Treating London-Dispersion Effects with the Latest Minnesota Density Functionals: Problems and Possible Solutions

Correcting Dispersion Corrections with Density-Corrected DFT

Almost all empirical parametrizations of dispersion corrections in DFT use only energy errors, thereby mixing functional and density-driven errors. We introduce density and dispersion-corrected DFT (D2C-DFT), a dual-calibration approach that accounts for density delocalization errors when parametrizing dispersion interactions. We simply exclude density-sensitive reactions from the training data. We find a significant reduction in both errors and variation among several semilocal functionals and their global hybrids when tailored dispersion corrections are employed with Hartree-Fock densities.

Origins of the unphysical noncovalent interaction energy curves obtained with the 2011 and 2012 Minnesota density functionals

With the noncovalent interaction energy curves of the methane dimer [(CH4)2], we have clarified two different origins of the unphysical noncovalent interaction energy curves obtained with the Minnesota density functionals of M11-L, MN12-L, and MN12-SX. For the M11-L functional, the unphysical inflection point on the (CH4)2 interaction energy curve originates from the inclusion of the long-range exchange. As to the MN12-L and MN12-SX functionals, the lack of smoothness restraints results in unphysical inflection points on the corresponding (CH4)2 interaction energy curves. As a result, exchange functionals are as important as dispersion corrections for density functionals to map noncovalent interaction energy surfaces reasonably. Moreover, very highly parameterized functionals with smoothness restraints are suggested for investigating noncovalent interaction energy surfaces.

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder

The accurate representation of the structural and dynamical properties of water is essential for simulating the unique behavior of this ubiquitous solvent. Here we assess the current status of describing liquid water using ab initio molecular dynamics, with a special focus on the performance of all the later generation Minnesota functionals. Findings are contextualized within the current knowledge on DFT for describing bulk water under ambient conditions and compared to experimental data. We find that, contrary to the prevalent idea that local and semilocal functionals overstructure water and underestimate dynamical properties, M06-L, revM06-L, and M11-L understructure water, while MN12-L and MN15-L overdistance water molecules due to weak cohesive effects. This can be attributed to a weakening of the hydrogen bond network, which leads to dynamical fingerprints that are over fast. While most of the hybrid Minnesota functionals (M06, M08-HX, M08-SO, M11, MN12-SX, and MN15) also yield understructured water, their dynamical properties generally improve over their semilocal counterparts. It emerges that exact exchange is a crucial component for accurately describing hydrogen bonds, which ultimately leads to corrections in both the dynamical and structural properties. However, an excessive amount of exact exchange strengthens hydrogen bonds and causes overstructuring and slow dynamics (M06-HF). As a compromise, M06-2X is the best performing Minnesota functional for water, and its D3 corrected variant shows very good structural agreement. From previous studies considering nuclear quantum effects (NQEs), the hybrid revPBE0-D3, and the rung-5 RPA (RPA@PBE) have been identified as the only two approximations that closely agree with experiments. Our results suggest that the M06-2X(-D3) functionals have the potential to further improve the reproduction of experimental properties when incorporating NQEs through path integral approaches. This work provides further proof that accurate modeling of water interactions requires the inclusion of both exact exchange and balanced (non-local) correlation, highlighting the need for higher rungs on Jacob's ladder to achieve predictive simulations of complex biological systems in aqueous environments.

Axial-equatorial equilibrium in substituted cyclohexanes: a DFT perspective on a small but complex problem

