Implementation of nuclear gradients of range-separated hybrid density functionals and benchmarking on rotational constants for organic molecules

Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers

Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.

Simulating chemical reactions promoted by self-assembled peptides with catalytic properties

Peptides that self-assemble exhibit distinct three-dimensional structures and attributes, positioning them as promising candidates for biocatalysts. Exploring their catalytic processes enhances our comprehension of the catalytic actions inherent to self-assembling peptides, laying a theoretical foundation for creating novel biocatalysts. The investigation into the intricate reaction mechanisms of these entities is rendered challenging due to the vast variability in peptide sequences, their aggregated formations, supportive elements, structures of active sites, types of catalytic reactions, and the interplay between these variables. This complexity hampers the elucidation of the linkage between sequence, structure, and catalytic efficiency in self-assembling peptide catalysts. This chapter delves into the latest progress in understanding the mechanisms behind peptide self-assembly, serving as a catalyst in hydrolysis and oxidation reactions, and employing computational analyses. It discusses the establishment of models, selection of computational strategies, and analysis of computational procedures, emphasizing the application of modeling techniques in probing the catalytic mechanisms of peptide self-assemblies. It also looks ahead to the potential future trajectories within this research domain. Despite facing numerous obstacles, a thorough investigation into the structural and catalytic mechanisms of peptide self-assemblies, combined with the ongoing advancement in computational simulations and experimental methodologies, is set to offer valuable theoretical insights for the development of new biocatalysts, thereby significantly advancing the biocatalysis field.

Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT

The unfavorable scaling (N5) of the conventional second-order Møller-Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.; Riplinger, C.; Valeev, E. F.; Neese, F. J. Chem. Phys. 2015, 143, 034108.] paved the way for DLPNO-based DH (DLPNO-DH) methods. In this work, we assess the accuracy of the DLPNO-DH approximation compared to conventional DHs on a large number of 7925 data points for thermochemistry and 239 data points for structural features, including main-group and transition-metal systems. It is shown that DLPNO-DH-DFT can be applied successfully to perform energy calculations and geometry optimizations for large molecules at a drastically reduced computational cost. Furthermore, PNO space extrapolation is shown to be applicable, similar to its DLPNO-CCSD(T) counterpart, to reduce the remaining error.

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

Informing geometric deep learning with electronic interactions to accelerate quantum chemistry

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. However, existing machine learning techniques are challenged by the scarcity of training data when exploring unknown chemical spaces. We overcome this barrier by systematically incorporating knowledge of molecular electronic structure into deep learning. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high-fidelity physical quantities. OrbNet-Equi accurately models a wide spectrum of target properties while being several orders of magnitude faster than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional semiempirical and machine learning-based methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.

Optimization of the r2SCAN-3c Composite Electronic-Structure Method for Use with Slater-Type Orbital Basis Sets

The "Swiss army knife" composite density functional electronic-structure method r²SCAN-3c (J. Chem. Phys. 2021, 154, 064103) is extended and optimized for the use with Slater-type orbital basis sets. The meta generalized-gradient approximation (meta-GGA) functional r²SCAN by Furness et al. is combined with a tailor-made polarized triple-ζ Slater-type atomic orbital (STO) basis set (mTZ2P), the semiclassical London dispersion correction (D4), and a geometrical counterpoise (gCP) correction. Relativistic effects are treated explicitly with the scalar-relativistic zeroth-order regular approximation (SR-ZORA). The performance of the new implementation is assessed on eight geometry and 74 energy benchmark sets, including the extensive GMTKN55 database as well as recent sets such as ROST61 and IONPI19. In geometry optimizations, the STO-based r²SCAN-3c is either on par with or more accurate than the hybrid density functional approximation M06-2X-D3(0)/TZP. In energy calculations, the overall accuracy is similar to the original implementation of r²SCAN-3c with Gaussian-type atomic orbitals (GTO), but basic properties, intermolecular noncovalent interactions, and barrier heights are better described with the STO approach, resulting in a lower weighted mean absolute deviation (WTMAD-2(STO) = 7.15 vs 7.50 kcal mol^-1 with the original method) for the GMTKN55 database. The STO-optimized r²SCAN-3c outperforms many conventional hybrid/QZ approaches in most common applications at a fraction of their cost. The reliable, robust, and accurate r²SCAN-3c implementation with STOs is a promising alternative to the original implementation with GTOs and can be generally used for a broad field of quantum chemical problems.

