*J Chem Phys ; 152(16): 161103, 2020 Apr 30.*

**| MEDLINE**| ID: mdl-32357762

##### RESUMO

Efficient Boltzmann-sampling using first-principles methods is challenging for extended systems due to the steep scaling of electronic structure methods with the system size. Stochastic approaches provide a gentler system-size dependency at the cost of introducing "noisy" forces, which could limit the efficiency of the sampling. When the forces are deterministic, the first-order Langevin dynamics (FOLD) offers efficient sampling by combining a well-chosen preconditioning matrix S with a time-step-bias-mitigating propagator [G. Mazzola and S. Sorella, Phys. Rev. Lett. 118, 015703 (2017)]. However, when forces are noisy, S is set equal to the force-covariance matrix, a procedure that severely limits the efficiency and the stability of the sampling. Here, we develop a new, general, optimal, and stable sampling approach for FOLD under noisy forces. We apply it for silicon nanocrystals treated with stochastic density functional theory and show efficiency improvements by an order-of-magnitude.

*J Chem Theory Comput ; 16(2): 1064-1072, 2020 Feb 11.*

**| MEDLINE**| ID: mdl-31899638

##### RESUMO

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 (â¼1500 electrons), whose excitation energy, exciton charge density, and (excited state) geometric relaxation are determined in the absence and presence of a point defect.

*J Chem Phys ; 151(17): 174115, 2019 Nov 07.*

**| MEDLINE**| ID: mdl-31703523

##### RESUMO

Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT.

*J Chem Theory Comput ; 15(12): 6703-6711, 2019 Dec 10.*

**| MEDLINE**| ID: mdl-31652067

##### RESUMO

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.

*J Chem Phys ; 151(11): 114116, 2019 Sep 21.*

**| MEDLINE**| ID: mdl-31542024

##### RESUMO

Linear scaling density functional theory is important for understanding electronic structure properties of nanometer scale systems. Recently developed stochastic density functional theory can achieve linear or even sublinear scaling for various electronic properties without relying on the sparsity of the density matrix. The basic idea relies on projecting stochastic orbitals onto the occupied space by expanding the Fermi-Dirac operator and repeating this for Nχ stochastic orbitals. Often, a large number of stochastic orbitals are required to reduce the statistical fluctuations (which scale as Nχ -1/2) below a tolerable threshold. In this work, we introduce a new stochastic density functional theory that can efficiently reduce the statistical fluctuations for certain observable and can also be integrated with an embedded fragmentation scheme. The approach is based on dividing the occupied space into energy windows and projecting the stochastic orbitals with a single expansion onto all windows simultaneously. This allows for a significant reduction of the noise as illustrated for bulk silicon with a large supercell. We also provide theoretical analysis to rationalize why the noise can be reduced only for a certain class of ground state properties, such as the forces and electron density.

*J Am Chem Soc ; 141(34): 13487-13496, 2019 Aug 28.*

**| MEDLINE**| ID: mdl-31379152

##### RESUMO

In contrast to molecular systems, which are defined with atomic precision, nanomaterials generally show some heterogeneity in size, shape, and composition. The sample inhomogeneity translates into a distribution of energy levels, band gaps, work functions, and other characteristics, which detrimentally affect practically every property of functional nanomaterials. We discuss a novel synthetic strategy, colloidal atomic layer deposition (c-ALD) with stationary reactant phases, which largely circumvents the limitations of traditional colloidal syntheses of nano-heterostructures with atomic precision. This approach allows for significant reduction of inhomogeneity in nanomaterials in complex nanostructures without compromising their structural perfection and enables the synthesis of epitaxial nano-heterostructures of unprecedented complexity. The improved synthetic control ultimately enables bandgap and strain engineering in colloidal nanomaterials with close to atomic accuracy. To demonstrate the power of the new c-ALD method, we synthesize a library of complex II-VI semiconductor nanoplatelet heterostructures. By combining spectroscopic and computational studies, we elucidate the subtle interplay between quantum confinement and strain effects on the optical properties of semiconductor nanostructures.

*J Chem Phys ; 151(4): 044114, 2019 Jul 28.*

**| MEDLINE**| ID: mdl-31370516

##### RESUMO

We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.

