Neural quantum states (NQS) are a promising ansatz for solving many-body quantum problems due to their inherent expressiveness. Yet this expressiveness can only be harnessed efficiently for treating identical particles if the suitable physical knowledge is hardwired into the neural network itself. For electronic structure, NQS based on backflow determinants have been shown to be a powerful ansatz for capturing strong correlation. By contrast, the analogue for bosons, backflow permanents, is unpractical due to the steep cost of computing the matrix permanent and due to the lack of particle conservation in common bosonic problems. To circumvent these obstacles, we introduce a modal backflow (MBF) NQS design and demonstrate its efficacy by solving the anharmonic vibrational problem. To accommodate the demand of high accuracy in spectroscopic calculations, we implement a selected-configuration scheme for evaluating physical observables and gradients, replacing the standard stochastic approach based on Monte Carlo sampling. A vibrational self-consistent field calculation is conveniently carried out within the MBF network, which serves as a pretraining step to accelerate and stabilize the optimization. In applications to both artificial and ab initio Hamiltonians, we find that the MBF network is capable of delivering spectroscopically accurate zero-point energies and vibrational transitions in all anharmonic regimes.

Classical simulation of quantum computers is essential for designing and benchmarking quantum algorithms. Here we present phase2, a full-state-vector simulator optimised for sequences of many-qubit Pauli rotations on distributed CPU and GPU clusters. Exploiting the common-suffix structure of Pauli-rotation circuits, the implementation reduces inter-node communication and achieves two orders of magnitude speedup for grouped rotations. We demonstrate weak and strong scaling to 40 qubits across 512 NVIDIA H100 GPUs using 32 TB of distributed memory. Applying the simulator to Hamiltonian time evolution of ruthenium-ligand active spaces up to 40 qubits, we find that the empirical Trotter error lies more than two orders of magnitude below the rigorous analytic upper bound for every active space in which the fit converged (up to 32 qubits). Practical circuit depths and simulation costs are therefore substantially smaller than the conservative estimates suggest.

Neural quantum states (NQS) provide a flexible and highly expressive parametrization of wave functions for strongly correlated problems in quantum chemistry. Despite rapid advances in network architectures, the evaluation of electronic energies remains almost exclusively based on variational Monte Carlo (VMC). While VMC is effective for structured systems such as spin chains, its accuracy and efficiency for electronic Hamiltonians are hindered by sharply peaked distributions, stochastic gradient noise, and slow convergence with sample size. In this Letter, we assess the capability of NQS-VMC to efficiently capture correlation in electronic ground states by comparing it to a recently developed NQS-based selected configuration (NQS-SC) approach. We set up a systematic comparison of the ground-state optimizations obtained with NQS-VMC and NQS-SC for molecular systems dominated by either static or dynamical correlation. The comparison demonstrates a clear advantage of NQS-SC over NQS-VMC in both energy accuracy and wave function coefficients, particularly for statically correlated molecules. Moreover, NQS-SC exhibits robust systematic improvability, whereas NQS-VMC does not. These findings position NQS-SC as the new default approach over NQS-VMC for electronic structure calculations. We further observe that neither NQS-SC nor NQS-VMC can efficiently capture dynamical correlation, highlighting the need for future hybrid methods, such as multiconfigurational perturbation theories built on top of NQS solutions.

Quantum chemistry provides accurate and reliable methods to investigate reaction pathways of reactive molecular systems relevant to the interstellar medium. However, the exhaustive exploration of a reactive network is often a daunting task, resulting in unexplored reactive channels that affect kinetic outcomes and branching ratios. Here, an automated workflow for exploring reactive potential energy surfaces (PESs) is employed for the first time to study the oxirane (C _2 H _4 O) plus methylidyne ( ^• CH) reaction. The ultimate goal is to comprehensively map its PES and, subsequently, derive rate constants for the most important reaction channels. In addition to its astrochemical relevance, this reaction has been considered because it is a challenging test case, its network being very extended, with 60 exothermic bimolecular products lying below the reactant’s energy. Kinetic simulations indicate that the main product of the reaction is the HCO radical plus ethene (C _2 H _4 ), while formation of s-trans-propenal (acrolein) and 2H-oxetene is also possible, but to a lesser extent. Based on the present study and other references in the literature, we suggest that the slightly higher relative abundance of s-trans-propenal compared to methyl ketene in the interstellar medium is a gas-phase kinetic effect, the former being a more easily accessible product on the C _3 H _5 O ^• PES.