In Chemistry, complexity is not necessarily associated to large systems, as illustrated by the textbook example of axial-equatorial equilibrium in mono-substituted cyclohexanes. The difficulty in modelling such a simple isomerization is related to the need for reproducing the delicate balance between two forces, with opposite effects, namely the attractive London dispersion and the repulsive steric interactions. Such balance is a stimulating challenge for density-functional approximations and it is systematically explored here by considering 20 mono-substituted cyclohexanes. In comparison to highly accurate CCSD(T) reference calculations, their axial-equatorial equilibrium is studied with a large set of 48 exchange-correlation approximations, spanning from semilocal to hybrid to more recent double hybrid functionals. This dataset, called SAV20 (as Steric A-values for 20 molecules), allows to highlight the difficulties encountered by common and more original DFT approaches, including those corrected for dispersion with empirical potentials, the 6-31G*-ACP model, and our cost-effective PBE-QIDH/DH-SVPD protocol, in modeling these challenging interactions. Interestingly, the performance of the approaches considered in this contribution on the SAV20 dataset does not correlate with that obtained with other more standard datasets, such as S66, IDISP or NC15, thus indicating that SAV20 covers physicochemical features not already considered in previous noncovalent interaction benchmarks.

Noncovalently bound excited-state dimers: a perspective on current time-dependent density functional theory approaches applied to aromatic excimer models

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for time-dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

An Anthracene-Thiolate-Ligated Ruthenium Complex: Computational Insights into Z-Stereoselective Cross Metathesis

Stereoselective control of the cross metathesis of olefins is a crucial aspect of synthetic procedures. In this study, we utilized density functional theory methods to calculate thermodynamic and kinetic descriptors to explore the stereoselectivity of cross metathesis between allylbenzene and 2-butene-1,4-diyl diacetate. A ruthenium-based complex, characterized primarily by an anthracene-9-thiolate ligand, was designed in silico to completely restrict the E conformation of olefins through a bottom-bound mechanism. Our investigation of the kinetics of all feasible propagation routes demonstrated that Z-stereoisomers of metathesis products can be synthesized with an energy cost of only 13 kcal/mol. As a result, we encourage further research into the synthetic strategies outlined in this work.

When catchers meet - a computational study on the dimerization of the Buckycatcher

We study the dimerization of the buckycatcher in gas phase and in toluene. We created an extensive library of 36 different complexes, which were characterized at semi-empirical and DFT levels. Semi-empirical geometries and dimerization energies compare well against reference data or Density Functional Theory calculations we performed. Born-Oppenheimer molecular dynamics was used to understand what happens when two molecules of the buckycatcher meet, allowing us to infer on the lack of kinetic barriers when dimers form. Thermodynamically, it is possible that room temperature solutions contain dimerized buckycatcher. Using a very simple exchange model, it is shown, however, that dimerization cannot compete thermodynamically against complexation with fullerenes, which accounts for experimental observations.

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.

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.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Electrophilicity of Hoveyda-Grubbs Olefin Metathesis Catalysts as the Driving Force that Controls Initiation Rates

The dissociative mechanism of initiation for a series of Hoveyda-Grubbs type metathesis catalysts modified at the para and meta positions in the isopropoxybenzylidene ligand is investigated by means of DFT calculations. The electron donating/withdrawing capacity of the ligand was screened through the incorporation of various substituents such as halogens, nitro, alkoxides, ketones, esters, amines, and amides. Variations in structural parameters, energy barriers for the Ru-O bond dissociation, and Ru-O bond strength were examined as a function of the Hammett constant. It was found that electronic properties of the catalysts such as chemical potential, hardness, and electrophilicity correlate linearly with the dissociative energy barriers. These findings enable a systematic rationalization and prediction of rate of precatalyst initiation through the calculation of only the HOMO-LUMO gap of catalysts, as the faster the initiation, the more electrophilic the catalyst.

