We consider a quantum-mechanical system, finite or extended, initially in its ground-state, exposed to a time-dependent potential pulse, with a slowly varying envelope and a carrier frequency \$\textbackslashomega\_0\$. By working out a rigorous solution of the time-dependent Schr\textbackslash"odinger equation in the high-\$\textbackslashomega\_0\$ limit, we show that the linear response is completely suppressed after the switch-off of the pulse. We show, at the same time, that to the lowest order in \$\textbackslashomega\_0ˆ\-1\\$, observables are given in terms of the linear density response function \$\textbackslashchi(\textbackslashrv,\textbackslashrv',\textbackslashomega)\$, despite the problem's nonlinearity. We propose a new spectroscopic technique based on these findings, which we name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). An analysis of the jellium slab and sphere models reveals very high surface sensitivity of NLHFPS, which produces a richer excitation spectrum than accessible within the linear-response regime. Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the conventional dipole selection rules, and the ease of theoretical interpretation by means of the linear response time-dependent density functional theory, NLHFPS has the potential to evolve into a powerful characterization method in nanoscience and nanotechnology.
Despite the abundance of data concerning single-photon double ionization of methanol, the spin state of the emitted electron pair has never been determined. Here we present the ﬁrst evidence that identiﬁes the emitted electron pair spin as overwhelmingly singlet when the dication forms in low-energy conﬁgurations. The experimental data show that while the yield of the CH2O+ + H3+ Coulomb explosion channel is abundant, the metastable methanol dication is largely absent. According to high-level ab initio simulations, these facts indicate that photoionization promptly forms singlet dication states, where they quickly decompose through various channels, with signiﬁcant H3+ yields on the low-lying states. In contrast, if we assume that the initial dication is formed in one of the low-lying triplet states, the ab initio simulations exhibit a metastable dication, contradicting the experimental ﬁndings. Comparing the average simulated branching ratios with the experimental data suggests a \textgreater3 order of magnitude enhancement of the singlet:triplet ratio compared with their respective 1:3 multiplicities.
Generalized Kohn−Sham density functional theory is a popular computational tool for the ground state of extended systems, particularly within range-separated hybrid (RSH) functionals that capture the long-range electronic interaction. Unfortunately, the heavy computational cost of the nonlocal exchange operator in RSH-DFT usually conﬁnes the approach to systems with at most a few hundred electrons. A signiﬁcant reduction in the computational cost is achieved by representing the density matrix with stochastic orbitals and a stochastic decomposition of the Coulomb convolution (J. Phys. Chem. A 2016, 120, 3071). Here, we extend the stochastic RSH approach to excited states within the framework of linear-response generalized Kohn−Sham time-dependent density functional theory (GKS-TDDFT) based on the plane-wave basis. As a validation of the stochastic GKS-TDDFT method, the excitation energies of small molecules N2 and CO are calculated and compared to the deterministic results. The computational eﬃciency of the stochastic method is demonstrated with a two-dimensional MoS2 sheet (∼1500 electrons), whose excitation energy, exciton charge density, and (excited state) geometric relaxation are determined in the absence and presence of a point defect.
We develop a stochastic resolution of identity approach to the real-time second-order Green’s function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green’s function [Takeshita et al. J. Chem. Phys. 2019, 151, 044114]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons.
Abstract The Kubo-Greenwood (KG) formula is often used in conjunction with Kohn-Sham (KS) density functional theory (DFT) to compute the optical conductivity, particularly for warm dense mater. For applying the KG formula, all KS eigenstates and eigenvalues up to an energy cutoff are required and thus the approach becomes expensive, especially for high temperatures and large systems, scaling cubically with both system size and temperature. Here, we develop an approach to calculate the KS conductivity within the stochastic DFT (sDFT) framework, which requires knowledge only of the KS Hamiltonian but not its eigenstates and values. We show that the computational effort associated with the method scales linearly with system size and reduces in proportion to the temperature unlike the cubic increase with traditional deterministic approaches. In addition, we find that the method allows an accurate description of the entire spectrum, including the high-frequency range, unlike the deterministic method which is compelled to introduce a high-frequency cut-off due to memory and computational time constraints. We apply the method to helium-hydrogen mixtures in the warm dense matter regime at temperatures of \textbackslashsim60\textbackslashtext\kK\ and find that the system displays two conductivity phases, where a transition from non-metal to metal occurs when hydrogen atoms constitute \textbackslashsim0.3 of the total atoms in the system.
