Size-Transferable Prediction of Excited State Properties for Molecular Assemblies with a Machine Learning Exciton Model

Computational modeling of the excited states of molecular aggregates faces significant computational challenges and size heterogeneity. Current machine learning (ML) models, typically trained on specific-sized aggregates, struggle with scalability. We found that the exciton model Hamiltonian of large aggregates can be decomposed into dimer pairs, allowing an ML model trained on dimers to reconstruct Hamiltonians for aggregates of any size. We also proposed a new method to address the phase-correction problem by introducing coupling terms' approximations. Our model accurately predicted the excitation energies of the trimer and tetramer of perylene and tetracene and estimated S1 oscillator strengths of perylene aggregates. Leveraging our ML model, the optical gaps of nanosized perylene aggregates with up to 50 monomers are analyzed, qualitatively revealing the role of different couplings on their size dependency. Future work will explore transferability across different monomers to predict optical properties in heterogeneous assemblies.

Accelerated linear algebra for large scale DFT calculations of materials on CPU/GPU architectures with CRYSTAL

We discuss the implementation strategy, numerical accuracy, and computational performance of the acceleration of linear algebra operations through graphics processing units (GPUs) for the self-consistent field driver of the Crystal electronic structure package for solid state density functional theory simulations. Accelerated tasks include matrix multiplication, diagonalization, and inversion, as well as Cholesky decomposition. The scaling of the implemented strategy over multiple accelerating devices is assessed in the range of 1-8 GPUs per node and found to be remarkably regular. Tests are performed on three systems: α-quartz, a microporous zeolitic imidazolate framework (ZIF-8), and a giant mesoporous metal-organic framework (bio-MOF). Scaling with system size is investigated via supercells of increasing size of both α-quartz and ZIF-8 (up to 648 and 2208 atoms per cell, respectively). The bio-MOF model structure has 2808 atoms per cell, with 33 672 basis functions. We test the performance of the accelerated code with both generalized gradient approximation (GGA) and hybrid GGA exchange-correlation functionals. The efficiency of the new accelerated code is compared to the previous central processing unit (CPU)-only parallelization strategies based on MPI or MPI/OpenMP within either replicated or distributed memory (i.e., massively parallel) approaches. Such a comparison highlights how the new GPU-accelerated code enables calculations on large systems at a significantly reduced computational cost relative to CPU-only strategies. For instance, we find that for the bio-MOF system, the computing time of the linear algebra tasks from a single GPU is comparable to that from the reference approach in the range of 512-1024 CPU cores and 4-8 nodes.

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.

Neural Network Potential with Multiresolution Approach Enables Accurate Prediction of Reaction Free Energies in Solution

We present the design and implementation of a novel neural network potential (NNP) and its combination with an electrostatic embedding scheme, commonly used within the context of hybrid quantum-mechanical/molecular-mechanical (QM/MM) simulations. Substitution of a computationally expensive QM Hamiltonian by an NNP with the same accuracy largely reduces the computational cost and enables efficient sampling in prospective MD simulations, the main limitation faced by traditional QM/MM setups. The model relies on the recently introduced anisotropic message passing (AMP) formalism to compute atomic interactions and encode symmetries found in QM systems. AMP is shown to be highly efficient in terms of both data and computational costs and can be readily scaled to sample systems involving more than 350 solute and 40,000 solvent atoms for hundreds of nanoseconds using umbrella sampling. Most deviations of AMP predictions from the underlying DFT ground truth lie within chemical accuracy (4.184 kJ mol-1). The performance and broad applicability of our approach are showcased by calculating the free-energy surface of alanine dipeptide, the preferred ligation states of nickel phosphine complexes, and dissociation free energies of charged pyridine and quinoline dimers. Results with this ML/MM approach show excellent agreement with experimental data and reach chemical accuracy in most cases. In contrast, free energies calculated with static DFT calculations paired with implicit solvent models or QM/MM MD simulations using cheaper semiempirical methods show up to ten times higher deviation from the experimental ground truth and sometimes even fail to reproduce qualitative trends.

Digging out the Molecular Connections between the Catalytic Mechanism of Human Lysosomal α-Mannosidase and Its Pathophysiology

Human lysosomal α-mannosidase (hLAMAN) is a paradigmatic example of how a few missense mutations can critically affect normal catabolism in the lysosome and cause the severe condition named α-mannosidosis. Here, using extensive quantum mechanical/molecular mechanical metadynamics calculations, we show how four reported pathological orthosteric and allosteric single-point mutations alter substrate puckering in the Michaelis complex and how the D74E mutation doubles the energy barrier of the rate-limiting step compared to the wild-type enzyme.

Extreme Isotopic Fractionation in CO and H2 Formed in Formaldehyde Photolysis: Theory and Experiment

Formaldehyde (HCHO) is an important intermediate in the breakdown of organic molecules in the atmosphere. It is the most abundant atmospheric carbonyl, and a major source of CO and H2 upon degradation. Isotopic analysis offers valuable insights into molecular processes, deepening our understanding of atmospheric transformations. We present a model of the isotope-dependent photolytic isotopic fractionation of formaldehyde incorporating Rice-Ramsperger-Kassel-Marcus (RRKM) analysis, validate the model with new and pre-existing experimental data, and use it to describe photolytic kinetic isotope effects (KIEs) and their pressure dependencies. RRKM theory was used to calculate decomposition rates of the S0, S1, and T1 states, using CCSD(T)/aug-cc-pVTZ, ωB97X-D/aug-cc-pVTZ, and CASPT2/aug-cc-pVTZ, respectively. We considered isotopologues HCHO, DCHO, DCDO, D13CHO, H13CHO, HCH17O, HCH18O, H13CH17O, and H13CH18O. We find that isotopic substitution notably affects the density of states, influencing rates of unimolecular decomposition and collisional energy transfer. Experimental photolysis rates ranged from j H C H O / j H C H 18 O = 1.027 ± 0.006 at 50 mbar to jHCHO/jDCDO = 1.418 ± 0.108 at 1000 mbar using a xenon lamp. The model accurately reproduced experimental pressure trends in KIEs, revealing that altitude-dependent deuterium enrichment in H2 cannot be explained by pressure effects alone and must also consider wavelength dependence.

pyVPT2: Interoperable software for anharmonic vibrational frequency calculations

We present pyVPT2, a program to perform second-order vibrational perturbation theory (VPT2) computations to obtain anharmonic vibrational frequencies. This program is written in Python and can utilize any of the several quantum chemistry programs that have been interfaced to the QCEngine project of the Molecular Sciences Software Institute (MolSSI). The requisite single point energy, gradient, or Hessian computations can be automatically performed in a distributed-parallel fashion by optionally using the MolSSI's QCFractal software. With pyVPT2, VPT2 anharmonic frequencies can now be computed using quantum chemistry programs that lack their own VPT2 capabilities.

