear Combination of Atomic Orbitals and fitting the bandstructure to {\it ab-initio} results. The parametrized TB Hamiltonian was used to model large finite Si(100) boxes (slabs) with number of atoms exceeding present capabilities of {\it ab-initio} calculations. The removal of one hydrogen atom from the reconstructed surface resulted in a DBQD state with wave function strongly localized around the Si atom and energy in the silicon bandgap. The DBQD could be charged with zero, one and two electrons. The Coulomb matrix elements were calculated and the charging energy of a two electron complex in a DBQD obtained., 20 Pages, 10 Figures

The electron localization function (ELF) by Becke and Edgecombe [A.D. Becke, K.E. Edgecombe, J. Chem. Phys. 92, 5397 (1990)] is routinely adopted as a descriptor of atomic shells and covalent bonds. Since the ELF and its related quantities find useful exploitation also in the construction of modern density functionals, the interest in complementing the ELF is linked to both the quests of improving electronic structure descriptors and density functional approximations. The ELF uses information which is available by considering parallel-spin electron pairs in single-reference many-body states. In this work, we complement this construction with information obtained by considering antiparallel-spin pairs whose short-range correlations are modeled by a density functional approximation. As a result, the approach requires only a contained computational effort. Applications to a variety of systems show that, in this way, we gain a spatial description of the bond in H2 (which is not available with the ELF) together with some trends not optimally captured by the ELF in other prototypical situations.

Atomically thin semiconducting transition-metal dichalcogenides enable new insight into physics of many-body effects mediated by Coulomb and electron-phonon interactions. We report photoluminescence (PL) and reflectivity contrast (RC) measurements of excitons ($X$) and trions ($T$) and Raman spectra of phonons in monolayers (MLs) of $\mathrm{Mo}{({\mathrm{S}}_{y}{\mathrm{Se}}_{1\ensuremath{-}y})}_{2}$ alloys with sulfur mole content up to $y=0.5$. We find the phonon energy crossing the trion binding energy with the sulfur mole content. Binary ${\mathrm{MoSe}}_{2}$ and ternary $\mathrm{Mo}{({\mathrm{S}}_{y}{\mathrm{Se}}_{1\ensuremath{-}y})}_{2}$ alloys exhibit contrasting behavior in the temperature evolution of excitons and trions PL intensity from $T=7$ to 295 K. In ${\mathrm{MoSe}}_{2}$, the trion dominates PL spectra at low temperatures but the exciton dominates PL at higher temperature. In contrast, in ternary $\mathrm{Mo}{({\mathrm{S}}_{y}{\mathrm{Se}}_{1\ensuremath{-}y})}_{2}$ alloys trions dominate PL spectra at all measured temperatures, with the trion to exciton PL intensity ratio increasing with sulfur content. We attribute the strong increase of the trion PL intensity in $\mathrm{Mo}{({\mathrm{S}}_{y}{\mathrm{Se}}_{1\ensuremath{-}y})}_{2}$ MLs with increase of sulfur mole content to two effects: (i) strong increase of exciton-trion coupling mediated by the optical phonon, which is realized by tuning phonon energy through trion binding energy, and (ii) significant increase of two-dimensional electron gas concentration. We also demonstrate that increasing sulfur content in $\mathrm{Mo}{({\mathrm{S}}_{y}{\mathrm{Se}}_{1\ensuremath{-}y})}_{2}$ alloys increases total PL intensity at high temperature. With the temperature growth from 7 to 295 K, the total PL in ${\mathrm{MoSe}}_{2}$ decreases about three orders of magnitude more than in $\mathrm{Mo}{({\mathrm{S}}_{0.5}{\mathrm{Se}}_{0.5})}_{2}$.

Resonance energy transfer (RET) is an inherently anisotropic process. Even the simplest, well-known F\"orster theory, based on the transition dipole-dipole coupling, implicitly incorporates the anisotropic character of RET. In this theoretical work, we study possible signatures of the fundamental anisotropic character of RET in hybrid nanomaterials composed of a semiconductor nanoparticle (NP) decorated with molecular dyes. In particular, by means of a realistic kinetic model, we show that the analysis of the dye photoluminescence difference for orthogonal input polarizations reveals the anisotropic character of the dye-NP RET which arises from the intrinsic anisotropy of the NP lattice. In a prototypical core/shell wurtzite CdSe/ZnS NP functionalized with cyanine dyes (Cy3B), this difference is predicted to be as large as 75\% and it is strongly dependent in amplitude and sign on the dye-NP distance. We account for all the possible RET processes within the system, together with competing decay pathways in the separate segments. In addition, we show that the anisotropic signature of RET is persistent up to a large number of dyes per NP., Comment: 9 pages, 5 figures. Supplementary information available at http://pubs.rsc.org/en/content/articlelanding/2016/ra/c6ra22433d/unauth#!divAbstract