Quantification of Geometric Errors Made Simple: Application to Main-Group Molecular Structures

Nearly all electronic structure simulations begin with obtaining approximate geometries, making a systematic quantification of errors in approximate molecular structures of key importance. Recently, the geometric energy offset (GEO) framework based on a single and natural measure for quantifying and analyzing these errors has been proposed ( J. Phys. Chem. Lett. 2020, 11, 99579964). An accurate and far less costly approximation to GEO is utilized here to readily quantify errors in main-group structures and analyze them in a chemically intuitive way. The use of semiexperimental geometries as a reference further simplifies the analysis. The analysis reveals new insights into the geometric performance of methods, their rankings, as well as patterns across different classes of methods and basis sets that arise from the analysis.

Anharmonicity and Spectra-Structure Correlations in MIR and NIR Spectra of Crystalline Menadione (Vitamin K3)

Mid-infrared (MIR) and near-infrared (NIR) spectra of crystalline menadione (vitamin K3) were measured and analyzed with aid of quantum chemical calculations. The calculations were carried out using the harmonic approach for the periodic model of crystal lattice and the anharmonic DVPT2 calculations applied for the single molecule model. The theoretical spectra accurately reconstructed the experimental ones permitting for reliable assignment of the MIR and NIR bands. For the first time, a detailed analysis of the NIR spectrum of a molecular system based on a naphthoquinone moiety was performed to elucidate the relationship between the chemical structure of menadione and the origin of the overtones and combination bands. In addition, the importance of these bands during interpretation of the MIR spectrum was demonstrated. The overtones and combination bands contribute to 46.4% of the total intensity of menadione in the range of 3600-2600 cm-1. Evidently, these bands play a key role in shaping of the C-H stretching region of MIR spectrum. We have shown also that the spectral regions without fundamentals may provide valuable structural information. For example, the theoretical calculations reliably reconstructed numerous overtones and combination bands in the 4000-3600 and 2800-1800 cm-1 ranges. These results, provide a comprehensive origin of the fundamentals, overtones and combination bands in the NIR and MIR spectra of menadione, and the relationship of these spectral features with the molecular structure.

r2SCAN-3c: A "Swiss army knife" composite electronic-structure method

The recently proposed r²SCAN meta-generalized-gradient approximation (mGGA) of Furness and co-workers is used to construct an efficient composite electronic-structure method termed r²SCAN-3c. To this end, the unaltered r²SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error. The performance of the new method is evaluated for the GMTKN55 database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for non-covalent interactions, organometallic reactions, and lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r²SCAN-3c: It by far surpasses its predecessor B97-3c at only twice the cost and provides one of the best results of all semi-local density-functional theory (DFT)/QZ methods ever tested for the GMTKN55 database at one-tenth of the cost. Specifically, for reaction and conformational energies as well as non-covalent interactions, it outperforms prominent hybrid-DFT/QZ approaches at two to three orders of magnitude lower cost. Perhaps, the most relevant remaining issue of r²SCAN-3c is self-interaction error (SIE), owing to its mGGA nature. However, SIE is slightly reduced compared to other (m)GGAs, as is demonstrated in two examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous composite DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.

Automated exploration of the low-energy chemical space with fast quantum chemical methods

We propose and discuss an efficient scheme for the in silico sampling for parts of the molecular chemical space by semiempirical tight-binding methods combined with a meta-dynamics driven search algorithm. The focus of this work is set on the generation of proper thermodynamic ensembles at a quantum chemical level for conformers, but similar procedures for protonation states, tautomerism and non-covalent complex geometries are also discussed. The conformational ensembles consisting of all significantly populated minimum energy structures normally form the basis of further, mostly DFT computational work, such as the calculation of spectra or macroscopic properties. By using basic quantum chemical methods, electronic effects or possible bond breaking/formation are accounted for and a very reasonable initial energetic ranking of the candidate structures is obtained. Due to the huge computational speedup gained by the fast low-cost quantum chemical methods, overall short computation times even for systems with hundreds of atoms (typically drug-sized molecules) are achieved. Furthermore, specialized applications, such as sampling with implicit solvation models or constrained conformational sampling for transition-states, metal-, surface-, or noncovalently bound complexes are discussed, opening many possible applications in modern computational chemistry and drug discovery. The procedures have been implemented in a freely available computer code called CREST, that makes use of the fast and reliable GFNn-xTB methods.