VeloxChem: GPU-Accelerated Fock Matrix Construction Enabling Complex Polarization Propagator Simulations of Circular Dichroism Spectra of G-Quadruplexes

An automatic code generated C++/HIP/CUDA implementation of the (auxiliary) Fock, or Kohn-Sham, matrix construction for execution in GPU-accelerated hardware environments is presented. The module is developed as part of the quantum chemistry software package VeloxChem, employing localized Gaussian atomic orbitals. The performance and scaling characteristics are analyzed in view of the specific requirements for self-consistent field optimization and response theory calculations. As an example, the electronic circular dichroism spectrum of a G-quadruplex is calculated at the level of time-dependent density functional theory in conjunction with the range-separated CAM-B3LYP exchange-correlation functional. Computational issues due to the high-density of states following the adoption of large-scale model systems are here bypassed with use of the complex polarization propagator approach. The origin of the negative Cotton effect in the long-wavelength onset of the experimental spectrum is elucidated in large-scale modeling and shown to be associated with the TTA nucleobase linkers in the G-quadruplex.

Acceleration of Diffusion in Ab Initio Nanoreactor Molecular Dynamics and Application to Hydrogen Sulfide Oxidation

The computational description of chemical reactivity can become extremely complex when multiple different reaction products and intermediates come into play, forming a chemical reaction network. Therefore, computational methods for the automated construction of chemical reaction networks have been developed in the last decades. One of these methods, ab initio nanoreactor molecular dynamics (NMD), is based on external forces enhancing reactivity by e.g., periodically compressing the system and allowing it to relax. However, during the relaxation process, a significant simulation time is required to allow energy to dissipate and molecules to diffuse, making this part of the NMD simulation computationally intensive. This work aims to improve NMD by accelerating the diffusion process in the relaxation phase. We systematically investigate the speedup of reaction discovery gained by diffusion acceleration, leading to a factor of up to 28 in discovery frequency. Diffusion-accelerated nanoreactor molecular dynamics (DA-NMD) is then used to construct a reaction network of hydrogen sulfide oxidation under atmospheric conditions, where reactions are automatically detected by a change in the bond order and bond distance. A reaction network of 108 molecular species and 399 elementary reactions was constructed starting from hydrogen sulfide, hydroxy radicals, and molecular oxygen covering a broad variety of sulfur-oxygen chemistry and oxidation states of the sulfur atom ranging from -II to +VI.

Factors governing H 3 + formation from methyl halogens and pseudohalogens

The formation ofH 3 + following the double ionization of small organic compounds via a roaming mechanism, which involves the generation of H2 and subsequent proton abstraction, has recently garnered significant attention. Nonetheless, a cohesive model explaining trends in the yield ofH 3 + characterizing these unimolecular reactions is yet to be established. We report yield and femtosecond time-resolved measurements following the strong-field double ionization of CH3X molecules, where X = OD, Cl, NCS, CN, SCN, and I. These measurements, combined with double-ionization-potential equation-of-motion coupled-cluster ab initio calculations used to determine the geometries and energetics of CH3X2+ dications, are employed to identify the key factors governing the formation ofH 3 + in certain doubly ionized CH3X species and its absence in others. We also carry out ab initio molecular dynamics simulations to obtain detailed microscopic insights into the mechanism, yields, and timescales ofH 3 + production. We find that the excess relaxation energy released after double ionization of CH3X molecules combined with substantial geometrical distortion that favors H2 formation prior to proton abstraction boost the generation ofH 3 + . Our study provides useful guidelines for examining alternative sources ofH 3 + in the universe.

Acceleration without Disruption: DFT Software as a Service

Density functional theory (DFT) has been a cornerstone in computational chemistry, physics, and materials science for decades, benefiting from advancements in computational power and theoretical methods. This paper introduces a novel, cloud-native application, Accelerated DFT, which offers an order of magnitude acceleration in DFT simulations. By integrating state-of-the-art cloud infrastructure and redesigning algorithms for graphic processing units (GPUs), Accelerated DFT achieves high-speed calculations without sacrificing accuracy. It provides a user-friendly and scalable solution for the increasing demands of DFT calculations in scientific communities. The implementation details, examples, and benchmark results illustrate how Accelerated DFT can significantly expedite scientific discovery across various domains.

Ligand Many-Body Expansion as a General Approach for Accelerating Transition Metal Complex Discovery

Methods that accelerate the evaluation of molecular properties are essential for chemical discovery. While some degree of ligand additivity has been established for transition metal complexes, it is underutilized in asymmetric complexes, such as the square pyramidal coordination geometries highly relevant to catalysis. To develop predictive methods beyond simple additivity, we apply a many-body expansion to octahedral and square pyramidal complexes and introduce a correction based on adjacent ligands (i.e., the cis interaction model). We first test the cis interaction model on adiabatic spin-splitting energies of octahedral Fe(II) complexes, predicting DFT-calculated values of unseen binary complexes to within an average error of 1.4 kcal/mol. Uncertainty analysis reveals the optimal basis, comprising the homoleptic and mer symmetric complexes. We next show that the cis model (i.e., the cis interaction model solved for the optimal basis) infers both DFT- and CCSD(T)-calculated model catalytic reaction energies to within 1 kcal/mol on average. The cis model predicts low-symmetry complexes with reaction energies outside the range of binary complex reaction energies. We observe that trans interactions are unnecessary for most monodentate systems but can be important for some combinations of ligands, such as complexes containing a mixture of bidentate and monodentate ligands. Finally, we demonstrate that the cis model may be combined with Δ-learning to predict CCSD(T) reaction energies from exhaustively calculated DFT reaction energies and the same fraction of CCSD(T) reaction energies needed for the cis model, achieving around 30% of the error from using the CCSD(T) reaction energies in the cis model alone.

