Corrected small basis set Hartree-Fock method for large systems

The Quality of Embedding Charges Is Critical for Convergence of Many-Body Expansions When BSSE Is Absent

There is conflicting evidence in the literature concerning the benefits of charge embedding on the convergence of many-body expansions (MBEs). Using a systematic series of water and ion-water clusters of varying size, this study indicates that the effects of charge embedding can be masked by basis set superposition error (BSSE). When BSSE is removed, this study demonstrates that charge embedding can significantly accelerate MBE convergence, where the electrostatically embedded two-body method, EE-MBE(2), can often yield accuracy close to the four-body method, MBE(4). Contrary to previous studies on smaller systems, this work shows that the performance of EE-MBE is highly sensitive to the charge model, with the best performance obtained when the natural population analysis (NPA) charge model is used and generated at the same level of theory used in the subsystem and supersystem calculations. It was demonstrated that the "3c" composite method, PBEh-3c, yields NPA atomic charges that are in excellent agreement with those obtained from supersystem density functional theory calculations. The linear-scaling X-Polarization method provides a more general approach to estimating these supersystem QM atomic charges, but its performance depends on how the fragments are defined.

Optimization of damping function parameters for -D3 and -D4 dispersion models for Hartree-Fock based symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) directly computes intermolecular interaction energy in terms of electrostatics, exchange-repulsion, induction/polarization, and London dispersion components. In SAPT based on Hartree-Fock ("SAPT0") or based on density functional theory, the most time-consuming step is the computation of the dispersion terms. Previous work has explored the replacement of these expensive dispersion terms with simple damped asymptotic models. We recently examined [Schriber et al. J. Chem. Phys. 154, 234107 (2021)] the accuracy of SAPT0 when replacing its dispersion term with Grimme's popular -D3 correction, reducing the computational cost scaling from O(N5) to O(N3). That work optimized damping function parameters for SAPT0-D3/jun-cc-pVDZ using estimates of the coupled-cluster complete basis set limit [CCSD(T)/CBS] on a 8299 dimer dataset. Here, we explore the accuracy of SAPT0-D3 with additional basis sets, along with an analogous model using -D4. Damping parameters are rather insensitive to basis sets, and the resulting SAPT0-D models are more accurate on average for total interaction energies than SAPT0. Our results are surprising in several respects: (1) improvement of -D4 over -D3 is negligible for these systems, even charged systems where -D4 should, in principle, be more accurate; (2) addition of Axilrod-Teller-Muto terms for three-body dispersion does not improve error statistics for this test set; and (3) SAPT0-D is even more accurate on average for total interaction energies than the much more computationally costly density functional theory based SAPT [SAPT(DFT)] in an aug-cc-pVDZ basis. However, SAPT0 and SAPT0-D3/D4 interaction energies benefit from significant error cancellation between exchange and dispersion terms.

Synergetic Effect of β-Cyclodextrin and Its Simple Carbohydrate Substituents on Complexation of Folic Acid and Its Structural Analog Methotrexate

Folic acid (FA) and its structural analog, anticancer medicine methotrexate (MTX), are known to form host/guest complexes with native cyclodextrins, of which the most stable are formed with the medium-sized β-cyclodextrin. Based on our research, proving that simple sugars (D-glucose, D-galactose, and D-mannose) can form adducts with folic acid, we envisioned that combining these two types of molecular receptors (cyclodextrin and simple carbohydrates) into one may be beneficial for the complexation of FA and MTX. We designed and obtained host/guest inclusion complexes of FA and MTX with two monoderivatives of β-cyclodextrin-substituted at position 6 with monosaccharide (glucose, G-β-CD) and disaccharide (maltose, Ma-β-CD). The complexation was proved by experimental (NMR, UV-vis, IR, TG, DSC) and theoretical methods. We proved that derivatization of β-cyclodextrin with glucose and maltose has a significant impact on the complexation with FA and MTX, as the addition of one glucose subunit to the structure of the receptor significantly increases the value of association constant for both FA/G-β-CD and MTX/G-β-CD, while further extending a pendant chain (incorporation of maltose subunit) results in no additional changes.

Small basis set density functional theory method for cost-efficient, large-scale condensed matter simulations

We present an efficient first-principles based method geared toward reliably predicting the structures of solid materials across the Periodic Table. To this end, we use a density functional theory baseline with a compact, near-minimal min+s basis set, yielding low computational costs and memory demands. Since the use of such a small basis set leads to systematic errors in chemical bond lengths, we develop a linear pairwise correction, available for elements Z = 1-86 (excluding the lanthanide series), parameterized for use with the Perdew-Burke-Ernzerhof exchange-correlation functional. We demonstrate the reliability of this corrected approach for equilibrium volumes across the Periodic Table and the transferability to differently coordinated environments and multi-elemental crystals. We examine relative energies, forces, and stresses in geometry optimizations and molecular dynamics simulations.

Benchmarking Quantum Mechanical Levels of Theory for Valence Parametrization in Force Fields

A wide range of density functional methods and basis sets are available to derive the electronic structure and properties of molecules. Quantum mechanical calculations are too computationally intensive for routine simulation of molecules in the condensed phase, prompting the development of computationally efficient force fields based on quantum mechanical data. Parametrizing general force fields, which cover a vast chemical space, necessitates the generation of sizable quantum mechanical data sets with optimized geometries and torsion scans. To achieve this efficiently, choosing a quantum mechanical method that balances computational cost and accuracy is crucial. In this study, we seek to assess the accuracy of quantum mechanical theory for specific properties such as conformer energies and torsion energetics. To comprehensively evaluate various methods, we focus on a representative set of 59 diverse small molecules, comparing approximately 25 combinations of functional and basis sets against the reference level coupled cluster calculations at the complete basis set limit.