Improving IDP theoretical chemical shift accuracy and efficiency through a combined MD/ADMA/DFT and machine learning approach

This work extends the multi-scale computational scheme for the quantum mechanics (QM) calculations of Nuclear Magnetic Resonance (NMR) chemical shifts (CSs) in proteins that lack a well-defined 3D structure. The scheme couples the sampling of an intrinsically disordered protein (IDP) by classical molecular dynamics (MD) with protein fragmentation using the adjustable density matrix assembler (ADMA) and density functional theory (DFT) calculations. In contrast to our early investigation on IDPs (Pavlíková Přecechtělová et al., J. Chem. Theory Comput., 2019, 15, 5642-5658) and the state-of-the art NMR calculations for structured proteins, a partial re-optimization was implemented on the raw MD geometries in vibrational normal mode coordinates to enhance the accuracy of the MD/ADMA/DFT computational scheme. In addition, machine-learning based cluster analysis was performed on the scheme to explore its potential in producing protein structure ensembles (CLUSTER ensembles) that yield accurate CSs at a reduced computational cost. The performance of the cluster-based calculations is validated against results obtained with conventional structural ensembles consisting of MD snapshots extracted from the MD trajectory at regular time intervals (REGULAR ensembles). CS calculations performed with the refined MD/ADMA/DFT framework employed the 6-311++G(d,p) basis set that outperformed IGLO-III calculations with the same density functional approximation (B3LYP) and both explicit and implicit solvation. The partial geometry optimization did not universally improve the agreement of computed CSs with the experiment but substantially decreased errors associated with the ensemble averaging. A CLUSTER ensemble with 50 structures yielded ensemble averages close to those obtained with a REGULAR ensemble consisting of 500 MD frames. The cluster based calculations thus required only a fraction of the computational time.

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.

Systematic Evaluation of Counterpoise Correction in Density Functional Theory

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ∼150 atoms and ligand-protein models with ∼300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. This is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.

Probing the Directionality of S···O/N Chalcogen Bond and Its Interplay with Weak C-H···O/N/S Hydrogen Bond Using Molecular Electrostatic Potential

The directionality of the chalcogen bond (Ch-bond) formed by S and its interplay with other weak interactions have important chemical and biological implications. Here, dimers made of CH₃-S-X and O/N containing nucleophiles are studied and found to be stabilized by coexisting S···O/N and C-H···O/N interactions. Based on experimentally accessible electron density and molecular electrostatic potentials (MESPs), we showed that reciprocity between S···O/N and C-H···O/N interactions in the stability of cumulative molecular interaction (ΔE) was dependent on the strength of the σ-hole on S (V_s,max). Direct correlation between ΔE of dimers with V_s,max of S supports the electrostatic nature of the Ch-bond. Such interplay of the Ch-bond is necessary for its directionality in complex nucleophiles (carbonyl groups) with multiple electron-rich centers, which is explained using MESP. A correlation between the MESP minima in the π-region and the strength of the S-π interaction explains the directional selectivity of the Ch-bond.

Noncovalently bound excited-state dimers: a perspective on current time-dependent density functional theory approaches applied to aromatic excimer models

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for Time-Dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

Olefin Metathesis Catalyzed by a Hoveyda-Grubbs-like Complex Chelated to Bis(2-mercaptoimidazolyl) Methane: A Predictive DFT Study

Although highly selective complexes for the cross-metathesis of olefins, particularly oriented toward the productive metathesis of Z-olefins, have been reported in recent years, there is a constant need to design and prepare new and improved catalysts for this challenging reaction. In this work, guided by density functional theory (DFT) calculations, the performance of a Ru-based catalyst chelated to a sulfurated pincer in the olefin metathesis was computationally assessed. The catalyst was designed based on the Hoveyda–Grubbs catalyst (SIMes)Cl₂Ru(=CH–o–OiPrC₆H₄) through the substitution of chlorides with the chelator bis(2-mercaptoimidazolyl)methane. The obtained thermodynamic and kinetic data of the initiation phase through side- and bottom-bound mechanisms suggest that this system is a versatile catalyst for olefin metathesis, as DFT predicts the highest energy barrier of the catalytic cycle of ca. 20 kcal/mol, which is comparable to those corresponding to the Hoveyda–Grubbs-type catalysts. Moreover, in terms of the stereoselectivity evaluated through the propagation phase in the metathesis of propene–propene to 2-butene, our study reveals that the Z isomer can be formed under a kinetic control. We believe that this is an interesting outcome in the context of future exploration of Ru-based catalysts with sulfurated chelates in the search for high stereoselectivity in selected reactions.