Theoretical predictions of photochemical processes are essential for interpreting and understanding spectral features. Reliable quantum dynamics calculations of vibronic systems require precise modeling of anharmonic effects in the potential energy surfaces and off-diagonal nonadiabatic coupling terms. In this work, we present the n-mode quantization of all vibronic Hamiltonian terms comprised of general high-dimensional model representations. We expand the existing vibrational DMRG formalism by applying the n-mode quantization to all potential energy surfaces entering the Hamiltonian as well as to all off-diagonal coupling terms. This is accompanied by the introduction of a novel matrix product state architecture employing tailored local site operators, which allow an effective encoding of the vibronic wave function in a tensor-train format. This results in a second-quantized framework for accurate vibronic calculations employing the density matrix renormalization group algorithm. We demonstrate the accuracy and reliability of this approach by calculating the excited-state quantum dynamics of maleimide. We analyze convergence and the choice of parameters of the underlying time-dependent density matrix renormalization group algorithm for the n-mode vibronic Hamiltonian, demonstrating that it enables accurate calculations of complex photochemical dynamics.

Automated explorations of chemical reaction networks (CRNs) guided by quantum chemistry (QC) calculations are undergoing rapid development that enables numerous applications. However, CRNs are accessible primarily through specialized quantum chemistry software without interface for cheminformatic exploitation of the generated data. Here, we present VizChemoton, an open-source module within the reaction exploration framework Software for Chemical Interaction Networks. VizChemoton enables visualization of CRNs and serves as an interface for cheminformatics applications based on conversion of molecular structures that accounts for radicals, zwitterions, and molecular complexes into string-based representations via RDKit mol objects. The conversion performance exceeded 90% of QC-generated compounds based on the evaluation of four CRNs constructed with density functional theory and extended tight-binding methods. We find that compounds absent from public structural databases correspond primarily to molecular complexes and unstable reaction intermediates. All essential QC and associated cheminformatics data are distributed in interoperable CSV and JSON formats to support downstream machine learning applications whereas reaction networks are readily visualized through a browser-based standalone HTML interface.

Chemistry and materials science are widely regarded as leading application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt to the evolving constraints of the emerging quantum hardware in order to accomplish any advantage for the computational chemistry practice. At the same time, the continuous advancement of classical wavefunction-theory methods narrows the window for a broad quantum advantage. Here, we explore potential benefits of quantum computation from the broader perspective of utility-scale applications. We argue that quantum algorithms need not only enable accurate calculations for a few challenging, that is, strongly correlated, molecular structures, which might be hard to describe with traditional methods. Instead, they must also support the practical integration of quantum-accelerated computations into high-throughput pipelines for routine calculations on arbitrary molecules, ultimately delivering a tangible value to society.

Accurately solving the Schrödinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding direct reference to a wave function. In particular, we develop a rigorous approximation framework that enables precise frequency estimation from a finite number of signal samples. Our analysis builds on results involving prolate spheroidal wave functions and yields error bounds that reveal a sharp accuracy transition governed by the observation time and spectral density of the signal. These results are very general and thus carry far. As one important example application, we consider the quantum computation for molecular systems. By combining our spectral method with a quantum subroutine for signal generation, we define quantum prolate diagonalization (QPD)—a hybrid classical-quantum algorithm. QPD simultaneously estimates ground- and excited-state energies within chemical accuracy at the Heisenberg limit. An analysis of different input states demonstrates the robustness of the method, showing that high precision can be retained even under imperfect state preparation.

Computational chemistry has become an indispensable tool for generating data and insights, pervading all branches of experimental chemistry. Its most central concept is the potential energy hypersurface, key to all chemistry and materials science, as it assigns an energy to a molecular structure, the necessary ingredient for reaction mechanism elucidation and reaction rate calculation. Density functional theory (DFT) has been the most important method in practice for obtaining such energies, which is mirrored in the use of high-performance computing hardware. In the last two decades, a new class of surrogate potential energy functions has been evolving with remarkable properties: quantum accuracy combined with force-field speed. Until very recently, their application was hampered by the fact that they needed to be trained on truly large system-specific data sets, generated before a computational chemistry study could be started (in sharp contrast to DFT, which, as a first-principles method, works out of the box, but at a far higher price of computational cost). Very recently, this roadblock has been overcome by so-called foundation machine learning interatomic potentials, which are poised to completely change the way we do computational chemistry, likely prompting us to abandon DFT as the prime method of choice for this purpose in less than a decade.