Extension of the D3 and D4 London dispersion corrections to the full actinides series

Efficient dispersion corrections are an indispensable component of modern density functional theory, semi-empirical quantum mechanical, and even force field methods. In this work, we extend the well established D3 and D4 London dispersion corrections to the full actinides series, francium, and radium. To keep consistency with the existing versions, the original parameterization strategy of the D4 model was only slightly modified. This includes improved reference Hirshfeld atomic partial charges at the ωB97M-V/ma-def-TZVP level to fit the required electronegativity equilibration charge (EEQ) model. In this context, we developed a new actinide data set called AcQM, which covers the most common molecular actinide compound space. Furthermore, the efficient calculation of dynamic polarizabilities that are needed to construct CAB6 dispersion coefficients was implemented into the ORCA program package. The extended models are assessed for the computation of dissociation curves of actinide atoms and ions, geometry optimizations of crystal structure cutouts, gas-phase structures of small uranium compounds, and an example extracted from a small actinide complex protein assembly. We found that the novel parameterizations perform on par with the computationally more demanding density-dependent VV10 dispersion correction. With the presented extension, the excellent cost-accuracy ratio of the D3 and D4 models can now be utilized in various fields of computational actinide chemistry and, e.g., in efficient composite DFT methods such as r2SCAN-3c. They are implemented in our freely available standalone codes (dftd4, s-dftd3) and the D4 version will be also available in the upcoming ORCA 6.0 program package.

Machine Learning Approach to Vertical Energy Gap in Redox Processes

A straightforward approach to calculating the free energy change (ΔG) and reorganization energy of a redox process is linear response approximation (LRA). However, accurate prediction of redox properties is still challenging due to difficulties in conformational sampling and vertical energy-gap sampling. Expensive hybrid quantum mechanical/molecular mechanical (QM/MM) calculations are typically employed in sampling energy gaps using conformations from simulations. To alleviate the computational cost associated with the expensive QM method in the QM/MM calculation, we propose machine learning (ML) methods to predict the vertical energy gaps (VEGs). We tested several ML models to predict the VEGs and observed that simple models like linear regression show excellent performance (mean absolute error ∼0.1 eV) in predicting VEGs in all test systems, even when using features extracted from cheaper semiempirical methods. Our best ML model (extra trees regressor) shows a mean absolute error of around 0.1 eV while using features from the cheapest QM method. We anticipate our approach can be generalized to larger macromolecular systems with more complex redox centers.

Mechanical Tuning of Fluorescence Lifetime and Bandgap in an Elastically Flexible Molecular Semiconductor Crystal

Despite having superior transport properties, lack of mechanical flexibility is a major drawback of crystalline molecular semiconductors as compared to their polymer analogues. Here single crystals of an organic semiconductor are reported that are not only flexible but exhibit systematic tuning of bandgaps, fluorescence lifetime, and emission wavelengths upon elastically bending. Spatially resolved fluorescence lifetime imaging and confocal fluorescence microscopy reveals systematic trends in the lifetime decay across the bent crystal region along with shifts in the emission wavelength. From the outer arc to the inner arc of the bent crystal, a significant decrease in the lifetime of ≈1.9 ns is observed, with a gradual bathochromic shift of ≈10 nm in the emission wavelength. For the crystal having a bandgap of 2.73 eV, the directional stress arising from bending leads to molecular reorientation effects and variations in the extent of intermolecular interactions- which are correlated to the lowering of bandgap and the evolution of the projected density of states. The systematic changes in the interactions quantified using electron density topological analysis in the compressed inner arc and elongated outer arc region are correlated to the non-radiative decay processes, thus rationalizing the tuning of fluorescence lifetime.

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

Evaluating Noncovalent Interactions in Halogenated Molecules with Double-Hybrid Functionals and a Dedicated Small Basis Set

We present here an extension of our recently developed PBE-QIDH/DH-SVPD basis set to halogen atoms, with the aim of obtaining, for weakly interacting halogenated molecules, interaction energies close to those provided by a large basis set (def2-TZVPP) coupled to empirical dispersion potential. The core of our approach is the split-valence basis set, DH-SVPD, that has been developed for F, Cl, Br, and I atoms using a self-consistent formula, containing only energy terms computed for dimers and the corresponding monomers at the same level of theory. The basis set developed considering four systems, one for each halogen atoms, has been then tested on the X40, X4 × 10 benchmarks as well as on other two, less standard, data sets. Finally, a large system (380 atoms) has been also considered as a "crash" test. Our results show that the simple and nonempirical PBE-QIDH/DH-SVPD approach is able to provide accurate results for interaction energies of all the considered systems and can thus be considered as a cheaper alternative to DH functionals paired with empirical dispersion corrections and a large basis set of triple-ζ quality.

Assessment of the applicability of DFT methods to [Cp*Rh]-catalyzed hydrogen evolution processes

The present computational study provides a benchmark of density functional theory (DFT) methods in describing hydrogen evolution processes catalyzed by [Cp*Rh]-containing organometallic complexes. A test set was composed of 26 elementary reactions featuring chemical transformations and bonding situations essential for the field, including the emerging concept of non-innocent Cp* behavior. Reference values were obtained from a highly accurate 3/4 complete basis set and 6/7 complete PNO space extrapolated DLPNO-CCSD(T) energies. The performance of lower-level extrapolation procedures was also assessed. We considered 84 density functionals (DF) (including 13 generalized gradient approximations (GGA), nine meta-GGAs, 33 hybrids, and 29 double-hybrids) and three composite methods (HF-3c, PBEh-3c, and r2SCAN-3c), combined with different types of dispersion corrections (D3(0), D3BJ, D4, and VV10). The most accurate approach is the PBE0-DH-D3BJ (MAD of 1.36 kcal mol-1) followed by TPSS0-D3BJ (MAD of 1.60 kcal mol-1). Low-cost r2SCAN-3c composite provides a less accurate but much faster alternative (MAD of 2.39 kcal mol-1). The widely used Minnesota-family M06-L, M06, and M06-2X DFs should be avoided (MADs of 3.70, 3.94, and 4.01 kcal mol-1, respectively).