How Accurate Are Approximate Density Functionals for Noncovalent Interaction of Very Large Molecular Systems?

Noncovalent intermolecular interactions are very important in many research areas. Therefore, it is vital to understand the extent to which approximate density functionals give a proper description of noncovalent interactions. Previous research has demonstrated that some approximate density functionals can predict usefully accurate interaction energies for many noncovalent systems; however, most of that work is limited to small and moderate-sized molecules. Very recently though, accurate benchmarks have become available for some very large molecules. The present work applies 21 approximate density functionals to compute the binding energies of seven large molecular systems that have a number of atoms ranging from 200 to 910. The results are judged by comparison to the recently published CIM-DLPNO-CCSD(T) results, which are assumed to provide a reliable benchmark. The five most accurate methods among those tested are found to be PW6B95-D4, PW6B95-D3(BJ), revM11, M06-L, and MN15.

Requirements for an accurate dispersion-corrected density functional

Post-self-consistent dispersion corrections are now the norm when applying density-functional theory to systems where non-covalent interactions play an important role. However, there is a wide range of base functionals and dispersion corrections available from which to choose. In this work, we opine on the most desirable requirements to ensure that both the base functional and dispersion correction, individually, are as accurate as possible for non-bonded repulsion and dispersion attraction. The base functional should be dispersionless, numerically stable, and involve minimal delocalization error. Simultaneously, the dispersion correction should include finite damping, higher-order pairwise dispersion terms, and electronic many-body effects. These criteria are essential for avoiding reliance on error cancellation and obtaining correct results from correct physics.

Comment on "The Nature of Chalcogen-Bonding-Type Tellurium-Nitrogen Interactions": Fixing the Description of Finite-Temperature Effects Restores the Agreement Between Experiment and Theory

Mitzel and co-workers recently presented an intriguing molecule displaying a tellurium-nitrogen interaction. Structural data obtained in the solid and in gas phase indicated a large increase of the Te-N equilibrium distance re from 2.64 to 2.92 Å, respectively. Although some DFT calculations appear to support the large re in gas phase, we argue that the lions share of the increase is due to an incomplete description of finite-temperature effects in the back-corrected experimental data. This hypothesis is based on high-level coupled-cluster (CC) and periodic DFT calculations, which consistently point towards a much smaller re in the isolated molecule. Further support comes through MD simulations with a tuned GFN2-xTB Hamiltonian: Calibrated against a CC reference, these show a six-times larger influence of temperature than with the originally used GFN1-xTB. Taking this into account, the back-corrected re in gas phase becomes 2.67±0.08 Å, in good agreement with high-level CC theory and most DFT methods.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

A molecular dynamics simulation study on the propensity of Asn-Gly-containing heptapeptides towards β-turn structures: Comparison with ab initio quantum mechanical calculations

Both molecular mechanical and quantum mechanical calculations play an important role in describing the behavior and structure of molecules. In this work, we compare for the same peptide systems the results obtained from folding molecular dynamics simulations with previously reported results from quantum mechanical calculations. More specifically, three molecular dynamics simulations of 5 μs each in explicit water solvent were carried out for three Asn-Gly-containing heptapeptides, in order to study their folding and dynamics. Previous data, based on quantum mechanical calculations within the DFT framework have shown that these peptides adopt β-turn structures in aqueous solution, with type I’ β-turn being the most preferred motif. The results from our analyses indicate that at least for the given systems, force field and simulation protocol, the two methods diverge in their predictions. The possibility of a force field-dependent deficiency is examined as a possible source of the observed discrepancy.

