Density functional theory (DFT) offers an exceptional balance between accuracy and efficiency, but practical density functional approximations face an unavoidable trade-off among simplicity, accuracy, and transferability. A systematic protocol is therefore needed to develop functionals that are reliably most accurate within a chosen application domain. Here we present such a protocol by combining constraint enforcement, flexible functional forms, and modern optimization. Applying this strategy to the range-separated hybrid (RSH) meta-GGA framework, we obtain the carefully optimized and appropriately constrained hybrid (COACH) functional. Across broad molecular benchmarks, COACH improves both accuracy and transferability relative to leading RSH meta-GGAs, including 97M-V, while retaining the computational practicality of its rung. Finally, our analysis of the remaining trade-offs and saturation behavior suggests that further systematic progress will likely require the incorporation of genuinely nonlocal information.

Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-ζ (QZ) size are required to adequately converge Kohn-Sham density functional theory (DFT) calculations toward the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. In this work, we develop and test a threshold-based natural atomic orbital (NAO) scheme in which ϵ-NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. This enables compression of the AO basis that is optimal for a given threshold, 10-ϵ, by discarding NAOs with occupation numbers below that threshold. Extensive pilot test calculations using the Hartree-Fock functional and taking the converged density matrix as input suggest that a threshold of 10-5 can yield a compression factor (ratio of AO to compressed ϵ-NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold 10-7, while the compression factor is typically between 2 and 2.5.

Zero-field (ZF) nuclear magnetic resonance (NMR) spectroscopy probes scalar J-couplings between nuclei while dispensing with large homogeneous magnetic fields, enabling low-cost and geometrically flexible detection, including through conductive enclosures. Despite these advantages, its broader use for chemical analysis has been limited by sensitivity and by the difficulty of predicting the dense spectral multiplets that arise at zero field. Here we demonstrate natural-abundance (1.1

Second-order Moller-Plesset perturbation theory (MP2) provides accurate correlation energies for periodic systems but suffers from finite-size errors (FSEs) that have inverse volume scaling due to the Coulomb kernel singularity in reciprocal space. This error scaling limits the routine applicability of MP2 to real materials, requiring prohibitively dense k-point meshes for convergence toward the thermodynamic limit (TDL). We introduce MP2 singularity subtraction (MP2SS), a systematic approach that applies the singularity subtraction strategy to reduce MP2 FSEs. The method employs auxiliary functions and fitting procedures that consider both the singularities present at the origin in reciprocal space and also the discontinuities in the MP2 structure factor that arise from finite k-point sampling. We present three possible MP2SS configurations (Gaussian, exponential, and tuned) which use different combinations of decay functions and demonstrate their performance for gapped systems. All MP2SS configurations consistently achieve millihartree accuracy for correlation energies at coarser k-point meshes than with no correction. Our results establish singularity subtraction as a powerful and flexible approach for mitigating finite-size errors in periodic correlation methods and provide a foundation for extending the technique to higher-order perturbation theories and other post-SCF methods.

Water-to-oil charge transfer (CT) across weak C-H···O hydrogen bonds is localized for hexane and hexadecane, and is too small to explain oil-droplet stability and electrokinetic experiments. Collective intraphase density rearrangements should not be confused with interfacial CT. Spectroscopic evidence cannot simultaneously imply weak CT for the C-H blue shift and large CT for the O-H/D red shift. A weakness of the C-H···O CT mechanism is that it can't explain other oil emulsion chemistry without this specific chemical motif.

Second-order Møller-Plesset theory (MP2) is the simplest wavefunction-based treatment of electron correlation and is a good compromise between accuracy and efficiency for evaluating the strength of many non-covalent intermolecular interactions. It has also been improved in accuracy and robustness by regularized methods, such as the size-consistent second order Brillouin-Wigner perturbation theory (BWs2) and κ-MP2. This work presents a non-technical summary of the recently developed second-generation absolutely localized molecular orbital (ALMO) energy decomposition analysis (EDA) method at the post-SCF level of MP2 and regularized MP2. The so-called frozen term is redefined to ensure that long range correlation contributions to electrostatics are correctly captured. The resulting EDA provides useful basis set limits to the correlation corrections for all physical contributions: donor-acceptor charge transfer, electrical polarization, dispersion, and Pauli repulsions and electrostatic interactions associated with frozen monomer orbitals. EDA calculations using MP2 are reported on several classes of systems: model systems to assess correlation effects on permanent and induced electrostatics, hydrogen bonds between water and model carbohydrate molecules, tetrel bonds ranging from 15 to 90 kJ mol-1 in strength, two halogen bonds - one of which is known to be solvent resistant, and a pair of "anti-electrostatic" halogen bonds. Several general conclusions emerge. First, to obtain physically reasonable conclusions, it is essential that the correlation contribution is not identified with dispersion alone: large corrections to the frozen term corresponding to changes in electrostatics are observed due to correlation. Second, the fingerprint of intermolecular interactions provided by the EDA reveals a range of interesting trends in the character of intermolecular interactions as a function of their type and strength. For example, the solvent-stable halogen bond is confirmed to be dominated by charge-transfer stabilization. On the other hand, the strongest tetrel bonds studied here are dominated by contributions from polarization, while more conventional hydrogen bonds between water and model carbohydrates represent a synergy between electrostatics, dispersion, and charge transfer. The metastability (or stability) of nominally antielectrostatic interactions depends strongly on the differing distance dependence of attractive and repulsive terms, and we demonstrated tuning based on changes in permanent electrostatics by increasing charge-separation through use of phenyl linkers.

