Recent developments in the PySCF program package

Modeling electronic absorption spectra with nuclear quantum effects in constrained nuclear-electronic orbital framework

Electronic absorption spectra serve as versatile and powerful tools in experiments. Accurate theoretical simulation of electronic absorption spectra is challenging because multiple factors such as environmental effects and nuclear quantum effects contribute to spectrum lineshapes. This work proposes a protocol to model electronic absorption spectra in the constrained nuclear-electronic orbital framework. Solvent effects, temperature effects, and particularly nuclear quantum effects can be taken into consideration in this unified framework. This protocol is applied to investigate the electronic absorption spectrum of the pyridine molecule in water. Nuclear quantum effects are found to induce a broadening and red shift of the absorption spectrum of pyridine.

Equation-of-motion internally contracted multireference unitary coupled-cluster theory

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM) extension of the internally contracted multireference unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows the transform-then-diagonalize approach, in analogy to its non-unitary counterpart [Datta and Nooijen, J. Chem. Phys. 137, 204107 (2012)]. By employing a projective approach to optimize the ground state, the method retains additive separability and proper scaling with system size. We show that excitation energies are size-intensive if the EOM operator satisfies the "killer" and the projective conditions. Furthermore, we propose to represent changes in the reference state upon electron excitation via projected many-body operators that span the active orbitals and show that the EOM equations formulated in this way are invariant with respect to active orbital rotations. We test the EOM-ic-MRUCC method truncated to single and double excitations by computing the potential energy curves for several excited states of a BeH2 model system, the HF molecule, and water undergoing symmetric dissociation. Across these systems, our method delivers accurate excitation energies and potential energy curves within 5 mEh (∼0.14 eV) from full configuration interaction. We find that truncating the Baker-Campbell-Hausdorff series to fourfold commutators contributes negligible errors (on the order of 10-5Eh or less), offering a practical route to highly accurate excited-state calculations with reduced computational overhead.

Impact of Parametrizations of the One-Body Reduced Density Matrix on the Energy Landscape

Many electronic structure methods rely on the minimization of the energy of the system with respect to the one-body reduced density matrix (1-RDM). To formulate a minimization algorithm, the 1-RDM is often expressed in terms of its eigenvectors via an orthonormal transformation and its eigenvalues. This transformation drastically alters the energy landscape. Especially in 1-RDM functional theory this means that the convexity of the energy functional is lost. We show that degeneracies in the occupation numbers can lead to additional critical points which are classified as saddle points. Using a Cayley or Householder parametrization for the orthonormal transformation, no extra critical points arise. In the case of Given's rotations or the exponential, additional critical points can arise, which are of no concern in practical minimization. These findings provide an explanation for the success of recent minimization procedures using second-order information.

Fully Analytic G0W0 Nuclear Gradients

In this letter, we present the first fully analytic derivation and implementation of nuclear gradients for the G0W0 method. For this, we leverage the recently established connection between the G0W0 approach and equation-of-motion unitary coupled-cluster theory for charged excitations. Analytic gradients are obtained through the Lagrangian technique and are implemented and validated by comparison with finite-difference calculations. For G0W0, we examine the effect of the Tamm-Dancoff approximation for evaluating the screened Coulomb interaction. Finally, we compare G0W0 adiabatic ionization potential and electron affinities to wave function-based electronic structure methods and experimental values.

Multiscale Embedding for Quantum Computing

We present a novel multiscale embedding scheme that links conventional QM/MM embedding and bootstrap embedding (BE) to allow simulations of large chemical systems on limited quantum devices. We also propose a mixed-basis BE scheme that facilitates BE calculations on extended systems using classical computers with limited memory resources. Benchmark data suggest the combination of these two strategies as a robust path in attaining the correlation energies of large realistic systems, combining the proven accuracy of BE with chemical and biological systems of interest in a lower computational cost method. Due to the flexible tunability of the resource requirements and systematic fragment construction, future developments in the realization of quantum computers naturally offer improved accuracy for multiscale BE calculations.

Exploring the origin of electron spin polarization in metal-containing chromophore-radical systems via multireference calculations

The electron spin polarization (ESP) phenomenon in photoexcited chromophore-radical connected systems was analyzed by multireference electronic structure calculations. We focused on bpy-M-CAT-mPh-NN (bpy = 4,4'-di-tert-butyl-2,2'-bipyridine, M = Pt or Pd, CAT = 3-tert-butylcatecholate, mPh = meta-phenylene, and NN = nitronyl nitroxide) reported by Kirk et al., which is a connected system consisting of a donor-acceptor complex and a radical, and elucidated the mechanism behind the reversal of the sign of photoinduced ESP depending on the metal species. The low-lying electronic states of these molecules were revealed through the multireference theory, suggesting that the ligand-to-ligand charge-transfer states play a significant role. Additionally, several structural factors that influence the energies of the excited states were identified. To enhance our understanding of the ESP, we incorporated spin-orbit coupling as a direct transition term between excited states and explicitly considered its effects on the ESP. The results of evaluating transition rates through a transition simulation indicate that when the influence of spin-orbit coupling is significant, the sign of the ESP in the ground state can reverse. This novel ESP mechanism mediated by spin-orbit coupling may offer fundamental insights for designing molecules to precisely control electron distribution across multiple spin states.

Mechanistic Insights into the Nonenzymatic Biosynthesis of Artemisinin and Related Natural Products: A Quantum Chemical Study

Artemisinin (Qinghaosu) is an important antimalaria natural medicine containing a unique endoperoxide bridge in its sesquiterpene structure. The last phase of artemisinin biosynthesis involves conversion of dihydroartemisinic acid (DHAA) to artemisinin, and the detailed mechanism remains unclear. Based on previous experimental studies, this work investigated the possible mechanism of nonenzymatic conversion of DHAA to artemisinin and identified the most chemically plausible reaction pathway using quantum chemical computations. The rate-determining step in this pathway is acid-catalyzed oxidation of the enol by triplet O2, with an overall free energy barrier of 22.5 kcal/mol. This pathway also gives byproducts dihydroarteannuin B and dihydro-epi-arteannuin B. In addition, the nonenzymatic formation mechanism of 21 natural products from Artemisia annua was discussed in this work. These results provide fundamental knowledge of the biosynthetic processes of artemisinin and related natural products, as well as important references for semisynthesis and structural modification studies of artemisinin.