Advanced Techniques for High-Performance Fock Matrix Construction on GPU Clusters

This Article presents two optimized multi-GPU algorithms for Fock matrix construction, building on the work of Ufimtsev and Martinez [ J. Chem. Theory Comput. 2009, 5, 1004-1015] and Barca et al. [ J. Chem. Theory Comput. 2021, 17, 7486-7503]. The novel algorithms, opt-UM and opt-Brc, introduce significant enhancements, including improved integral screening, exploitation of sparsity and symmetry, a linear scaling exchange matrix assembly algorithm, and extended capabilities for Hartree-Fock caculations up to f-type angular momentum functions. Opt-Brc excels for smaller systems and for highly contracted triple-ζ basis sets, while opt-UM is advantageous for large molecular systems. Performance benchmarks on NVIDIA A100 GPUs show that our algorithms in the EXtreme-scale Electronic Structure System (EXESS), when combined, outperform all current GPU and CPU Fock build implementations in TeraChem, QUICK, GPU4PySCF, LibIntX, ORCA, and Q-Chem. The implementations were benchmarked on linear and globular systems and average speed ups across three double-ζ basis sets of 1.4×, 8.4×, and 9.4× were observed compared to TeraChem, QUICK, and GPU4PySCF respectively. An increased average speedup of 2.1× over TeraChem is observed when using four A100 GPUs. Strong scaling analysis reveals over 91% parallel efficiency on four GPUs for opt-Brc, making it typically faster for multi-GPU execution. Single-compute-node comparisons with CPU-based software like ORCA and Q-Chem show speedups of up to 42× and 31×, respectively, enhancing power efficiency by up to 18×.

Delving into Macrolide Binding Affinities and Associated Structural Modulations in Erythromycin Esterase C: Insights into the Venus Flytrap Mechanism

Since their inception in antibacterial therapy, macrolide-based antibiotics have significantly shaped the evolutionary pathways of pathogenic bacteria, driving them to develop diverse antimicrobial resistance (AMR) mechanisms. Among these, macrolide esterase, commonly referred to as erythromycin esterase, emerged as a critical defense mechanism, enabling bacteria to detoxify macrolides by hydrolyzing the macrolactone ring within the bacterial cell. In this study, we delve into the intricate interactions and conformational dynamics of erythromycin esterase C (EreC), a key member of the Ere enzyme family. We have focused on three FDA-approved and widely prescribed macrolides─erythromycin, clarithromycin, and azithromycin─by employing classical molecular dynamics, absolute binding free energy calculations, and 2D well-tempered metadynamics simulations to explore their interactions with EreC. To estimate the absolute binding free energies, we have used the recently developed and robust "Streamlined Alchemical Free Energy Perturbation (SAFEP)" protocol. The results from our molecular dynamics simulations and advanced analyses portrayed the crucial role of hydrophobic interactions within the macrolide binding cleft of EreC, along with the significant influence of the minor lobe in facilitating overall structural fluctuation. In silico alanine scanning identified top three hydrophobic residues, i.e., PHE248, MET333, and PHE344, responsible for macrolide binding inside that cleft. According to the free energy calculations, azithromycin and clarithromycin showed greater binding affinities toward EreC than the parent macrolide erythromycin. Moreover, 2D metadynamics simulations along with graph theory-based eigenvector centrality analyses revealed a metastable "semiopen" state during the hypothesized "active loop closure" of the EreC protein triggered by subtle conformational changes of an important histidine residue, HIS289, upon macrolide capture, drawing a fascinating parallel to the renowned "Venus flytrap" mechanism.

Force-Assisted Orbital Crossing in Mechanochemical Oxirane Ring Opening

Polymer mechanochemistry induces chemical reactivity by applying a directed force, which can lead to unexpected reaction mechanisms. Strained cyclic molecules are often used in force-sensitive motifs because of the strong force coupling of ring-opening reactions. In this computational study, the force dependence of the ring-opening reactions of oxirane will be investigated. Density functional theory and multireference methods were used to investigate the electronic character of both symmetry-allowed and symmetry-forbidden reactions. In the latter case, an orbital crossing occurs during the reaction course, forcing the Woodward-Hoffmann-forbidden reaction to proceed via a diradical pathway. The performance of broken-symmetry density functional theory is evaluated and compares well to high-accuracy CASPT2, MRCI, and ic-MRCC computations. Due to the high ring strain, the barrier heights of both ring-opening reactions are steeply reduced by the application of an external force. Furthermore, the use of unsaturated linkers was shown to yield a significant reduction of the barrier heights, explaining previous experimental findings. Finally, we show through analysis of the PES topology how the external force transforms characteristic points such as saddle points and bifurcations, providing insights into force-dependent mechanism changes.

Catching the π-Stacks: Prediction of Aggregate Structures of Porphyrin

π-π interactions decisively shape the supramolecular structure and functionality of π-conjugated molecular semiconductor materials. Despite the customizable molecular building blocks, predicting their supramolecular structure remains a challenge. Traditionally, force field methods have been used due to the complexity of these structures, but advances in computational power have enabled ab initio approaches such as density functional theory (DFT). DFT is particularly suitable for finding energetically favorable structures of dye aggregates, which are determined by a large number of different interactions, but a systematic aggregate search can still be very challenging due to the large number of possible geometries. In this work, we show ways to overcome this challenge. We investigate how finely translational and rotational lattices must be structured to identify all energetic minima of π-stack structures, focusing on porphyrins as a prototype challenge. Our approach involves single-point DFT calculations of systematically varied dimer geometries, identification of local energy minima, hierarchical grouping of geometrically similar structures, and optimization of the energetically favorable representatives of each geometric family. This ab initio method provides a general framework for the systematic prediction of aggregate structures and reveals geometrically diverse and energetically favorable dimers.