Counterintuitive torsional barriers controlled by hydrogen bonding

The torsional barriers along the Caryl-Caryl axis of a pair of isosteric disubstituted biphenyls were determined by variable temperature 1H NMR spectroscopy in three solvents with contrasted hydrogen bond accepting abilities (1,1,2,2-tetrachloroethane-d2, nitrobenzene-d5 and dimethyl sulfoxide-d6). One of the biphenyl scaffolds was substituted at its ortho and ortho' positions with N'-acylcarbohydrazide groups that could engage in a pair of intramolecular N-HO=C hydrogen bonding interactions at the ground state, but not at the transition state of the torsional isomerization pathway. The torsional barrier of this biphenyl was exceedingly low despite the presence of the hydrogen bonds (16.1, 15.6 and 13.4 kcal mol-1 in the three aforementioned solvents), compared to the barrier of the reference biphenyl (15.3 ± 0.1 kcal mol-1 on average). Density functional theory and the solvation model developed by Hunter were used to decipher the various forces at play. They highlighted the strong stabilization of hydrogen bond donating solutes not only by hydrogen bond accepting solvents, but also by weakly polar, yet polarizable solvents. As fast exchanges on the NMR time scale were observed above the melting point of dimethyl sulfoxide-d6, a simple but accurate model was also proposed to extrapolate low free activation energies in a pure solvent (dimethyl sulfoxide-d6) from higher ones determined in mixtures of solvents (dimethyl sulfoxide-d6 in nitrobenzene-d5).

On-Surface Chemistry Induced by Long-Lived Excitons: (NO)2 Dissociation on C60

Solid-state excitonic excitations play an increasingly important role in optoelectronic and light harvesting processes due to their ubiquitous presence in dipolar two-dimensional materials. Here we show that long-lived solid-state excitons induce chemical reactions in adsorbed molecules and thus convert light into chemical energy. For the model system (NO)₂ dimer adsorbed on ordered c(4×4) C₆₀ films, time-of-flight measurements following UV laser excitation reveal a slow and a fast dissociative desorption channel, which are assigned to intersystem crossing and internal conversion, respectively, by time-dependent density functional theory calculations.

Difficulties of Popular Density Functionals to Describe the Conformational Isomerism in Iodoacetic Acid

Matrix isolation studies in solid argon and neon at 4.2 K reveal that iodoacetic acid initially only exists as its ground state (c,x) conformer with an almost perpendicular I-C-C═O dihedral angle, but UV irradiation in the 240-255 nm range leads to population of the 0.8 kcal mol^-1 less stable (c,c) isomer. The latter structure exhibits a close 3.23 Å contact of the iodine and carbonyl oxygen atoms decidedly below the sum of their van der Waals radii (3.50 Å). Increasing the matrix temperature by only a few Kelvin triggers the thermal back reaction of (c,c) to (c,x) and leads to an estimated upper limit of 0.38 kcal mol^-1 for the associated torsional barrier. While wave function methods including completely uncorrelated Hartree-Fock theory have no problem to identify (c,c) as a proper minimum, many popular density functionals fail to describe the C-C torsional potential in cis-iodoacetic acid qualitatively correct. We assessed the performance of 12 density functionals of different levels of sophistication, namely, the BLYP, PBE, TPSS, B3LYP, BHandHLYP, PBE0, M06-2X, CAM-B3LYP, ωB97X-D3, B2-PLYP, B2GP-PLYP, and DSD-PBEP86 methods, against accurate extrapolated CCSD(T)/CBS(T-Q)//MP2/def2-TZVPP energies and found that almost all of them yield acceptable relative energies. Still, even some of the best performers fail to find a reasonably deep minimum in the region of the (c,c) conformer, and addition of the empirical D3-dispersion correction does not remedy the qualitative shortcoming. Instead, inclusion of a sufficient amount of (long-range) exact exchange and likely a proper treatment of medium-range correlation effects all along the torsional coordinate play an important role in the proper description of the sub-van der Waals iodine-oxygen contact. More modern, recommended functionals do not suffer from the described shortcoming.