Pentaphosphorylation via the Anhydride of Dihydrogen Pentametaphosphate: Access to Nucleoside Hexa- and Heptaphosphates and Study of Their Interaction with Ribonuclease A

Pentametaphosphate is the little studied cyclic pentamer of the metaphosphate ion, [PO3]5 5-. We show that the doubly protonated form of this pentamer can be selectively dehydrated to provide the anhydride [P5O14]3- (1). This trianion is the well-defined condensed phosphate component of a novel reagent for attachment of a pentaphosphate chain to biomolecules all in one go. Here, we demonstrate by extending adenosine monophosphate (AMP) and uridine monophosphate (UMP) to their corresponding nucleoside hexaphosphates, while adenosine diphosphate (ADP) and uridine diphosphate (UDP) are phosphate chain-extended to the corresponding nucleoside heptaphosphates. Such constructs are of interest for their potential biological function with respect to RNA-processing enzymes. Thus, we go on to investigate in detail the interaction of the polyanionic constructs with ribonuclease A, a model protein containing a polycationic active site and for which X-ray crystal structures are relatively straightforward to obtain. This work presents a combined experimental and quantum chemical approach to understanding the interactions of RNase A with the new nucleoside hexa- and heptaphosphate constructs.

In-depth exploration of catalytic sites on amorphous solid water: I. The astrosynthesis of aminomethanol

Chemical processes taking place on ice-grain mantles are pivotal to the complex chemistry of interstellar environments. In this study, we conducted a comprehensive analysis of the catalytic effects of an amorphous solid water (ASW) surface on the reaction between ammonia (NH3) and formaldehyde (H2CO) to form aminomethanol (NH2CH2OH) using density functional theory. We identified potential catalytic sites based on the binding energy distribution of NH3 and H2CO reactants, on a set-of-clusters surface model composed of 22 water molecules and found a total of 14 reaction paths. Our results indicate that the catalytic sites can be categorized into four groups, depending on the interactions of the carbonyl oxygen and the amino group with the ice surface in the reactant complex. A detailed analysis of the reaction mechanism using Intrinsic Reaction Coordinate and reaction force analysis, revealed three distinct chemical events for this reaction: formation of the C-N bond, breaking of the N-H bond, and formation of the O-H hydroxyl bond. Depending on the type of catalytic site, these events can occur within a single, concerted, albeit asynchronous, step, or can be isolated in a step-wise mechanism, with the lowest overall transition state energy observed at 1.3 kcal mol-1. A key requirement for the low-energy mechanism is the presence of a pair of dangling OH bonds on the surface, found at 5% of the potential catalytic sites on an ASW porous surface.

Binding energies of ethanol and ethylamine on interstellar water ices: synergy between theory and experiments

Experimental and computational chemistry are two disciplines used to conduct research in astrochemistry, providing essential reference data for both astronomical observations and modeling. These approaches not only mutually support each other, but also serve as complementary tools to overcome their respective limitations. Leveraging on such synergy, we characterized the binding energies (BEs) of ethanol (CH3CH2OH) and ethylamine (CH3CH2NH2), two interstellar complex organic molecules (iCOMs), on crystalline and amorphous water ices through density functional theory (DFT) calculations and temperature-programmed desorption (TPD) experiments. Experimentally, CH3CH2OH and CH3CH2NH2 behave similarly, in which desorption temperatures are higher on the water ices than on a bare gold surface. Computed cohesive energies of pure ethanol and ethylamine bulk structures allow describing of the BEs of the pure species deposited on the gold surface, as extracted from the TPD curve analyses. The BEs of submonolayer coverages of CH3CH2OH and CH3CH2NH2 on the water ices cannot be directly extracted from TPD due to their co-desorption with water, but they are computed through DFT calculations, and found to be greater than the cohesive energy of water. The behaviour of CH3CH2OH and CH3CH2NH2 is different when depositing adsorbate multilayers on the amorphous ice, in that, according to their computed cohesive energies, ethylamine layers present weaker interactions compared to ethanol and water. Finally, from the computed BEs of ethanol, ethylamine and water, we can infer that the snow-lines of these three species in protoplanetary disks will be situated at different distances from the central star. It appears that a fraction of ethanol and ethylamine is already frozen on the grains in the water snow-lines, causing their incorporation in water-rich planetesimals.

Low-cost quantum mechanical descriptors for data efficient skin sensitization QSAR models

Quantitative Structure Activity Relationship modelling methodologies need to incorporate relevant mechanistic information to have high predictive performance and validity. Electrophilic reactivity is a common mechanistic feature of skin sensitization endpoints which could be concisely characterized with electronic descriptors which is key to enabling the modelling of small datasets in this domain. However, quantum mechanical methodologies have previously featured high computational costs which would exclude the use of large datasets. Consequently, we investigate the use of electronic descriptors calculated using the Hartree Fock with 3 corrections (Hf-3c) method, a low-cost ab initio methodology that has higher chemical accuracy than previous semiempirical methodologies for modelling in vitro skin sensitization assay outcomes. We also model the Ames assay as a surrogate for determining skin sensitization outcomes. The quantum chemical descriptors calculated using the Hf-3c method with conductor-like polarizable continuum model (CPCM) implicit solvation found improved QSAR model performance for the in vitro Ames (n = 6049, 0.770 AUC), KeratinoSens (n = 164, 0.763 AUC), and Direct Peptide Reactivity Assay (n = 122, 0.750 AUC) datasets, with their combination producing high predictive performance for unseen in vivo Local Lymph Node Assay (n = 86, 0.789 AUC) and Human Repeated Insult Patch Test (n = 86, 0.791 AUC) assay toxicant outcomes.

Simulations predict preferred Mg2+ coordination in a nonenzymatic primer-extension reaction center

The mechanism by which genetic information was copied prior to the evolution of ribozymes is of great interest because of its importance to the origin of life. The most effective known process for the nonenzymatic copying of an RNA template is primer extension by a two-step pathway in which 2-aminoimidazole-activated nucleotides first react with each other to form an imidazolium-bridged intermediate that subsequently reacts with the primer. Reaction kinetics, structure-activity relationships, and X-ray crystallography have provided insight into the overall reaction mechanism, but many puzzles remain. In particular, high concentrations of Mg2+ are required for efficient primer extension, but the mechanism by which Mg2+ accelerates primer extension remains unknown. By analogy with the mechanism of DNA and RNA polymerases, a role for Mg2+ in facilitating the deprotonation of the primer 3'-hydroxyl is often assumed, but no catalytic metal ion is seen in crystal structures of the primer-extension complex. To explore the potential effects of Mg2+ binding in the reaction center, we performed atomistic molecular dynamics simulations of a series of modeled complexes in which a Mg2+ ion was placed in the reaction center with inner-sphere coordination with different sets of functional groups. Our simulations suggest that coordination of a Mg2+ ion with both O3' of the terminal primer nucleotide and the pro-Sp nonbridging oxygen of the reactive phosphate of an imidazolium-bridged dinucleotide would help to pre-organize the structure of the primer/template substrate complex to favor the primer-extension reaction. Our results suggest that the catalytic metal ion may play an important role in overcoming electrostatic repulsion between a deprotonated O3' and the reactive phosphate of the bridged dinucleotide and lead to testable predictions of the mode of Mg2+ binding that is most relevant to catalysis of primer extension.