Parallel Implementation of the Density Matrix Renormalization Group Method Achieving a Quarter petaFLOPS Performance on a Single DGX-H100 GPU Node

We report cutting edge performance results on a single node hybrid CPU-multi-GPU implementation of the spin adapted ab initio Density Matrix Renormalization Group (DMRG) method on current state-of-the-art NVIDIA DGX-H100 architectures. We evaluate the performance of the DMRG electronic structure calculations for the active compounds of the FeMoco, the primary cofactor of nitrogenase, and cytochrome P450 (CYP) enzymes with complete active space (CAS) sizes of up to 113 electrons in 76 orbitals [CAS(113, 76)] and 63 electrons in 58 orbitals [CAS(63, 58)], respectively. We achieve 246 teraFLOPS of sustained performance, an improvement of more than 2.5× compared to the performance achieved on the DGX-A100 architectures and an 80× acceleration compared to an OpenMP parallelized implementation on a 128-core CPU architecture. Our work highlights the ability of tensor network algorithms to efficiently utilize high-performance multi-GPU hardware and shows that the combination of tensor networks with modern large-scale GPU accelerators can pave the way toward solving some of the most challenging problems in quantum chemistry and beyond.

Unravelling the prebiotic origins of the simplest α-ketoacids in cometary ices: a computational investigation

We have employed the ab initio nanoreactor (AINR) and DFT calculations to explore how the soft impact of comets entering early earth's dense atmosphere could induce chemical reactions in trapped interstellar ice components, leading to the origin of glyoxylic and pyruvic acids the simplest α-ketoacids essential for prebiotic metabolic cycles.

Molecular Basis of the Substrate Specificity of Phosphotriesterase from Pseudomonas diminuta: A Combined QM/MM MD and Electron Density Study

The occurrence of organophosphorus compounds, pesticides, and flame-retardants in wastes is an emerging ecological problem. Bacterial phosphotriesterases are capable of hydrolyzing some of them. We utilize modern molecular modeling tools to study the hydrolysis mechanism of organophosphorus compounds with good and poor leaving groups by phosphotriesterase from Pseudomonas diminuta (Pd-PTE). We compute Gibbs energy profiles for enzymes with different cations in the active site: native Zn2+cations and Co2+cations, which increase the steady-state rate constant. Hydrolysis occurs in two elementary steps via an associative mechanism and formation of the pentacoordinated intermediate. The first step, a nucleophilic attack, occurs with a low energy barrier independently of the substrate. The second step has a low energy barrier and considerable stabilization of products for substrates with good leaving groups. For substrates with poor leaving groups, the reaction products are destabilized relative to the ES complex that suppresses the reaction. The reaction proceeds with low energy barriers for substrates with good leaving groups with both Zn2+and Co2+cations in the active site; thus, the product release is likely to be a limiting step. Electron density and geometry analysis of the QM/MM MD trajectories of the intermediate states with all considered compounds allow us to discriminate substrates by their ability to be hydrolyzed by the Pd-PTE. For hydrolyzable substrates, the cleaving bond between a phosphorus atom and a leaving group is elongated, and electron density depletion is observed on the Laplacian of electron density maps.

Multi-GPU RI-HF Energies and Analytic Gradients─Toward High-Throughput Ab Initio Molecular Dynamics

This article presents an optimized algorithm and implementation for calculating resolution-of-the-identity Hartree-Fock (RI-HF) energies and analytic gradients using multiple graphics processing units (GPUs). The algorithm is especially designed for high throughput ab initio molecular dynamics simulations of small and medium size molecules (10-100 atoms). Key innovations of this work include the exploitation of multi-GPU parallelism and a workload balancing scheme that efficiently distributes computational tasks among GPUs. Our implementation also employs techniques for symmetry utilization, integral screening, and leveraging sparsity to optimize memory usage. Computational results show that the implementation achieves significant performance improvements, including over 3 × speedups in single GPU AIMD throughput compared to previous GPU-accelerated RI-HF and traditional HF methods. Furthermore, utilizing multiple GPUs can provide superlinear speedup when the additional aggregate GPU memory allows for the storage of decompressed three-center integrals.

A novel approach for low-temperature synthesis of nanostructured rutile-like Ti1-x Fe x O2 solid solutions

We present a straightforward method for synthesizing rutile-like Ti1-x Fe x O2 solid solutions at 90 °C, with x = 0.02, 0.04, 0.06, and 0.08. Additionally, for reference, we synthesized Fe-free rutile under identical conditions. All samples were characterized using XRPD, Rietveld refinement, elemental analysis, and specific surface area. Further characterization of the pure rutile and the solid solution with x = 0.04 was conducted using HRTEM, SEM-EDS, Raman spectroscopy, UV-vis DRS, and Mössbauer spectroscopy. The results indicated that Fe atoms incorporated into the crystalline structure of rutile, replacing Ti atoms. All phases exhibited a tetragonal crystalline structure with lattice parameters that increased with Fe content. Rietveld refinement and the electron microscopy revealed that the crystallites had a morphology elongated along the c-axis. Experimental evidence showed that the incorporation of iron into the crystalline structure altered the optical properties, as corroborated through DFT calculations on a Fe-free rutile cluster and one doped with Fe. These calculations also suggest enhancement of the stability of the solid solutions.

GPU-accelerated on-the-fly nonadiabatic semiclassical dynamics

GPU-accelerated on-the-fly nonadiabatic dynamics is enabled by interfacing the linearized semiclassical dynamics approach with the TeraChem electronic structure program. We describe the computational workflow of the "PySCES" code interface, a Python code for semiclassical dynamics with on-the-fly electronic structure, including parallelization over multiple GPU nodes. We showcase the abilities of this code and present timings for two benchmark systems: fulvene solvated in acetonitrile and a charge transfer system in which a photoexcited zinc-phthalocyanine donor transfers charge to a fullerene acceptor through multiple electronic states on an ultrafast timescale. Our implementation paves the way for an efficient semiclassical approach to model the nonadiabatic excited state dynamics of complex molecules, materials, and condensed phase systems.