Soft experimental constraints for soft interactions: a spectroscopic benchmark data set for weak and strong hydrogen bonds

An experimental benchmark data base on rotational constants, vibrational properties and energy differences for weakly and more strongly hydrogen-bonded complexes and their constituents from the spectroscopic literature is assembled. It is characterized in detail and finally contracted to a more compact, discriminatory set (ENCH-51, for Experimental Non-Covalent Harmonic with 51 entries). The meeting points between theory and experiment consist of equilibrium rotational constants and harmonic frequencies and energies, which are back-corrected from experimental observables and are very easily accessible by quantum chemical calculations. The relative performance of B3LYP-D3, PBE0-D3 and M06-2X density functional theory predictions with a quadruple-zeta basis set is used to illustrate systematic errors, error compensation and selective performance for structural, vibrational and energetical observables. The current focus is on perspectives and different benchmarking methodologies, rather than on a specific theoretical method or a specific class of compounds. Extension of the data base in chemical, observable and quantum chemical method space is encouraged.

Structure Optimisation of Large Transition-Metal Complexes with Extended Tight-Binding Methods

Large transition-metal complexes are used in numerous areas of chemistry. Computer-aided theoretical investigations of such complexes are limited by the sheer size of real systems often consisting of hundreds to thousands of atoms. Accordingly, the development and thorough evaluation of fast semi-empirical quantum chemistry methods that are universally applicable to a large part of the periodic table is indispensable. Herein, we report on the capability of the recently developed GFNn-xTB method family for full quantum-mechanical geometry optimisation of medium to very large transition-metal complexes and organometallic supramolecular structures. The results for a specially compiled benchmark set of 145 diverse closed-shell transition-metal complex structures for all metals up to Hg are presented. Further the GFNn-xTB methods are tested on three established benchmark sets regarding reaction energies and barrier heights of organometallic reactions.

A generally applicable atomic-charge dependent London dispersion correction

The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.

The role of dispersion and anharmonic corrections in conformational analysis of flexible molecules: the allyl group rotamerization of matrix isolated safrole

Conformational changes of the monomeric safrole (5-(2-propenyl)-1,3-benzodioxole) isolated in low temperature xenon matrices were induced thermally or using narrow-band UV radiation. The rotation of the allyl group taking place in the studied matrices was followed by FTIR spectroscopy. Safrole represents a challenging example of a flexible molecule highlighting the importance of dispersion interactions and anharmonic effects in the structural, spectroscopic and energetic analysis. Structures of the safrole conformers, their energetics and infrared spectra have been calculated using various computational methods ranging from density functional theory (DFT) to coupled cluster (CC). The best theoretical results were obtained by integrating CCSD(T) energies including complete basis set extrapolation and core-valence corrections with B2PLYP-D3 equilibrium structures and hybrid B2PLYP-D3/B3LYP-D3 anharmonic computations for IR spectra and thermodynamics.

GFN2-xTB-An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions

An extended semiempirical tight-binding model is presented, which is primarily designed for the fast calculation of structures and noncovalent interaction energies for molecular systems with roughly 1000 atoms. The essential novelty in this so-called GFN2-xTB method is the inclusion of anisotropic second order density fluctuation effects via short-range damped interactions of cumulative atomic multipole moments. Without noticeable increase in the computational demands, this results in a less empirical and overall more physically sound method, which does not require any classical halogen or hydrogen bonding corrections and which relies solely on global and element-specific parameters (available up to radon, Z = 86). Moreover, the atomic partial charge dependent D4 London dispersion model is incorporated self-consistently, which can be naturally obtained in a tight-binding picture from second order density fluctuations. Fully analytical and numerically precise gradients (nuclear forces) are implemented. The accuracy of the method is benchmarked for a wide variety of systems and compared with other semiempirical methods. Along with excellent performance for the "target" properties, we also find lower errors for "off-target" properties such as barrier heights and molecular dipole moments. High computational efficiency along with the improved physics compared to its precursor GFN-xTB makes this method well-suited to explore the conformational space of molecular systems. Significant improvements are furthermore observed for various benchmark sets, which are prototypical for biomolecular systems in aqueous solution.