*ACS Nano ; 13(11): 12322-12344, 2019 Nov 26.*

**| MEDLINE**| ID: mdl-31246407

##### RESUMO

The goal of this work is to identify favored pathways for preparation of defect-resilient attached wurtzite CdX (X = S, Se, Te) nanocrystals. We seek guidelines for oriented attachment of faceted nanocrystals that are most likely to yield pairs of nanocrystals with either few or no electronic defects or electronic defects that are in and of themselves desirable and stable. Using a combination of in situ high-resolution transmission electron microscopy (HRTEM) and electronic structure calculations, we evaluate the relative merits of atomic attachment of wurtzite CdSe nanocrystals on the {11Ì 00} or {112Ì 0} family of facets. Pairwise attachment on either facet can lead to perfect interfaces, provided the nanocrystal facets are perfectly flat and the angles between the nanocrystals can adjust during the assembly. Considering defective attachment, we observe for {11Ì 00} facet attachment that only one type of edge dislocation forms, creating deep hole traps. For {112Ì 0} facet attachment, we observe that four distinct types of extended defects form, some of which lead to deep hole traps whereas others only to shallow hole traps. HRTEM movies of the dislocation dynamics show that dislocations at {11Ì 00} interfaces can be removed, albeit slowly. Whereas only some extended defects at {112Ì 0} interfaces could be removed, others were trapped at the interface. Based on these insights, we identify the most resilient pathways to atomic attachment of pairs of wurtzite CdX nanocrystals and consider how these insights can translate to the creation of electronically useful materials from quantum dots with other crystal structures.

*J Chem Phys ; 150(23): 234112, 2019 Jun 21.*

**| MEDLINE**| ID: mdl-31228895

##### RESUMO

We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. The numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.

*ACS Nano ; 13(8): 8589-8596, 2019 Aug 27.*

**| MEDLINE**| ID: mdl-31251582

##### RESUMO

Colloidal, two-dimensional semiconductor nanoplatelets (NPLs) exhibit quantum confinement in only one dimension, which results in an electronic structure that is significantly altered compared to that of other quantum-confined nanomaterials. Whereas it is often assumed that the lack of quantum confinement in the lateral plane yields a spatially extended exciton, reduced dielectric screening potentially challenges this picture. Here, we implement absorption spectroscopy in pulsed magnetic fields up to 60 T for three different CdSe NPL thicknesses and lateral areas. Based on diamagnetic shifts, we find that the exciton lateral extent is comparable to NPL thickness, indicating that the quantum confinement and reduced screening concomitant with few-monolayer thickness strongly reduces the exciton lateral extent. Atomistic electronic structure calculations of the exciton size for varying lengths, widths, and thicknesses support the substantially smaller in-plane exciton extent.

*Nano Lett ; 19(7): 4804-4810, 2019 Jul 10.*

**| MEDLINE**| ID: mdl-31244231

##### RESUMO

In this report, we show that a new mechanism for carrier transport in solution-processed colloidal semiconductor nanocrystal arrays exists at high excitation intensity on ultrafast time scales and allows for facile intrinsic transport between as-prepared nanocrystals over long distances. By combining a high speed photoconductive switch with an ultrafast laser excitation in a sub-40 ps photoconductor, we observed transient photocurrents with peak densities of 3 × 104 - 106 mA/cm2 in self-assembled PbSe nanocrystals capped with long native oleic acid ligands. The ratio between the transient photocurrent peak and the steady-state dark current is 10 orders of magnitude. The transient mobility at the peak current is estimated to range between 0.5-17.5 cm2/(V s) for the various nanocrystal sizes studied, which is 6 to 9 orders of magnitude higher than the dark current steady-state mobility in PbSe, CdSe, and CdTe nanocrystals capped with native ligands. The results are analyzed using a kinetic model which attributes the ultrahigh transient photocurrent to multiple photogenerated excitons undergoing on-particle Auger recombination, followed by rapid tunneling at high energies. This mechanism is demonstrated for a wide range of PbSe nanocrystals sizes (diameters from 2.7 to 7.1 nm) and experimental parameters. Our observations indicate that native ligand-capped nanocrystal arrays are promising for optoelectronics applications wherein multiple carriers are photoinjected to interband states.

*J Chem Phys ; 150(3): 034106, 2019 Jan 21.*

**| MEDLINE**| ID: mdl-30660162

##### RESUMO

The stochastic density functional theory (DFT) [R. Baer et al., Phys. Rev. Lett. 111, 106402 (2013)] is a valuable linear-scaling approach to Kohn-Sham DFT that does not rely on the sparsity of the density matrix. Linear (and often sub-linear) scaling is achieved by introducing a controlled statistical error in the density, energy, and forces. The statistical error (noise) is proportional to the inverse square root of the number of stochastic orbitals and thus decreases slowly; however, by dividing the system into fragments that are embedded stochastically, the statistical error can be reduced significantly. This has been shown to provide remarkable results for non-covalently-bonded systems; however, the application to covalently bonded systems had limited success, particularly for delocalized electrons. Here, we show that the statistical error in the density correlates with both the density and the density matrix of the system and propose a new fragmentation scheme that elegantly interpolates between overlapped fragments. We assess the performance of the approach for bulk silicon of varying supercell sizes (up to Ne = 16 384 electrons) and show that overlapped fragments reduce significantly the statistical noise even for systems with a delocalized density matrix.