LibERI-A portable and performant multi-GPU accelerated library for electron repulsion integrals via OpenMP offloading and standard language parallelism

A portable and performant graphics processing unit (GPU)-accelerated library for electron repulsion integral (ERI) evaluation, named LibERI, has been developed and implemented via directive-based (e.g., OpenMP and OpenACC) and standard language parallelism (e.g., Fortran DO CONCURRENT). Offloaded ERIs consist of integrals over low and high contraction s, p, and d functions using the rotated-axis and Rys quadrature methods. GPU codes are factorized based on previous developments [Pham et al., J. Chem. Theory Comput. 19(8), 2213-2221 (2023)] with two layers of integral screening and quartet presorting. In this work, the density screening is moved to the GPU to enhance the computational efficacy for large molecular systems. The L-shells in the Pople basis set are also separated into pure S and P shells to increase the ERI homogeneity and reduce atomic operations and the memory footprint. LibERI is compatible with any quantum chemistry drivers supporting the MolSSI Driver Interface. Benchmark calculations of LibERI interfaced with the GAMESS software package were carried out on various GPU architectures and molecular systems. The results show that the LibERI performance is comparable to other state-of-the-art GPU-accelerated codes (e.g., TeraChem and GMSHPC) and, in some cases, outperforms conventionally developed ERI CUDA kernels (e.g., QUICK) while fully maintaining portability.

Perspective on Theoretical and Experimental Advances in Atmospheric Photochemistry

Research that explores the chemistry of Earth's atmosphere is central to the current understanding of global challenges such as climate change, stratospheric ozone depletion, and poor air quality in urban areas. This research is a synergistic combination of three established domains: earth observation, for example, using satellites, and in situ field measurements; computer modeling of the atmosphere and its chemistry; and laboratory measurements of the properties and reactivity of gas-phase molecules and aerosol particles. The complexity of the interconnected chemical and photochemical reactions which determine the composition of the atmosphere challenges the capacity of laboratory studies to provide the spectroscopic, photochemical, and kinetic data required for computer models. Here, we consider whether predictions from computational chemistry using modern electronic structure theory and nonadiabatic dynamics simulations are becoming sufficiently accurate to supplement quantitative laboratory data for wavelength-dependent absorption cross-sections, photochemical quantum yields, and reaction rate coefficients. Drawing on presentations and discussions from the CECAM workshop on Theoretical and Experimental Advances in Atmospheric Photochemistry held in March 2024, we describe key concepts in the theory of photochemistry, survey the state-of-the-art in computational photochemistry methods, and compare their capabilities with modern experimental laboratory techniques. From such considerations, we offer a perspective on the scope of computational (photo)chemistry methods based on rigorous electronic structure theory to become a fourth core domain of research in atmospheric chemistry.

Boosting the Modeling of Infrared and Raman Spectra of Bulk Phase Chromophores with Machine Learning

In the field of vibrational spectroscopy simulation, hybrid approximations to Kohn-Sham density-functional theory (KS-DFT) are often considered computationally prohibitive due to the significant effort required to evaluate the exchange-correlation potential in planewave codes. In this Letter, we show that by leveraging the porting of KS-DFT on GPU and incorporating machine-learning techniques, simulating IR and Raman spectra of real-life chromophores in bulk aqueous solution becomes a routine application at this level of theory.

Ultrafast studies of elusive chemical reactions in the gas phase

The chemical composition of the interstellar medium and planetary atmospheres is constantly in flux as atoms and molecules collide and interact with high-energy particles such as electrons, protons, and photons. These transformative processes ultimately lead to the coalescence of molecules and eventually the birth of stars. Our understanding of these chemical ecosystems relies on models that synthesize data from gas-phase experiments, providing insights into reaction cross sections. This Review examines efforts to delve into the fundamental bond-forming and bond-breaking dynamics that occur during bimolecular and electron-initiated reactions. These experiments involve clever approaches to establish a time reference and the collision geometry necessary for tracking atomic motion with femtosecond time resolution. Findings from these efforts enhance present models and improve predictions for molecule-molecule and electron-molecule collisions.

Advancing biomolecular simulation through exascale HPC, AI and quantum computing

Biomolecular simulation can act as both a digital microscope and a crystal ball; offering the potential for a deeper understanding of experimental observations whilst also presenting a forward-looking avenue for the in silico design and evaluation of hitherto unsynthesized compounds. Indeed, as the intricacy of our scientific inquiries has grown, so too has the computational prowess we seek to deploy in our pursuit of answers. As we enter the Exascale era, this mini-review surveys the computational landscape from both the point of view of the development of new and ever more powerful systems, and the simulations that are run on them. Moreover, as we stand on the cusp of a transformative phase in computational biology, this article offers a contemplative glance into the future, speculating on the profound implications of artificial intelligence and quantum computing for large-scale biomolecular simulations.

A Polarizable QM/MM Model That Combines the State-Averaged CASSCF and AMOEBA Force Field for Photoreactions in Proteins

This study presents the polarizable quantum mechanics/molecular mechanics (QM/MM) embedding of the state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field for the purpose of studying photoreactions in protein environments. We describe two extensions of our previous work that combine SA-CASSCF with AMOEBA water models, allowing it to be generalized to AMOEBA models for proteins and other macromolecules. First, we discuss how our QM/MM model accounts for the discrepancy between the direct and polarization electric fields that arises in the AMOEBA description of intramolecular polarization. A second improvement is the incorporation of link atom schemes to treat instances in which the QM/MM boundary goes through covalent bonds. A single-link atom scheme and double-link atom scheme are considered in this work, and we will discuss how electrostatic interaction, van der Waals interaction, and various kinds of valence terms are treated across the boundary. To test the accuracy of the link atom scheme, we will compare QM/MM with full QM calculations and study how the errors in ground state properties, excited state properties, and excitation energies change when tuning the parameters in the link atom scheme. We will also test the new SA-CASSCF/AMOEBA method on an elementary reaction step in NanoLuc, an artificial bioluminescence luciferase. We will show how the reaction mechanism is different when calculated in the gas phase, in polarizable continuum medium (PCM), versus in protein AMOEBA models.

