Unfavorable Scaling Research Articles

Fluorine-Doped Carbon Support Enables Superfast Oxygen Reduction Kinetics by Breaking the Scaling Relationship.

It is well-established that Pt-based catalysts suffer from the unfavorable linear scaling relationship (LSR) between *OOH and *OH (ΔG(*OOH)=ΔG(*OH)+3.2±0.2 eV) for the oxygen reduction reaction (ORR), resulting in a great challenge to significantly reduced ORR overpotentials. Herein, we propose a universal and feasible strategy of fluorine-doped carbon supports, which optimize interfacial microenvironment of Pt-based catalysts and thus significantly enhance their reactive kinetics. The introduction of C-F bonds not only weakens the *OH binding energy, but also stabilizes the *OOH intermediate, resulting in a break of LSR. Furthermore, fluorine-doped carbon constructs a local super-hydrophobic interface that facilitates the diffusion of H2O and the mass transfer of O2. Electrochemical tests show that the F-doped carbon-supported Pt catalysts exhibit over 2-fold higher mass activities than those without F modification. More importantly, those catalysts also demonstrate excellent stability in both rotating disk electrode (RDE) and membrane electrode assembly (MEA) tests. This study not only validates the feasibility of tuning the electrocatalytic microenvironment to improve mass transport and to break the scaling relationship, but also provides a universal catalyst design paradigm for other gas-involving electrocatalytic reactions.

Fluorine‐Doped Carbon Support Enables Superfast Oxygen Reduction Kinetics by Breaking the Scaling Relationship

AbstractIt is well‐established that Pt‐based catalysts suffer from the unfavorable linear scaling relationship (LSR) between *OOH and *OH (ΔG(*OOH)=ΔG(*OH)+3.2±0.2 eV) for the oxygen reduction reaction (ORR), resulting in a great challenge to significantly reduced ORR overpotentials. Herein, we propose a universal and feasible strategy of fluorine‐doped carbon supports, which optimize interfacial microenvironment of Pt‐based catalysts and thus significantly enhance their reactive kinetics. The introduction of C−F bonds not only weakens the *OH binding energy, but also stabilizes the *OOH intermediate, resulting in a break of LSR. Furthermore, fluorine‐doped carbon constructs a local super‐hydrophobic interface that facilitates the diffusion of H2O and the mass transfer of O2. Electrochemical tests show that the F‐doped carbon‐supported Pt catalysts exhibit over 2‐fold higher mass activities than those without F modification. More importantly, those catalysts also demonstrate excellent stability in both rotating disk electrode (RDE) and membrane electrode assembly (MEA) tests. This study not only validates the feasibility of tuning the electrocatalytic microenvironment to improve mass transport and to break the scaling relationship, but also provides a universal catalyst design paradigm for other gas‐involving electrocatalytic reactions.

Error Control and Automatic Detection of Reference Active Spaces in Many-Body Expanded Full Configuration Interaction.

We present a wide-reaching revamp of the generalized many-body expanded full configuration interaction (MBE-FCI) method. First, we outline how to automatize the selection of reference active spaces, whereby the inherent bias introduced through a manual identification is reduced, also within the context of traditional complete active space methods. Second, we allow for the use of compact orbital clusters as expansion objects, which works to circumvent the unfavorable scaling with the number of orbitals included in the space complementary to the reference orbitals. Finally, we present a new algorithm for ensuring that many-body expansions can be efficiently terminated while conservatively accounting for resulting errors. These developments are all tested on a variety of molecular systems and different orbital representations to illustrate the abilities of our algorithm to produce correlation energies within predetermined error bounds, significantly broadening the overall applicability of the MBE-FCI method.

Classical and quantum theory of fluctuations for many‐particle systems out of equilibrium