Spin-Free Exact Two-Component Linear Response Coupled Cluster Theory for the Estimation of Frequency-Dependent Second-Order Properties

We have presented the theory, implementation, and benchmark results for the one-electronic variant of spin-free exact two-component (SFX2C1e) linear response coupled cluster (LRCCSD) theory for static and dynamic polarizabilities of atoms and molecules in the spin-summed formulation. The resolution of identity (RI) approximation for two-electron integrals has been used to reduce the computational cost of the calculation and has been shown to have a negligible effect on accuracy. The calculated static and dynamic polarizability values agree very well with the more expensive X2C-LRCCSD and the experimental results. Our calculated results show that accurate predictions of polarizabilities of atoms and molecules containing heavy atoms require the use of a large basis set containing an adequate number of diffuse functions, in addition to accounting for electron correlation and relativistic effects.

Electronic insights into the role of nuclear quantum effects in proton transfer reactions of nucleobase pairs

Double proton transfer in nucleobase pairs leads to point mutations in nucleic acids. A series of constrained nuclear-electronic orbital calculations combined with natural bond orbital and non-covalent interaction analyses, and kinetic studies have quantitatively revealed the importance of nuclear quantum effects (NQEs) in the reaction. Compared with the classical treatment of the nuclei, the probability of forming the tautomeric isomers of Cytosine-Guanine, when explicitly accounting for NQEs, increased by a factor of 8.0. This outcome can be attributed to enhancing the interaction between the orbitals at the reactive site due to NQEs, which increased the number of electrons occupying the antibonding orbitals.

Improving Aufbau Suppressed Coupled Cluster through Perturbative Analysis

Guided by perturbative analysis, we improve the accuracy of Aufbau suppressed coupled cluster theory in simple single excitations, multiconfigurational single excitations, and charge transfer excitations while keeping the cost of its leading-order terms precisely in line with ground-state coupled cluster. Combining these accuracy improvements with a more efficient implementation based on spin adaptation, we observe high accuracy in a large test set of single excitations and, in particular, a mean unsigned error for charge transfer states that outperforms equation-of-motion coupled cluster theory by 0.25 eV. We discuss how these results are achieved via a systematic identification of which amplitudes to prioritize for single- and multiconfigurational excited states, and how this prioritization differs in important ways from the ground-state theory. In particular, our data show that a partial linearization of the theory increases accuracy by mitigating unwanted side effects of Aufbau suppression.

Classical Preoptimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications

The ADAPT-VQE algorithm is a promising method for generating a compact ansatz based on derivatives of the underlying cost function, and it yields accurate predictions of electronic energies for molecules. In this work, we report the implementation and performance of ADAPT-VQE with our recently developed sparse wave function circuit solver (SWCS) in terms of accuracy and efficiency for molecular systems with up to 52 spin orbitals. The SWCS can be tuned to balance computational cost and accuracy, which extends the application of ADAPT-VQE for molecular electronic structure calculations to larger basis sets and a larger number of qubits. Using this tunable feature of the SWCS, we propose an alternative optimization procedure for ADAPT-VQE to reduce the computational cost of the optimization. By preoptimizing a quantum simulation with a parametrized ansatz generated with ADAPT-VQE/SWCS, we aim to utilize the power of classical high-performance computing in order to minimize the work required on noisy intermediate-scale quantum hardware, which offers a promising path toward demonstrating quantum advantage for chemical applications.

Calculating the Energy Profile of an Enzymatic Reaction on a Quantum Computer

Quantum computing (QC) provides a promising avenue for enabling quantum chemistry calculations, which are classically impossible due to computational complexity that increases exponentially with system size. As fully fault-tolerant algorithms and hardware, for which an exponential speedup is predicted, are currently out of reach, recent research efforts have been dedicated to developing and scaling algorithms for Noisy Intermediate-Scale Quantum (NISQ) devices to showcase the practical usefulness of such machines. To demonstrate the usefulness of NISQ devices in the field of chemistry, we apply our recently developed FAST-VQE algorithm and a state-of-the-art quantum gate reduction strategy based on propositional satisfiability together with standard optimization tools for the simulation of the rate-determining proton transfer step for CO2 hydration catalyzed by carbonic anhydrase resulting in the first application of a quantum computing device for the simulation of an enzymatic reaction. To this end, we have combined classical force field simulations with quantum mechanical methods on classical and quantum computers in a hybrid calculation approach. The presented technique significantly enhances the accuracy and capabilities of QC-based molecular modeling and finally pushes it into compelling and realistic applications. The framework is general and can be applied beyond the case of computational enzymology.

Bridging the Gap between Transformer-Based Neural Networks and Tensor Networks for Quantum Chemistry

The neural network quantum state (NNQS) method has demonstrated promising results in ab initio quantum chemistry, achieving remarkable accuracy in molecular systems. However, efficient calculation of systems with large active spaces remains challenging. This study introduces a novel approach that bridges tensor network states with the transformer-based NNQS-Transformer (QiankunNet) to enhance accuracy and convergence for systems with relatively large active spaces. By transforming tensor network states into active space configuration interaction type wave functions, QiankunNet achieves accuracy surpassing both the pretraining density matrix renormalization group (DMRG) results and traditional coupled cluster methods, particularly in strongly correlated regimes. We investigate two configuration transformation methods: the sweep-based direct conversion (Conv.) method and the entanglement-driven genetic algorithm (EDGA) method, with Conv. showing superior efficiency. The effectiveness of this approach is validated on H2O with a large active space (10e, 24o) in the cc-pVDZ basis set, demonstrating an efficient routine between DMRG and QiankunNet and also offering a promising direction for advancing quantum state representation in complex molecular systems.

Optimal-Reference Excited State Methods: Static Correlation at Polynomial Cost with Single-Reference Coupled-Cluster Approaches

Accurate yet efficient modeling of chemical systems with pronounced static correlation in their excited states remains a significant challenge in quantum chemistry, as most electronic structure methods that can adequately capture static correlation scale factorially with system size. Researchers are often left with no option but to use more affordable methods that may lack the accuracy required to model critical processes in photochemistry such as photolysis, photocatalysis, and nonadiabatic relaxation. A great deal of work has been dedicated to refining single-reference descriptions of static correlation in the ground state via "addition-by-subtraction" coupled cluster methods such as pair coupled cluster with double substitutions (pCCD), singlet-paired CCD (CCD0), triplet-paired CCD (CCD1), and CCD with frozen singlet- or triplet-paired amplitudes (CCDf0/CCDf1). By combining wave functions derived from these methods with the intermediate state representation (ISR), we gain insights into the extensibility of single-reference coupled cluster theory's coverage of static correlation to the excited state problem. Our CCDf1-ISR(2) approach is robust in the face of static correlation and provides enough dynamical correlation to accurately predict excitation energies to within about 0.2 eV in small organic molecules. We also highlight distinct advantages of the Hermitian ISR construction, such as the avoidance of pathological failures of equation-of-motion methods for excited state potential energy surface topology. Our results prompt us to continue exploring optimal single-reference theories (excited state approaches that leverage dependence on the initial reference wave function) as a potentially economical approach to the excited state static correlation problem.