Accurate modeling of noncovalent protein-ligand interactions is critical for applications such as enzyme engineering and drug discovery. Here, we present a data set of 14,905 protein-ligand interaction energies using experimental structures derived from HiQBind, a high-quality protein-ligand structural database, and subsequently fragmented into dimer configurations that are classified into noncovalent interaction (NCI) types, including hydrogen bonds, hydrophobic contacts, halogen bonds, salt bridges, cation-π, and π-π interactions. Each NCI category was further evaluated with energy decomposition analysis (EDA)1 as a powerful framework to partition total protein-ligand energies into physically meaningful NCI components for electrostatics, Pauli repulsion, dispersion, polarization, and charge transfer. We further use this data to benchmark the performance of current classical force fields and the current state-of-the-art machine-learned interaction potential (MLIP). Together, this data set provides a quantitative quantum mechanical survey of protein-ligand energetics, offering new insights into the molecular origins of protein-ligand NCIs to inform drug design while establishing benchmarks for next-generation force field and MLIP development.

We present a shadow-tomography-enhanced Non-Orthogonal Quantum Eigensolver (NOQE) for more efficient and accurate electronic structure calculations on near-term quantum devices. By integrating shadow tomography into the NOQE, the measurement cost scales linearly rather than quadratically with the number of reference states, while also reducing the required qubits and circuit depth by half. This approach enables extraction of all matrix elements via randomized measurements and classical postprocessing. We analyze its sample complexity and show that, for small systems, it remains constant in the high-precision regime, while for larger systems, it scales linearly with the system size. We further apply shadow-based error mitigation to suppress noise-induced bias without increasing quantum resources. Demonstrations on the hydrogen molecule in the strongly correlated regime achieve chemical accuracy under realistic noise, showing that our method is both resource-efficient and noise-resilient for practical quantum chemistry simulations in the near term.

We incorporate a solver for the fragment problem with accuracy beyond coupled cluster singles and doubles (CCSD) into the previously proposed static embedding framework, MPCC. To this end, we employ a CCSDT solver for the fragment subsystem. For the environment subsystem, we construct a perturbative estimate of the triples amplitudes, explicitly accounting for feedback from all fragment amplitudes. The resulting approach is denoted MPCCSDT(pt). We further introduce a more complete formulation in which feedback from the environment amplitudes to the fragment amplitudes is also included. This scheme involves an iterative treatment of the environment triples amplitudes and is denoted MPCCSDT(it). In addition, we assess the accuracy of the previously proposed low-level method by introducing a modified low-level approach that incorporates a lowest-order treatment of selected long-range effects, including spin fluctuations and charge polarization. All resulting approaches may be viewed as post-CCSD(T) methods. We therefore consider test cases for which CCSD(T) exhibits substantial deviations from CCSDT. Our results demonstrate that inclusion of triples amplitudes at the fragment level alone is insufficient; a perturbative treatment of the environment triples amplitudes is required. For many energy-difference applications, feedback from the environment triples amplitudes to the fragment amplitudes, is not essential, but it does play a role in the very challenging molecules. A very interesting finding from our study is that in some challenging cases, we need an improved (second-order) perturbative method for the SD amplitudes, going beyond the first-order one used in our earlier work.

Given the power of large language and large vision models, it is of profound and fundamental interest to ask if a foundational model based on data and parameter scaling laws and pre-training strategies is possible for learned simulations of chemistry and materials. The scaling of large and diverse datasets and highly expressive architectures for chemical and materials sciences should result in a foundation model that is more efficient and broadly transferable, robust to out-of-distribution challenges, and easily fine-tuned to a variety of downstream observables, when compared to specific training from scratch on targeted applications in atomistic simulation. In this Perspective we aim to cover the rapidly advancing field of machine learned interatomic potentials (MLIP), and to illustrate a path to create chemistry and materials MLIP foundation models at larger scale.