Combining low-cost electronic structure theory and low-cost parallel computing architecture

The computational efficiency of low-cost electronic structure methods can be further improved by leveraging heterogenous computing architectures. The software package TeraChem has been developed since 2008 to make use of graphical processing units (GPUs), particularly their strong single-precision performance, for the acceleration of quantum chemical calculations. Here, we present the implementation of three low-cost methods, namely HF-3c, PBEh-3c, and the recently introduced ωB97X-3c. We show that these can benefit in terms of performance when combined with "consumer grade" GPUs by leveraging the mixed precision integral handling in TeraChem. The current limitation of the latter's GPU integral library is that Gaussian integrals only for functions with angular momentum l < 3 can be computed, which generally restricts the achievable accuracy in terms of the one-particle basis set. Particularly, the implementation of the ωB97X-3c method now enables higher accuracy with this setting which, in turn, provides the most efficient implementation accessible with consumer-grade hardware. We furthermore show that the implemented 3c methods can be combined with the hh-TDA formalism. This gives new and efficient low-cost multi-configurational excited states methods, which are benchmarked for the description of lowest vertical excitation energies in this work. All in all, the combination of these efficient electronic structure theory methods with affordable highly parallelized computing hardware provides an optimal computational and monetary cost to accuracy ratio.

Alternative CNDOL Fockians for fast and accurate description of molecular exciton properties

CNDOL is an a priori, approximate Fockian for molecular wave functions. In this study, we employ several modes of singly excited configuration interaction (CIS) to model molecular excitation properties by using four combinations of the one electron operator terms. Those options are compared to the experimental and theoretical data for a carefully selected set of molecules. The resulting excitons are represented by CIS wave functions that encompass all valence electrons in the system for each excited state energy. The Coulomb-exchange term associated to the calculated excitation energies is rationalized to evaluate theoretical exciton binding energies. This property is shown to be useful for discriminating the charge donation ability of molecular and supermolecular systems. Multielectronic 3D maps of exciton formal charges are showcased, demonstrating the applicability of these approximate wave functions for modeling properties of large molecules and clusters at nanoscales. This modeling proves useful in designing molecular photovoltaic devices. Our methodology holds potential applications in systematic evaluations of such systems and the development of fundamental artificial intelligence databases for predicting related properties.

Development of a multi-step screening procedure for redox active molecules in organic radical polymer anodes and as redox flow anolytes

Benzo[d]-X-zolyl-pyridinyl (XO, S, NH) radicals represent a promising class of redox-active molecules for organic batteries. We present a multistep screening procedure to identify the most promising radical candidates. Experimental investigations and highly correlated wave function-based calculations are performed to determine benchmark redox potentials. Based on these, the accuracies of different methods (semi-empirical, density functional theory, wave function-based), solvent models, dispersion corrections, and basis sets are evaluated. The developed screening procedure consists of three steps: First, a conformer search is performed with CREST. The molecules are selected based on the redox potentials calculated using GFN2-xTB. Second, HOMO energies calculated with reparametrized B3LYP-D3(BJ) and the def2-SVP basis set are used as selection criteria. The final molecules are selected based on the redox potentials calculated from Gibbs energies using BP86-D3(BJ)/def2-TZVP. With this multistep screening approach, promising molecules can be suggested for synthesis, and structure-property relationships can be derived.

In Search of the Best Low-Cost Methods for Efficient Screening of Conformers

Locating the lowest energy conformer is crucial for the accurate computation of equilibrium properties of molecular systems. This paper examines the performance of efficient low-cost methods in terms of the alignment and relative energies of their energy minima against the benchmark revDSD-PBEP86-D4/def2-TZVPP//MP2/cc-pVTZ potential energy surface. The low-cost methods considered include GFN-FF, GFN2-xTB, DFTB3, HF-3c, B97-3c, PBEh-3c, and r2SCAN-3c composite methods against a diverse test set of 20 compounds including alkanes, perfluoroalkyl molecules, peptides, open-shell radicals, and Zn(II) complexes of varying sizes. The "3c" composite methods are generally more accurate, but are at least 2-3 orders of magnitude more expensive than tight-binding methods which have energy minima that align well with the benchmark potential energy surface. The findings of this paper were further exploited to introduce a simple strategy involving Grimme's CENSO energy-sorting algorithm that resulted in up to an order of magnitude reduction in computational time for locating the lowest energy conformer on the revDSD-PBEP86-D4/def2-TZVPP//MP2/cc-pVTZ surface.

Stepping-Stone CBH: Benchmark and Application of a Multilayered Isodesmic-Based Correction Scheme

We present a generalization of the connectivity-based hierarchy (CBH) of isodesmic-based correction schemes to a multilayered fragmentation platform for overall cost reduction while retaining high accuracy. The newly developed multilayered CBH approach, called stepping-stone CBH (SSCBH), is benchmarked on a diverse set of 959 medium-sized organic molecules. Applying SSCBH corrections to the PBEh-D3 density functional resulted in an average error of 0.76 kcal/mol for the full test set compared to accurate CCSD(T)-quality enthalpies and an even lower error of 0.44 kcal/mol on a subset containing only acyclic molecules. These results rival the traditional CBH-3 approach at a greatly reduced cost, allowing larger fragment corrections to be made at the MP2 level of theory rather than with G4. Our SSCBH approach will enable more widespread applications of CBH methods to a broader range of organic and biomolecular systems.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Enhancement of energy decomposition analysis in fragment molecular orbital calculations

Energy decomposition analysis is one of the most attractive features of fragment molecular orbital (FMO) calculations from the point of view of practical applications. Here we report some enhancements for PIEDA in the ABINIT-MP program. One is a separation of the dispersion-type stabilization from the electron correlation energy, traditionally referred to as the "dispersion interaction" (DI). Another is an alternative evaluation of the electrostatic (ES) interaction using the restrained electrostatic potential (RESP) charges. The GA:CT stacked base pair and the Trp-Cage miniprotein were used as illustrative examples.

Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals

σ-Functionals belong to the class of Kohn-Sham (KS) correlation functionals based on the adiabatic-connection fluctuation-dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to triple-ζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.

CREST-A program for the exploration of low-energy molecular chemical space

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Conformational energies of biomolecules in solution: Extending the MPCONF196 benchmark with explicit water molecules

A prerequisite for the computational prediction of molecular properties like conformational energies of biomolecules is a reliable, robust, and computationally affordable method usually selected according to its performance for relevant benchmark sets. However, most of these sets comprise molecules in the gas phase and do not cover interactions with a solvent, even though biomolecules typically occur in aqueous solution. To address this issue, we introduce a with explicit water molecules solvated version of a gas-phase benchmark set containing 196 conformers of 13 peptides and other relevant macrocycles, namely MPCONF196 [J. Řezáč et al., JCTC 2018, 14, 1254-1266], and provide very accurate PNO-LCCSD(T)-F12b/AVQZ' reference values. The novel solvMPCONF196 benchmark set features two additional challenges beyond the description of conformers in the gas phase: conformer-water and water-water interactions. The overall best performing method for this set is the double hybrid revDSDPBEP86-D4/def2-QZVPP yielding conformational energies of almost coupled cluster quality. Furthermore, some (meta-)GGAs and hybrid functionals like B97M-V and ω B97M-D with a large basis set reproduce the coupled cluster reference with an MAD below 1 kcal mol- 1  . If more efficient methods are required, the composite DFT-method r2 SCAN-3c (MAD of 1.2 kcal mol- 1 ) is a good alternative, and when conformational energies of polypeptides or macrocycles with more than 500-1000 atoms are in the focus, the semi-empirical GFN2-xTB or the MMFF94 force field (for very large systems) are recommended.

Encapsulation in Charged Droplets Generates Distorted Host-Guest Complexes

The ability of various hydrogen-bonded resorcinarene-based capsules to bind α,ω-alkylbisDABCOnium (DnD) guests of different lengths was investigated in solution and in the gas-phase. While no host-guest interactions were detected in solution, encapsulation could be achieved in the charged droplets formed during electrospray ionisation (ESI). This included guests, which are far too long in their most stable conformation to fit inside the cavity of the capsules. A combination of three mass spectrometric techniques, namely, collision-induced dissociation, hydrogen/deuterium exchange, and ion-mobility mass spectrometry, together with computational modelling allow us to determine the binding mode of the DnD guests inside the cavity of the capsules. Significant distortions of the guest into horseshoe-like arrangements are required to optimise cation-π interactions with the host, which also adopt distorted geometries with partially open hydrogen-bonding seams when binding longer guests. Such quasi "spring-loaded" capsules can form in the charged droplets during the ESI process as there is no competition between guest encapsulation and ion pair formation with the counterions that preclude encapsulation in solution. The encapsulation complexes are sufficiently stable in the gas-phase - even when strained - because non-covalent interactions significantly strengthen in the absence of solvent.

Nuclear Quantum Effects Made Accessible: Local Density Fitting in Multicomponent Methods

The simulation of nuclear quantum effects (NQEs) is crucial for an accurate description of systems and processes involving light nuclei, such as hydrogen atoms. Within the last years, the importance of those effects has been highlighted for a vast range of systems with tremendous implications in chemistry, biology, physics, and materials sciences. However, while electronic structure theory methods have become routine tools for quantum chemical investigations, there is still a lack of approaches to address NQEs that are computationally accessible and straightforward to use. To address this, we present the first combination of the nuclear-electronic orbital Hartree-Fock approach with both local and density fitting approximations (LDF-NEO-HF). This results in a low-order scaling approach that enables the inclusion of NQEs for large systems within a fraction of a day and for small to medium size systems in minutes. Moreover, we demonstrate the qualitative accuracy and robustness of our approach to retrieve NQEs for three real-use cases motivated by chemical, biological, and materials science applications.

Gas-Phase vs. Grain-Surface Formation of Interstellar Complex Organic Molecules: A Comprehensive Quantum-Chemical Study

Several organic chemical compounds (the so-called interstellar complex organic molecules, iCOMs) have been identified in the interstellar medium (ISM). Examples of iCOMs are formamide (HCONH2), acetaldehyde (CH3CHO), methyl formate (CH3OCHO), or formic acid (HCOOH). iCOMs can serve as precursors of other organic molecules of enhanced complexity, and hence they are key species in chemical evolution in the ISM. The formation of iCOMs is still a subject of a vivid debate, in which gas-phase or grain-surface syntheses have been postulated. In this study, we investigate the grain-surface-formation pathways for the four above-mentioned iCOMs by transferring their primary gas-phase synthetic routes onto water ice surfaces. Our objective is twofold: (i) to identify potential grain-surface-reaction mechanisms leading to the formation of these iCOMs, and (ii) to decipher either parallelisms or disparities between the gas-phase and the grain-surface reactions. Results obtained indicate that the presence of the icy surface modifies the energetic features of the reactions compared to the gas-phase scenario, by increasing some of the energy barriers. Therefore, the investigated gas-phase mechanisms seem unlikely to occur on the icy grains, highlighting the distinctiveness between the gas-phase and the grain-surface chemistry.