Strong Coupling Møller-Plesset Perturbation Theory

Perturbative approaches are methods to efficiently tackle many-body problems, offering both intuitive insights and analysis of correlation effects. However, their application to systems where light and matter are strongly coupled is nontrivial. Specifically, the definition of suitable orbitals for the zeroth-order Hamiltonian represents a significant theoretical challenge. While reviewing previously investigated orbital choices, this work presents an alternative polaritonic orbital basis suitable for the strong coupling regime. We develop a quantum electrodynamical (QED) Møller-Plesset perturbation theory using orbitals obtained from the strong coupling QED Hartree-Fock. We assess the strengths and limitations of the different approaches with emphasis on frequency and coupling strength dispersions, intermolecular interactions and polarization orientational effects. The results show the essential role of using a consistent molecular orbital framework in order to achieve an accurate description of cavity-induced electron-photon correlation effects.

Strongly Correlated States of Transition Metal Spin Defects: The Case of an Iron Impurity in Aluminum Nitride

We investigate the electronic properties of an exemplar transition metal impurity in an insulator, with the goal of accurately describing strongly correlated defect states. We consider iron in aluminum nitride, a material of interest for hybrid quantum technologies, and we carry out calculations with quantum embedding methods, density matrix embedding theory (DMET) and quantum defect embedding theory (QDET), and with spin-flip time-dependent density functional theory (TDDFT). We show that both DMET and QDET accurately describe the ground state and low-lying excited states of the defect and that TDDFT yields photoluminescence spectra in agreement with experiments. In addition, we provide a detailed discussion of the convergence of our results as a function of the active space used in the embedding methods, thus defining a protocol to obtain converged data directly comparable with experiments.

Generalized Many-Body Perturbation Theory for the Electron Correlation Energy: Multireference Random Phase Approximation via Diagrammatic Resummation

Many-body perturbation theory (MBPT) based on Green's functions and Feynman diagrams provides a fundamental theoretical framework for various ab initio computational approaches in molecular and materials science, including the random phase approximation (RPA) and GW approximation. Unfortunately, this perturbation expansion often fails in systems with strong multireference characters. Extending diagrammatic MBPT to the multireference case is highly nontrivial and remains largely unexplored, primarily due to the breakdown of Wick's theorem. In this work, we develop a diagrammatic multireference generalization of MBPT for computing correlation energies of strongly correlated systems, by using the cumulant expansion of many-body Green's functions in place of Wick's theorem. This theoretical framework bridges the gap between MBPT in condensed matter physics and multireference perturbation theories (MRPT) in quantum chemistry, which had been almost exclusively formulated within time-independent wave function frameworks prior to this work. Our formulation enables the explicit incorporation of strong correlation effects from the outset as in MRPT, while treating residual weak interactions through a generalized diagrammatic perturbation expansion as in MBPT. As a concrete demonstration, we formulate a multireference (MR) extension of the standard single-reference (SR) RPA by systematically resumming generalized ring diagrams, which naturally leads to a unified set of equations applicable to both SR and MR cases. Benchmark calculations on prototypical molecular systems reveal that MR-RPA successfully resolves the well-known failure of SR-RPA in strongly correlated systems. This theoretical advancement paves the way for advancing ab initio computational methods through diagrammatic resummation techniques in future.

Efficient Computational Strategies of the Cluster-in-Molecule Local Correlation Approach for Interaction Energies of Large Host-Guest Systems

We propose a heterogeneously accelerated reduced cluster-in-molecule (CIM) local correlation approach for calculating host-guest interaction energies. The essence of this method is to compute only the clusters that make significant contributions to the interaction energies while approximately neglecting those clusters with smaller contributions. Benchmark calculations at the CIM resolution-of-identity second-order Mo̷ller-Plesset perturbation (CIM-RI-MP2) or CIM spin-component-scaled RI-MP2 (CIM-SCS-RI-MP2) levels, involving three medium-sized protein-ligand structures, demonstrate that the reduced CIM method achieves over 48% time savings without compromising accuracy, as the interaction energy error remains within 0.5 kcal/mol compared to the full CIM method. To further enhance cluster computation efficiency, we developed a heterogeneous parallel version of the CIM-(SCS-)RI-MP2 method. It achieves over 93% internode parallel efficiency and over 98% multi-GPU card parallel efficiency for the tested large complexes. Ultimately, the hardware-accelerated reduced CIM-(SCS-)RI-MP2 method is applied to calculate the interaction energies of six protein-ligand systems, ranging from 913 to 1425 atoms. Remarkably, the method requires only 4.3-22.8% of the clusters to achieve accurate results, and under the condition of using only a single node, the wall time is within 2 days. Additionally, the reduced CIM domain-based local pair natural orbital coupled cluster with singles, doubles, and perturbative triples [CIM-DLPNO-CCSD(T)] method is successfully applied to the calculation of a 1425-atom protein-ligand system. These computations demonstrate the capability of a specific electronic structure to accurately calculate interaction energies for large host-guest systems.

Efficient Grouped-Bath Ansatz for Spin-Flip Nonorthogonal Configuration Interaction in Transition-Metal Charge-Transfer Complexes

We introduce a novel grouped-bath ansatz that approximates the spin-flip nonorthogonal configuration interaction (SF-NOCI) ansatz, named SF-GNOCI, which significantly reduces computational cost while preserving accuracy. SF-NOCI, originally developed by Mayhall et al., is a robust and nearly "black-box" electronic structure theory well suited for studying charge-transfer phenomena. It captures orbital relaxation effects for all configurations within the active space, providing a balanced correlation among charge transfer and other states. However, including these relaxation effects for all configurations results in a sharp increase in computational cost, especially for the large active spaces commonly encountered in transition metal complexes. To overcome this challenge, we grouped configurations based on the number of electrons associated with each atom. Configurations within each group share a common set of bath orbitals, significantly reducing computational overhead. We demonstrate the performance of SF-GNOCI through benchmark calculations on two systems: the avoided crossing of the lowest singlet states in LiF dissociation and the low-lying charge transfer states of [Fe(SCH3)4]2-/1-. Our results show that SF-GNOCI achieves accuracy comparable to standard SF-NOCI while reducing computational cost by a factor of 10 for [ F e ( S C H 3 ) 4 ] 2 - and 15 for [ F e ( S C H 3 ) 4 ] 1 - . We believe that the SF-GNOCI ansatz is a promising reference state for efficiently describing charge transfer phenomena in transition metal complexes.

