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Quantum computers can accurately compute ground state energies using phase estimation, but this requires a guiding state which has significant overlap with the true ground state.For large molecules and extended materials, it becomes difficult to find guiding states with good ground state overlap for growing molecule sizes. Additionally, the required number of qubits and quantum gates may become prohibitively large. One approach for dealing with these challenges is to use a quantum embedding method, which allows a reduction to one or multiple smaller quantum cores embedded in a larger quantum region. In such situations it is unclear how the embedding method affects the hardness of constructing good guiding states. In this work, we therefore investigate the preparation of guiding states in the context of quantum embedding methods. We extend previous work on quantum impurity problems, a framework in which we can rigorously analyze the embedding of a subset of orbitals. While there exist results for optimal active orbital space selection in terms of energy minimization, we rigorously demonstrate how the same principles can be used to define selected orbital spaces for state preparation in terms of the overlap with the ground state. Moreover, we perform numerical studies of molecular systems relevant to biochemistry, one field in which quantum embedding methods are required due to the large size of biomacromolecules such as proteins and nucleic acids. We investigate two different embedding strategies which can exhibit qualitatively different orbital entanglement. In all cases we demonstrate that the easy-to-obtain mean-field state will have a sufficiently high overlap with the target state to perform quantum phase estimation., Comment: 25 pages, 9 figures

While silicon solar cells dominate global photovoltaic energy production, their continued improvement is hindered by the single junction limit. One potential solution is to use molecular singlet exciton fission to generate two electrons from each absorbed high-energy photon. We demonstrate that the long-standing challenge of coupling molecular excited states to silicon solar cells can be overcome using sequential charge transfer. Combining zinc phthalocyanine, aluminum oxide, and a shallow junction crystalline silicon microwire solar cell, the peak charge generation efficiency per photon absorbed in tetracene is (138 +- 6)%, comfortably surpassing the quantum efficiency limit for conventional silicon solar cells and establishing a new, scalable approach to low cost, high efficiency photovoltaics., Comment: 34 pages, 14 figures

Modern graphics processing units (GPUs) provide an unprecedented level of computing power. In this study, we present a high-performance, multi-GPU implementation of the analytical nuclear gradient for Kohn-Sham time-dependent density functional theory (TDDFT), employing the Tamm-Dancoff approximation (TDA) and Gaussian-type atomic orbitals as basis functions. We discuss GPU-efficient algorithms for the derivatives of electron repulsion integrals and exchange-correlation functionals within the range-separated scheme. As an illustrative example, we calculated the TDA-TDDFT gradient of the S1 state of a full-scale green fluorescent protein with explicit water solvent molecules, totaling 4353 atoms, at the wB97X/def2-SVP level of theory. Our algorithm demonstrates favorable parallel efficiencies on a high-speed distributed system equipped with 256 Nvidia A100 GPUs, achieving >70% with up to 64 GPUs and 31% with 256 GPUs, effectively leveraging the capabilities of modern high-performance computing systems., Comment: 13 pages, 9 figures

X-ray photoelectron spectroscopy (XPS) measures core-electron binding energies (CEBEs) to reveal element-specific insights into chemical environment and bonding. Accurate theoretical CEBE prediction aids XPS interpretation but requires proper modeling of orbital relaxation and electron correlation upon core-ionization. This work systematically investigates basis set selection for extrapolation to the complete basis set (CBS) limit of CEBEs from $\Delta$MP2 and $\Delta$CC energies across 94 K-edges in diverse organic molecules. We demonstrate that an alternative composite scheme using $\Delta$MP2 in a large basis corrected by $\Delta$CC-$\Delta$MP2 difference in a small basis can quantitatively recover optimally extrapolated $\Delta$CC CEBEs within 0.02 eV. Unlike $\Delta$CC, MP2 calculations do not suffer from convergence issues and are computationally cheaper, and, thus, the composite $\Delta$MP2/$\Delta$CC scheme balances accuracy and cost, overcoming limitations of solely using either method. We conclude by providing a comprehensive analysis of the choice of small and large basis sets for the composite schemes and provide practical recommendations for highly accurate (within 0.10-0.15 eV MAE) ab initio prediction of XPS spectra.

