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Reduced density matrix functional theory (RDMFT) and coupled cluster theory restricted to paired double excitations (pCCD) are emerging as efficient methodologies for accounting for the so-called non-dynamic electronic correlation effects. Up to now, molecular calculations have been performed with real-valued orbitals. However, before extending the applicability of these methodologies to extended systems, where Bloch states are employed, the subtleties of working with complex-valued orbitals and the consequences of imposing time-reversal symmetry must be carefully addressed. In this work, we describe the theoretical and practical implications of adopting time-reversal symmetry in RDMFT and pCCD when allowing for complex-valued orbital coefficients. The theoretical considerations primarily affect the optimization algorithms, while the practical implications raise fundamental questions about the stability of solutions. Specifically, we find that complex solutions lower the energy when non-dynamic electronic correlation effects are pronounced. We present numerical examples to illustrate and discuss these instabilities and possible problems introduced by N-representability violations.

To establish general principles of optimal control of active matter, we study the elementary problem of moving an active particle by a trap with minimum work input. We show analytically that (open-loop) optimal protocols are not affected by activity, but work fluctuations are always increased. For closed-loop protocols, which rely on initial measurements of the self-propulsion, the average work has a minimum for a finite persistence time. Using these insights, we derive an optimal cyclic active information engine, which is found to have a higher precision and information efficiency when operated with a run-and-tumble particle than for an active Ornstein-Uhlenbeck particle and, we argue, than for any other type of active particle., Comment: 7 pages, 3 figures

To expand the QUEST database of highly-accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly-accurate excitation energies. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both $G_0W_0$ and ev$GW$ quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models amongst those with respective $\mathcal{O}(N^5)$ and $\mathcal{O}(N^6)$ scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, $\omega$B97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-$\omega$B88PP86 and SOS-$\omega$PBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/ev$GW$ calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts., Comment: 27 pages, 10 figures (Supporting Information available)

Electronic resonances are metastable states that can decay by electron loss. They are ubiquitous across various fields of science, such as chemistry, physics, and biology. However, current theoretical and computational models for resonances cannot yet rival the level of accuracy achieved by bound-state methodologies. Here, we generalize selected configuration interaction (SCI) to treat resonances using the complex absorbing potential (CAP) technique. By modifying the selection procedure and the extrapolation protocol of standard SCI, the resulting CAP-SCI method yields resonance positions and widths of full configuration interaction quality. Initial results for the shape resonances of \ce{N2-} and \ce{CO-} reveal the important effect of high-order correlation, which shifts the values obtained with CAP-augmented equation-of-motion coupled-cluster with singles and doubles by more than \SI{0.1}{\eV}. The present CAP-SCI approach represents a cornerstone in the development of highly-accurate methodologies for resonances., Comment: 10 pages, 2 figures (supporting information available)

Medical image segmentation is a critical task in healthcare applications, and U-Nets have demonstrated promising results. This work delves into the understudied aspect of receptive field (RF) size and its impact on the U-Net and Attention U-Net architectures. This work explores several critical elements including the relationship between RF size, characteristics of the region of interest, and model performance, as well as the balance between RF size and computational costs for U-Net and Attention U-Net methods for different datasets. This work also proposes a mathematical notation for representing the theoretical receptive field (TRF) of a given layer in a network and proposes two new metrics - effective receptive field (ERF) rate and the Object rate to quantify the fraction of significantly contributing pixels within the ERF against the TRF area and assessing the relative size of the segmentation object compared to the TRF size respectively. The results demonstrate that there exists an optimal TRF size that successfully strikes a balance between capturing a wider global context and maintaining computational efficiency, thereby optimizing model performance. Interestingly, a distinct correlation is observed between the data complexity and the required TRF size; segmentation based solely on contrast achieved peak performance even with smaller TRF sizes, whereas more complex segmentation tasks necessitated larger TRFs. Attention U-Net models consistently outperformed their U-Net counterparts, highlighting the value of attention mechanisms regardless of TRF size. These novel insights present an invaluable resource for developing more efficient U-Net-based architectures for medical imaging and pave the way for future exploration. A tool is also developed that calculates the TRF for a U-Net (and Attention U-Net) model, and also suggest an appropriate TRF size for a given model and dataset.