Impact of the olefin structure on the catalytic cycle and decomposition rates of Hoveyda-Grubbs metathesis catalysts

A relatively fast degradation of ruthenium catalysts in the presence of selected olefins, and ethylene in particular, is one of the bottlenecks in their use in metathesis reactions. Here we explore the structure-activity relationships between the rate of degradation of Hoveyda-Grubbs catalysts and the structure of olefins by means of DFT calculations. We show that (Z)-1,2-dichloroethene can't form stable complexes with a 14-electron active complex due to a strong inductive electron withdrawal effect. Hoveyda-Grubbs catalysts can be, however, used to convert (Z)-1,2-dichloroethene to (E)-1,2-dichloroethene due to differences in crucial barriers in the catalytic cycle for E/Z isomers. Hoveyda-Grubbs catalysts in the presence of both isomers of 1,2-dimethoxyethene and 1,2-dichloroethene are predicted to be very stable in the unproductive metathesis, while for monosubstituted olefins the methoxyethene presence gives relatively low barriers for crucial degradation transition states and can readily undergo decomposition.

Theoretical Study of the Mechanism of Catalytic Enanteoselective N-H and O-H Insertion Reactions

Theoretical density functional theory (DFT) calculations were carried out to study bond insertion reactions using a copper(I)-Box-carbenoid as a bond activator. In order to understand the reaction mechanism where N-H and O-H bonds actively participate, the reaction force (RF) and activation strain model (ASM) were used. Results indicate that the first step of the reaction is barrierless for both bond insertions (N-H and O-H), and the second step of the insertion reaction in the phenol (O-H bond) is favored kinetically and thermodynamically with regard to the aniline substrate (N-H bond). The enantioselectivity is driven by the ligand of the catalyst by steric repulsion, favoring the formation of the R isomer. The analysis of the reaction force and ASM exhibited that the higher energy barrier in aniline is mainly due to a higher W₂ contribution together with repulsive interactions, which hinders the insertion process.

DFT Computed Dielectric Response and THz Spectra of Organic Co-Crystals and Their Constituent Components

Terahertz (THz) spectroscopy has been put forth as a non-contact, analytical probe to characterize the intermolecular interactions of biologically active molecules, specifically as a way to understand, better develop, and use active pharmaceutical ingredients. An obstacle towards fully utilizing this technique as a probe is the need to couple features in the THz regions to specific vibrational modes and interactions. One solution is to use density functional theory (DFT) methods to assign specific vibrational modes to signals in the THz region, coupling atomistic insights to spectral features. Here, we use open source planewave DFT packages that employ ultrasoft pseudopotentials to assess the infrared (IR) response of organic compounds and complex co-crystal formulations in the solid state, with and without dispersion corrections. We compare our DFT computed lattice parameters and vibrational modes to experiment and comment on how to improve the agreement between theory and modeling to allow for THz spectroscopy to be used as an analytical probe in complex biologically relevant systems.

Growth Mechanism, Ambient Stability, and Charge Trapping Ability of Ti-Based Maleic Acid Hybrid Films by Molecular Layer Deposition

Ti-based maleic acid (MA) hybrid films were successfully fabricated by molecular layer deposition (MLD) using organic precursor MA and inorganic precursor TiCl₄. The effect of deposition temperature on the growth rate, composition, and bonding mode of hybrid thin films has been investigated systematically. With increasing temperature from 140 to 280 °C, the growth rate decreases from 1.42 to 0.16 Å per MLD cycle with basically unchanged composition ratio of C:O:Ti in the films. Fourier transform infrared spectra indicate that all hybrid films show preference for bidentate bonding mode. Further analyses of X-ray photoelectron spectroscopy and in situ quartz crystal microbalance elucidate that as-deposited MLD Ti-MA hybrid films consist of inorganic Ti-O-Ti units and organic-inorganic Ti-MA units. In addition, the density functional theory calculation was performed to investigate the possible reaction mechanism of the TiCl₄-MA MLD process, which is well consistent with experimental results. More importantly, upon comparison with the TiCl₄-fumaric acid MLD system, it is demonstrated that the cis- and trans-configurations of butenedioic acid influence the MLD growth, bonding mode, stability, and charging ability of MLD hybrid films. Ti-MA hybrid films exhibit better stability and charging ability than Ti-FA hybrid films, benefiting from the inorganic Ti-O-Ti units in the hybrid films.

