Hybrid interfaces combining inorganic and organic materials underpin the operation of many optoelectronic and photocatalytic systems and allow for innovative approaches to photon up- and down-conversion. However, the mechanism of exchange-mediated energy transfer of spin-triplet excitons across these interfaces remains obscure, particularly when both the macroscopic donor and acceptor are composed of many separately interacting nanoscopic moieties. Here, we study the transfer of excitons from colloidal lead sulfide (PbS) nanocrystals to the spin-triplet state of rubrene molecules. By reducing the length of the carboxylic acid ligands on the nanocrystal surface from 18 to 4 carbon atoms, thinning the effective ligand shell from 13 to 6 Å, we are able to increase the characteristic transfer rate by an order of magnitude. However, we observe that the energy transfer rate asymptotes for shorter separation distances (≤10 Å) which we attribute to the reduced Dexter coupling brought on by the increased effective dielectric constant of these solid-state devices when the aliphatic ligands are short. This implies that the shortest ligands, which hinder long-term colloidal stability, offer little advantage for energy transfer. Indeed, we find that hexanoic acid ligands are already sufficient for near-unity transfer efficiency. Using nanocrystals with these optimal-length ligands in an improved solid-state device structure, we obtain an upconversion efficiency of (7 ± 1)% with excitation at λ = 808 nm.

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.

Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a newly developed stochastic technique, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which samples the exact wavefunction expanded in plane wave Slater determinants. Despite the introduction of a basis set incompleteness error, we obtain a finite-basis energy which is significantly, and variationally lower than any previously published work for the 54-electron HEG at rs = 0.5 a.u., in a Hilbert space of 10 108 Slater determinants. At this value of rs, as well as of 1.0 a.u., we remove the remaining basis set incompleteness error by extrapolation, yielding results comparable or better than state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in sizable periodic systems.

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green’s functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0.

Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete basis set (CBS) limit in methods utilising plane-wave wavefunction expansions. Simple analytic and numerical results from second-order Møller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis set truncation when constructing many-electron wavefunctions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wavefunction methods, from MP2 to coupled-cluster doubles theory (CCD) and the random-phase approximation plus second-order screened exchange (RPA+SOSEX). Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane wave basis and thereby allow application of these methods to more realistic physical problems. PACS numbers: 71.10.-w,71.10.Ca, 71.15.-m,71.15.Ap * Electronic address: js615@cam.ac.uk † Electronic address: asa10@cam.ac.uk © 0.30 © 0.28 © 0.26 © 0.24 © 0.22 © 0.20 © 0.18 © 0.16 MP2 CCD RPA+SOSEX i -FCIQMC M −1 Correlation energy (a.u.) 66 −1

Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the 'initiator' adaptation to Full Configuration Interaction Quantum Monte Carlo (i -FCIQMC), with a view to accelerating convergence. In particular we find that the fixed shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i -FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N = 14 over a range of densities 0.5 ≤ rs ≤ 5.0 a.u. A single-point extrapolation scheme is introduced to produce complete basis energies for 14, 38 and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed shift strategy to reduce the computational cost of many i -FCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

We investigate the accuracy of a number of wave function based methods at the heart of quantum chemistry for metallic systems. Using the Hartree-Fock wave function as a reference, perturbative (Møller-Plesset) and coupled cluster theories are used to study the uniform electron gas model. Our findings suggest that nonperturbative coupled cluster theories are acceptable for modeling electronic interactions in metals while perturbative coupled cluster theories are not. Using screened interactions, we propose a simple modification to the widely used coupled cluster singles and doubles plus perturbative triples method that lifts the divergent behavior and is shown to give very accurate correlation energies for the homogeneous electron gas.

The density matrix quantum Monte Carlo (DMQMC) method is used to sample exact-on-average N-body density matrices for uniform electron gas systems of up to 10 124 matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the k-space configuration pathintegral formalism disagree by up to ∼10% at certain reduced temperatures T=T F ≤ 0.5 and densities r s ≤ 1. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that the DMQMC method can calculate free energies directly and present exact free energies for T=T F ≥ 1 and r s ≤ 2. DOI: 10.1103/PhysRevLett.117.115701 The uniform electron gas is perhaps the most fundamental model in condensed matter physics. Core concepts such as Fermi liquid theory [1], quasiparticles and collective excitations [2,3], screening [4], the BCS theory of superconductivity [5], and Hohenberg-Kohn-Sham density-functional theory (DFT) [6,7], were all built on our understanding of the electron gas at low temperature. A growing interest in matter at extreme conditions, especially in the warm dense regime [8] found in inertial confinement fusion experiments [9], planetary interiors [10], and laser-irradiated solids [11], has sparked efforts to extend this understanding to much higher temperatures. Here, the electron gas also represents a useful model for hot lower density plasmas where electron-ion effects are less important [12]. This Letter concerns the properties of the electron gas at temperatures comparable to the Fermi energy.The quantitative successes of ground-state DFT rest on parametrizations of the correlation energy of the electron gas at zero temperature [13][14][15]. Errors of a few percent in the correlation functional have large effects on chemical bonding and phase diagrams, so these parametrizations are based on accurate quantum Monte Carlo (QMC) data [16]. Thermal DFT [17] treats thermal, quantum mechanical, many-body, and material effects explicitly and has emerged as a viable tool [18] for the study of warm dense matter, but requires as input a similarly accurate parametrization of the exchange-correlation free energy in the entire temperature-density plane [17,19,20]. A significant step towards providing these much needed data was recently made by Brown et al. [21] using the restricted path-integral Monte Carlo method, with local density parametrizations quickly following [22][23][24]. Soon after this, however, an alternative technique, configuration PIMC, was applied to the same problem and gave substantially different results [25,26].This Letter resolves the disagreement between the two p...