London Dispersion Corrections Research Articles

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.

Dispersion-corrected r2SCAN based double-hybrid functionals

The regularized and restored semi-local meta-generalized gradient approximation (meta-GGA) exchange–correlation functional r2SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208–8215 (2020)] is used to create adiabatic-connection-derived global double-hybrid functionals employing spin-opposite-scaled MP2. The 0-DH, CIDH, QIDH, and 0–2 type double-hybrid functionals are assessed as a starting point for further modification. Variants with 50% and 69% Hartree–Fock exchange (HFX) are empirically optimized (Pr2SCAN50 and Pr2SCAN69), and the effect of MP2-regularization (κPr2SCAN50) and range-separated HFX (ωPr2SCAN50) is evaluated. All optimized functionals are combined with the state-of-the-art London dispersion corrections D4 and NL. The resulting functionals are assessed comprehensively for their performance on main-group and metal-organic thermochemistry on 90 different benchmark sets containing 25 800 data points. These include the extensive GMTKN55 database, additional sets for main-group chemistry, and multiple sets for transition-metal complexes, including the ROST61, the MOR41, and the MOBH35 sets. As the main target of this study is the development of a broadly applicable, robust functional with low empiricism, special focus is put on variants with moderate amounts of HFX (50%), which are compared to the so far successful PWPB95-D4 (50% HFX, 20% MP2 correlation) functional. The overall best variant, ωPr2SCAN50-D4, performs well on main-group and metal-organic thermochemistry, followed by Pr2SCAN69-D4 that offers a slight edge for metal-organic thermochemistry and by the low HFX global double-hybrid Pr2SCAN50-D4 that performs robustly across all tested sets. All four optimized functionals, Pr2SCAN69-D4, Pr2SCAN50-D4, κPr2SCAN50-D4, and ωPr2SCAN50-D4, outperform the PWPB95-D4 functional.

Effects of dispersion corrections on the theoretical description of bulk metals

The addition of a London dispersion correction to standard Kohn-Sham density-functional theory is essential for an accurate description of noncovalent interactions. While several dispersion-corrected density functionals (DC-DFs) have shown excellent performance for hard solids at ambient conditions, their transferability to metallic systems at ambient conditions or under isotropic compression has not been systematically examined. In this study, we assess the ability of selected DC-DFs to describe the equations of state (EOSs) of selected elemental metals and intermetallic compounds up to several gigapascals of pressure. EOS-derived properties, such as the unit-cell volume, the bulk modulus, and its pressure derivative, were then evaluated with and without thermal effects and the results compared with experimental reference data. We also assess the ability of the DC-DFs to predict the phase-transition pressures for a set of intermetallic compounds. The results of this study establish that London dispersion physics, and even dispersion contributions from the core electrons, is important in the description of bulk metals.

Subtle hydrogen bond preference and dual Franck-Condon activity - the interesting pairing of 2-naphthol with anisole.

The hydrogen-bonded complexes between 2-naphthol (or β-naphthol) and anisole are explored by detecting their IR absorption in the OH stretching range as well as their UV absorption by means of laser-induced fluorescence and resonance-enhanced two-photon UV ionisation. For the more stable cis and the metastable trans conformations of the OH group in 2-naphthol, hydrogen bonding to the oxygen atom of anisole is consistently detected in different supersonic jet expansions. Alternative hydrogen bonding to the aromatic ring of anisole remains elusive, although the majority of state-of-the-art hybrid DFT functionals with London dispersion correction and - less surprisingly - MP2 wavefunction theory predict it to be slightly more stable at zero-point level, unless three-body dispersion correction is added to the B3LYP-D3(BJ) approach. This changes at the CCSD(T) level, which forecasts an energy advantage of 1-3 kJ mol-1 for the classical hydrogen bond arrangement even after including (DFT) zero-point energy contributions. The UV and IR spectra of the cis complex exhibit clear evidence for intensity redistribution of the primary OH stretch oscillator to combination states with the same low-frequency intermolecular bending mode by Franck-Condon-type vertical excitation mechanisms. This rare case of dual (vibronic and vibrational) Franck-Condon activity of a low-frequency mode invites future studies of homologues where aromatic ring docking of the OH group may be further stabilised, e.g. through anisole ring methylation.