Far-IR and UV spectral signatures of controlled complexation and microhydration of the polycyclic aromatic hydrocarbon acenaphthene

UV and IR spectroscopic study of the controlled complexation and microhydration of a polycyclic aromatic hydrocarbon under isolated conditions using free electron laser FELIX.

Strained hydrogen bonding in imidazole trimer: a combined infrared, Raman, and theory study

This is not how three imidazole molecules prefer to arrange, as a combined IR, Raman and computational analysis unambiguously shows.

Extension of the D3 dispersion coefficient model

A new model, termed D4, for the efficient computation of molecular dipole-dipole dispersion coefficients is presented. As in the related, well established D3 scheme, these are obtained as a sum of atom-in-molecule dispersion coefficients over atom pairs. Both models make use of dynamic polarizabilities obtained from first-principles time-dependent density functional theory calculations for atoms in different chemical environments employing fractional atomic coordination numbers for interpolation. Different from the D3 model, the coefficients are obtained on-the-fly by numerical Casimir-Polder integration of the dynamic, atomic polarizabilities α(iω). Most importantly, electronic density information is now incorporated via atomic partial charges computed at a semi-empirical quantum mechanical tight-binding level, which is used to scale the polarizabilities. Extended statistical measures show that errors for dispersion coefficients with the proposed D4 method are significantly lower than with D3 and other, computationally more involved schemes. Alongside, accurate isotropic charge and hybridization dependent, atom-in-molecule static polarizabilities are obtained with an unprecedented efficiency. Damping function parameters are provided for three standard density functionals, i.e., TPSS, PBE0, and B3LYP, allowing evaluation of the new DFT-D4 model for common non-covalent interaction energy benchmark sets.

Diving for Accurate Structures in the Ocean of Molecular Systems with the Help of Spectroscopy and Quantum Chemistry

The prediction and interpretation of structural properties are the starting points for a deep understanding of thermochemistry, kinetics, and spectroscopic signatures of molecular systems. To give an example, detailed knowledge of the conformational behavior of the main building blocks of biomolecules in the gas phase (i.e., without the perturbing effect of the environment) is a mandatory prerequisite toward the understanding of the role played by different interactions in determining the biological activity in terms of structure-activity relationships. The first step to take is an unambiguous definition of molecular structure. We address the so-called Born-Oppenheimer equilibrium structure, which is defined in a rigorous manner and isotopically independent, and the target accuracy. For the latter, we aim at so-called "spectroscopic" accuracy, which implies uncertainties of a few milliangstroms for bond lengths and smaller than a tenth of degree for angles. If on one side the continuous enhancements of the experimental techniques give access to new and unprecedented spectroscopic determinations, on the other side they require increasing efforts for an unbiased interpretation and analysis. Among the pieces of information, accurate molecular structures play a particularly important role. Indeed, there is a strong relationship between the experimental outcome and the electronic structure of the system. Spectroscopic techniques, in particular those exploited in the gas phase, are therefore accurate and reliable sources for structural information. However, it is seldom straightforward to derive molecular structures directly from the experimental information. Indeed, even in the favorable case of investigations in the gas phase, vibrational effects are always present, and disentangling their contributions requires collection of information for all vibrational modes, a nearly impossible task. To overcome these limitations, joint theory-spectroscopy strategies can be identified, which are referred to as "top-down" and "bottom-up". The first approach, denoted as the semiexperimental approach, relies on extracting from experimental outcomes the equilibrium structure by using quantum-chemical computations to recover vibrational effects. The bottom-up approach consists in verifying the computed equilibrium geometry by means of a comparison between calculated and experimental spectroscopic parameters that probe structural characteristics. In this contribution, we try to review the most important challenges in accurate molecular structure determinations, with particular emphasis on the "solution" provided by a joint theoretical-experimental approach and on the current state of the art. Starting from the illustration of different strategies, we proceed by addressing the increasing complexity in the derivation of equilibrium geometries: we start from the construction of a database of accurate structures, we then face the problem of extending the dimension of the systems amenable to accurate structural determinations, and finally we move to the challenge of understanding the nature of intermolecular interactions.