An Analysis of Regularized Second-Order Energy Expressions in the Context of Post-HF and KS-DFT Calculations: What Do We Gain and What Do We Lose?

Møller-Plesset second-order (MP2) perturbation energy expression has been a workhorse for quantum chemistry methods for many years due to its very appealing accuracy/cost ratio compared to more advanced methods. It has been widely utilized in the post-Hartree-Fock (post-HF) calculations and Kohn-Sham density functional theory (KS-DFT) to define, e.g., the double-hybrid class of density functional approximations. Although the list of successful applications of the MP2 method is quite long, it suffers from various limitations, e.g., in strongly correlated systems, divergence in small energy gap systems, or overestimation of binding energies for large noncovalently bonded species. In this work, we analyze a few of the most commonly utilized forms of regularized MP2 correlation energy expression in the context of post-HF and KS-DFT calculations. To this end, we perform various tests for model systems, e.g., homogeneous electron gas, one-dimensional Hubbard model, Harmonium atoms, and some real-life examples, to trace back the advantages and disadvantages of these formulas, providing practical guidelines for their utilization in everyday quantum chemical calculations.

GW Plus Cumulant Approach for Predicting Core-Level Shakeup Satellites in Large Molecules

Recently, the GW approach has emerged as a valuable tool for computing deep core-level binding energies as measured in X-ray photoemission spectroscopy. However, GW fails to accurately predict shakeup satellite features, which arise from charge-neutral excitations accompanying the ionization. In this work, we extend the GW plus cumulant (GW + C) approach to molecular 1s excitations, deriving conditions under which GW + C can be reliably applied to shakeup processes. We present an efficient implementation with O(N4) scaling with respect to the system size N, within an all-electron framework based on numeric atom-centered orbitals. We demonstrate that decoupling the core and valence spaces is crucial when using localized basis functions. Additionally, we meticulously validate the basis set convergence of the satellite spectrum for 65 spectral functions and identify the importance of diffuse augmenting functions. To assess the accuracy, we apply our GW + C scheme to π-conjugated molecules containing up to 40 atoms, predicting dominant satellite features within 0.5 eV of experimental values. For the acene series, from benzene to pentacene, we demonstrate how GW + C provides critical insights into the interpretation of experimentally observed satellite features.

Efficient Implementation of the Random Phase Approximation with Domain-Based Local Pair Natural Orbitals

We present an efficient implementation of the direct random phase approximation (RPA) for molecular systems within the domain-based local pair natural orbital (DLPNO) framework. With recommended loose, normal, and tight parameter settings, DLPNO-RPA achieves approximately 99.7-99.95% accuracy in the total correlation energy compared to a canonical implementation, enabling highly accurate reaction energies and potential energy surfaces to be computed while substantially reducing computational costs. As an application, we demonstrate the capability of DLPNO-RPA to efficiently calculate basis set-converged binding energies for a set of large molecules, with results showing excellent agreement with high-level reference data from both coupled cluster and diffusion Monte Carlo. This development paves the way for the routine use of RPA-based methods in molecular quantum chemistry.

Analytic Gradient for Spin-Flip TDDFT Using Noncollinear Functionals in the Multicollinear Approach

Spin-flip time-dependent density functional theory (TDDFT) is an efficient tool for describing ground and excited states, especially when they exhibit significant multiconfigurational effects. Currently, most implementations and applications rely on collinear functionals. Using noncollinear functionals in spin-flip TDDFT is a more natural and appropriate choice, which preserves energy degeneracy and spin symmetry better. However, its development has been hindered by numerical instabilities in the second-order functional derivatives. We recently proposed a new approach for constructing noncollinear functionals, the multicollinear approach, which provides numerically stable higher-order functional derivatives and has been applied to spin-flip TDDFT calculations. In this study, we apply the multicollinear approach to the spin-flip TDDFT analytic gradient to address its main challenge: calculating the third-order derivatives of noncollinear functionals. Since these derivatives for generalized gradient approximation (GGA) and meta-GGA functionals may have been implemented for the first time, we validated the implementation through benchmark tests, comparing the results with numerical gradients and the analytic gradients of spin-conserving excited states with the same energy. Finally, we demonstrate the application of spin-flip TDDFT analytic gradients in optimizing the geometries of the lower singlet states, including double-excitation states, and calculating the adiabatic excitation energies and dissociation curves. The analytic gradients of spin-flip TDDFT also serve as a reference for studying analytic derivative couplings and provide a new potential option for on-the-fly molecular dynamics simulations. Furthermore, this work provides useful references for the study of other first-order properties and the development of relativistic TDDFT gradients.

Local hybrid alternatives to the orbital density approximation reduce the orbital dependence of self-interaction corrected DFT and the overbinding of DFT-corrected correlated wavefunctions

This work presents local hybrid alternatives to the orbital density approximation employed in self-interaction corrected density functional theory (SIC-DFT) and extended for use in DFT-corrected correlated wavefunction approaches (CAS-DFT). When combined with standard approximate density functionals, the orbital density approximation leaves SIC-DFT energies strongly dependent on unitary transforms among occupied orbitals and leaves CAS-DFT energies overbound. The alternatives presented here reduce both errors. The orbital density approximation and the local hybrid alternatives are shown to approximate an underlying nondiagonal exchange-correlation hole. A preliminary extension is presented to active-virtual correlation. These results motivate exploration of local hybrid concepts in SIC-DFT and CAS-DFT.

Overview on Building Blocks and Applications of Efficient and Robust Extended Tight Binding

The extended tight binding (xTB) family of methods opened many new possibilities in the field of computational chemistry. Within just 5 years, the GFN2-xTB parametrization for all elements up to Z = 86 enabled more than a thousand applications, which were previously not feasible with other electronic structure methods. The xTB methods provide a robust and efficient way to apply quantum mechanics-based approaches for obtaining molecular geometries, computing free energy corrections or describing noncovalent interactions and found applicability for many more targets. A crucial contribution to the success of the xTB methods is the availability within many simulation packages and frameworks, supported by the open source development of its program library and packages. We present a comprehensive summary of the applications and capabilities of xTB methods in different fields of chemistry. Moreover, we consider the main software packages for xTB calculations, covering their current ecosystem, novel features, and usage by the scientific community.