Molecular Basis of Influence of A501X Mutations in Penicillin-Binding Protein 2 of Neisseria gonorrhoeae Strain 35/02 on Ceftriaxone Resistance

The increase in the resistance of mutant strains of Neisseria gonorrhoeae to the antibiotic ceftriaxone is pronounced in the decrease in the second-order acylation rate constant, k2/KS, by penicillin-binding protein 2 (PBP2). These changes can be caused by both the decrease in the acylation rate constant, k2, and the weakening of the binding affinity, i.e., an increase in the substrate constant, KS. A501X mutations in PBP2 affect second-order acylation rate constants. The PBP2A501V variant exhibits a higher k2/KS value, whereas for PBP2A501R and PBP2A501P variants, these values are lower. We performed molecular dynamic simulations with both classical and QM/MM potentials to model both acylation energy profiles and conformational dynamics of four PBP2 variants to explain the origin of k2/KS changes. The acylation reaction occurs in two elementary steps, specifically, a nucleophilic attack by the oxygen atom of the Ser310 residue and C-N bond cleavage in the β-lactam ring accompanied by the elimination of the leaving group of ceftriaxone. The energy barrier of the first step increases for PBP2 variants with a decrease in the observed k2/KS value. Submicrosecond classic molecular dynamic trajectories with subsequent cluster analysis reveal that the conformation of the β3-β4 loop switches from open to closed and its flexibility decreases for PBP2 variants with a lower k2/KS value. Thus, the experimentally observed decrease in the k2/KS in A501X variants of PBP2 occurs due to both the decrease in the acylation rate constant, k2, and the increase in KS.

Calculating absorption and fluorescence spectra for chromophores in solution with ensemble Franck-Condon methods

Accurately modeling absorption and fluorescence spectra for molecules in solution poses a challenge due to the need to incorporate both vibronic and environmental effects, as well as the necessity of accurate excited state electronic structure calculations. Nuclear ensemble approaches capture explicit environmental effects, Franck-Condon methods capture vibronic effects, and recently introduced ensemble-Franck-Condon approaches combine the advantages of both methods. In this study, we present and analyze simulated absorption and fluorescence spectra generated with combined ensemble-Franck-Condon approaches for three chromophore-solvent systems and compare them to standard ensemble and Franck-Condon spectra, as well as to the experiment. Employing configurations obtained from ground and excited state ab initio molecular dynamics, three combined ensemble-Franck-Condon approaches are directly compared to each other to assess the accuracy and relative computational time. We find that the approach employing an average finite-temperature Franck-Condon line shape generates spectra nearly identical to the direct summation of an ensemble of Franck-Condon spectra at one-fourth of the computational cost. We analyze how the spectral simulation method, as well as the level of electronic structure theory, affects spectral line shapes and associated Stokes shifts for 7-nitrobenz-2-oxa-1,3-diazol-4-yl and Nile red in dimethyl sulfoxide and 7-methoxy coumarin-4-acetic acid in methanol. For the first time, our studies show the capability of combined ensemble-Franck-Condon methods for both absorption and fluorescence spectroscopy and provide a powerful tool for simulating linear optical spectra.

STORMM: Structure and topology replica molecular mechanics for chemical simulations

The Structure and TOpology Replica Molecular Mechanics (STORMM) code is a next-generation molecular simulation engine and associated libraries optimized for performance on fast, vectorized central processor units and graphics processing units (GPUs) with independent memory and tens of thousands of threads. STORMM is built to run thousands of independent molecular mechanical calculations on a single GPU with novel implementations that tune numerical precision, mathematical operations, and scarce on-chip memory resources to optimize throughput. The libraries are built around accessible classes with detailed documentation, supporting fine-grained parallelism and algorithm development as well as copying or swapping groups of systems on and off of the GPU. A primary intention of the STORMM libraries is to provide developers of atomic simulation methods with access to a high-performance molecular mechanics engine with extensive facilities to prototype and develop bespoke tools aimed toward drug discovery applications. In its present state, STORMM delivers molecular dynamics simulations of small molecules and small proteins in implicit solvent with tens to hundreds of times the throughput of conventional codes. The engineering paradigm transforms two of the most memory bandwidth-intensive aspects of condensed-phase dynamics, particle-mesh mapping, and valence interactions, into compute-bound problems for several times the scalability of existing programs. Numerical methods for compressing and streamlining the information present in stored coordinates and lookup tables are also presented, delivering improved accuracy over methods implemented in other molecular dynamics engines. The open-source code is released under the MIT license.

Closing Kok's cycle of nature's water oxidation catalysis

The Mn4CaO5(6) cluster in photosystem II catalyzes water splitting through the Si state cycle (i = 0-4). Molecular O2 is formed and the natural catalyst is reset during the final S3 → (S4) → S0 transition. Only recently experimental breakthroughs have emerged for this transition but without explicit information on the S0-state reconstitution, thus the progression after O2 release remains elusive. In this report, our molecular dynamics simulations combined with density functional calculations suggest a likely missing link for closing the cycle, i.e., restoring the first catalytic state. Specifically, the formation of closed-cubane intermediates with all hexa-coordinate Mn is observed, which would undergo proton release, water dissociation, and ligand transfer to produce the open-cubane structure of the S0 state. Thereby, we theoretically identify the previously unknown structural isomerism in the S0 state that acts as the origin of the proposed structural flexibility prevailing in the cycle, which may be functionally important for nature's water oxidation catalysis.

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning

Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S2). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. We use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.

GENESIS 2.1: High-Performance Molecular Dynamics Software for Enhanced Sampling and Free-Energy Calculations for Atomistic, Coarse-Grained, and Quantum Mechanics/Molecular Mechanics Models

GENeralized-Ensemble SImulation System (GENESIS) is a molecular dynamics (MD) software developed to simulate the conformational dynamics of a single biomolecule, as well as molecular interactions in large biomolecular assemblies and between multiple biomolecules in cellular environments. To achieve the latter purpose, the earlier versions of GENESIS emphasized high performance in atomistic MD simulations on massively parallel supercomputers, with or without graphics processing units (GPUs). Here, we implemented multiscale MD simulations that include atomistic, coarse-grained, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. They demonstrate high performance and are integrated with enhanced conformational sampling algorithms and free-energy calculations without using external programs except for the QM programs. In this article, we review new functions, molecular models, and other essential features in GENESIS version 2.1 and discuss ongoing developments for future releases.