The widespread application of III-V colloidal quantum dots (QDs) as non-toxic, highly tunable emitters is stymied by their high density of trap states. Here, we utilize density functional theory (DFT) to investigate trap state formation in a diverse set of realistically passivated core-only InP and GaP QDs. Through orbital localization techniques, we deconvolute the dense manifold of trap states to allow for detailed assignment of surface defects. We find that the three-coordinate species dominate trapping in III-V QDs and identify features in the geometry and charge environment of trap centers capable of deepening, or sometimes passivating, traps. Furthermore, we observe stark differences in surface reconstruction between InP and GaP, where the more labile InP reconstructs to passivate three-coordinate indium at the cost of distortion elsewhere. These results offer explanations for experimentally observed trapping behavior and suggest new avenues for controlling trap states in III-V QDs., Comment: 14 pages, 5 figures

Given the growing significance of 2D materials in various optoelectronic applications, it is imperative to have simulation tools that can accurately and efficiently describe electron correlation effects in these systems. Here, we show that the recently developed bootstrap embedding (BE) accurately predicts electron correlation energies and structural properties for 2D systems. Without explicit dependence on the reciprocal space sum ($k$-points) in the correlation calculation, BE can typically recover $\sim$99.5% of the total electron correlation energy in 2D semi-metal, insulator and semiconductors. We demonstrate that BE can predict lattice constants and bulk moduli for 2D systems with high precision. Furthermore, we highlight the capability of BE to treat electron correlation in twisted bilayer graphene superlattices with large unit cells containing hundreds of carbon atoms. We find that as the twist angle decreases towards the magic angle, the correlation energy initially decreases in magnitude, followed by a subsequent increase. We conclude that BE is a promising electronic structure method for future applications to 2D materials.

Bootstrap embedding (BE) is a recently developed electronic structure method that has shown great success at treating electron correlation in molecules. Here, we extend BE to treat surfaces and solids where the wave function is represented in periodic boundary conditions using reciprocal space sums (i.e. $k$-point sampling). The major benefit of this approach is that the resulting fragment Hamiltonians carry no explicit dependence on the reciprocal space sums, allowing one to apply traditional non-periodic electronic structure codes to the fragments even though the entire system requires careful consideration of periodic boundary conditions. Using coupled cluster singles and doubles (CCSD) as an example method to solve the fragment Hamiltonians, we present minimal basis set CCSD-in-HF results on 1D conducting polymers. We show that periodic BE-CCSD can typically recover $\sim$99.9% of the electron correlation energy. We further demonstrate that periodic BE-CCSD is feasible even for complex donor-acceptor polymers of interest to organic solar cells - despite the fact that the monomers are sufficiently large that even a $\Gamma-$point periodic CCSD calculation is prohibitive. We conclude that BE is a promising new tool for applying molecular electronic structure tools to solids and interfaces.

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match -- at little additional computational cost -- full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching., Comment: 58+24 pages, 8+9 figures

Despite the long history of spectroscopic studies of the C$_2$ molecule, fundamental questions about its chemical bonding are still being hotly debated. The complex electronic structure of C$_2$ is a consequence of its dense manifold of near-degenerate, low-lying electronic states. A global multi-state diabatic model is proposed here to disentangle the numerous configuration interactions within four symmetry manifolds of C$_2$ ($^{1}\Pi_g$, $^{3}\Pi_g$, $^{1}\Sigma_u^+$, and $^{3}\Sigma_u^+$). The key concept of our model is the existence of two "valence-hole" configurations, $2\sigma_g^22\sigma_u^11\pi_{u}^33\sigma_g^2$ for $^{1,3}\Pi_g$ states and $2\sigma_g^22\sigma_u^11\pi_{u}^43\sigma_g^1$ for $^{1,3}\Sigma_u^+$ states that derive from $3\sigma_g\leftarrow2\sigma_u$ electron promotion. The lowest-energy state from each of the four C$_2$ symmetry species is dominated by this type of valence-hole configuration at its equilibrium internuclear separation. As a result of their large binding energy (nominal bond order of 3) and correlation with the 2s$^2$2p$^2$+2s2p$^3$ separated-atom configurations, the presence of these valence-hole configurations has a profound impact on the $global$ electronic structure and unimolecular dynamics of C$_2$.