Automated Multireference Vertical Excitations for Transition-Metal Compounds

Excited states of transition metal complexes are generally strongly correlated due to the near-degeneracy of the metal d orbitals. Consequently, electronic structure calculations of such species often necessitate multireference approaches. However, widespread use of multireference methods is hindered due to the active space selection problem, which has historically required system-specific chemical knowledge and a trial-and-error approach. Here, we address this issue with an automated method combining the approximate pair coefficient (APC) scheme for estimating orbital entropies with the discrete variational selection (DVS) approach for evaluating active space quality. We apply DVS-APC to the calculation of 67 vertical excitations in transition metal diatomics as well as to two larger complexes. We show DVS-APC generated active spaces yield NEVPT2 mean absolute errors of 0.18 eV, in line with previous accuracies obtained for organic systems, but larger than errors achieved with hand-selected active spaces (0.14 eV). If instead of using DVS we identify the best results from our trial wave functions, we find improved performance (mean absolute error of 0.1 eV) over the manually selected results. We highlight this deviation between DVS and hand selected active spaces as a possible measure of bias introduced when hand selecting active spaces. However, we find that multiconfiguration pair-density functional theory (MC-PDFT) using the tPBE and tPBE0 functionals is roughly 0.15 eV less accurate than NEVPT2 across this class of diatomic systems, potentially accounting for the decreased performance of DVS-APC, which uses MC-PDFT energies to select between active spaces. We also showcase an ability to "down-sample" the DVS-APC wave functions using natural orbital occupancies to achieve smaller minimal active spaces which retain the accuracy of the larger starting active spaces. Finally, DVS-APC and tPBE0 are proven to be effective when applied to modeling excited states in two larger transition metal complexes, suggesting that the transition metal diatomics may be a particular outstanding challenge for DVS-APC and MC-PDFT approaches.

AtomDB: A Python Library and Database for Atomic and Promolecular Properties

AtomDB is a free and open-source Python library for accessing and manipulating neutral and charged atomic species and their promolecular properties. It serves as a computational toolset, operating on an accompanying "extended periodic table" database, with experimental and computational data covering atomic species with a wide range of charges and multiplicities. AtomDB includes facilities for computing promolecules: local promolecular properties, constructed from the corresponding atomic densities, and scalar promolecular properties, computed from the corresponding scalar atomic properties, both taking into account whether properties are extensive or intensive. AtomDB is designed to be easy to use, extend, and maintain: it follows best practices for modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. This article is the official release note for the AtomDB library.

PyPWDFT: A Lightweight Python Software for Single-Node 10K Atom Plane-Wave Density Functional Theory Calculations

PyPWDFT is a Python software designed for performing plane-wave density functional theory (DFT) calculations. It can perform large-scale DFT calculations using only a single process on a single node, including local density functional for 10,000 atoms and nonlocal hybrid functional for 4096 atoms. Our benchmark test results demonstrate that PyPWDFT achieves performance comparable to that of Fortran/C++ codes, despite being developed in a native Python environment. In addition, it requires only NumPy, SciPy, and CuPy, enabling CPU-GPU heterogeneous computing, achieving a two-order-of-magnitude speedup compared to single-threaded CPU execution. Due to its excellent cross-platform compatibility, medium-scale DFT calculations can be performed through a graphical user interface on personal computers and Windows systems using consumer-grade GPUs, such as the NVIDIA GeForce RTX 4090. The computational efficiency is comparable to that of professional-grade GPUs such as the NVIDIA V100. The efficient performance, scalability to handle large-scale systems, high numerical accuracy, and different interfaces for molecular dynamics collectively underscore the considerable potential of PyPWDFT to develop into versatile DFT software.

Algebraic Diagrammatic Construction Theory of Charged Excitations with Consistent Treatment of Spin-Orbit Coupling and Dynamic Correlation

We present algebraic diagrammatic construction theory for simulating spin-orbit coupling and electron correlation in charged electronic states and photoelectron spectra. Our implementation supports Hartree-Fock and multiconfigurational reference wave functions, enabling efficient correlated calculations of relativistic effects using single-reference (SR-) and multireference-algebraic diagrammatic construction (MR-ADC). We combine the SR- and MR-ADC methods with three flavors of spin-orbit two-component Hamiltonians and benchmark their performance for a variety of atoms and small molecules. When multireference effects are not important, the SR-ADC approximations are competitive in accuracy to MR-ADC, often showing closer agreement with experimental results. However, for electronic states with multiconfigurational character and in nonequilibrium regions of potential energy surfaces, the MR-ADC methods are more reliable, predicting accurate excitation energies and zero-field splittings. Our results demonstrate that the spin-orbit ADC methods are promising approaches for interpreting and predicting the results of modern spectroscopies.

Multiscale Force Field Model Based on a Graph Neural Network for Complex Chemical Systems

Inspired by the QM/MM methodology, the ML/MM approach introduces a new opportunity for multiscale simulation, improving the balance between accuracy and computational efficiency. Benefited from the rapid advancements in molecular embedding methods, density functional theory level quantum mechanical (QM) calculations within the QM/MM framework can be accelerated by several orders of magnitude through the application of machine learning (ML) potential energy surfaces. As a problem inherited from the QM/MM methodology, challenges exist in designing the interactions between machine learning and molecular mechanics (MM) regions. In this study, electrostatic interactions between machine learning and MM atoms are treated by using a graphical neural network based on stationary perturbation theory. In this protocol, we process coordinates and MM charges to yield electrostatic energy and forces, resulting in a high-performance electrostatic embedding ML/MM architecture. The accuracy of the ML/MM energy was validated in aqueous solutions of alanine dipeptide and allyl vinyl ether (AVE). We investigated the transferability of parameters trained from AVE in a single solvent to various other solvents, including water, methanol, dimethyl sulfoxide, toluene, ionic liquids, and water-toluene interface environments. We then established a solvent-free protocol for data set preparation. Comparison of the free energy landscapes of the Claisen rearrangement of AVE in different solvation environments showed the catalytic effect of aqueous solutions, consistent with experiments.

Accurate and efficient prediction of double excitation energies using the particle-particle random phase approximation

Double excitations are crucial to understanding numerous chemical, physical, and biological processes, but accurately predicting them remains a challenge. In this work, we explore the particle-particle random phase approximation (ppRPA) as an efficient and accurate approach for computing double excitation energies. We benchmark ppRPA using various exchange-correlation functionals for 21 molecular systems and two point defect systems. Our results show that ppRPA with functionals containing appropriate amounts of exact exchange provides accuracy comparable to high-level wave function methods such as CCSDT and CASPT2, with significantly reduced computational cost. Furthermore, we demonstrate the use of ppRPA starting from an excited (N - 2)-electron state calculated by ΔSCF for the first time, as well as its application to double excitations in bulk periodic systems. These findings suggest that ppRPA is a promising tool for the efficient calculation of double and partial double excitation energies in both molecular and bulk systems.