AbstractCorrelated classical and quantum many‐particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging both, conceptionally and with respect to computational resources. While for classical systems, in principle, exact simulations are possible via molecular dynamics, this is not the case for quantum systems. Alternatively, one can use many‐particle approaches such as hydrodynamics, kinetic theory, or nonequilibrium Green functions (NEGF). However, NEGF exhibit a very unfavorable cubic scaling of the CPU time with the number of time steps. An alternative is the G1–G2 scheme [N. Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)] which allows for NEGF simulations with time linear scaling, however, at the cost of large memory consumption. The reason is the need to store the two‐particle correlation function. This problem can be overcome for a number of approximations by reformulating the kinetic equations in terms of fluctuations – an approach that was developed, for classical systems, by Yu.L. Klimontovich [JETP 33, 982 (1957)]. Here, we present an overview of his ideas and extend them to quantum systems. In particular, we demonstrate that this quantum fluctuations approach can reproduce the nonequilibrium GW approximation [E. Schroedter et al., Cond. Matt. Phys. 25, 23401 (2022)] promising high accuracy at low computational cost which arises from an effective semiclassical stochastic sampling procedure. We also demonstrate how to extend the approach to the two‐time exchange‐correlation functions and the density response properties. [E. Schroedter et al., Phys. Rev. B 108, 205109 (2023)]. The results are equivalent to the Bethe–Salpeter equation for the two‐time exchange‐correlation function when the generalized Kadanoff‐Baym ansatz with Hartree‐Fock propagators is applied [E. Schroedter and M. Bonitz, phys. stat. sol. (b) 2024, 2300564].

Solving Intractable Chemical Problems by Tensor Decomposition.

Many complex chemical problems encoded in terms of physics-based models become computationally intractable for traditional numerical approaches due to their unfavorable scaling with increasing molecular size. Tensor decomposition techniques can overcome such challenges by decomposing unattainably large numerical representations of chemical problems into smaller, tractable ones. In the first two decades of this century, algorithms based on such tensor factorizations have become state-of-the-art methods in various branches of computational chemistry, ranging from molecular quantum dynamics to electronic structure theory and machine learning. Here, we consider the role that tensor decomposition schemes have played in expanding the scope of computational chemistry. We relate some of the most prominent methods to their common underlying tensor network formalisms, providing a unified perspective on leading tensor-based approaches in chemistry and materials science.

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra.

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT.

The unfavorable scaling (N5) of the conventional second-order Møller-Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.; Riplinger, C.; Valeev, E. F.; Neese, F. J. Chem. Phys. 2015, 143, 034108.] paved the way for DLPNO-based DH (DLPNO-DH) methods. In this work, we assess the accuracy of the DLPNO-DH approximation compared to conventional DHs on a large number of 7925 data points for thermochemistry and 239 data points for structural features, including main-group and transition-metal systems. It is shown that DLPNO-DH-DFT can be applied successfully to perform energy calculations and geometry optimizations for large molecules at a drastically reduced computational cost. Furthermore, PNO space extrapolation is shown to be applicable, similar to its DLPNO-CCSD(T) counterpart, to reduce the remaining error.

Honeybee comb-inspired stiffness gradient-amplified catapult for solid particle repellency.

Natural surfaces that repel foreign matter are ubiquitous and crucial for living organisms. Despite remarkable liquid repellency driven by surface energy in many organisms, repelling tiny solid particles from surfaces is rare. The main challenge lies in the unfavourable scaling of inertia versus adhesion in the microscale and the inability of solids to release surface energy. Here we report a previously unexplored solid repellency on a honeybee's comb: a catapult-like effect to immediately eject pollen after grooming dirty antennae for self-cleaning. Nanoindentation tests revealed the 38-μm-long comb features a stiffness gradient spanning nearly two orders of magnitude from ~25 MPa at the tip to ~645 MPa at the base. This significantly augments the elastic energy storage and accelerates the subsequent conversion into kinetic energy. The reinforcement in energy storage and conversion allows the particle's otherwise weak inertia to outweigh its adhesion, thereby suppressing the unfavourable scaling effect and realizing solid repellency that is impossible in conventional uniform designs. We capitalize on this to build an elastomeric bioinspired stiffness-gradient catapult and demonstrate its generality and practicality. Our findings advance the fundamental understanding of natural catapult phenomena with the potential to develop bioinspired stiffness-gradient materials, catapult-based actuators and robotic cleaners.

Correlations between the Electronic Structure and Energetics of the Catalytic Steps in Homogeneous Water Oxidation Catalysis.