Intramolecular London Dispersion Interaction Effects on Gas-Phase and Solid-State Structures of Diamondoid Dimers

The covalent diamantyl (C₂₈H₃₈) and oxadiamantyl (C₂₆H₃₄O₂) dimers are stabilized by London dispersion attractions between the dimer moieties. Their solid-state and gas-phase structures were studied using a multitechnique approach, including single-crystal X-ray diffraction (XRD), gas-phase electron diffraction (GED), a combined GED/microwave (MW) spectroscopy study, and quantum chemical calculations. The inclusion of medium-range electron correlation as well as the London dispersion energy in density functional theory is essential to reproduce the experimental geometries. The conformational dynamics computed for C₂₆H₃₄O₂ agree well with solution NMR data and help in the assignment of the gas-phase MW data to individual diastereomers. Both in the solid state and the gas phase the central C-C bond is of similar length for the diamantyl [XRD, 1.642(2) Å; GED, 1.630(5) Å] and the oxadiamantyl dimers [XRD, 1.643(1) Å; GED, 1.632(9) Å; GED+MW, 1.632(5) Å], despite the presence of two oxygen atoms. Out of a larger series of quantum chemical computations, the best match with the experimental reference data is achieved with the PBEh-3c, PBE0-D3, PBE0, B3PW91-D3, and M06-2X approaches. This is the first gas-phase confirmation that the markedly elongated C-C bond is an intrinsic feature of the molecule and that crystal packing effects have only a minor influence.

Conformational energy range of ligands in protein crystal structures: The difficult quest for accurate understanding

In this review, we address a fundamental question: What is the range of conformational energies seen in ligands in protein-ligand crystal structures? This value is important biophysically, for better understanding the protein-ligand binding process; and practically, for providing a parameter to be used in many computational drug design methods such as docking and pharmacophore searches. We synthesize a selection of previously reported conflicting results from computational studies of this issue and conclude that high ligand conformational energies really are present in some crystal structures. The main source of disagreement between different analyses appears to be due to divergent treatments of electrostatics and solvation. At the same time, however, for many ligands, a high conformational energy is in error, due to either crystal structure inaccuracies or incorrect determination of the reference state. Aside from simple chemistry mistakes, we argue that crystal structure error may mainly be because of the heuristic weighting of ligand stereochemical restraints relative to the fit of the structure to the electron density. This problem cannot be fixed with improvements to electron density fitting or with simple ligand geometry checks, though better metrics are needed for evaluating ligand and binding site chemistry in addition to geometry during structure refinement. The ultimate solution for accurately determining ligand conformational energies lies in ultrahigh-resolution crystal structures that can be refined without restraints.

A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions

We present the updated and extended GMTKN55 benchmark database for more accurate and extensive energetic evaluation of density functionals and other electronic structure methods with detailed guidelines for method users.

Small Atomic Orbital Basis Set First-Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources

In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.

Reliable vibrational wavenumbers for C=O and N-H stretchings of isolated and hydrogen-bonded nucleic acid bases

The accurate prediction of vibrational wavenumbers for functional groups involved in hydrogen-bonded bridges remains an important challenge for computational spectroscopy. For the specific case of the C=O and N-H stretching modes of nucleobases and their oligomers, the paucity of experimental reference values needs to be compensated by reliable computational data, which require the use of approaches going beyond the standard harmonic oscillator model. Test computations performed for model systems (formamide, acetamide and their cyclic homodimers) in the framework of the second order vibrational perturbation theory (VPT2) confirmed that anharmonic corrections can be safely computed by global hybrid (GHF) or double hybrid (DHF) functionals, whereas the harmonic part is particularly challenging. As a matter of fact, GHFs perform quite poorly and even DHFs, while fully satisfactory for C=O stretchings, face unexpected difficulties when dealing with N-H stretchings. On these grounds, a linear regression for N-H stretchings has been obtained and validated for the heterodimers formed by 4-aminopyrimidine with 6-methyl-4-pyrimidinone (4APM-M4PMN) and by uracil with water. In view of the good performance of this computational model, we have built a training set of B2PLYP-D3/maug-cc-pVTZ harmonic wavenumbers (including linear regression scaling for N-H) for six-different uracil dimers and a validation set including 4APM-M4PMN, one of the most stable hydrogen-bonded adenine homodimers, as well as the adenine-uracil, adenine-thymine, guanine-cytosine and adenine-4-thiouracil heterodimers. Because of the unfavourable scaling of DHF harmonic wavenumbers with the dimensions of the investigated systems, we have optimized a linear regression of B3LYP-D3/N07D harmonic wavenumbers for the training set, which has been next checked against the validation set. This relatively cheap model, which shows very good agreement with experimental data (average errors of about 10 cm(-1)), paves the route toward a reliable analysis of spectroscopic signatures for larger polynucleotides.