Design, Synthesis, and Biological Evaluation of Novel Orally Available Covalent CDK12/13 Dual Inhibitors for the Treatment of Tumors

Cyclin-dependent kinases 12 and 13 (CDK12/13) safeguard genomic integrity by preferentially regulating gene expression in the DNA damage response (DDR). The CDK12/13-mediated upregulation of DDR genes and pathways significantly contributes to both tumorigenesis and the development of resistance to antitumor therapies. Thus, the functional inhibition of CDK12/13 offers an attractive strategy to combat carcinogenesis, particularly for refractory and treatment-resistant cancers. Here, we report the discovery of compound 12b as a novel, potent, orally available covalent CDK12/13 dual inhibitor with a promising safety profile and robust in vivo antitumor properties.

Accuracy of the diffusion quantum Monte Carlo method on dissociation curves of van der Waals systems with the single-Slater-Jastrow trial wavefunction

Non-covalent interactions, particularly van der Waals (vdW) interactions, are crucial in chemistry, physics, and life sciences. Accurate calculation of both the repulsive and attractive parts of vdW potentials is essential for a reliable description of dissociation curves in vdW systems. The diffuse quantum Monte Carlo (DMC) method is known to be able to calculate vdW interactions accurately at equilibrium distances. However, its performance on vdW interaction energies at non-equilibrium distances has not been investigated. In this work, dissociation curves for ten vdW interacting systems with dispersion interactions, dipole-induced dipole interactions and dipole-dipole interactions are calculated using the DMC and some low-level methods, i.e., MP2 and CCSD, to illustrate their accuracy for the attractive and repulsion potentials of vdW potentials. Our results indicate that while MP2 and CCSD provide reliable descriptions of the attractive potential in vdW interactions, they exhibit larger errors in the repulsive region. On the other hand, DMC employing a single-Slater-Jastrow trial wavefunction with the DLA approximation for the non-local part of pseudopotentials demonstrates high accuracy in both repulsive and attractive potentials. Additionally, reliable DMC results can be achieved with T-moves if the Jastrow factor is optimized carefully. These results emphasize the capability of the DMC with DLA to accurately compute vdW interaction energies at non-equilibrium distances.

Interpolating numerically exact many-body wave functions for accelerated molecular dynamics

While there have been many developments in computational probes of both strongly-correlated molecular systems and machine-learning accelerated molecular dynamics, there remains a significant gap in capabilities in simulating accurate non-local electronic structure over timescales on which atoms move. We develop an approach to bridge these fields with a practical interpolation scheme for the correlated many-electron state through the space of atomic configurations, whilst avoiding the exponential complexity of these underlying electronic states. With a small number of accurate correlated wave functions as a training set, we demonstrate provable convergence to near-exact potential energy surfaces for subsequent dynamics with propagation of a valid many-body wave function and inference of its variational energy whilst retaining a mean-field computational scaling. This represents a profoundly different paradigm to the direct interpolation of potential energy surfaces in established machine-learning approaches. We combine this with modern electronic structure approaches to systematically resolve molecular dynamics trajectories and converge thermodynamic quantities with a high-throughput of several million interpolated wave functions with explicit validation of their accuracy from only a few numerically exact quantum chemical calculations. We also highlight the comparison to traditional machine-learned potentials or dynamics on mean-field surfaces.

Exploring Intrinsic Bond Properties with the Fukui Matrix from Conceptual Density Matrix Functional Theory

We extend the traditional conceptual density functional theory (CDFT) to conceptual density matrix functional theory (CDMFT) by replacing the external potential v(r) by the one-electron integral hrs in the energy functional. This approach provides a new path for investigating intrinsic bond properties such as bond reactivity. The derivation of the Fukui matrix, i.e., derivative of the density matrix P with respect to the number of electrons N, is elucidated, and the result is illustrated in a case study on H2O. The matrix is shown to play a crucial role in quantifying changes of bond strength for electron removal or addition processes via the bond order derivative ( ∂ B ∂ N ) - . Using the Mayer bond order and different atoms-in-molecules partitioning methods, we show that as a first-order response quantity, the bond order derivative agrees well with the finite difference bond order changes. The bond order derivative (bond Fukui function) is a bond reactivity descriptor. We demonstrate this by predicting the regioselectivity of a classical electrophilic addition reaction (the bromination of alkenes) and predicting the initial electron-driven bond cleavage in mass spectrometry. Specifically, the bond order derivative captures all of the major signals from the experimental mass spectra for a series of small molecules with a variety of functional groups.

easyPARM: Automated, Versatile, and Reliable Force Field Parameters for Metal-Containing Molecules with Unique Labeling of Coordinating Atoms

The dynamics of metal centers are challenging to describe due to the vast variety of ligands, metals, and coordination spheres, hampering the existence of general databases of transferable force field parameters for classical molecular dynamics simulations. Here, we present easyPARM, a Python-based tool that can calculate force field parameters for a wide range of metal complexes from routine frequency calculations with electronic structure methods. The approach is based on a unique labeling strategy, in which each ligand atom that coordinates the metal receives a unique atom type. This design prevents parameter shortage, labeling duplication, and the necessity to post-process output files, even for very complicated coordination spheres, whose parametrization process remain automatic. The program requires the Cartesian Hessian matrix, the geometry xyz file, and the atomic charges to provide reliable force-field parameters extensively benchmarked against density functional theory dynamics in both the gas and condensed phases. The procedure allows the classical description of metal complexes at a low computational cost with an accuracy as good as the quality of the Hessian matrix obtained by quantum chemistry methods. easyPARM v2.00 reads vibrational frequencies and charges in Gaussian (version 09 or 16) or ORCA (version 5 or 6) format and provides refined force-field parameters in Amber format. These can be directly used in Amber and NAMD molecular dynamics engines or converted to other formats. The tool is available free of charge in the GitHub platform (https://github.com/Abdelazim-Abdelgawwad/easyPARM.git).

Grassmann Extrapolation for Accelerating Geometry Optimization

This study extends the Grassmann extrapolation (G-Ext) method, which was introduced for Born-Oppenheimer molecular dynamics, to the context of geometry optimization. Using density matrices from previous optimization steps, the G-Ext approach applies a nonlinear, structure-preserving mapping onto the Grassmann manifold to provide an initial guess which accelerates the convergence of the self-consistent field (SCF) procedure. Using the optimal parameters identified by employing various descriptors and computational strategies across a diverse set of molecules, G-Ext shows excellent performance improvements, particularly with large molecular systems.