The development of an efficient electrocatalyst for the water oxidation reaction is limited by unfavorable scaling relations between catalytic intermediates, resulting in an overpotential. In contrast to heterogeneous catalysts, the electronic structure of homogeneous catalysts can be modified to a great extent due to a tailored ligand design. However, studies utilizing the tunability of organic ligands have rarely been conducted in a systematic manner and, as of yet, have not produced catalytic paths that avoid the aforementioned unfavorable scaling relations. To investigate the influence of electron-donating groups (EDGs) or electron-withdrawing groups (EWGs) on elementary steps in electrochemical water oxidation catalysis, cis-[Ru(bpy)2(H2O)]2+ (bpy = 2,2'-bipyridine) was selected as the scaffold that was modified with methyl, methoxy, chloro, and trifluoromethyl groups. This catalyst can undergo several electron transfer (ET), proton transfer (PT), and proton-coupled electron transfer (PCET) steps that were all probed experimentally. In this systematic study, it was found that PCET steps are relatively insensitive with respect to the presence of EDGs or EWGs, while the decoupled ET and PT steps are more heavily affected. However, the influence of the substituents decreases with an increasing oxidation state of Ru due to a lack of d-electrons available at the Ru center for π-backbonding to the bipyridine ligand. Therefore, the RuV/VI redox couple appears to be relatively unaffected by the substituent. Nevertheless, the implementation of EWGs can shift all oxidation events to a very narrow potential window. Not only do our findings illustrate how electronic substituents affect the entire potential energy landscape of the catalytic water oxidation reaction, but they also show that the cis-[Ru(bpy)2(H2O)]2+ compounds follow different design rules and scaling relations, as has been reported for every other oxygen evolution catalyst thus far.

Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansätze for Hybrid Variational Quantum Computing.

One of the commonly used chemically inspired approaches in variational quantum computing is the unitary coupled-cluster (UCC) ansätze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansätze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of the UCC ansätze with better scaling. In this paper, we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansätze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. We also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.

Magnetic Interactions in a [Co(II)3Er(III)(OR)4] Model Cubane through Forefront Multiconfigurational Methods

Strong electron correlation effects are one of the major challenges in modern quantum chemistry. Polynuclear transition metal clusters are peculiar examples of systems featuring such forms of electron correlation. Multireference strategies, often based on but not limited to the concept of complete active space, are adopted to accurately account for strong electron correlation and to resolve their complex electronic structures. However, transition metal clusters already containing four magnetic centers with multiple unpaired electrons make conventional active space based strategies prohibitively expensive, due to their unfavorable scaling with the size of the active space. In this work, forefront techniques, such as density matrix renormalization group (DMRG), full configuration interaction quantum Monte Carlo (FCIQMC), and multiconfiguration pair-density functional theory (MCPDFT), are employed to overcome the computational limitation of conventional multireference approaches and to accurately investigate the magnetic interactions taking place in a [Co(II)3Er(III)(OR)4] (chemical formula [Co(II)3Er(III)(hmp)4(μ2-OAc)2(OH)3(H2O)], hmp = 2-(hydroxymethyl)-pyridine) model cubane water oxidation catalyst. Complete active spaces with up to 56 electrons in 56 orbitals have been constructed for the seven energetically lowest different spin states. Relative energies, local spin, and spin-spin correlation values are reported and provide crucial insights on the spin interactions for this model system, pivotal in the rationalization of the catalytic activity of this system in the water-splitting reaction. A ferromagnetic ground state is found with a very small, ∼50 cm-1, highest-to-lowest spin gap. Moreover, for the energetically lowest states, S = 3-6, the three Co(II) sites exhibit parallel aligned spins, and for the lower states, S = 0-2, two Co(II) sites retain strong parallel spin alignment.

Solving the Schrödinger Equation in the Configuration Space with Generative Machine Learning.

The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schrödinger equation for realistic molecules and materials but is characterized by an unfavorable scaling, which strongly limits its practical applicability. Effectively selecting only the configurations that actually contribute to the wave function is a fundamental step toward practical applications. We propose a machine learning approach that iteratively trains a generative model to preferentially generate the important configurations. By considering molecular applications it is shown that convergence to chemical accuracy can be achieved much more rapidly with respect to random sampling or the Monte Carlo configuration interaction method. This work paves the way to a broader use of generative models to solve the electronic structure problem.

Toward Accurate yet Effective Computations of Rotational Spectroscopy Parameters for Biomolecule Building Blocks.