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

Development of Parallel On-the-Fly Algorithm for Global Exploration of Conical Intersection Seam Space

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

Multiscale biomolecular simulations in the exascale era

The complexity of biological systems and processes, spanning molecular to macroscopic scales, necessitates the use of multiscale simulations to get a comprehensive understanding. Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations are crucial for capturing processes beyond the reach of classical MD simulations. The advent of exascale computing offers unprecedented opportunities for scientific exploration, not least within life sciences, where simulations are essential to unravel intricate molecular mechanisms underlying biological processes. However, leveraging the immense computational power of exascale computing requires innovative algorithms and software designs. In this context, we discuss the current status and future prospects of multiscale biomolecular simulations on exascale supercomputers with a focus on QM/MM MD. We highlight our own efforts in developing a versatile and high-performance multiscale simulation framework with the aim of efficient utilization of state-of-the-art supercomputers. We showcase its application in uncovering complex biological mechanisms and its potential for leveraging exascale computing.

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

Kinetic View of Enzyme Catalysis from Enhanced Sampling QM/MM Simulations

The rate constants of enzyme-catalyzed reactions (kcat) are often approximated from the barrier height of the reactive step. We introduce an enhanced sampling QM/MM approach that directly calculates the kinetics of enzymatic reactions, without introducing the transition-state theory assumptions, and takes into account the dynamical equilibrium between the reactive and non-reactive conformations of the enzyme/substrate complex. Our computed kcat values are in order-of-magnitude agreement with the experimental data for two representative enzymatic reactions.

Coherence mapping to identify the intermediates of multi-channel dissociative ionization

Identifying the short-lived intermediates and reaction mechanisms of multi-channel radical cation fragmentation processes remains a current and important challenge to understanding and predicting mass spectra. We find that coherent oscillations in the femtosecond time-dependent yields of several product ions following ultrafast strong-field ionization represent spectroscopic signatures that elucidate their mechanism of formation and identify the intermediate(s) they originate from. Experiments on endo-dicyclopentadiene show that vibrational frequencies from various intermediates are mapped onto their resulting products. Aided by ab initio methods, we identify the vibrational modes of both the cleaved and intact molecular ion intermediates. These results confirm stepwise and concerted fragmentation pathways of the dicyclopentadiene ion. This study highlights the power of tracking the femtosecond dynamics of all product ions simultaneously and sheds further light onto one of the fundamental reaction mechanisms in mass spectrometry, the retro-Diels Alder reaction.

Structure and Ultrafast X-ray Diffraction of the Hydrated Metaphosphate

We study the pathway of metaphosphate hydration when a metaphosphate anion is dissolved in liquid water with an explicit water model. For this purpose, we propose a sequential Monte Carlo algorithm incorporated with the ab initio quantum mechanics/molecular mechanics (QM/MM) method, which can reduce the amount of ab initio QM/MM sampling while retaining the accuracy of the simulation. We demonstrate the numerical calculation of the standard enthalpy change for the successive addition reaction PO3-·2H2O + H2O ⇌ PO3-·3H2O in the liquid phase, which helps to clarify the hydration pathway of the metaphosphate. With the obtained hydrated structure of the metaphosphate anion, we perform ab initio calculations for its relaxation dynamics upon vibrational excitation and characterize the energy transfer process in solution with simulated ultrafast X-ray diffraction signals, which can be experimentally implemented with X-ray free-electron lasers.

Massively scalable workflows for quantum chemistry: BigChem and ChemCloud

Electronic structure theory, i.e., quantum chemistry, is the fundamental building block for many problems in computational chemistry. We present a new distributed computing framework (BigChem), which allows for an efficient solution of many quantum chemistry problems in parallel. BigChem is designed to be easily composable and leverages industry-standard middleware (e.g., Celery, RabbitMQ, and Redis) for distributed approaches to large scale problems. BigChem can harness any collection of worker nodes, including ones on cloud providers (such as AWS or Azure), local clusters, or supercomputer centers (and any mixture of these). BigChem builds upon MolSSI packages, such as QCEngine to standardize the operation of numerous computational chemistry programs, demonstrated here with Psi4, xtb, geomeTRIC, and TeraChem. BigChem delivers full utilization of compute resources at scale, offers a programable canvas for designing sophisticated quantum chemistry workflows, and is fault tolerant to node failures and network disruptions. We demonstrate linear scalability of BigChem running computational chemistry workloads on up to 125 GPUs. Finally, we present ChemCloud, a web API to BigChem and successor to TeraChem Cloud. ChemCloud delivers scalable and secure access to BigChem over the Internet.

The variational quantum eigensolver self-consistent field method within a polarizable embedded framework

We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example.

New physical insights into the supporting subspace factorization of XMS-CASPT2 and generalization to multiple spin states via spin-free formulation

This paper introduces a spin-free formulation of the supporting subspace factorization [C. Song and T. J. Martínez, J. Chem. Phys. 149, 044108 (2018)], enabling a reduction in the computational scaling of the extended multi-state complete active space second-order perturbation (XMS-CASPT2) method for arbitrary spins. Compared to the original formulation that is defined in the spin orbitals and is limited to singlet states, the spin-free formulation in this work treats different spin states equivalently, thus naturally generalizing the idea beyond singlet states. In addition, we will present a new way of deriving the supporting subspace factorization with the purpose of understanding its physical interpretation. In this new derivation, we separate the sources that make CASPT2 difficult into the "same-site interactions" and "inter-site interactions." We will first show how the Kronecker sum can be used to remove the same-site interactions in the absence of inter-site interactions, leading to MP2 energy in dressed orbitals. We will then show how the inter-site interactions can be exactly recovered using Löwdin partition, where the supporting subspace concept will naturally arise. The new spin-free formulation maintains the main advantage of the supporting subspace factorization, i.e., allowing XMS-CASPT2 energies to be computed using highly optimized MP2 energy codes and Fock build codes, thus reducing the scaling of XMS-CASPT2 to the same scaling as MP2. We will present and discuss results that benchmark the accuracy and performance of the new method. To demonstrate how the new method can be useful in studying real photochemical systems, the supporting subspace XMS-CASPT2 is applied to a photoreaction sensitive to magnetic field effects. The new spin-free formulation makes it possible to calculate the doublet and quartet states required in this particular photoreaction mechanism.