The conjecture that, as in bulk semiconductors, hot multiexcitons in nanocrystals cool rapidly to the lowest available energy levels is tested here by recording the eﬀects of a single cold “spectator” exciton on the relaxation dynamics of a subsequently deposited hot counterpart. Results in CdSe/CdS nanodots show that a preexisting cold “spectator exciton” allows only half of the photoexcited electrons to relax directly to the band-edge. The rest are blocked in an excited quantum state due to conﬂicts in spin orientation. The latter fully relax in this sample only after ∼25 ps as the blocked electrons spins ﬂip, prolonging the temporal window of opportunity for harvesting the retained energy more than 100 fold! Common to all quantum-conﬁned nanocrystals, this process will delay cooling and impact the spectroscopic signatures of hot multiexcitons in all envisioned generation scenarios. How the spin-ﬂipping rate scales with particle size and temperature remains to be determined.
A multifaceted agreement between ab initio theoretical predictions and experimental measurements, including branching ratios, channel-speciﬁc kinetic energy release, and three-body momentum correlation spectra, leads to the identiﬁcation of new mechanisms in Coulomb-explosion (CE) induced two- and three-body breakup processes in methanol. These identiﬁed mechanisms include direct nonadiabatic Coulomb explosion responsible for CO bond-breaking, a long-range “ inverse harpooning” dominating the production of H2+ + HCOH+, a transient proton migration leading to surprising energy partitioning in three-body fragmentation and other complex dynamics forming products such as H2O+ and H3+. These mechanisms provide general concepts that should be useful for analyzing future time-resolved Coulomb explosion imaging of methanol as well as other molecular systems. These advances are enabled by a combination of recently developed experimental and computational techniques, using weak ultrafast EUV pulses to initiate the CE and a high-level quantum chemistry approach to follow the resulting ﬁeld-free nonadiabatic molecular dynamics.
Absorption cross-section spectra for gold nanoparticles were calculated using fully quantum Stochastic Density Functional Theory and a classical Finite-Difference Time Domain Maxwell solver. Spectral shifts were monitored as a function of size (1.3–) and shape (octahedron, cubeoctahedron and truncated cube). Even though the classical approach is forced to fit the quantum time-dependent density functional theory at , at smaller sizes there is a significant deviation as the classical theory is unable to account for peak splitting and spectral blueshifts even after quantum spectral corrections. We attribute the failure of classical methods at predicting these features to quantum effects and low density of states in small nanoparticles. Classically, plasmon resonances are modelled as collective conduction electron excitations, but at small nanoparticle size these excitations transition to few or even individual conductive electron excitations, as indicated by our results.
Single-photon Coulomb explosion of methanol is instigated using the broad bandwidth pulse achieved through high-order harmonics generation. Using 3D coincidence fragment imaging of one molecule at a time, the kinetic energy release (KER) and angular distributions of the products are measured in different Coulomb explosion (CE) channels. Two-body CE channels breaking either the C–O or the C–H bonds are described as well as a proton migration channel forming H2O+, which is shown to exhibit higher KER. The results are compared to intense-field Coulomb explosion measurements in the literature. The interpretation of broad bandwidth single-photon CE data is discussed and supported by ab initio calculations of the predominant C–O bond breaking CE channel. We discuss the importance of these findings for achieving time resolved imaging of ultrafast dynamics.
Multiexciton generation, by which more than a single electron–hole pair is generated on optical excitation, is a promising paradigm for pushing the efficiency of solar cells beyond the Shockley–Queisser limit of 31%. Utilizing this paradigm, however, requires the onset energy of multiexciton generation to be close to twice the band gap energy and the efficiency to increase rapidly above this onset. This challenge remains unattainable even using confined nanocrystals, nanorods or nanowires. Here, we show how both goals can be achieved in a nanorod heterostructure with type-II band offsets. Using pseudopotential atomistic calculation on a model type-II semiconductor heterostructure we predict the optimal conditions for controlling multiexciton generation efficiencies at twice the band gap energy. For a finite band offset, this requires a sharp interface along with a reduction of the exciton cooling and may enable a route for breaking the Shockley–Queisser limit.
Using a combination of density functional theory and quantum master equations approach, we study the effect of electromagnetic (EM) coupling on the nonequilibrium steady-state behavior of a recently introduced gated molecular junction. This junction was demonstrated in a previous publication to exhibit sharp current switching near a certain critical DC field Ez*, which induces intramolecular charge transfer, and here, we analyze the steady-state population and current when an AC EM field (EMF) is present. The AC EMF at frequency $ømega_0$ produces pronounced population and current features at gate fields Ez = Ez* ± $\hbar ømega_0/ez$ (where $e_z$ is the dipole of the charge-transfer state) and thus allows additional sharp switching capability at lower gate fields. We found that even when EMF is absent, the EM coupling itself changes the overall steady-state population and current distributions because it allows for relaxation via spontaneous emission
We study how shape affects multiexciton generation rates in a semiconducting nanocrystal by considering CdSe nanorods with varying diameters and aspect ratios. The calculations employ an atomistic semiempirical pseudopotential model combined with an efficacious stochastic approach applied to systems containing up to 20 000 atoms. The effect of nanorod diameter and aspect ratio on multiexciton generation rates is analyzed in terms of the scaling of the density of trion states and the scaling of the Coulomb couplings. Both show distinct scaling from spherical nanocrystals leading to a surprising result where the multiexciton generation rates are roughly independent of the nanorod length.