The interplay of high-resolution rotational spectroscopy and quantum-chemical computations plays an invaluable role in the investigation of biomolecule building blocks in the gas phase. However, quantum-chemical methods suffer from unfavorable scaling with the dimension of the system under consideration. While a complete characterization of flexible systems requires an elaborate multi-step strategy, in this work, we demonstrate that the accuracy obtained by quantum-chemical composite approaches in the prediction of rotational spectroscopy parameters can be approached by a model based on density functional theory. Glycine and serine are employed to demonstrate that, despite its limited cost, such a model is able to predict rotational constants with an accuracy of 0.3% or better, thus paving the way toward the accurate characterization of larger flexible building blocks of biomolecules.

Challenges in Elucidating the Free Energy Scheme of the Laccase Catalyzed Reduction of Oxygen.

Artificial redox catalysts are typically limited by unfavorable scaling relations of reaction intermediates leading to a significant overpotential in multi-electron redox reactions such as for example the oxygen reduction reaction (ORR). The multicopper oxidase laccase is able to catalyze the ORR in nature. In particular the high-potential variants show a remarkably low overpotential for the ORR and apparently do not suffer from such unfavorable scaling relations. Although laccases are intensively studied, it is presently unknown why the overpotential for ORR is so low and a clear description regarding the thermodynamics of the catalytic cycle and the underlying design principles is lacking. In order to understand the laccase catalyzed ORR from an electrochemical perspective, elucidation of the free energy scheme would be of high value. This article reviews the energetics of the proposed laccase catalyzed ORR mechanisms based on experimental and computational studies. However, there are still remaining challenges to overcome to elucidate the free energy scheme of laccase. Obtaining thermodynamic data on intermediates is hard or even impossible with analytical techniques. On the other hand, several computational studies have been performed with significantly different parameters and conditions, thus making a direct comparison difficult. For these reasons, a consensus on a clear free energy scheme is still lacking. We anticipate that ultimately conquering these challenges will result in a better understanding of laccase catalyzed ORR and will allow for the design of low overpotential redox catalysts.

Gas-Phase Computational Spectroscopy: The Challenge of the Molecular Bricks of Life.

Gas-phase molecular spectroscopy is a natural playground for accurate quantum-chemical computations. However, the molecular bricks of life (e.g., DNA bases or amino acids) are challenging systems because of the unfavorable scaling of quantum-chemical models with the molecular size (active electrons) and/or the presence of large-amplitude internal motions. From the theoretical point of view, both aspects prevent the brute-force use of very accurate but very expensive state-of-the-art quantum-chemical methodologies. From the experimental point of view, both features lead to congested gas-phase spectra, whose assignment and interpretation are not at all straightforward. Based on these premises, this review focuses on the current status and perspectives of the fully a priori prediction of the spectral signatures of medium-sized molecules (containing up to two dozen atoms) in the gas phase with special reference to rotational and vibrational spectroscopies of some representative molecular bricks of life.

Quantum dynamics using path integral coarse-graining.

The vibrational spectra of condensed and gas-phase systems are influenced by thequantum-mechanical behavior of light nuclei. Full-dimensional simulations of approximate quantum dynamics are possible thanks to the imaginary time path-integral (PI) formulation of quantum statistical mechanics, albeit at a high computational cost which increases sharply with decreasing temperature. By leveraging advances in machine-learned coarse-graining, we develop a PI method with the reduced computational cost of a classical simulation. We also propose a simple temperature elevation scheme to significantly attenuate the artifacts of standard PI approaches as well as eliminate the unfavorable temperature scaling of the computational cost. We illustrate the approach, by calculating vibrational spectra using standard models of water molecules and bulk water, demonstrating significant computational savings and dramatically improved accuracy compared to more expensive reference approaches. Our simple, efficient, and accurate method has prospects for routine calculations of vibrational spectra for a wide range of molecular systems - with an explicit treatment of the quantum nature of nuclei.

Beyond Hard-Core Bosons in Transmon Arrays

Arrays of transmons have proven to be a viable medium for quantum information science and quantum simulations. Despite their widespread popularity as qubit arrays, there remains yet untapped potential beyond the two-level approximation or, equivalently, the hard-core boson model. With the higher excited levels included, coupled transmons naturally realize the attractive Bose-Hubbard model. The dynamics of the model has been difficult to study due to unfavorable scaling of the dimensionality of the Hilbert space with the system size. In this work, we present a framework for describing the effective unitary dynamics of highly-excited states of coupled transmons based on high-order degenerate perturbation theory. This allows us to describe various collective phenomena -- such as bosons stacked onto a single site behaving as a single particle, edge-localization, and effective longer-range interactions -- in a unified, compact and accurate manner. While our examples deal with one-dimensional chains of transmons for the sake of clarity, the theory can be readily applied to more general geometries.