A transferable quantum mechanical energy model for intermolecular interactions using a single empirical parameter

The calculation of intermolecular interactions in molecular crystals using model energies provides a unified route to understanding the complex interplay of driving forces in crystallization, elastic properties and more. Presented here is a new single-parameter interaction energy model (CE-1p), extending the previous CrystalExplorer energy model and calibrated using density functional theory (DFT) calculations at the ωB97M-V/def2-QZVP level over 1157 intermolecular interactions from 147 crystal structures. The new model incorporates an improved treatment of dispersion interactions and polarizabilities using the exchange-hole dipole model (XDM), along with the use of effective core potentials (ECPs), facilitating application to molecules containing elements across the periodic table (from H to Rn). This new model is validated against high-level reference data with outstanding performance, comparable to state-of-the-art DFT methods for molecular crystal lattice energies over the X23 set (mean absolute deviation 3.6 kJ mol-1) and for intermolecular interactions in the S66x8 benchmark set (root mean-square deviation 3.3 kJ mol-1). The performance of this model is further examined compared to the GFN2-xTB tight-binding model, providing recommendations for the evaluation of intermolecular interactions in molecular crystal systems.

CRYSTAL23: A Program for Computational Solid State Physics and Chemistry

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

Reliable and accurate prediction of basic pK[Formula: see text] values in nitrogen compounds: the pK[Formula: see text] shift in supramolecular systems as a case study

This article presents a quantitative structure-activity relationship (QSAR) approach for predicting the acid dissociation constant (pK[Formula: see text]) of nitrogenous compounds, including those within supramolecular complexes based on cucurbiturils. The model combines low-cost quantum mechanical calculations with QSAR methodology and linear regressions to achieve accurate predictions for a broad range of nitrogen-containing compounds. The model was developed using a diverse dataset of 130 nitrogenous compounds and exhibits excellent predictive performance, with a high coefficient of determination (R[Formula: see text]) of 0.9905, low standard error (s) of 0.3066, and high Fisher statistic (F) of 2142. The model outperforms existing methods, such as Chemaxon software and previous studies, in terms of accuracy and its ability to handle heterogeneous datasets. External validation on pharmaceutical ingredients, dyes, and supramolecular complexes based on cucurbiturils confirms the reliability of the model. To enhance usability, a script-like tool has been developed, providing a streamlined process for users to access the model. This study represents a significant advancement in pK[Formula: see text] prediction, offering valuable insights for drug design and supramolecular system optimization.

Gaussian process regression adaptive density-guided approach: Toward calculations of potential energy surfaces for larger molecules

We present a new program implementation of the Gaussian process regression adaptive density-guided approach [Schmitz et al., J. Chem. Phys. 153, 064105 (2020)] for automatic and cost-efficient potential energy surface construction in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach toward calculations of larger molecular systems than those previously accessible and maintain the very high accuracy of constructed potential energy surfaces. On the methodological side, improvements were made by using a Δ-learning approach, predicting the difference against a fully harmonic potential, and employing a computationally more efficient hyperparameter optimization procedure. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80% of single point calculations could be avoided, introducing a root mean square deviation in fundamental excitations of about 3 cm-1. A much higher accuracy with errors below 1 cm-1 could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68%. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly accurate vibrational spectra simulations.

Development of NOTCH, an all-electron, beyond-NDDO semiempirical method: Application to diatomic molecules

In this work, we develop a new semiempirical method, dubbed NOTCH (Natural Orbital Tied Constructed Hamiltonian). Compared to existing semiempirical methods, NOTCH is less empirical in its functional form as well as parameterization. Specifically, in NOTCH, (1) the core electrons are treated explicitly; (2) the nuclear-nuclear repulsion term is calculated analytically, without any empirical parameterization; (3) the contraction coefficients of the atomic orbital (AO) basis depend on the coordinates of the neighboring atoms, which allows the size of AOs to depend on the molecular environment, despite the fact that a minimal basis set is used; (4) the one-center integrals of free atoms are derived from scalar relativistic multireference equation-of-motion coupled cluster calculations instead of empirical fitting, drastically reducing the number of necessary empirical parameters; (5) the (AA|AB) and (AB|AB)-type two-center integrals are explicitly included, going beyond the neglect of differential diatomic overlap approximation; and (6) the integrals depend on the atomic charges, effectively mimicking the "breathing" of AOs when the atomic charge varies. For this preliminary report, the model has been parameterized for the elements H-Ne, giving only 8 empirical global parameters. Preliminary results on the ionization potentials, electron affinities, and excitation energies of atoms and diatomic molecules, as well as the equilibrium geometries, vibrational frequencies dipole moments, and bond dissociation energies of diatomic molecules, show that the accuracy of NOTCH rivals or exceeds those of popular semiempirical methods (including PM3, PM7, OM2, OM3, GFN-xTB, and GFN2-xTB) as well as the cost-effective ab initio method Hartree-Fock-3c.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

Comparison of the Performance of Density Functional Methods for the Description of Spin States and Binding Energies of Porphyrins

This work analyzes the performance of 250 electronic structure theory methods (including 240 density functional approximations) for the description of spin states and the binding properties of iron, manganese, and cobalt porphyrins. The assessment employs the Por21 database of high-level computational data (CASPT2 reference energies taken from the literature). Results show that current approximations fail to achieve the "chemical accuracy" target of 1.0 kcal/mol by a long margin. The best-performing methods achieve a mean unsigned error (MUE) <15.0 kcal/mol, but the errors are at least twice as large for most methods. Semilocal functionals and global hybrid functionals with a low percentage of exact exchange are found to be the least problematic for spin states and binding energies, in agreement with the general knowledge in transition metal computational chemistry. Approximations with high percentages of exact exchange (including range-separated and double-hybrid functionals) can lead to catastrophic failures. More modern approximations usually perform better than older functionals. An accurate statistical analysis of the results also casts doubts on some of the reference energies calculated using multireference methods. Suggestions and general guidelines for users are provided in the conclusions. These results hopefully stimulate advances for both the wave function and the density functional side of electronic structure calculations.