ipie is a Python-based auxiliary-field quantum Monte Carlo (AFQMC) package that has undergone substantial improvements since its initial release [J. Chem. Theory Comput., 2022, 19(1): 109-121]. This paper outlines the improved modularity and new capabilities implemented in ipie. We highlight the ease of incorporating different trial and walker types and the seamless integration of ipie with external libraries. We enable distributed Hamiltonian simulations, allowing for multi-GPU simulations of large systems. This development enabled us to compute the interaction energy of a benzene dimer with 84 electrons and 1512 orbitals, which otherwise would not have fit on a single GPU. We also support GPU-accelerated multi-slater determinant trial wavefunctions [arXiv:2406.08314] to enable efficient and highly accurate simulations of large-scale systems. This allows for near-exact ground state energies of multi-reference clusters, [Cu$_2$O$_2$]$^{2+}$ and [Fe$_2$S$_2$(SCH$_3$)]$^{2-}$. We also describe implementations of free projection AFQMC, finite temperature AFQMC, AFQMC for electron-phonon systems, and automatic differentiation in AFQMC for calculating physical properties. These advancements position ipie as a leading platform for AFQMC research in quantum chemistry, facilitating more complex and ambitious computational method development and their applications., Comment: 17 pages, 13 figures

Hedin's equations provide an elegant route to compute the exact one-body Green's function (or propagator) via the self-consistent iteration of a set of non-linear equations. Its first-order approximation, known as $GW$, corresponds to a resummation of ring diagrams and has shown to be extremely successful in physics and chemistry. Systematic improvement is possible, although challenging, via the introduction of vertex corrections. Considering anomalous propagators and an external pairing potential, we derive a new self-consistent set of closed equations equivalent to the famous Hedin equations but having as a first-order approximation the particle-particle (pp) $T$-matrix approximation where one performs a resummation of the ladder diagrams. This pp version of Hedin's equations offers a way to go systematically beyond the $T$-matrix approximation by accounting for low-order pp vertex corrections., Comment: 12 pages, 5 figures (Supp. Mat. available)

Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects., Comment: 18 pages, 10 figures (supporting information available)

In the realm of photochemistry, the significance of double excitations (also known as doubly-excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [http://dx.doi.org/10.1021/acs.jctc.8b01205; Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly-excited states where the transitions almost exclusively involve doubly-excited configurations and (ii) 19 "partial" doubly-excited states which exhibit a more balanced character between singly- and doubly-excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition ($\%T_1$) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies., Comment: 25 pages, 3 figures (Supporting Information available)

Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems that interact with each other by reciprocal or nonreciprocal, instantaneous or time-delayed interactions. We present a simple approach that combines Markov state models with directed information-theoretical measures for causal inference that can accurately infer the underlying interactions from noisy time series of the dynamical system states alone. Remarkably, this is possible despite the built-in simplification of a Markov assumption and the choice of a very coarse discretization at the level of probability estimation. Our test systems are an Ising chain with nonreciprocal coupling imposed by local driving of a single spin, and a system of delay-coupled linear stochastic processes. Stepping away from physical systems, the approach infers cause-effect relationships, or more generally, the direction of mutual or one-way influence. The presented method is agnostic to the number of interacting entities and details of the dynamics, so that it is widely applicable to problems in various fields., Comment: 11 pages, 4 figure; plus Supplemental Material (3 pages, 1 supplemental figure)

The cumulant expansion of the Green's function is a computationally efficient beyond-$GW$ approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous $GW$ approximation of many-body perturbation theory, \textit{ab initio} cumulant expansions performed on top of $GW$ ($GW$+C) have demonstrated the capability to handle multi-particle processes by incorporating higher-order correlation effects or vertex corrections, yielding better agreements between experiment and theory for satellite structures. While widely employed in condensed matter physics, very few applications of $GW$+C have been published on molecular systems. Here, we assess the performance of this scheme on a series of 10-electron molecular systems (\ce{Ne}, \ce{HF}, \ce{H2O}, \ce{NH3}, and \ce{CH4}) where full configuration interaction estimates of the outer-valence quasiparticle and satellite energies are available., Comment: 11 pages, 3 figures (supporting information available)