Wind farm array cable layout optimisation for complex offshore sites—A decomposition based heuristic approach

As the number of turbines in offshore wind farms increases, so does the complexity of cable routing optimisation problems. Optimising the collector network is a crucial task for developers contributing between 15% and 30% of initial investment costs. For some algorithms, increasing the number of turbines leads to unfavourable scaling of the computational time and memory required to reach optimal solutions. Heuristics offer an alternative but are likely to incur increases in total costs relative to the optimal solution since heuristic searching cannot guarantee optimality. This study proposes a novel optimisation algorithm based on the ant-colony heuristic by introducing decomposition techniques informed by the problem formulation to improve the computational performance. The new algorithm can reach near-optimal solutions and requires little computational resource. Three algorithms are compared on a set of six case studies, including mixed-integer linear programming (MILP), classical ant-colony optimisation (ACO) algorithm, and the proposed ACO with decomposition, ACOsp. Optimal solutions were found using the MILP algorithm. ACO algorithm solutions cost 0.4–7.6% more than optimal solutions, whereas ACOsp solutions cost only 0.0–1.4% more than optimal solutions. The proposed ACOsp algorithm has shown to be a robust approach for large-scale cable layout optimisation problems (>100 turbines) without requiring high-performance computing facilities.

Plane-wave-based stochastic-deterministic density functional theory for extended systems

Traditional finite-temperature Kohn-Sham density functional theory (KSDFT) has an unfavorable scaling with respect to the electron number or at high temperatures. The evaluation of the ground-state density in KSDFT can be replaced by the Chebyshev trace (CT) method. In addition, the use of stochastic orbitals within the CT method leads to the stochastic density functional theory [Phys. Rev. Lett. 111, 106402 (2013)] (SDFT) and its improved theory, mixed stochastic-deterministic density functional theory [Phys. Rev. Lett. 125, 055002 (2020)] (MDFT). We have implemented the above four methods within the first-principles package ABACUS. All of the four methods are based on the plane-wave basis set with the use of norm-conserving pseudopotentials and the periodic boundary conditions with the use of $k$-point sampling in the Brillouin zone. By using the KSDFT calculation results as benchmarks, we systematically evaluate the accuracy and efficiency of the CT, SDFT, and MDFT methods via examining a series of physical properties, which include the electron density, the free energy, the atomic forces, stress, and density of states for a few condensed phase systems. The results suggest that our implementations of CT, SDFT, and MDFT not only reproduce the KSDFT results with a high accuracy, but also exhibit several advantages over the tradition KSDFT method. We expect these methods can be of great help in studying high-temperature and large-size extended systems such as warm dense matter and dense plasma.

Hierarchical autoregressive neural networks for statistical systems

It was recently proposed that neural networks could be used to approximate many-dimensional probability distributions that appear e.g. in lattice field theories or statistical mechanics. Subsequently they can be used as variational approximators to assess extensive properties of statistical systems, like free energy, and also as neural samplers used in Monte Carlo simulations. The practical application of this approach is unfortunately limited by its unfavourable scaling both of the numerical cost required for training, and the memory requirements with the system size. This is due to the fact that the original proposition involved a neural network of width which scaled with the total number of degrees of freedom, e.g. L2 in case of a two dimensional L×L lattice. In this work we propose a hierarchical association of physical degrees of freedom, for instance spins, to neurons which replaces it with the scaling with the linear extent L of the system. We demonstrate our approach on the two-dimensional Ising model by simulating lattices of various sizes up to 128×128 spins, with time benchmarks reaching lattices of size 512×512. We observe that our proposal improves the quality of neural network training, i.e. the approximated probability distribution is closer to the target that could be previously achieved. As a consequence, the variational free energy reaches a value closer to its theoretical expectation and, if applied in a Markov Chain Monte Carlo algorithm, the resulting autocorrelation time is smaller. Finally, the replacement of a single neural network by a hierarchy of smaller networks considerably reduces the memory requirements.