Statistically representative databases for density functional theory via data science

Cluster analysis applied to quantum chemistry: a new broad database of chemical properties with a reasonable computational cost.

A Trip to the Density Functional Theory Zoo: Warnings and Recommendations for the User

This account is written for general users of density functional theory (DFT) methods as well as experimental researchers who are new to the field and would like to conduct such calculations. Its main emphasis lies on how to find a way through the confusing ‘zoo’ of DFT by addressing common misconceptions and highlighting those modern methods that should ideally be used in calculations of energetic properties and geometries. A particular focus is on highly popular methods and the important fact that popularity does not imply accuracy. In this context, we present a new analysis of the openly available data published in Swart and co-workers’ famous annual ‘DFT poll’ (http://www.marcelswart.eu/dft-poll/) to demonstrate the existing communication gap between the DFT user and developer communities. We show that despite considerable methodological advances in the field, the perception of some parts of the user community regarding their favourite approaches has changed little. It is hoped that this account makes a contribution towards changing this status and that users are inspired to adjust their current computational protocols to accommodate strategies that are based on proven robustness, accuracy, and efficiency rather than popularity.

The influence of the cationic carbenes on the initiation kinetics of ruthenium-based metathesis catalysts; a DFT study

Cationic carbenes are a relatively new and rare group of ancillary ligands, which have shown their superior activity in a number of challenging catalytic reactions. In ruthenium-based metathesis catalysis they are often used as ammonium tags, to provide water-soluble, environment-friendly catalysts. In this work we performed computational studies on three cationic carbenes with the formal positive charge located at different distances from the carbene carbon. We show that the predicted initiation rates of Grubbs, indenylidene, and Hoveyda–Grubbs-like complexes incorporating these carbenes show little variance and are similar to initiation rates of standard Grubbs, indenylidene, and Hoveyda–Grubbs catalysts. In all investigated cases the partial charge of the carbene carbon atom is similar, resulting in comparable C_carbene–Ru bond strengths and Ru–P/O dissociation Gibbs free energies.

Semi-empirical or non-empirical double-hybrid density functionals: which are more robust?

The development of non-empirical double-hybrid density functionals (DHDFs) is a very active research area with the number of approaches in this field having increased rapidly. At the same time, there is a lack of published work that provides a fair assessment and comparison between non-empirical and semi-empirical DHDFs on an equal footing. Herein, we close this gap and present a thorough analysis of both classes of DHDFs on the large GMTKN55 benchmark database for general main-group thermochemistry, kinetics, and noncovalent interactions [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184-32215]. In total, 115 variations of dispersion-corrected and -uncorrected DHDFs are tested, which will be condensed to an in-depth assessment of 31 methods: 19 non-empirical and 12 semi-empirical DHDFs. As such, our study represents the largest DHDF study ever conducted and can serve as an important benchmark informing method developers and users alike. Our results show that semi-empirical DHDFs are the most robust density functional approximations and more reliable and accurate than non-empirical ones. In fact, some non-empirical approaches are even outperformed by hybrid approaches or even dispersion-corrected and -uncorrected MP2 and SCS-MP2. SOS0-PBE0-2-D3(BJ) is the only exception and the only non-empirical DHDF that we can safely recommend for general applicability. However, it is still outperformed by six semi-empirical DHDFs, of which we would like to particularly recommend the following five: ωB97X-2-D3(BJ), DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), B2NC-PLYP-D3(BJ), and B2GPPLYP-D3(BJ). Our findings seriously question current trends in the field and they highlight that novel strategies have to be found in order to outperform the currently best density functional theory methods on the market. We hope that our study can function as an important cornerstone inspiring such a change of direction in the field.