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shake-up transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials of full configuration interaction (FCI) quality computed in small molecular systems. Following the protocol developed for the quest database [https://doi.org/10.1002/wcms.1517, V\'eril et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions ($GW$, GF2, and $T$-matrix) for ionization potentials are also analyzed. Their limitations in correctly modeling satellite transitions are discussed., Comment: 22 pages, 3 figures (supporting information available)

Recently, a new distributed implementation of the full configuration interaction (FCI) method has been reported [Gao et al. J. Chem Theory Comput. 2024, 20, 1185]. Thanks to a hybrid parallelization scheme, the authors were able to compute the exact energy of propane (\ce{C3H8}) in the minimal basis STO-3G. This formidable task involves handling an active space of 26 electrons in 23 orbitals or a Hilbert space of \SI{1.3d12} determinants. This is, by far, the largest FCI calculation reported to date. Here, we illustrate how, from a general point of view, selected configuration interaction (SCI) can achieve microhartree accuracy at a fraction of the computational and memory cost, via a sparse exploration of the FCI space. The present SCI calculations are performed with the \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) algorithm, as implemented in a determinant-driven way in the \textsc{quantum package} software. The present study reinforces the common wisdom that among the exponentially large number of determinants in the FCI space, only a tiny fraction of them significantly contribute to the energy. More importantly, it demonstrates the feasibility of achieving comparable accuracy using more reasonable and sustainable computational resources, hence reducing the ever-growing carbon footprint of computational chemistry., Comment: 5 pages, 2 figures (supporting information available)

The high-luminosity upgrade of the LHC brings unprecedented requirements for real-time and precision bunch-by-bunch online luminosity measurement and beam-induced background monitoring. A key component of the CMS Beam Radiation, Instrumentation and Luminosity system is a stand-alone luminometer, the Fast Beam Condition Monitor (FBCM), which is fully independent from the CMS central trigger and data acquisition services and able to operate at all times with a triggerless readout. FBCM utilizes a dedicated front-end application-specific integrated circuit (ASIC) to amplify the signals from CO$_2$-cooled silicon-pad sensors with a timing resolution of a few nanoseconds, which enables the measurement of the beam-induced background. FBCM uses a modular design with two half-disks of twelve modules at each end of CMS, with four service modules placed close to the outer edge to reduce radiation-induced aging. The electronics system design adapts several components from the CMS Tracker for power, control and read-out functionalities. The dedicated FBCM23 ASIC contains six channels and adjustable shaping time to optimize the noise with regards to sensor leakage current. Each ASIC channel outputs a single binary high-speed asynchronous signal carrying time-of-arrival and time-over-threshold information. The chip output signal is digitized, encoded and sent via a radiation-hard gigabit transceiver and an optical link to the back-end electronics for analysis. This paper reports on the updated design of the FBCM detector and the ongoing testing program., Comment: 16th Topical Seminar on Innovative Particle and Radiation Detectors (IPRD23) 2023 Sept 25-29 Siena, Italy

To expand the existing QUEST database of accurate vertical transition energies [\href{https://doi.org/10.1002/wcms.1517}{V\'eril et al.~\textit{WIREs Comput.~Mol.~Sci.} \textbf{2021}, \textit{11}, e1517}], we have modeled more than 100 electronic excited states of different natures (local, charge-transfer, Rydberg, singlet, and triplet) in a dozen of mono- and di-substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled-cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high-level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM-MP2, STEOM-CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a)$^\star$, and CCSDT-3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT-3 can provide consistent estimates, whereas among less expensive methods SCS-CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and \emph{vice versa}. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds., Comment: 14 pages, 4 figures