Performance of Density Functionals and Semiempirical 3c Methods for Small Gold-Thiolate Clusters

In light of the recent surge in computational studies of gold thiolate clusters, we present a comparison of popular density functionals (DFAs) and three-part corrected methods (3c-methods) on their performance by taking a data set named as AuSR18 consisting of 18 isomers of Au_n(SCH₃)_m (m ≤ n = 1-3). We have compared the efficiency and accuracy of the DFAs and 3c-methods in geometry optimization with RI-SCS-MP2 as the reference method. Similarly, the performance for accurate and efficient energy evaluation was compared with DLPNO-CCSD(T) as the reference method. The lowest energy structure among the isomers of the largest stoichiometry from our data set, AuSR18, i.e., Au₃(SCH₃)₃, is considered to evaluate the computational time for SCF and gradient evaluations. Alongside this, the numbers of optimization steps to locate the most stable minima of Au₃(SCH₃)₃ are compared to assess the efficiency of the methods. A comparison of relevant bond lengths with the reference geometries was made to estimate the accuracy in geometry optimization. Some methods, such as LC-BLYP, ωB97M-D3BJ, M06-2X, and PBEh-3c, could not locate many of the minima found by most of the other methods; thus, the versatility in locating various minima is also an important criterion in choosing a method for the given project. To determine the accuracy of the methods, we compared the relative energies of the isomers in each stoichiometry and the interaction energy of the gold core with the ligands. The dependence of basis set size and relativistic effects on energies are also compared. The following are some of the highlights. TPSS has shown accuracy, while mPWPW shows comparable speed and accuracy. For the relative energies of the clusters, the hybrid range-separated DFAs are the best option. CAM-B3LYP excels, whereas B3LYP performs poorly. Overall, LC-BLYP is a balanced performer considering both the geometry and relative stability of the structures, but it lacks diversity. The 3c-methods, although fast, are less impressive in relative stability.

Electronic structure theory on modeling short-range noncovalent interactions between amino acids

While short-range noncovalent interactions (NCIs) are proving to be of importance in many chemical and biological systems, these atypical bindings happen within the so-called van der Waals envelope and pose an enormous challenge for current computational methods. We introduce SNCIAA, a database of 723 benchmark interaction energies of short-range noncovalent interactions between neutral/charged amino acids originated from protein x-ray crystal structures at the "gold standard" coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory with a mean absolute binding uncertainty less than 0.1 kcal/mol. Subsequently, a systematic assessment of commonly used computational methods, such as the second-order Møller-Plesset theory (MP2), density functional theory (DFT), symmetry-adapted perturbation theory (SAPT), composite electronic-structure methods, semiempirical approaches, and the physical-based potentials with machine learning (IPML) on SNCIAA is carried out. It is shown that the inclusion of dispersion corrections is essential even though these dimers are dominated by electrostatics, such as hydrogen bondings and salt bridges. Overall, MP2, ωB97M-V, and B3LYP+D4 turned out to be the most reliable methods for the description of short-range NCIs even in strongly attractive/repulsive complexes. SAPT is also recommended in describing short-range NCIs only if the δMP2 correction has been included. The good performance of IPML for dimers at close-equilibrium and long-range conditions is not transferable to the short-range. We expect that SNCIAA will assist the development/improvement/validation of computational methods, such as DFT, force-fields, and ML models, in describing NCIs across entire potential energy surfaces (short-, intermediate-, and long-range NCIs) on the same footing.

Theoretical and Experimental Investigation of Autoxidation Propensity of Selected Drugs in Solution State

The C-H bond dissociation energy (BDE) of drug molecules is often used to estimate their relative propensities to undergo autoxidation. BDE calculations based on electronic structures provide a convenient means to estimate the risk for a given compound to degrade via autoxidation. This study aimed to verify the utility of calculated C-H BDEs of a range of drug molecules in predicting their autoxidation propensities, in the solution state. For the autoxidation study, 2,2'-azobis (2-methylpropionitrile) was employed as the solution state stressor, and the experimental reaction rate constants were determined employing ultraperformance liquid chromatographic (UPLC) methods. Reaction rates in the solution state were compared to the calculated C-H BDE values of the respective compounds. The results indicated a poor correlation for compounds in the solution state, and their relative stabilities could not be explained with C-H BDE. On the other hand, a favorable relationship was observed between the relative extent of ionization and the autoxidation rates of the selected compounds. In the solution state, factors such as the type and extent of drug ionization, degree and type of solvation have been shown to contribute to differences in reactivity. By applying the computational method involving the effect of H-atom abstraction and potential ionization sites in the molecule, the calculated C-H BDE should relate better to the experimental autoxidation rates.

Automated handling of complex chemical structures in Z-matrix coordinates-The chemcoord library

In this work, we present a fully automated method for the construction of chemically meaningful sets of hierarchical nonredundant internal coordinates (ICs; also commonly denoted as Z-matrices) from the Cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to Cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimizations with nonlinear constraints. Analytical gradients for the transformation between the coordinate systems were derived for analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimization was coupled with a Symbolic Algebra package to support arbitrary nonlinear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. The difference to the commonly used nonhierarchical IC transformations is discussed. Sample applications are provided for a number of common chemical reactions and illustrative examples.

Benchmarking two-body contributions to crystal lattice energies and a range-dependent assessment of approximate methods

Using the many-body expansion to predict crystal lattice energies (CLEs), a pleasantly parallel process, allows for flexibility in the choice of theoretical methods. Benchmark-level two-body contributions to CLEs of 23 molecular crystals have been computed using interaction energies of dimers with minimum inter-monomer separations (i.e., closest contact distances) up to 30 Å. In a search for ways to reduce the computational expense of calculating accurate CLEs, we have computed these two-body contributions with 15 different quantum chemical levels of theory and compared these energies to those computed with coupled-cluster in the complete basis set (CBS) limit. Interaction energies of the more distant dimers are easier to compute accurately and several of the methods tested are suitable as replacements for coupled-cluster through perturbative triples for all but the closest dimers. For our dataset, sub-kJ mol^-1 accuracy can be obtained when calculating two-body interaction energies of dimers with separations shorter than 4 Å with coupled-cluster with single, double, and perturbative triple excitations/CBS and dimers with separations longer than 4 Å with MP2.5/aug-cc-pVDZ, among other schemes, reducing the number of dimers to be computed with coupled-cluster by as much as 98%.

Quantum computing in pharma: A multilayer embedding approach for near future applications

Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F₂ in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.