A computationally efficient double hybrid density functional based on the random phase approximation

A new double hybrid density functional (PWRB95) based on GGA orbitals and RPA is presented and its performance is investigated compared to standard DFT and wavefunction methods.

Screened exchange hybrid density functional for accurate and efficient structures and interaction energies

HSE-3c: a computationally efficient and numerically robust screened hybrid functional that can be applied to periodic small gap systems.

Consistent structures and interactions by density functional theory with small atomic orbital basis sets

A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust "high-speed" computational tool in theoretical chemistry and physics.

CC/DFT Route toward Accurate Structures and Spectroscopic Features for Observed and Elusive Conformers of Flexible Molecules: Pyruvic Acid as a Case Study

The structures and relative stabilities as well as the rotational and vibrational spectra of the three low-energy conformers of pyruvic acid (PA) have been characterized using a state-of-the-art quantum-mechanical approach designed for flexible molecules. By making use of the available experimental rotational constants for several isotopologues of the most stable PA conformer, Tc-PA, the semiexperimental equilibrium structure has been derived. The latter provides a reference for the pure theoretical determination of the equilibrium geometries for all conformers, thus confirming for these structures an accuracy of 0.001 Å and 0.1 deg for bond lengths and angles, respectively. Highly accurate relative energies of all conformers (Tc-, Tt-, and Ct-PA) and of the transition states connecting them are provided along with the thermodynamic properties at low and high temperatures, thus leading to conformational enthalpies accurate to 1 kJ mol(-1). Concerning microwave spectroscopy, rotational constants accurate to about 20 MHz are provided for the Tt- and Ct-PA conformers, together with the computed centrifugal-distortion constants and dipole moments required to simulate their rotational spectra. For Ct-PA, vibrational frequencies in the mid-infrared region accurate to 10 cm(-1) are reported along with theoretical estimates for the transitions in the near-infrared range, and the corresponding infrared spectrum including fundamental transitions, overtones, and combination bands has been simulated. In addition to the new data described above, theoretical results for the Tc- and Tt-PA conformers are compared with all available experimental data to further confirm the accuracy of the hybrid coupled-cluster/density functional theory (CC/DFT) protocol applied in the present study. Finally, we discuss in detail the accuracy of computational models fully based on double-hybrid DFT functionals (mainly at the B2PLYP/aug-cc-pVTZ level) that avoid the use of very expensive CC calculations.

Unveiling the non-covalent interactions of molecular homodimers by dispersion-corrected DFT calculations and collision-induced broadening of ro-vibrational transitions: application to (CH2F2)2 and (SO2)2

(CH₂F₂)₂ and (SO₂)₂ are investigated using DFT-D3 computations, and experimental dissociation energies are determined by TDL-IR spectroscopy. DFT-D3 dramatically improves over uncorrected DFT.

Microsolvation of 2-thiouracil: molecular structure and spectroscopic parameters of the thiouracil-water complex

State-of-the-art quantum-chemical computations have been employed to accurately determine the equilibrium structure and interaction energy of the 2-thiouracil-water complex, thus extending available reference data for biomolecule solvation patterns. The coupled-cluster level of theory in conjunction with a triple-ζ basis set has been considered together with extrapolation to the basis set limit, performed by employing second-order Møller-Plesset perturbation theory, and inclusion of core-correlation and diffuse-function corrections. On the basis of the comparison of experiment and theory for 2-thiouracil [ Puzzarini et al. Phys. Chem. Chem. Phys. 2013 , 15 , 16965 - 16975 ], structural changes due to water complexation have been pointed out. Molecular and spectroscopic properties of the 2-thiouracil-water complex have then been studied by means of the composite computational approach introduced for the molecular structure evaluation. Among the results achieved, we mention the accurate determination of the molecular dipole moment and of the spectroscopic parameters required for predicting the rotational spectrum.