Quantum computation with Trotter product formulae is straightforward and requires little overhead in terms of logical qubits. The choice of the orbital basis significantly affects circuit depth, with localised orbitals yielding lowest circuit depths. However, literature results point to large Trotter errors incurred by localised orbitals. Here, we therefore investigate the effect of orbital transformations on Trotter error. We consider three strategies to reduce Trotter error by orbital transformation: (i) The a priori selection of an orbital basis that produces low Trotter error. (ii) The derivation of an orbital basis that produces a ground state energy free of Trotter error (as we observed that the Trotter error is a continuous function in the Givens-rotation parameter for index-based Trotter series-orderings, from which continuity of this error upon orbital transformation can be deduced). (iii) Application of propagators that change the computational basis between Trotter steps. Our numerical results show that reliably reducing Trotter error by orbital transformations is challenging. General recipes to produce low Trotter errors cannot be easily derived, despite analytical expressions which suggest ways to decrease Trotter error. Importantly, we found that localised orbital bases do not produce large Trotter errors in molecular calculations, which is an important result for efficient QPE set-ups.

Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite accuracy. In this perspective, we argue that this mismatch points to the need for a new mathematical program: a rigorous constructive theory for effective descriptions to identify essential degrees of freedom. We propose an observation-centered point of view in which signals are treated as the primary objects of analysis, while wave functions and Hamiltonians are reconstructed as auxiliary structures to rationalize the observed data. Our starting point is a signal-based spectral equation that reformulates frequency analysis as an operator problem. We connect this point of view to results on prolate Fourier theory, spectral analysis with finite observation time, and short-time quantum simulation. We highlight a sharp accuracy transition relating necessary observation time to the effective spectral density of a signal for achieving accurate resolution. The resulting framework integrates approximation as a fundamental necessity more directly into the foundations of quantum mechanics and points toward a broader program for the effective description of complex quantum systems, such as those found in the molecular sciences.

The construction of a grid-based potential energy surface (PES) can be prohibitively expensive as the number of grid points grows exponentially with molecular size. Molecular symmetry can reduce this cost by eliminating symmetry-equivalent points. We present an algebraic symmetry-based grid reduction method, ASyBGR, that is capable of handling non-Abelian and higher-order cyclic symmetry groups. Non-coordinate-mixing operations are encoded into a vector space bit-string, where Gaussian elimination and closure can identify all symmetry-valid sign change patterns and the coordinate axes whose grids can be halved about the origin. In the presence of degenerate subspaces, we optimize the coordinate basis to maximize reduction. The method was validated by comparing vibrational configuration interaction (VCI) energies calculated using the full and symmetry-reduced fourth-order HDMR PESs for molecules spanning a broad range of symmetries. The number of grid points required to construct the PES was reduced by as much as 81%, while VCI energies deviated below 1 1/cm for all test cases on average. The relative root-mean-square deviation (RRMSD) between the full and symmetry-reduced potential energy and dipole moment surfaces were at most on the order of 10^-3 and 10^-2, respectively.

For more than half a century SF6 has been the predominant gas insulation medium. Due to its high global warming potential it is now being replaced with mixtures of natural origin gases (NOG), namely N-2, O-2 and CO2, either alone or in combination with the strongly electron-attaching gas C4F7N. Information about the thermodynamic properties and reaction rates of these mixtures and their decomposition products is essential for predicting their electrical insulation performance. However, currently available reaction rate data is lacking. In this work, we employ an automated chemical network exploration tool to derive an internally consistent reaction mechanism for these mixtures. The mechanism captures the kinetically significant reactions between neutral species and includes the reaction rates for the decomposition of C4F7N, its reactions with its decomposition products, and their reactions with NOG. Our reaction mechanism contains all fluorinated by-products experimentally observed after arcing tests and reveals that the barrier-free decomposition rates of C4F7N reported in the literature appear to be significantly overestimated based on comparison with available experimental decomposition temperatures. We carry out chemical kinetics calculations to investigate the decomposition by-products of two different C4F7N, CO2, O-2 mixtures under different conditions and show that the presence of C4F7N promotes CO generation, whereas higher O-2 concentrations suppress it. We report the volumetric heat capacity (rho Cp) based on chemical kinetics rather than chemical equilibrium, as done in existing literature, and show that the peaks in rho Cp that are associated with high thermal interruption performance shift to lower temperatures when the gas is cooled. The full reaction mechanism file is provided to support and enable further studies. In the future, we aim to use this reaction mechanism to model the stepped leader dielectric breakdown process in these mixtures.