In conventional spectroscopy, transitions between electronic levels are governed by the electric dipole selection rule because electric quadrupole, magnetic dipole, and coupled electric dipole-magnetic dipole transitions are forbidden in a far field. We demonstrated that by using nanostructured electromagnetic fields, the selection rules of absorption spectroscopy could be fundamentally manipulated. We also show that forbidden transitions between discrete quantum levels in a semiconductor nanorod structure are allowed within the near-field of a noble metal nanoparticle. Atomistic simulations analyzed by an effective mass model reveal the breakdown of the dipolar selection rules where quadrupole and octupole transitions are allowed. Our demonstration could be generalized to the use of nanostructured near-fields for enhancing light-matter interactions that are typically weak or forbidden.
Systematically varying the optical gap that is associated with charge-transfer excitations is an important step in the design of light-harvesting molecules. So far the guidance that time-dependent density functional theory could give in this process was limited by the traditional functionals' inability to describe charge-transfer excitations. We show that a nonempirical range-separated hybrid approach allows to reliably predict charge-transfer excitations for molecules of practically relevant complexity. Calculated absorption energies agree with measured ones. We predict from theory that by varying the number of thiophenes in donor-acceptor-donor molecules, the energy of the lowest optical absorption can be tuned to the lower end of the visible spectrum. Saturation sets in at about five thiophene rings. (C) 2011 American Institute of Physics. [doi:10.1063/1.3581788]
We study the photodissociation of the H+2 molecule by ultrashort Fock-state electromagnetic pulses (EMPs). We use the Born-Oppenheimer treatment combined with an explicit photon number representation via diabatic electrophoton potential surfaces for simplification of the basic equations. We discuss the issue of the number of photon states required and show that six photon states enable good accuracy for photoproduct kinetic energies of up to 3 eV. We calculate photodissociation probabilities and nuclear kinetic-energy (KE) distributions of the photodissociation products for 800 nm, 50-TW/cm2 pulses. We show that KE distributions depend on three pulse durations of 10, 20, and 45 fs and on various initial vibrational states of the molecule. We compare the Fock-state results to those obtained by “conventional,” i.e., coherent-state, laser pulses of equivalent electric fields and durations. The effects of the quantum state of EMPs on the photodissociation dynamics are especially strong for high initial vibrational states of H+2. While coherent-state pulses suppress photodissociation for the high initial vibrational states of H+2, the Fock-state pulses enhance it.
We develop a generalized framework based on a Green’s function formalism to calculate the efficiency of multiexciton generation in nanocrystal quantum dots. The direct/indirect absorption and coherent/incoherent impact ionization mechanisms, often used to describe multiexciton generation in nanocrystals, are reviewed and rederived from the unified theory as certain approximations. In addition, two new limits are described systematically – the weak Coulomb coupling limit and the semi-wide band limit. We show that the description of multiexciton generation in nanocrystals can be described as incoherent process and we discuss the scaling of multiexciton generation with respect to the photon energy and nanocrystal size. Illustrations are given for three prototype systems: CdSe, InAs and silicon quantum dots.
We review density functional theory (DFT) within the Kohn-Sham (KS) and the generalized KS (GKS) frameworks from a theoretical perspective for both time-independent and time-dependent problems. We focus on the use of range-separated hybrids within a GKS approach as a practical remedy for dealing with the deleterious long-range self-repulsion plaguing many approximate implementations of DFT. This technique enables DFT to be widely relevant in new realms such as charge transfer, radical cation dimers, and Rydberg excitations. Emphasis is put on a new concept of system-specific range-parameter tuning, which introduces predictive power in applications considered until recently too difficult for DFT.
We study the description of charge-transfer excitations in a series of coumarin-based donor-bridge-acceptor dyes. We show that excellent predictive power for the excitation energies and oscillator strengths in these systems is obtained by using a range-separated hybrid functional within the generalized Kohn–Sham approach to time-dependent density functional theory. Key to this success is a step for tuning the range separation parameter from first principles. We explore different methods for this tuning step, which are variants of a recently suggested approach for charge-transfer excitations [T. Stein et al., J. Am. Chem. Soc. 131, 2818 (2009)]. We assess the quality of prediction by comparing to excitation energies previously published for the same systems using the approximate coupled-cluster singles and doubles (CC2) method.
We show how charge transfer excitations at molecular complexes can be calculated quantitatively using time-dependent density functional theory. Predictive power is obtained from range-separated hybrid functionals using nonempirical tuning of the range-splitting parameter. Excellent performance of this approach is obtained for a series of complexes composed of various aromatic donors and the tetracyanoethytene acceptor, paving the way to systematic nonempirical quantitative studies of charge-transfer excitations in real systems.