In quantum chemistry, obtaining a system's mean-field solution and incorporating electron correlation in a post Hartree-Fock (HF) manner comprise one of the standard protocols for ground-state calculations. In principle, this scheme can also describe excited states but is not widely used at present, primarily due to the difficulty of locating the mean-field excited states. With recent developments in excited-state orbital relaxation, self-consistent excited-state solutions can now be located routinely at various levels of theory. In this work, we explore the possibility of correcting HF excited states using M{\o}ller-Plesset perturbation theory to the second order. Among various PT2 variants, we find that the restricted open-shell MP2 (ROMP2) gives excitation energies comparable to the best density functional theory results, delivering $\sim 0.2$ eV mean unsigned error over a wide range of single-configuration state function excitations, at only non-iterative $O(N^5)$ computational scaling., Comment: 11 pages w/o references, 1 figure, 6 tables

We investigate the effect of lattice disorder and local correlation effects in finite and periodic silicene structures caused by carbon doping using first-principles calculations. For both finite and periodic silicene structures, the electronic properties carbon-doped monolayers are dramatically changed by controlling the doping sites in the structures, which is related to the amount of disorder introduced in the lattice and electron-electron correlation effects. By changing the position of the carbon dopants, we found that a Mott-Anderson transition is achieved. Moreover, the band gap is determined by the level of lattice disorder and electronic correlation effects. Finally, these structures are ferromagnetic even under disorder which has potential applications in Si-based nanoelectronics, such as field-effect transistors (FETs)., Comment: 10 pages, 6 figures

The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding methods mainly focus on systems composed of weakly correlated parts and are insufficient when division across chemical bonds is unavoidable. Recently, density matrix embedding theory (DMET) and other methods based on the Schmidt decomposition have emerged as a fresh approach to this problem. Despite their success on model systems, these methods can prove difficult for realistic systems because they rely on either a rigid, non-overlapping partition of the system or a specification of some special sites (i.e. `edge' and `center' sites), neither of which is well-defined in general for real molecules. In this work, we present a new Schmidt decomposition-based embedding scheme called Incremental Embedding that allows the combination of arbitrary overlapping fragments without the knowledge of edge sites. This method forms a convergent hierarchy in the sense that higher accuracy can be obtained by using fragments involving more sites. The computational scaling for the first few levels is lower than that of most correlated wave function methods. We present results for several small molecules in atom-centered Gaussian basis sets and demonstrate that Incremental Embedding converges quickly with fragment size and recovers most static correlation in small basis sets even when truncated at the second lowest level., Comment: 13 pages, 6 figures

In the framework of DFT, the lowest triplet excited state, T$_1$, can be evaluated using multiple formulations, the most straightforward of which are UDFT and TDDFT. Assuming the exact XC functional is applied, UDFT and TDDFT provide identical energies for T$_1$ ($E_{\rm T}$), which is also a constraint that we require our XC functionals to obey. However, this condition is not satisfied by most of the popular XC functionals, leading to inaccurate predictions of low-lying, spectroscopically and photochemically important excited states, such as T$_1$ and S$_1$. Inspired by the optimal tuning strategy for frontier orbital energies [Stein, Kronik, and Baer, {\it J. Am. Chem. Soc.} {\bf 2009}, 131, 2818], we proposed a novel and non-empirical prescription of constructing an XC functional in which the agreement between UDFT and TDDFT in $E_{\rm T}$ is strictly enforced. Referred to as "triplet tuning", our procedure allows us to formulate the XC functional on a case-by-case basis using the molecular structure as the exclusive input, without fitting to any experimental data. The first triplet tuned XC functional, TT-$\omega$PBEh, is formulated as a long-range-corrected hybrid of PBE and HF functionals [Rohrdanz, Martins, and Herbert, {\it J. Chem. Phys.} {\bf 2009}, 130, 054112] and tested on four sets of large organic molecules. Compared to existing functionals, TT-$\omega$PBEh manages to provide more accurate predictions for key spectroscopic and photochemical observables, including but not limited to $E_{\rm T}$, $E_{\rm S}$, $\Delta E_{\rm ST}$, and $I$, as it adjusts the effective electron-hole interactions to arrive at the correct excitation energies. This promising triplet tuning scheme can be applied to a broad range of systems that were notorious in DFT for being extremely challenging.

High-performance materials rely on small reorganization energies to facilitate both charge separation and charge transport. Here, we performed DFT calculations to predict small reorganization energies of rectangular silicene nanoclusters with hydrogen-passivated edges denoted by H-SiNC. We observe that across all geometries, H-SiNCs feature large electron affinities and highly stabilized anionic states, indicating their potential as n-type materials. Our findings suggest that fine-tuning the size of H-SiNCs along the zigzag and armchair directions may permit the design of novel n-type electronic materials and spinctronics devices that incorporate both high electron affinities and very low internal reorganization energies., Comment: 25 pages, 6 figures