In this paper, an efficient implementation of the renormalized internally-contracted multreference coupled cluster with singles and doubles (RIC-MRCCSD) into the ORCA quantum chemistry program suite is reported. To this end, Evangelista's Wick d equation generator was combined with ORCA's native AGE code generator in order to implement the many-body residuals required for the RIC-MRCCSD method. Substantial efficiency gains are realized by deriving a spin-free formulation instead of the previously reported spin-orbital version developed by some of us. Since AGE produces parallelized code, the resulting implementation can directly be run in parallel with substantial speedups when executed on multiple cores. In terms of runtime, the cost of RIC-MRCCSD is shown to be between single-reference RHF-CCSD and UHF-CCSD, even when active space spaces as large as CAS(14,14) are considered. This achievement is largely due to the fact that no reduced density matrices (RDM) or cumulants higher than three-body enter the formalism. The scalability of the method to large systems is furthermore demonstrated by computing the ground-state of a vitamin B12 model comprised of an active space of CAS(12, 12) and 809 orbitals. In terms of accuracy, RIC-MRCCSD is carefully compared to second- and approximate fourth-order n-electron valence state perturbation theories (NEVPT2, NEVPT4(SD)), to the multireference zeroth-order coupled-electron pair approximation (CEPA(0)), as well as to the IC-MRCCSD from Kohn. In contrast to RIC-MRCCSD, the IC-MRCCSD equations are entirely derived by AGE using the conventional projection-based approach, which, however, leads to much higher algorithmic complexity than the former as well as the necessity to calculate up to the five-body RDMs. Remaining challenges such as the variation of the results with the flow, a free parameter that enters the RIC-MRCCSD theory, are discussed.

Free energy calculations are at the heart of physics-based analyses of biochemical processes. They allow us to quantify molecular recognition mechanisms, which determine a wide range of biological phenomena, from how cells send and receive signals to how pharmaceutical compounds can be used to treat diseases. Quantitative and predictive free energy calculations require computational models that accurately capture both the varied and intricate electronic interactions between molecules as well as the entropic contributions from the motions of these molecules and their aqueous environment. However, accurate quantum-mechanical energies and forces can be obtained only for small atomistic models and not for large biomacromolecules. Here, we demonstrate how to consistently link accurate quantum-mechanical data obtained for substructures to the overall potential energy of biomolecular complexes using machine learning in an integrated algorithm. We do so using a two-fold quantum embedding strategy where the innermost quantum cores are treated at a very high level of accuracy. We demonstrate the viability of this approach for the molecular recognition of a ruthenium-based anticancer drug by its protein target by applying traditional quantum chemical methods. As such methods scale unfavorably with system size, we analyze the requirements for quantum computers to provide highly accurate energies that affect the resulting free energies. Once the requirements are met, our computational pipeline, FreeQuantum, is able to make efficient use of the quantum-computed energies, thereby enabling quantum computing-enhanced modeling of biochemical processes. This approach combines the exponential speedups of quantum computers for simulating interacting electrons with modern classical simulation techniques that incorporate machine learning to model large molecules.

Artificial intelligence (AI) and machine learning (ML) are rapidly reshaping the landscape of computational chemistry, offering new opportunities for accelerating catalyst discovery and deepening our understanding of chemical reactivity. This perspective highlights emerging methodologies ranging from machine learning potentials and reinforcement learning to generative AI and large language models that are poised to transform computational catalysis. We discuss challenges in developing robust molecular representations for transition-metal complexes, bridging mechanistic understanding with AI-driven predictions, and constructing reliable data sets that capture both successful and failed reactivity outcomes. By drawing on the authors' practical experience across computational, experimental, and AI-driven domains, we emphasize the importance of integrating chemical intuition and methodological expertise with data-driven approaches while remaining open to serendipitous discoveries enabled by automation and self-driving laboratories. Ultimately, the future of computational catalysis lies in balancing human intuition with algorithmic power, leveraging AI not as a replacement but as an accelerator of chemical insight, mechanistic understanding, and catalyst design.