Free energies of association determine chemical equilibria and thus control noncovalent binding. While traditional energy decomposition analysis (EDA) methods can provide a chemically or physically interpretive decomposition of noncovalent electronic binding energies, by definition they neglect entropic effects (and nuclear contributions to the enthalpy). With the objective of revealing the chemical origins of trends in free energies of binding, we introduce the concept of a free energy or Gibbs decomposition analysis (GDA), by coupling the absolutely localized molecular orbital (ALMO) treatment of electrons in non-covalent interactions with the simplest possible quantum treatment of nuclear motion at finite temperature, which is the rigid rotor-harmonic oscillator (RR-HO) model. The resulting pilot GDA is employed to decompose enthalpic and entropic contributions to the free energy of association of the water dimer, fluoride-water dimer, and the binding of water to an open metal site in a recently synthesized metal-organic framework (Cu(I)-MFU-4l). The results show enthalpic trends that generally track the energy of binding (i.e. EDA results), and entropic trends that reveal the increasing price of loss of translational and rotational degrees freedom with temperature. The GDA approach can be generalized to more sophisticated treatment of quantum nuclei, as well as to semiclassical or classical nuclear motion.

Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(II) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.

One approach to calculating electronic excited states treats both ground and excited states as single determinants, either by direct optimization or with the aid of constraints. In this work, we extend the theory of occupied-virtual orbitals for chemical valence (OVOCV) to analyze the orbital character of excitations computed in this way. An intermediate frozen state that is polarization-free is introduced to cleanly separate the primary excitation from the accompanying orbital relaxation of spectator orbitals. A variety of chemical examples are reported using the OVOCV excitation analysis on orbital-optimized density functional theory (OO-DFT) calculations, including charge-transfer excitations, core excitations and singly and doubly excited valence states. Orbital relaxation effects are typically collective, and can be as large as 4-5 eV (with roughly 0.1 e- promoted) in charge transfer states, and even larger in core excited states. OVOCV analysis differs from natural transition orbital (NTO) analysis; we show that direct use of NTOs can largely obscure the role of orbital relaxation in favor of the primary excitation.

We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin-Wigner (BW-s) partitioning instead of a Møller-Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree-Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. The main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.

The intersection of quantum computing and quantum chemistry represents a promising frontier for achieving quantum utility in domains of both scientific and societal relevance. Owing to the exponential growth of classical resource requirements for simulating quantum systems, quantum chemistry has long been recognized as a natural candidate for quantum computation. This perspective focuses on identifying scientifically meaningful use cases where early fault-tolerant quantum computers, which are considered to be equipped with approximately 25-100 logical qubits, could deliver tangible impact. While recent advances in classical computing have pushed the boundaries of tractable simulations to unprecedented scales, this logical-qubit regime represents the first window where quantum devices can pursue qualitatively distinct strategies, such as polynomial-scaling phase estimation, direct simulation of quantum dynamics, and active-space embedding, that remain challenging for classical solvers, such as multireference charge-transfer and conical-intersection states central to photochemistry and materials design. We highlight near-term opportunities in algorithm and software design, discuss representative chemical problems suited for quantum acceleration, and propose strategic roadmaps and collaborative pathways for advancing practical quantum utility in quantum chemistry.

Understanding the impact of O2 during a carbon capture process is vital for designing robust, cost-effective materials for carrying it out. However, mechanistic studies of the O2-induced degradation of materials are not easily undertaken owing to the complex sequential reaction pathways that arise. Here, we report comprehensive mechanistic investigations of the O2-induced degradation of diamine-appended metal-organic frameworks (MOFs) exhibiting cooperative CO2 adsorption. Oxygen exposure experiments were performed on seven different diamine-appended MOFs, including e-2-Mg2(dobpdc) (e-2 = N-ethylethylenediamine, dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate), under various temperatures and O2 pressures. These experiments show that diamine degradation inhibits CO2 chemisorption and that the degradation rate is significantly influenced by the diamine structure. In contrast, the parent frameworks remain essentially intact upon O2 exposure. Detailed characterization of O2-exposed e-2-Mg2(dobpdc) revealed the formation of various degradation products, including acetaldehyde, carbon dioxide, water, ethylamine, and other aldehyde- and imine-containing species. Together, these observations suggest that diamine degradation occurs via C-N bond cleavage through pathways involving C-centered radicals. Furthermore, computational evaluation of the initiation and propagation pathways for amine degradation in diamine-appended MOFs indicates that (i) degradation is likely initiated by OH•, (ii) carbon-centered radicals generated via radical transfer reactions react with O2, leading to amine degradation, and (iii) the rate-limiting step of the degradation reactions likely involves O-O bond cleavage. Overall, these mechanistic insights could inform strategies for mitigating O2-induced amine degradation in next-generation carbon capture technologies.