*Nano Lett ; 18(12): 7889-7895, 2018 12 12.*

**| MEDLINE**| ID: mdl-30403875

##### RESUMO

The fast nonradiative decay of multiexcitonic states via Auger recombination is a fundamental process affecting a variety of applications based on semiconductor nanostructures. From a theoretical perspective, the description of Auger recombination in confined semiconductor nanostructures is a challenging task due to the large number of valence electrons and exponentially growing number of excited excitonic and biexcitonic states that are coupled by the Coulomb interaction. These challenges have restricted the treatment of Auger recombination to simple, noninteracting electron-hole models. Herein we present a novel approach for calculating Auger recombination lifetimes in confined nanostructures having thousands to tens of thousands of electrons, explicitly including electron-hole interactions. We demonstrate that the inclusion of electron-hole correlations are imperative to capture the correct scaling of the Auger recombination lifetime with the size and shape of the nanostructure. In addition, correlation effects are required to obtain quantitatively accurate lifetimes even for systems smaller than the exciton Bohr radius. Neglecting such correlations can result in lifetimes that are two orders of magnitude too long. We establish the utility of the new approach for CdSe quantum dots of varying sizes and for CdSe nanorods of varying diameters and lengths. Our new approach is the first theoretical method to postdict the experimentally known "universal volume scaling law" for quantum dots and makes novel predictions for the scaling of the Auger recombination lifetimes in nanorods.

*J Chem Phys ; 149(17): 174107, 2018 Nov 07.*

**| MEDLINE**| ID: mdl-30409020

##### RESUMO

We show that a rigid scissors-like GW self-consistency approach, labeled here Δ ¯ G W 0 , can be trivially implemented at zero additional cost for large scale one-shot G 0 W 0 calculations. The method significantly improves one-shot G 0 W 0 and for large systems is very accurate. Δ ¯ G W 0 is similar in spirit to evGW 0 where the self-consistency is only applied on the eigenvalues entering Green's function, while both W and the eigenvectors of Green's function are held fixed. Δ ¯ G W 0 further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent G 0 W 0 self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-GW approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of Δ ¯ G W 0 increases with the system size. For molecules, it is up to 0.4-0.5 eV away from coupled-cluster single double triple (CCSD(T)), but for tetracene and hexacene, it matches the ionization energies from both CCSD(T) and evGW 0 to better than 0.05 eV. For solids, as exemplified here by periodic supercells of semiconductors and insulators with 6192 valence electrons, the method matches evGW 0 quite well and both methods are in good agreement with the experiment.

*J Chem Phys ; 149(10): 104105, 2018 Sep 14.*

**| MEDLINE**| ID: mdl-30219023

##### RESUMO

We relate the memory kernel in the Nakajima-Zwanzig-Mori time-convolution approach to the reduced system propagator which is often used to obtain the kernel in the Tokuyama-Mori time-convolutionless approach. The connection provides a robust and simple formalism to compute the memory kernel for a generalized system-bath model circumventing the need to compute high order system-bath observables, thus streamlining the use of numerically exact solvers for calculating the memory kernel. We illustrate this for a model system with electron-electron and electron-phonon couplings, driven away from equilibrium.

*Nano Lett ; 18(11): 6967-6973, 2018 11 14.*

**| MEDLINE**| ID: mdl-30265549

##### RESUMO

Surface condition plays an important role in the optical performance of semiconductor materials. As new types of semiconductors, the emerging metal-halide perovskites are promising for next-generation optoelectronic devices. We discover significantly improved light-emission efficiencies in lead halide perovskites due to surface oxygen passivation. The enhancement manifests close to 3 orders of magnitude as the perovskite dimensions decrease to the nanoscale, improving external quantum efficiencies from <0.02% to over 12%. Along with about a 4-fold increase in spontaneous carrier recombination lifetimes, we show that oxygen exposure enhances light emission by reducing the nonradiative recombination channel. Supported by X-ray surface characterization and theoretical modeling, we propose that excess lead atoms on the perovskite surface create deep-level trap states that can be passivated by oxygen adsorption.