A theoretical framework for the design of molecular crystal engines

Photomechanical molecular crystals have garnered attention for their ability to transform light into mechanical work, but difficulties in characterizing the structural changes and mechanical responses experimentally have hindered the development of practical organic crystal engines. This study proposes a new computational framework for predicting the solid-state crystal-to-crystal photochemical transformations entirely from first principles, and it establishes a photomechanical engine cycle that quantifies the anisotropic mechanical performance resulting from the transformation. The approach relies on crystal structure prediction, solid-state topochemical principles, and high-quality electronic structure methods. After validating the framework on the well-studied [4 + 4] cycloadditions in 9-methyl anthracene and 9-tert-butyl anthracene ester, the experimentally-unknown solid-state transformation of 9-carboxylic acid anthracene is predicted for the first time. The results illustrate how the mechanical work is done by relaxation of the crystal lattice to accommodate the photoproduct, rather than by the photochemistry itself. The large ∼10⁷ J m^-3 work densities computed for all three systems highlight the promise of photomechanical crystal engines. This study demonstrates the importance of crystal packing in determining molecular crystal engine performance and provides tools and insights to design improved materials in silico.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

A comprehensive benchmark investigation of quantum chemical methods for carbocations

The application of various density functional approximations (DFAs) and an emphasis on popular methods without any consensus have prevailed in computational studies dedicated to carbocations. More importantly, an extensive and rigorous benchmark investigation on density functionals for the class is still lacking. To close this gap, we present a comprehensive benchmark study of quantum chemical methods on a series of classical and nonclassical carbocations, the CARBO33 dataset. We evaluate a total of 107 DFT methods from all rungs giving particular attention to double hybrid density functionals as the potential of the class has been largely undermined in the context of carbocations. To support our findings, DLPNO-CCSD(T) at the complete basis set (CBS) limit and W1-F12 are used as reference methods. Our results indicate that the composite CBS-QB3 method performs poorly and should not be adopted for target energies. Oftentimes, the tested DFAs of a lower rung perform better than several DFAs in a higher rung of Perdew's "Jacob's ladder". Nonetheless, double hybrids DSD-PBEP86-NL and ωB97X-2-D3(BJ) stand out by showing the overall best performance. Among the hybrids evaluated, about half of them show mean absolute deviation (MAD) below 1.1 kcal mol^-1, including the popular hybrids M06-2X and mPW1PW91. In this family, MN15-D3(BJ) performs particularly well (MAD = 0.77 kcal mol^-1) displaying reliable results across various tests. Highly popular B3LYP exhibited one of the worst performances (MAD = 4.74 kcal mol^-1), and we do not recommend its application to carbocations. We also assess the 24 general-purpose basis sets of single- up to quadruple-ζ quality. The best compromise between accuracy and computational cost is achieved with cc-pVTZ followed by def2-TZVP. Computations on larger structures of general interest, including terpene carbocations, are also presented for selected DFT methods confirming general trends in the results.

ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set

A new composite density functional theory (DFT) method is presented. It is based on ωB97X-V as one of the best-performing density functionals for the GMTKN55 thermochemistry database and completes the family of "3c" methods toward range-separated hybrid DFT. This method is consistently available for all elements up to Rn (Z = 1-86). Its further key ingredients are a polarized valence double-ζ (vDZP) Gaussian basis set, which was fully optimized in molecular DFT calculations, in combination with large-core effective core potentials and a specially adapted D4 dispersion correction. Unlike most existing double-ζ atomic orbital sets, vDZP shows only small basis set superposition errors (BSSEs) and can compete with standard sets of triple-ζ quality. Small residual BSSE effects are efficiently absorbed by the D4 damping scheme, which overall eliminates the need for an explicit treatment or empirical corrections for BSSE. Thorough tests on a variety of thermochemistry benchmark sets show that the new composite method, dubbed ωB97X-3c, is on par with or even outperforms standard hybrid DFT methods in a quadruple-zeta basis set at a small fraction of the computational cost. Particular strengths of this method are the description of non-covalent interactions and barrier heights, for which it is among the best-performing density functionals overall.

Theoretical Study of Charge Mobility in Crystal Porphine and a Computer Design of a Porphine-Based Semiconductive Discotic Liquid Mesophase

Organic semiconductors are the focus of numerous studies; they are used in electronic devices. Modern research involves the production of neuromorphic organic materials, including those based on liquid crystal materials. The purpose of this work involves the theoretical modeling of molecules (the "core with branches" type) to construct a discotic mesophase capable of performing the functions of a neuromorphic material. For this purpose, the conductivity of crystal porphine, which can act as the nucleus of a molecule of the "core with branches" type, was investigated. The Marcus theory charge mobility values for the hole and electron were 0.148 and 0.088 cm2/V·s, respectively (the MOO method for calculating transfer integrals), and 0.561 and 0.160 cm2/V·s (DIPRO method). Based on TD-HF (HF-3c level of theory) calculations, possible structures of molecules for the formation of a discotic mesophase are proposed.

Parametrized quantum-mechanical approaches combined with the fragment molecular orbital method

Fast parameterized methods such as density-functional tight-binding (DFTB) facilitate realistic calculations of large molecular systems, which can be accelerated by the fragment molecular orbital (FMO) method. Fragmentation facilitates interaction analyses between functional parts of molecular systems. In addition to DFTB, other parameterized methods combined with FMO are also described. Applications of FMO methods to biochemical and inorganic systems are reviewed.

Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications

Computational chemistry is an essential tool in the pharmaceutical industry. Quantum computing is a fast evolving technology that promises to completely shift the computational capabilities in many areas of chemical research by bringing into reach currently impossible calculations. This perspective illustrates the near-future applicability of quantum computation of molecules to pharmaceutical problems. We briefly summarize and compare the scaling properties of state-of-the-art quantum algorithms and provide novel estimates of the quantum computational cost of simulating progressively larger embedding regions of a pharmaceutically relevant covalent protein-drug complex involving the drug Ibrutinib. Carrying out these calculations requires an error-corrected quantum architecture that we describe. Our estimates showcase that recent developments on quantum phase estimation algorithms have dramatically reduced the quantum resources needed to run fully quantum calculations in active spaces of around 50 orbitals and electrons, from estimated over 1000 years using the Trotterization approach to just a few days with sparse qubitization, painting a picture of fast and exciting progress in this nascent field.