Semiconductor nanocrystals are a promising class of materials for a variety of novel optoelectronic devices, since many of their properties, such as the electronic gap and conductivity, can be controlled. Much of this control is achieved via the organic ligand shell, through control of the size of the nanocrystal and the distance to other objects. We here simulate ligand-coated CdSe nanocrystals using atomistic molecular dynamics, allowing for the resolution of novel structural details about the ligand shell. We show that the ligands on the surface can lie flat to form a highly anisotropic 'wet hair' layer as opposed to the 'spiky ball' appearance typically considered. We discuss how this can give rise to a dot-to-dot packing distance of one ligand length since the thickness of the ligand shell is reduced to approximately one-half of the ligand length for the system sizes considered here; these distances imply that energy and charge transfer rates between dots and nearby objects will be enhanced due to the thinner than expected ligand shell. Our model predicts a non-linear scaling of ligand shell thickness as the ligands transition from 'spiky' to 'wet hair'. We verify this scaling using TEM on a PbS nanoarray, confirming that this theory gives a qualitatively correct picture of the ligand shell thickness of colloidal quantum dots., Comment: 17 Pages, 9 Figures

The spin-boson model is a simplified Hamiltonian often used to study non-adiabatic dynamics in large condensed phase systems, even though it has not been solved in a fully analytic fashion. Herein, we present an exact analytic expression for the dynamics of the spin-boson model in the infinitely slow bath limit and generalize it to approximate dynamics for faster baths. We achieve the latter by developing a hybrid approach that combines the exact slow-bath result with the popular NIBA method to generate a memory kernel that is formally exact to second order in the diabatic coupling but also contains higher-order contributions approximated from the second order term alone. This kernel has the same computational complexity as NIBA, but is found to yield dramatically superior dynamics in regimes where NIBA breaks down---such as systems with large diabatic coupling or energy bias. This indicates that this hybrid approach could be used to cheaply incorporate higher order effects into second order methods, and could potentially be generalized to develop alternate kernel resummation schemes.

The mean-field solutions of electronic excited states are much less accessible than ground state (e.g.\ Hartree-Fock) solutions. Energy-based optimization methods for excited states, like $\Delta$-scf, tend to fall into the lowest solution consistent with a given symmetry -- a problem known as "variational collapse". In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, $\sigma$-scf, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find \emph{all} excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states -- ground or excited -- are treated on an equal footing. Third, it provides an alternate approach to locate $\Delta$-scf solutions that are otherwise inaccessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF)., Comment: This paper has been withdrawn by the author due to a crucial sign error in equation 13

We present a novel method that appropriately handles both dynamical and static electron correlation in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order M{\o}ller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter., Comment: 5 pages, 3 figures, 2 tables

We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in neighbor interactions [J. Chen et al., Phys. Rev. Lett. 109, 036403 (2012)], we find that free probability continues to provide accurate approximations for systems with constant interactions on two- and three-dimensional lattices or with next-nearest-neighbor interactions, with the results being visually indistinguishable from the numerically exact solution. For systems with disordered interactions, we observe a small but visible degradation of the approximation. To explain this behavior of the free approximation, we develop and apply an asymptotic error analysis scheme to show that the approximation is accurate to the eighth moment in the density of states for systems with constant interactions, but is only accurate to sixth order for systems with disordered interactions. The error analysis also allows us to calculate asymptotic corrections to the density of states, allowing for systematically improvable approximations as well as insight into the sources of error without requiring a direct comparison to an exact solution.

Quantum--Mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the Frozen Density Embedding formulation of subsystem Density-Functional Theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against Coupled-Cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tents of {\AA}ngstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules., Comment: Accepted for publication by The Journal of Chemical Physics on Jan. 11th, 2013

We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of these rules. We provide a combinatorial interpretation for partial freeness as the presence of closed paths in Hilbert space defined by particular joint moments. We also discuss how asymptotic moment expansions provide an error term on the density of states. We present MATLAB code for the calculation of moments and free cumulants of arbitrary random matrices., Comment: 8 pages, 2 figures

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with the perturbation theory and isotropic entanglement theory., Comment: 5 pages, 3 figures, submitted to Phys. Rev. Lett

We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability.

A local approximation for dynamic polarizability leads to a nonlocal functional for the long-range dispersion interaction energy via an imaginary-frequency integral. We analyze several local polarizability approximations and argue that the form underlying the construction of our recent van der Waals functional [O. A. Vydrov and T. Van Voorhis, Phys. Rev. Lett. 103, 063004 (2009)] is particularly well physically justified. Using this improved formula, we compute dynamic dipole polarizabilities and van der Waals C_6 coefficients for a set of atoms and molecules. Good agreement with the benchmark values is obtained in most cases.