*Nano Lett ; 18(8): 5211-5216, 2018 08 08.*

**| MEDLINE**| ID: mdl-29985622

##### RESUMO

Hybrid semiconductor-metal nanoparticles (HNPs) manifest unique, synergistic electronic and optical properties as a result of combining semiconductor and metal physics via a controlled interface. These structures can exhibit spatial charge separation across the semiconductor-metal junction upon light absorption, enabling their use as photocatalysts. The combination of the photocatalytic activity of the metal domain with the ability to generate and accommodate multiple excitons in the semiconducting domain can lead to improved photocatalytic performance because injecting multiple charge carriers into the active catalytic sites can increase the quantum yield. Herein, we show a significant metal domain size dependence of the charge carrier dynamics as well as the photocatalytic hydrogen generation efficiencies under nonlinear excitation conditions. An understanding of this size dependence allows one to control the charge carrier dynamics following the absorption of light. Using a model hybrid semiconductor-metal CdS-Au nanorod system and combining transient absorption and hydrogen evolution kinetics, we reveal faster and more efficient charge separation and transfer under multiexciton excitation conditions for large metal domains compared to small ones. Theoretical modeling uncovers a competition between the kinetics of Auger recombination and charge separation. A crossover in the dominant process from Auger recombination to charge separation as the metal domain size increases allows for effective multiexciton dissociation and harvesting in large metal domain HNPs. This was also found to lead to relative improvement of their photocatalytic activity under nonlinear excitation conditions.

*J Chem Phys ; 146(22): 224111, 2017 Jun 14.*

**| MEDLINE**| ID: mdl-29166067

##### RESUMO

An ab initio Langevin dynamics approach is developed based on stochastic density functional theory (sDFT) within a new embedded saturated fragment formalism, applicable to covalently bonded systems. The forces on the nuclei generated by sDFT contain a random component natural to Langevin dynamics, and its standard deviation is used to estimate the friction term on each atom by satisfying the fluctuation-dissipation relation. The overall approach scales linearly with the system size even if the density matrix is not local and is thus applicable to ordered as well as disordered extended systems. We implement the approach for a series of silicon nanocrystals (NCs) of varying size with a diameter of up to 3 nm corresponding to Ne = 3000 electrons and generate a set of configurations that are distributed canonically at a fixed temperature, ranging from cryogenic to room temperature. We also analyze the structure properties of the NCs and discuss the reconstruction of the surface geometry.

*J Chem Theory Comput ; 13(10): 4997-5003, 2017 Oct 10.*

**| MEDLINE**| ID: mdl-28876912

##### RESUMO

Quasiparticle (QP) excitations are extremely important for understanding and predicting charge transfer and transport in molecules, nanostructures, and extended systems. Since density functional theory (DFT) within the Kohn-Sham (KS) formulation does not provide reliable QP energies, many-body perturbation techniques such as the GW approximation are essential. The main practical drawback of GW implementations is the high computational scaling with system size, prohibiting its use in extended, open boundary systems with many dozens of electrons or more. Recently, a stochastic formulation of GW (sGW) was presented (Phys. Rev. Lett. 2014, 113, 076402) with a near-linear-scaling complexity, illustrated for a series of silicon nanocrystals reaching systems of more than 3000 electrons. This advance provides a route for many-body calculations on very large systems that were impossible with previous approaches. While earlier we have shown the gentle scaling of sGW, its accuracy was not extensively demonstrated. Therefore, we show that this new sGW approach is very accurate by calculating the ionization energies of a group of sufficiently small molecules where a comparison to other GW codes is still possible. Using a set of 10 such molecules, we demonstrate that sGW provides reliable vertical ionization energies in close agreement with benchmark deterministic GW results (J. Chem. Theory Comput, 2015, 11, 5665), with mean (absolute) deviation of 0.05 and 0.09 eV. For completeness, we also provide a detailed review of the sGW theory and numerical implementation.

*J Chem Theory Comput ; 13(10): 4605-4610, 2017 Oct 10.*

**| MEDLINE**| ID: mdl-28914534

##### RESUMO

A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to second order Møller-Plesset perturbation theory (MP2) utilizing a multiple stochastic orbital approach. The introduction of multiple stochastic orbitals results in an O(NAO3) scaling for both the stochastic RI-ERIs and stochastic RI-MP2, NAO being the number of basis functions. For a range of water clusters we demonstrate that this method exhibits a small prefactor and observed scalings of O(Ne2.4) for total energies and O(Ne3.1) for forces (Ne being the number of correlated electrons), outperforming MP2 for clusters with as few as 21 water molecules.