Through systematic first-principles calculations, molecular dynamics, and Monte Carlo simulations, it is predicted that the MSeO3 (M = Ru, Rh, Pd, and Pt) single-layer sheets constitute a class of highly stable 2D materials, featuring a range of compelling properties. The mechanical exfoliation of MSeO3 monolayers from their bulk phases is experimentally feasible due to the ultralow exfoliation energies (less than 0.20 J/m2). Notably, the antiferromagnetic RhSeO3 monolayer exhibits an in-plane magnetic anisotropy with a large magnetic anisotropy energy (MAE) of 256.70 mu eV. By performing Heisenberg Monte Carlo (MC) simulations, the Neel temperature of RhSeO3 is predicted to be 370 K. The Berezinskii-Kosterlitz-Thouless (BKT) transition temperature of RhSeO3 is as high as 910.56 K. This makes it a potential candidate material for applications in low-dimensional spintronic devices. The RhSeO3 and PdSeO3 monolayers have considerable indirect bandgaps of 2.415 and 2.981 eV, respectively, and their valence and conduction bands perfectly align with the redox potentials of water. Furthermore, the rather pronounced optical absorption in the visible and ultraviolet regions further facilitates the RhSeO3 and PdSeO3 monolayers as promising photocatalysts for splitting pure water (pH = 7) into H2 and O2. Unexpectedly, the RuSeO3, PdSeO3, and PtSeO3 monolayers exhibit unusual negative Poisson's ratios (NPRs); notably the RuSeO3 monolayer has a remarkable NPR of-0.549. This class of multifunctional materials exhibit diverse and promising properties, thereby facilitating the path towards future applications in nanoelectronics, spintronics, optoelectronics, and photocatalysis.

Energy decomposition analysis (EDA) has become an important tool to relate electronic structure calculations to physically meaningful contributions. The second generation of the absolutely localized molecular orbitals (ALMO)-EDA accounts for polarization with a well-defined basis set limit using truncated virtual orbitals, namely fragment electric-field response functions (FERF). In this work, we introduce a hessian-free uncoupled FERF (uFERF) alternative that has very similar accuracy and is 5-10 times faster to evaluate. Furthermore, we investigate the use of monopole uFERFs (response to scaled nuclear charges) for intermolecular interactions and establish their role in strong ion-neutral interactions.

We present GSCDB137, a rigorously curated benchmark library of 137 data sets (8377 entries) covering main-group and transition-metal reaction energies and barrier heights, (intra- and intermolecular) noncovalent interactions, dipole moments, polarizabilities, electric-field response energies, and vibrational frequencies. Legacy data from GMTKN55 and MGCDB84 have been updated to today's best reference values; redundant or low-quality points were removed, and many new, property-focused sets were added. Testing 29 popular density functional approximations (DFAs) confirms the expected Jacob's-ladder hierarchy overall but also reveals notable exceptions: functional performance for frequencies and electric-field properties correlates poorly with that for other ground-state energetics. ωB97M-V and ωB97X-V are the most balanced hybrid meta-GGA and hybrid GGA, respectively; B97M-V and revPBE-D4 lead the meta-GGA and GGA classes. Double hybrids lower mean errors by about 30% versus their hybrid analogues but demand careful frozen-core, basis set, and spin contamination treatment. GSCDB137 offers a comprehensive, openly documented platform for rigorous validation of DFA and universal machine learning potentials, and training of the next generation of exchange-correlation functionals.

Quantum mechanical calculations of core electron binding energies (CEBEs) are relevant to interpreting X-ray photoelectron spectroscopy (XPS). Orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge CEBEs but is challenged by the presence of significant spin-orbit coupling (SOC) at L- and higher edges involving inner-shell orbitals with nonzero angular momentum. To extend OO-DFT to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted open-shell OO-DFT to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell (e.g., ionizing all six possible 2p spin orbitals). Nonorthogonal configuration interaction (NOCI) is then used to obtain the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. Using a screened 1-electron SOC operator parametrized with the Dirac-Coulomb-Breit (DCB) Hamiltonian results in doublet splitting (DS) values for third row elements that are nearly in quantitative agreement with experiment. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT CEBEs to yield CEBEs (split by SOC) corrected for dynamic correlation. Comparing calculations on gas phase molecules with experimental results establishes that NO-QDPT with the SCAN functional (NO-QDPT/SCAN), using the DCB screened 1-electron SOC operator is accurate to about 0.2 eV for L-edge CEBEs of molecules containing third row atoms. However, this NO-QDPT approach becomes less accurate for fourth-row elements starting in the middle of the 3d transition metal series, with errors increasing as atomic number increases.