High-Performance Multi-GPU Analytic RI-MP2 Energy Gradients

This article presents a novel algorithm for the calculation of analytic energy gradients from second-order Møller-Plesset perturbation theory within the Resolution-of-the-Identity approximation (RI-MP2), which is designed to achieve high performance on clusters with multiple graphical processing units (GPUs). The algorithm uses GPUs for all major steps of the calculation, including integral generation, formation of all required intermediate tensors, solution of the Z-vector equation and gradient accumulation. The implementation in the EXtreme Scale Electronic Structure System (EXESS) software package includes a tailored, highly efficient, multistream scheduling system to hide CPU-GPU data transfer latencies and allows nodes with 8 A100 GPUs to operate at over 80% of theoretical peak floating-point performance. Comparative performance analysis shows a significant reduction in computational time relative to traditional multicore CPU-based methods, with our approach achieving up to a 95-fold speedup over the single-node performance of established software such as Q-Chem and ORCA. Additionally, we demonstrate that pairing our implementation with the molecular fragmentation framework in EXESS can drastically lower the computational scaling of RI-MP2 gradient calculations from quintic to subquadratic, enabling further substantial savings in runtime while retaining high numerical accuracy in the resulting gradients.

Multistate, Polarizable QM/MM Embedding Scheme Based on the Direct Reaction Field Method: Solvatochromic Shifts, Analytical Gradients and Optimizations of Conical Intersections in Solution

We recently introduced a polarizable embedding scheme based on an integral-exact reformulation of the direct reaction field method (IEDRF) that accounts for the differential solvation of ground and excited states in QM/MM simulations. The polarization and dispersion interactions between the quantum-mechanical (QM) and molecular-mechanical (MM) regions are described by the DRF Hamiltonian, while the Pauli repulsion between explicitly treated QM electrons and the implicit electron density around MM atoms is modeled with effective core potentials. A single Hamiltonian is used for all electronic states so that Born-Oppenheimer states belonging to the same geometry are orthogonal and state crossings are well-defined. In this work, we describe the implementation of the method using graphical processing unit acceleration in TeraChem, where it is combined with multiple electronic structure methods, including Hartree-Fock, time-dependent density functional theory, and complete active space self-consistent field. In contrast with older implementations of the DRF method, integrals of the polarization operators are evaluated exactly. Expressions for ingredients needed to construct analytical gradients and nonadiabatic coupling vectors are derived and tested by optimizing a conical intersection between two excited states in the presence of a polarizable solvent shell. The method is applied to estimate the solvent shifts of absorption energies of a series of donor-acceptor dyes having low-lying charge-transfer states. Even for a nonpolar solvent such as n-hexane, the inclusion of its static polarizability leads to non-negligible shifts that improve the agreement to essentially quantitative levels (0.03 eV) with full-system calculations. Good agreement with the positions of the experimental absorption maxima measured in solution is also observed.

Exploring Chemical Space Using Ab Initio Hyperreactor Dynamics

In recent years, first-principles exploration of chemical reaction space has provided valuable insights into intricate reaction networks. Here, we introduce ab initio hyperreactor dynamics, which enables rapid screening of the accessible chemical space from a given set of initial molecular species, predicting new synthetic routes that can potentially guide subsequent experimental studies. For this purpose, different hyperdynamics derived bias potentials are applied along with pressure-inducing spherical confinement of the molecular system in ab initio molecular dynamics simulations to efficiently enhance reactivity under mild conditions. To showcase the advantages and flexibility of the hyperreactor approach, we present a systematic study of the method's parameters on a HCN toy model and apply it to a recently introduced experimental model for the prebiotic formation of glycinal and acetamide in interstellar ices, which yields results in line with experimental findings. In addition, we show how the developed framework enables the study of complicated transitions like the first step of a nonenzymatic DNA nucleoside synthesis in an aqueous environment, where the molecular fragmentation problem of earlier nanoreactor approaches is avoided.

Monitoring the Evolution of Relative Product Populations at Early Times during a Photochemical Reaction

Identifying multiple rival reaction products and transient species formed during ultrafast photochemical reactions and determining their time-evolving relative populations are key steps toward understanding and predicting photochemical outcomes. Yet, most contemporary ultrafast studies struggle with clearly identifying and quantifying competing molecular structures/species among the emerging reaction products. Here, we show that mega-electronvolt ultrafast electron diffraction in combination with ab initio molecular dynamics calculations offer a powerful route to determining time-resolved populations of the various isomeric products formed after UV (266 nm) excitation of the five-membered heterocyclic molecule 2(5H)-thiophenone. This strategy provides experimental validation of the predicted high (∼50%) yield of an episulfide isomer containing a strained three-membered ring within ∼1 ps of photoexcitation and highlights the rapidity of interconversion between the rival highly vibrationally excited photoproducts in their ground electronic state.

Accelerating Pythonic Coupled-Cluster Implementations: A Comparison Between CPUs and GPUs

In this work, we benchmark several Python routines for time and memory requirements to identify the optimal choice of the tensor contraction operations available. We scrutinize how to accelerate the bottleneck tensor operations of Pythonic coupled-cluster implementations in the Cholesky linear algebra domain, utilizing a NVIDIA Tesla V100S PCIe 32GB (rev 1a) graphics processing unit (GPU). The NVIDIA compute unified device architecture API interacts with CuPy, an open-source library for Python, designed as a NumPy drop-in replacement for GPUs. Due to the limitations of video memory, the GPU calculations must be performed batch-wise. Timing results of some contractions containing large tensors are presented. The CuPy implementation leads to a factor of 10-16 speed-up of the bottleneck tensor contractions compared to computations on 36 central processing unit (CPU) cores. Finally, we compare example CCSD and pCCD-LCCSD calculations performed solely on CPUs to their CPU-GPU hybrid implementation, which leads to a speed-up of a factor of 3-4 compared to the CPU-only variant.