We reexamine $\Delta$CCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain where the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here is to evaluate the effectiveness of $\Delta$CCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the $\Delta$CCSD and EOM-CCSD methods, for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly-excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our dataset, consisting of 276 excited states stemming from the \textsc{quest} database [V\'eril \textit{et al.}, \textit{WIREs Comput. Mol. Sci.} \textbf{2021}, 11, e1517], provides a significant base to draw general conclusions concerning the accuracy of $\Delta$CCSD. Except for the doubly-excited states, we found that $\Delta$CCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of \SI{0.10}{\eV} and \SI{0.07}{\eV}) is less pronounced than that obtained for singly-excited states of closed-shell systems (MAEs of \SI{0.15}{\eV} and \SI{0.08}{\eV}). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for $\Delta$CCSD., Comment: 16 pages, 6 figures

This work merges two different types of many-electron ensembles, namely the Theophilou-Gross-Oliveira-Kohn ensembles of ground and neutrally-excited states, and the more recent $N$-centered ensembles of neutral and charged ground states. On that basis, an in-principle exact and general, so-called extended $N$-centered, ensemble density-functional theory of charged and neutral electronic excitations is derived. We revisit in this context the concept of density-functional derivative discontinuity for neutral excitations, without ever invoking nor using the asymptotic behavior of the ensemble electronic density. The present mathematical construction fully relies on the weight dependence of the ensemble Hartree-exchange-correlation density-functional energy, which makes the theory applicable to lattice models and opens new perspectives for the description of gaps in mesoscopic systems., Comment: 21 pages, second revision

Due to the infinite summation of bubble diagrams, the $GW$ approximation of Green's function perturbation theory has proven particularly effective in the weak correlation regime, where this family of Feynman diagrams is important. However, the performance of $GW$ in multireference molecular systems, characterized by strong electron correlation, remains relatively unexplored. In the present study, we investigate the ability of $GW$ to handle closed-shell multireference systems in their singlet ground state by examining four paradigmatic scenarios. Firstly, we analyze a prototypical example of a chemical reaction involving strong correlation: the potential energy curve of \ce{BeH2} during the insertion of a beryllium atom into a hydrogen molecule. Secondly, we compute the electron detachment and attachment energies of a set of molecules that exhibit a variable degree of multireference character at their respective equilibrium geometries: \ce{LiF}, \ce{BeO}, \ce{BN}, \ce{C2}, \ce{B2}, and \ce{O3}. Thirdly, we consider a \ce{H6} cluster with a triangular arrangement, which features a notable degree of spin frustration. Finally, the dissociation curve of the \ce{HF} molecule is studied as an example of single bond breaking. These investigations highlight a nuanced perspective on the performance of $GW$ for strong correlation, depending on the level of self-consistency, the choice of initial guess, and the presence of spin-symmetry breaking at the Hartree-Fock level., Comment: 11 pages, 4 figures

Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their precision relies heavily on extrapolation procedures to produce a final estimate of the exact result. Using the structure of the exact electronic energy landscape, we provide a rationale for the common linear extrapolation of the variational energy as a function of the second-order perturbative correction. In particular, we demonstrate that the energy gap and the coupling between the so-called internal and external spaces are the key factors determining the rate at which the linear regime is reached. Starting from first principles, we also derive a new non-linear extrapolation formula that improves the post-processing of data generated from SCI methods and can be applied to both ground- and excited-state energies., Comment: 9 pages, 8 figures

We provide an in-depth examination of the $GW$ approximation of Green's function many-body perturbation theory by detailing both its theoretical and practical aspects in the realm of quantum chemistry. First, the quasiparticle context is introduced before delving into the derivation of Hedin's equations. From these, we explain how to derive the well-known $GW$ approximation of the self-energy. In a second time, we meticulously explain each step involved in a $GW$ calculation and what type of physical quantities can be computed. To illustrate its versatility, we consider two contrasting systems: the water molecule, a weakly correlated system, and the carbon dimer, a strongly correlated system. Each stage of the process is thoroughly detailed and explained alongside numerical results and illustrative plots. We hope that the contribution will facilitate the dissemination and democratization of Green's function-based formalisms within the computational and theoretical quantum chemistry community., Comment: 14 pages, 7 figures (supporting information available)

Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here we investigate experimentally and theoretically the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimal. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms., Comment: 16 pages with 10 figures, accepted for publication in PRX

Molecules that violate Hund's rule and exhibit an inverted gap between the lowest singlet $S_1$ and triplet $T_1$ excited states have attracted considerable attention due to their potential applications in optoelectronics. Amongst these molecules, the triangular-shaped heptazine, and its derivatives, have been in the limelight. However, conflicting reports have arisen regarding the relative energies of $S_1$ and $T_1$. Here, we employ highly accurate levels of theory, such as CC3, to not only resolve the debate concerning the sign but also quantify the magnitude of the $S_1$-$T_1$ gap. We also determine the 0-0 energies to evaluate the significance of the vertical approximation. In addition, we compute reference $S_1$-$T_1$ gaps for a series of 10 related molecules. This enables us to benchmark lower-order methods for future applications on larger systems within the same family of compounds. This contribution can serve as a reliable foundation for the design of triangular-shaped molecules with enhanced photophysical properties., Comment: 8 pages, 3 figures, supporting information available

Learning from Demonstration (LfD) is a framework that allows lay users to easily program robots. However, the efficiency of robot learning and the robot's ability to generalize to task variations hinges upon the quality and quantity of the provided demonstrations. Our objective is to guide human teachers to furnish more effective demonstrations, thus facilitating efficient robot learning. To achieve this, we propose to use a measure of uncertainty, namely task-related information entropy, as a criterion for suggesting informative demonstration examples to human teachers to improve their teaching skills. In a conducted experiment (N=24), an augmented reality (AR)-based guidance system was employed to train novice users to produce additional demonstrations from areas with the highest entropy within the workspace. These novice users were trained for a few trials to teach the robot a generalizable task using a limited number of demonstrations. Subsequently, the users' performance after training was assessed first on the same task (retention) and then on a novel task (transfer) without guidance. The results indicated a substantial improvement in robot learning efficiency from the teacher's demonstrations, with an improvement of up to 198% observed on the novel task. Furthermore, the proposed approach was compared to a state-of-the-art heuristic rule and found to improve robot learning efficiency by 210% compared to the heuristic rule.

To enrich and enhance the diversity of the \textsc{quest} database of highly-accurate excitation energies [\href{https://doi.org/10.1002/wcms.1517}{V\'eril \textit{et al.}, \textit{WIREs Comput.~Mol.~Sci.}~\textbf{11}, e1517 (2021)}], we report vertical transition energies in transition metal compounds. Eleven diatomic molecules with singlet or doublet ground state containing a fourth-row transition metal (\ce{CuCl}, \ce{CuF}, \ce{CuH}, \ce{ScF}, \ce{ScH}, \ce{ScO}, \ce{ScS}, \ce{TiN}, \ce{ZnH}, \ce{ZnO}, and \ce{ZnS}) are considered and the corresponding excitation energies are computed using high-level coupled-cluster (CC) methods, namely CC3, CCSDT, CC4, and CCSDTQ, as well as multiconfigurational methods such as CASPT2 and NEVPT2. In some cases, to provide more comprehensive benchmark data, we also provide full configuration interaction estimates computed with the \textit{"Configuration Interaction using a Perturbative Selection made Iteratively"} (CIPSI) method. Based on these calculations, theoretical best estimates of the transition energies are established in both the aug-cc-pVDZ and aug-cc-pVTZ basis sets. This allows us to accurately assess the performance of CC and multiconfigurational methods for this specific set of challenging transitions. Furthermore, comparisons with experimental data and previous theoretical results are also reported., Comment: 17 pages, 3 figures

We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known $GW$ self-energy, as well as the particle-particle and electron-hole $T$-matrix self-energies. Each of these can be easily computed via the eigenvalues and eigenvectors of a different random-phase approximation (RPA) linear eigenvalue problem that completely defines their corresponding response function. For illustrative and comparative purposes, we report the principal ionization potentials of a set of small molecules computed at each level of theory. The performance of these schemes on strongly correlated systems (\ce{B2} and \ce{C2}) is also discussed., Comment: 13 pages, 6 figures