Machine learning interatomic potentials (MLIPs) have become emerging tools in molecular modeling and computational chemistry. By learning high-dimensional potential energy surfaces from quantum chemical data, MLIPs enable accurate and efficient predictions of structural, thermodynamic, and dynamical properties. However, such models have limitations in predictions of electronic properties and the effects of static electron correlation due to their lack of electronic structure information. This work presents OrbGNN, an electronic structure graph architecture analogous to molecular graph and MLIP frameworks, where pair-orbital interactions constitute the graph representation, while orbital entanglement encodes the connectivity between them. By embedding information derived from orbital correlation metrics directly into the graph topology, OrbGNN provides a compact representation of a molecule s orbital landscape and electron correlation patterns. Analysis of the behavior of the feature space in an orbital graph are shown to demonstrate model robustness. The model is evaluated for the dissociation of nitrogen and for a larger dataset of diatomic molecules. Finally, the OrbGNN model is applied to a set of octahedral iron(II) complexes to predict spin-state energy gaps.

Radical S-adenosyl methionine enzymes catalyze a diverse repertoire of post-translational modifications in protein and peptide substrates. Among these, an exceptional and mechanistically obscure example is the installation of α-keto-β-amino acid residues by formal excision of a tyrosine-derived tyramine unit. The responsible spliceases are key maturases in a widespread family of natural products termed spliceotides that comprise potent protease inhibitors, with the installed β-residues being crucial for bioactivity. Here, we established the in vitro activity of the model splicease PcpXY to interrogate the mechanism of non-canonical protein splicing. Identification of shunt and coproducts, deuterium labeling studies, and density functional theory energy calculations of hypothesized intermediates support a mechanism involving hydrogen abstraction at tyrosine Cα as the initial site of peptide radical formation and release of 4-hydroxybenzaldehyde as the tyrosine-derived coproduct. The data illuminate key features of this unprecedented radical-mediated biotransformation yielding ketoamide pharmacophores that are also present in peptidomimetic therapeutics.

Recent developments in computational chemistry facilitate the automated quantum chemical exploration of chemical reaction networks for the in-silico prediction of synthesis pathways, yield, and selectivity. However, the underlying quantum chemical energy calculations require vast computational resources, limiting these explorations severely in practice. Machine learning potentials (MLPs) offer a solution to increase computational efficiency, while retaining the accuracy of reliable first-principles data used for their training. Unfortunately, MLPs will be limited in their generalization ability within chemical (reaction) space, if the underlying training data are not representative for a given application. Within the framework of automated reaction network exploration, where new reactants or reagents composed of any elements from the periodic table can be introduced, this lack of generalizability will be the rule rather than the exception. Here, we therefore evaluate the benefits of the lifelong MLP concept in this context. Lifelong MLPs push their adaptability by efficient continual learning of additional data. We propose an improved learning algorithm for lifelong adaptive data selection yielding efficient integration of new data while previous expertise is preserved. In this way, we can reach chemical accuracy in reaction search trials.

We present an implementation of a perturbative triples correction for the coupled cluster ansatz including single and double excitations based on the transcorrelated Hamiltonian. Transcorrelation introduces explicit electron correlation in the electronic Hamiltonian through similarity transformation with a correlation factor. Due to this transformation, the transcorrelated Hamiltonian includes up to three-body couplings and becomes non-Hermitian. Since the conventional coupled cluster equations are solved by projection, it is well suited to harbor non-Hermitian Hamiltonians. The arising three-body operator, however, creates a huge memory bottleneck and increases the runtime scaling of the coupled cluster equations. As it has been shown that the three-body operator can be approximated, by expressing the Hamiltonian in the normal-ordered form, we investigate this approximation for the perturbative triples correction. Results are compared with a code-generation based transcorrelated coupled cluster implementation up to quadruple excitations.