Quantum Computing Approach to Fixed-Node Monte Carlo Using Classical Shadows

Quantum Monte Carlo (QMC) methods are powerful approaches for solving electronic structure problems. Although they often provide high-accuracy solutions, the precision of most QMC methods is ultimately limited by the trial wave function that must be used. Recently, an approach has been demonstrated to allow the use of trial wave functions prepared on a quantum computer [Huggins et al., Unbiasing fermionic quantum Monte Carlo with a quantum computer. Nature 2022, 603, 416] in the auxiliary-field QMC (AFQMC) method using classical shadows to estimate the required overlaps. However, this approach has an exponential post-processing step to construct these overlaps when performing classical shadows obtained using random Clifford circuits. Here, we study an approach to avoid this exponential scaling step by using a fixed-node Monte Carlo method based on full configuration interaction quantum Monte Carlo. This method is applied to the local unitary cluster Jastrow ansatz. We consider H4, ferrocene, and benzene molecules using up to 12 qubits as examples. Circuits are compiled to native gates for typical near-term architectures, and we assess the impact of circuit-level depolarizing noise on the method. We also provide a comparison of AFQMC and fixed-node approaches, demonstrating that AFQMC is more robust to errors, although extrapolations of the fixed-node energy reduce this discrepancy. Although the method can be used to reach chemical accuracy, the sampling cost to achieve this is high even for small active spaces, suggesting caution about the prospect of outperforming conventional QMC approaches.

Accurate Neural Network Fine-Tuning Approach for Transferable Ab Initio Energy Prediction across Varying Molecular and Crystalline Scales

Existing machine learning models attempt to predict the energies of large molecules by training small molecules, but eventually fail to retain high accuracy as the errors increase with system size. Through an orbital pairwise decomposition of the correlation energy, a pretrained neural network model on hundred-scale data containing small molecules is demonstrated to be sufficiently transferable for accurately predicting large systems, including molecules and crystals. Our model introduces a residual connection to explicitly learn the pairwise energy corrections, and employs various low-rank retraining techniques to modestly adjust the learned network parameters. We demonstrate that with as few as only one larger molecule retraining the base model originally trained on only small molecules of (H2O)6, the MP2 correlation energy of the large liquid water (H2O)64 in a periodic supercell can be predicted at chemical accuracy. Similar performance is observed for large protonated clusters and periodic poly glycine chains. A demonstrative application is presented to predict the energy ordering of symmetrically inequivalent sublattices for distinct hydrogen orientations in the ice XV phase. Our work represents an important step forward in the quest for cost-effective, highly accurate and transferable neural network models in quantum chemistry, bridging the electronic structure patterns between small and large systems.

Improving Exchange-Correlation Potentials of Standard Density Functionals with the Optimized-Effective-Potential Method for Higher Accuracy of Excitation Energies

We present a general scheme to improve the exchange-correlation potential of standard Kohn-Sham methods, like the PBE (Perdew, Burke, Ernzerhof) or PBE0 method, by enforcing exact conditions the exchange-correlation potential has to obey during their calculation. The required modifications of the potentials are enabled by generating the potentials within the optimized-effective-potential (OEP) framework instead of directly taking the functional derivative with respect to the electron density on a real-space grid as usual. We generalize a condition for the exact exchange potential that involves the eigenvalues of the highest occupied molecular orbital such that it is applicable to arbitrary approximate exchange potentials. The new approach yields strongly improved exchange-correlation potentials which lead to qualitatively and quantitatively improved KS orbital and eigenvalue spectra containing a Rydberg series as required and obeying much better the Kohn-Sham ionization energy theorem. If the resulting orbitals and eigenvalues are used as input quantities in time-dependent density-functional theory (TDDFT) to calculate excitation energies then the accuracy of the latter is drastically improved, e.g., for TDDFT with the PBE functional the accuracy of excitation energies is improved by a factor of roughly three. This make the introduced approach highly attractive for generating input orbitals and eigenvalues for TDDFT but potentially also for high-rung correlation functionals that are typically evaluated in a post-SCF (post self-consistent-field) manner. We apply the new approach to calculate exchange-correlation potentials to the PBE and PBE0 functionals but the approach is generally applicable to any functional.

Large-scale sparse wave function circuit simulator for applications with the variational quantum eigensolver

The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized circuits, but this becomes increasingly challenging with circuit size. As a consequence, the utility of large-scale circuit optimization is relatively unknown. In this work we demonstrate that purely classical resources can be used to optimize quantum circuits in an approximate but robust manner such that we can bridge the resources that we have from high performance computing and see a direct transition to quantum advantage. We show this through the sparse wave function circuit solvers, which we detail here, and demonstrate a region of efficient classic simulation. With such tools, we can avoid the many problems that plague circuit optimization for circuits with hundreds of qubits using only practical and reasonable classical computing resources. These tools allow us to probe the true benefit of variational optimization approaches on quantum computers, thus opening the window to what can be expected with near term hardware for physical systems. We demonstrate this with a unitary coupled cluster ansatz on various molecules up to 64 qubits with tens of thousands of variational parameters.

Diffractive Imaging of Transient Electronic Coherences in Molecules with Electron Vortices

Direct imaging of transient electronic coherences in molecules has been challenging, with the potential to control electron motions and influence reaction outcomes. We propose a novel time-resolved vortex electron diffraction technique to spatially resolve transient electronic coherences in isolated molecules. By analyzing helical dichroism diffraction signals, the contribution of electronic populations cancels out, isolating the purely electronic coherence signals. This allows direct monitoring of the time evolution and decoherence of transient electronic coherences in molecules.

Mott Transition and Volume Law Entanglement with Neural Quantum States

The interplay between delocalization and repulsive interactions can cause electronic systems to undergo a Mott transition between a metal and an insulator. Here we use neural network hidden fermion determinantal states (HFDS) to uncover this transition in the disordered, fully connected Hubbard model. While dynamical mean-field theory (DMFT) provides exact solutions to physical observables of the model in the thermodynamic limit, our method allows us to directly access the wave function for finite system sizes well beyond the reach of exact diagonalization. We demonstrate how HFDS are able to obtain more accurate results in the metallic regime and in the vicinity of the transition than calculations based on a matrix product state (MPS) ansatz, for which the volume law of entanglement exhibited by the system is prohibitive. We use the HFDS method to calculate the energy and double occupancy, the quasiparticle weight and the energy gap and, importantly, the amplitudes of the wave function that provide a novel insight into this model. Our work paves the way for the study of strongly correlated electron systems with neural quantum states.