We introduce \textsc{qcmath}, a user-friendly quantum chemistry software tailored for electronic structure calculations, implemented using the Wolfram Mathematica language and available at \url{https://github.com/LCPQ/qcmath}. This software, designed with accessibility in mind, takes advantage of the symbolic capabilities intrinsic to Mathematica. Its primary goal is to provide a supportive environment for newcomers to the field of quantum chemistry, enabling them to easily conceptualize, develop, and test their own ideas. The functionalities of \textsc{qcmath} encompass a broad spectrum of methods, catering to both ground- and excited-state calculations. We provide a comprehensive overview of these capabilities, complemented by essential theoretical insights. To facilitate ease of use, we offer an exhaustive blueprint of the software's architecture. Furthermore, we provide users with comprehensive guides, addressing both the operational aspects and the more intricate programming facets of \textsc{qcmath}., Comment: 9 pages

Hierarchy configuration interaction (hCI) has been recently introduced as an alternative configuration interaction (CI) route combining excitation degree and seniority number, which showed to efficiently recover both dynamic and static correlations for closed-shell molecular systems [\href{https://doi.org/10.1021/acs.jpclett.2c00730}{\textit{J.~Phys.~Chem.~Lett.}~\textbf{2022}, \textit{13}, 4342}]. Here, we generalize hCI for an arbitrary reference determinant, allowing calculations for radicals and for excited states in a state-specific way. We gauge this route against excitation-based CI (eCI) and seniority-based CI (sCI) by evaluating how different ground-state properties of radicals converge to the full CI limit. We find that hCI outperforms or matches eCI, whereas sCI is far less accurate, in line with previous observations for closed-shell molecules. Employing the second-order Epstein-Nesbet (EN2) perturbation theory as a correction significantly accelerates the convergence of hCI and eCI. We further explore various hCI and sCI models to calculate excitation energies of closed- and open-shell systems. Our results underline that both the choice of the reference determinant and the set of orbitals drive the fine balance between correlation of ground and excited states. State-specific hCI2 and higher order models perform similarly to their eCI counterparts, whereas lower orders of hCI deliver poor results, unless supplemented by the EN2 correction, which substantially improves their accuracy. In turn, sCI1 produces decent excitation energies for radicals, encouraging the development of related seniority-based coupled-cluster methods., Comment: 18 pages, 5 figures

Due to their high energy density (2600 Wh/kg), low cost, and low environmental impact, lithium-sulfur batteries are considered a promising alternative to lithium-ion batteries. However, their commercial viability remains a formidable scientific challenge mainly because of the sluggish reaction kinetics at the cathode and the so-called "shuttling effect" of soluble polysulfides, which results in capacity decay and a shortened lifespan. Herein, molecular imprinting with Li$_2$S$_8$ as a target molecule in combination with a two-dimensional material, MXene, is proposed to overcome these issues. Molecularly imprinted polymer-coated nitrogen-doped Ti-based MXene was successfully synthesized and demonstrated to exhibit an appealing electrochemical performance, namely a high specific capacity of 1095 mAh/g at 0.1 C and an extended cycling stability (300 mAh/g at 1.0 C after 300 cycles). X-ray photoelectron spectroscopy was applied to elucidate the underlying mechanisms and proved that Li$_2$S$_8$-imprinted polymer polyacrylamide serves as a polysulfide trap through strong chemical affinity towards the long-chain lithium polysulfides, while N-doped Ti-based MXene promotes the redox kinetics by accelerating the conversion of lithium polysulfides. This distinct interfacial strategy is expected to result in more effective and stable Li-S batteries.