The challenge of simulating many-body models with analogue physical systems requires both experimental precision and very low operational temperatures. Atomically precise placement of dopants in Si permits the construction of nanowires by design. We investigate the suitability of these interacting electron systems as simulators of a fermionic extended Hubbard model on demand. We describe the single-particle wavefunctions as a linear combination of dopant orbitals (LCDO). The electronic states are calculated within configuration interaction (CI). Due to the peculiar oscillatory behavior of each basis orbital, properties of these chains are strongly affected by the interdonor distance R0, in a non-monotonic way. Ground state (T = 0 K) properties such as charge and spin correlations are shown to remain robust under temperatures up to 4 K for specific values of R0. The robustness of the model against disorder is also tested, allowing some fluctuation of the placement site around the target position. We suggest that finite donor chains in Si may serve as an analog simulator for strongly correlated model Hamiltonians. This simulator is, in many ways, complementary to those based on cold atoms in optical lattices—the trade-off between the tunability achievable in the latter and the survival of correlation at higher operation temperatures for the former suggests that both technologies are applicable for different regimes. Precisely positioned impurities in silicon could perform quantum simulations of models that are intractable for classical computers. Amintor Dusko and co-workers from Brazil’s Universidade Federal do Rio de Janeiro and the University of Ottawa in Canada have shown numerically that if phosphorus atoms in silicon devices are arranged in a line, their electrons can provide an experimental realization of the many-body Fermi-Hubbard model. This model, first presented in 1963, provides a heavily simplified description of high-temperature superconductors. However, a theoretical solution cannot be obtained for large systems. By simulating the model experimentally, Dusko et al.’s proposed system circumvents these computational limitations, and could reach temperature regimes that are not accessible with state-of-the-art cold atom simulators. Successful experimental realization could therefore provide new insights into a model that has been intensively studied since the 1960s.

The UV absorption spectrum of C-60 in n-hexane solvent has been revised by means of numerical analysis and time-dependent density functional theory (TDDFT). The absorption spectrum in the range 3-7 eV has been fitted by a spectral function that includes fourteen transitions with Gaussian lineshape, providing reference transition energies and intensities. The agreement between the experimental and theoretical UV absorption intensities has been considerably improved with respect to previous calculations, by including the solvent dielectric response via the polarizable continuum model (PCM). (C) 2014 Elsevier B.V. All rights reserved.

We develop a novel approach to treat excitation energy transfer in hybrid nanosystems composed by an organic molecule attached to a semiconductor nanoparticle. Our approach extends the customary Förster theory by considering interaction between transition multipole moments of the nanoparticle at all orders and a point-like transition dipole moment representing the molecule. Optical excitations of the nanoparticle are described through an envelope-function configuration interaction method for a single electron-hole pair. We applied the method to the prototypical case of a core/shell CdSe/ZnS semiconductor quantum dot which shows a complete suppression of the energy transfer for specific transitions which could not be captured by Förster theory.

The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the Van der Waals solute surface. In a real-space representation this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the Octopus code and present results for the electrostatic contribution to the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water., Version submitted to The Journal of Chemical Physics 10 pages, 7 Figures + supplemental material

A general methodology is presented to model the opto-electronic properties of a dye molecule in the presence of a semiconductor nanoparticle (NP), a model system for the architecture of dye-sensitized solar cells. The method is applied to the L0 organic dye solvated with acetonitrile in the neighborhood of a TiO2 NP. The total reaction potential due to the polarization of the solvent and the metal oxide is calculated by extending the polarizable continuum model integral equation formalism. The ground state energy is computed by using density functional theory (DFT) while the vertical electronic excitations are obtained by time-dependent DFT in a state-specific corrected linear response scheme. We calculate the excited state oxidation potential (ESOP) for the protonated and deprotonated forms of the L0 dye at different distances and configurations with respect to the NP surface. The stronger renormalizations of the ESOP values due to the presence of the TiO2 nanostructure are found for the protonated dye, reaching a maximum of about -0.15 eV. The role of protonation effect is discussed in terms of the atomic Lowdin charges of the oxidized and reduced species. On the other hand, we observed a weak effect on the L0 optical excitation gap due to the polarization response of the NP. (C) 2013 AIP Publishing LLC.

We report on ab-initio calculations of the electronic structure and optical absorption response of the black dye sensitizer in gas phase. We show that, despite the large size of this molecule, the second-order multiconfiguration quasi-degenerate perturbation theory (MC-QDPT) can be used to calculate vertical excitation energies, oscillator strengths and optical absorption spectra. The zeroth-order reference states entering perturbation calculations are complete active space (CAS) configuration interaction (CI) wave functions computed for 12 active electrons distributed in 12 active orbitals. We found that the CI approach is not enough for taking into account the strong dynamical correlation effects in this system. In fact, the excitation energies of the CAS-CI target states are strongly renormalized by the MC-QDPT calculations. In the calculated absorption spectra, the analysis of the perturbed wavefunctions revealed that the stronger absorption bands correspond to metal-to-ligand and ligand-to-ligand charge transfer processes. Comparison with independent time-dependent extension (TDDFT) calculations performed with different functionals shows that corrections to the long-range behavior of the functional is pivotal to achieve agreement with the MC-QDPT results.

We find an unexpected scaling in the correlation energy of artificial atoms, i.e., harmonically confined two-dimensional quantum dots. The scaling relation is found through extensive numerical examinations including Hartree-Fock, variational quantum Monte Carlo, density-functional, and full configuration-interaction calculations. We show that the correlation energy, i.e., the true ground-state total energy subtracted by the Hartree-Fock total energy, follows a simple function of the Coulomb energy, confimenent strength and, the number of electrons. We find an analytic expression for this function, as well as for the correlation energy per particle and for the ratio between the correlation and total energies. Our tests for independent diffusion Monte Carlo and coupled-cluster results for quantum dots -- including open-shell data -- confirm the generality of the obtained scaling. As the scaling is also well applicable to $\gtrsim$ 100 electrons, our results give interesting prospects for the development of correlation functionals within density-functional theory., Comment: Accepted to Journal of Physics: Condensed Matter