Photon Many-Body Dispersion: Exchange-Correlation Functional for Strongly Coupled Light-Matter Systems

We introduce an electron-photon exchange-correlation functional for quantum electrodynamical density-functional theory (QEDFT). The approach, photon MBD (pMBD), is inspired by the many-body dispersion (MBD) method for weak intermolecular interactions, which is generalized to include both electronic and photonic (electromagnetic) degrees of freedom on the same footing. We demonstrate that pMBD accurately captures effects that arise in the context of strong light-matter interactions, such as anisotropic electron-photon interactions, beyond single-photon effects, and cavity-modulated van der Waals interactions. Moreover, we show that pMBD is computationally efficient and allows simulations of large complex systems coupled to optical cavities.

Double ionization potential equation-of-motion coupled-cluster approach with full inclusion of 4-hole-2-particle excitations and three-body clusters

The double ionization potential (DIP) equation-of-motion (EOM) coupled-cluster (CC) method with a full treatment of 4-hole-2-particle (4h-2p) correlations and triply excited clusters, abbreviated as DIP-EOMCCSDT(4h-2p), and its approximate form called DIP-EOMCCSD(T)(a)(4h-2p) have been formulated and implemented in the open-source CCpy package available on GitHub. The resulting codes work with both nonrelativistic and spin-free scalar-relativistic Hamiltonians. By examining the DIPs of a few small molecules, for which accurate reference data are available, we demonstrate that the DIP-EOMCCSDT(4h-2p) and DIP-EOMCCSD(T)(a)(4h-2p) approaches improve the results obtained using the DIP-EOMCC methods truncated at 3h-1p or 4h-2p excitations on top of the CC calculations with singles and doubles.

On the entanglement of chromophore and solvent orbitals

Among various types of chromophore-solvent interactions, the entanglement of chromophore and solvent orbitals, when significant, can cause the chromophore frontier orbitals to spread over to nearby solvent molecules, introducing partial charge-transfer character to the lowest excitations of the chromophore and lowering the excitation energies. While highly intuitive, the physical details of such orbital entanglement effects on the excitation energies of chromophores have yet to be fully explored. Here, using two well-known biochromophores (oxyluciferin and p-hydroxybenzyledene imidazolinone) as examples, we show that the chromophore-solvent orbital entanglements can be elucidated using two quantum mechanical embedding schemes: density matrix embedding theory and absolutely localized molecular orbitals. However, there remains a great challenge to incorporate the orbital entanglement effect in combined quantum mechanical molecular mechanical (QM/MM) calculations, and we hope that our findings will stimulate the development of new methods in that direction.

An Implicit Solvation Model for Binding Free Energy Estimation in Nonaqueous Solution

Implicit solvation models permit the approximate description of solute-solvent interactions, where water is the most often considered solvent due to its relevance in biological systems. The use of other solvents is less common but is relevant for applications such as in nuclear magnetic resonance (NMR) or chromatography. As an example, chloroform is commonly used in anisotropic NMR to measure residual dipolar couplings (RDCs) of chiral analytes weakly aligned by an alignment medium. They can be calculated from molecular dynamics (MD) simulations with explicit solvent, but it is computationally expensive, because tens of microseconds-long MD trajectories should be collected. Here, we develop a computational protocol and numerical implementation for binding free energies of rigid organic molecules to poly-γ-benzyl-l-glutamate using an implicit solvation model of chloroform. The model parameters are fit to alchemical binding free energies obtained from MD simulations in explicit chloroform and compared to the MD results and another implicit solvation model. Possible applications of the method are docking or Monte Carlo simulations based on a physically meaningful scoring function for the fast prediction of interaction poses of ligands for selective binding or the alignment of analytes.

Capturing Strong Correlation in Molecules with Phaseless Auxiliary-Field Quantum Monte Carlo Using Generalized Hartree-Fock Trial Wave Functions

Generalized Hartree-Fock (GHF) is a long-established electronic structure method that can lower the energy (compared to spin-restricted variants) by breaking physical wave function symmetries, namely S ^ 2 and S ^ z . After an exposition of GHF theory, we assess the use of GHF trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC-G) calculations of strongly correlated molecular systems including symmetrically stretched hydrogen rings, carbon dioxide, and dioxygen. Imaginary time propagation is able to restore S ^ 2 symmetry and yields energies of comparable or better accuracy than CCSD(T) with unrestricted HF and GHF references, and consistently smooth dissociation curves─a remarkable result given the relative scalability of ph-AFQMC-G to larger system sizes. The present exploration of model strongly correlated systems marks a promising starting point for future studies of more chemically relevant molecules, and demonstrates that ph-AFQMC-G provides a highly accurate (and, in contrast to active-space-based trials, relatively black box and always size-consistent) description of challenging systems exhibiting, e.g., antiferromagnetic coupling and/or geometric spin frustration.

Minimum Energy Conical Intersection Optimization Using DFT/MRCI(2)

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a semiempirical electronic structure approach that is both computationally efficient and has predictive accuracy for the calculation of electronic excited states and for the simulation of electronic spectroscopies. However, given that the reference space is generated via a selected-CI procedure, a challenge arises in the construction of smooth potential energy surfaces. To address this issue, we treat the local discontinuities that arise as noise within the Gaussian progress regression framework and learn the surfaces by explicitly incorporating and optimizing a white-noise kernel. The characteristic polynomial coefficient surfaces of the potential matrix, which are smooth functions of nuclear coordinates even at conical intersections, are learned in place of the adiabatic energies and are used to optimize the DFT/MRCI(2) minimum energy conical intersection geometries for representative intersection motifs in the molecules ethylene, butadiene, and fulvene. One consequence of explicitly treating the noise in the surfaces is that the energy difference cannot be made arbitrarily small at points of nominal intersection. Despite the limitations, however, we find the structures as well as the branching spaces to compare well with ab initio MRCI and conclude that this approach is a viable method to learn a smooth representation of DFT/MRCI(2) surfaces.

Bayesian Flow Network Framework for Chemistry Tasks

In this work, we introduce ChemBFN, a language model that handles chemistry tasks based on Bayesian flow networks working with discrete data. A new accuracy schedule is proposed to improve sampling quality by significantly reducing reconstruction loss. We show evidence that our method is appropriate for generating molecules with satisfied diversity, even when a smaller number of sampling steps is used. A classifier-free guidance method is adapted for conditional generation. It is also worthwhile to point out that after generative training, our model can be fine-tuned on regression and classification tasks with state-of-the-art performance, which opens the gate of building all-in-one models in a single module style. Our model has been open sourced at https://github.com/Augus1999/bayesian-flow-network-for-chemistry.