We present an equation generator algorithm that utilizes second-quantized operators in normal order with respect to a correlated or non-correlated reference and the corresponding Wick theorem. The algorithm proposed here, written with \textsc{mathematica}, enables the generation of non-redundant strings of second-quantized operators that, after classification, are directly assigned to intermediate quantities used to construct the coupled-cluster (CC) effective Hamiltonian. We demonstrate the capabilities of the algorithm by computing the CC amplitude equations and various blocks of the equation-of-motion CC effective Hamiltonian. A comprehensive description of this four-step algorithm is provided alongside concrete examples., Comment: 15 pages, 2 figures

In recent years, Green's function methods have garnered considerable interest due to their ability to target both charged and neutral excitations. Among them, the well-established $GW$ approximation provides accurate ionization potentials and electron affinities and can be extended to neutral excitations using the Bethe-Salpeter equation (BSE) formalism. Here, we investigate the connections between various Green's function methods and evaluate their performance for charged and neutral excitations. Comparisons with other widely-known second-order wave function methods are also reported. Additionally, we calculate the singlet-triplet gap of cycl[3,3,3]azine, a model molecular emitter for thermally activated delayed fluorescence, which has the particularity of having an inverted gap thanks to a substantial contribution from the double excitations. We demonstrate that, within the $GW$ approximation, a second-order BSE kernel with dynamical correction is required to predict this distinctive characteristic., Comment: 18 pages, 1 figure

We develop a framework for the stochastic thermodynamics of a probe coupled to a fluctuating medium with spatio-temporal correlations, described by a scalar field. For a Brownian particle dragged by a harmonic trap through a fluctuating Gaussian field, we show that near criticality (where the field displays long-range spatial correlations) the spatially-resolved average heat flux develops a dipolar structure, where heat is absorbed in front and dissipated behind the dragged particle. Moreover, a perturbative calculation reveals that the dissipated power displays three distinct dynamical regimes depending on the drag velocity., Comment: 7 pages, 3 figures (main) + 21 pages, 1 figure (SM)

We study time-reversal symmetry breaking in non-Hermitian fluctuating field theories with conserved dynamics, comprising the mesoscopic descriptions of a wide range of nonequilibrium phenomena. They exhibit continuous parity-time ($\mathcal{PT}$) symmetry breaking phase transitions to dynamical phases. For two concrete transition scenarios, exclusive to non-Hermitian dynamics, namely oscillatory instabilities and critical exceptional points, a low-noise expansion exposes a pre-transitional surge of the mesoscale (informatic) entropy production rate, inside the static phases. Its scaling in the susceptibility contrasts conventional critical points (such as second-order phase transitions), where the susceptibility also diverges, but the entropy production generally remains finite. The difference can be attributed to active fluctuations in the wavelengths that become unstable. For critical exceptional points, we identify the coupling of eigenmodes as the entropy-generating mechanism, causing a drastic noise amplification in the Goldstone mode., Comment: 21 pages, 2 figures. Two companion articles are available at arXiv:2303.16701 and arXiv:2305.00744

We study the nonreciprocal Cahn-Hilliard model with thermal noise as a prototypical example of a generic class of non-Hermitian stochastic field theories, analyzed in two companion papers [Suchanek, Kroy, Loos, ArXiv:2303.16701 (2023); Suchanek, Kroy, Loos, ArXiv:2305.05633 (2023)]. Due to the nonreciprocal coupling between two field components, the model is inherently out of equilibrium and can be regarded as an active field theory. Beyond the conventional homogeneous and static-demixed phases, it exhibits a traveling-wave phase, which can be entered via either an oscillatory instability or a critical exceptional point. By means of a Fourier decomposition of the entropy production rate, we quantify the associated scale-resolved time-reversal symmetry breaking, in all phases and across the transitions, in the low-noise regime. Our perturbative calculation reveals its dependence on the strength of the nonreciprocal coupling. Surging entropy production near the static-dynamic transitions can be attributed to entropy-generating fluctuations in the longest wavelength mode and heralds the emerging traveling wave. Its translational dynamics can be mapped on the dissipative ballistic motion of an active (quasi)particle., Comment: 17 pages, 6 Figures. Two companion articles are available at arXiv:2303.16701 and arXiv:2305.05633