Upon DFT-D3 dispersion correction and ECD spectral confirmation, only several conformers can stably coexist for three fungal cycloaspeptides (A, D, G)

Dispersion correction in theoretical determination of cyclopeptide conformations is emphasized. Whether in gas approximation or in solvation simulation, the density functional theory with London dispersion correction (DFT-D3) demonstrates that only 2–3 conformers can stably coexist for cycloaspeptides (A, D, G) at B3LYP-D3 and CAM-B3LYP-D3. Conformational rationality is confirmed by electronic circular dichroism (ECD). Whether for Cotton effect or for excitation energy, TD-B3LYP-D3 has better performances than TD-CAM-B3LYP-D3 because the former can better reproduce the experiment. A molecular orbital analysis is used to interpret ECD, where two energy bands observed in experiment originates from the ππ* transitions other than the σπ* transitions. Long-range correction and solvent effect make H-bonds shorten, and dispersion correction makes them further shorten.

Exploiting Phase Transitions in Catalysis: Adsorption of CO on doped VO2 -Polymorphs.

VO2 is well known for its low-temperature metal-insulator transition between two phases with tetragonal rutile and monoclinic structure. The adsorption of CO on the two polymorphs of Mo-doped VO2 is calculated to investigate the effect of a substrate phase change on the adsorption energy. The system is investigated theoretically at density-functional theory level using a hybrid functional with London dispersion correction. We establish a computational protocol applicable for the study of physisorption on open-shell transition metal oxides. The main task is to control the spin state of open-shell slab models used to model adsorption of closed-shell molecules in order to obtain numerically stable adsorption energies and to reduce spin contamination within the broken-symmetry unrestricted Kohn-Sham approximation. Applying this procedure, it is possible to identify the most stable adsorption positions of CO on both phases of VO2 . CO adsorbs vertically with the C atom on a surface V atom in the monoclinic phase with an adsorption energy of -56 kJ/mol. The same adsorption position has an adsorption energy of only -46 kJ/mol on the rutile phase. Similar differences were obtained with multireference methods using an embedded cluster model. This effect may inspire experimental strategies exploiting the rutile monoclinic VO2 phase transition in catalytic processes where CO is formed as product or as an intermediate.

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.

London Dispersion‐Corrected Density Functionals Applied to van der Waals Stacked Layered Materials: Validation of Structure, Energy, and Electronic Properties

AbstractMost density functionals lack to correctly account for long‐range London dispersion interactions, and numerous a posteriori correction schemes have been proposed in recent years. In van der Waals structures, the interlayer distance controls the proximity effect on the electronic structure, and the interlayer interaction energy indicates the possibility to mechanically exfoliate a layered material. For upcoming twisted van der Waals heterostructures, a reliable but efficient and scalable theoretical scheme to correctly predict the interlayer distance is required. Therefore, the performance of a series of popular London dispersion corrections combined with computationally affordable density functionals is validated. As reference data, the experimental interlayer distance of layered bulk materials is used, and corresponding interlayer interaction energies are calculated using the random phase approximation. We demonstrate that the SCAN‐rVV10 and PBE‐rVV10L functionals predict interlayer interaction energies and interlayer distances of the studied layered systems within the range of the defined error limits of 10 meV per atom and 0.12 Å, respectively. Semi‐empirical and empirical dispersion‐corrected functionals show significantly larger error bars, with PBE+dDsC performing best with comparable quality of geometries, but with higher interlayer interaction energy error limits of ≈20 meV per atom.

Dispersion corrected r2SCAN based global hybrid functionals: r2SCANh, r2SCAN0, and r2SCAN50.

The regularized and restored semilocal meta-generalized gradient approximation (meta-GGA) exchange-correlation functional r2SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208-8215 (2020)] is used to create three global hybrid functionals with varying admixtures of Hartree-Fock "exact" exchange (HFX). The resulting functionals r2SCANh (10% HFX), r2SCAN0 (25% HFX), and r2SCAN50 (50% HFX) are combined with the semi-classical D4 London dispersion correction. The new functionals are assessed for the calculation of molecular geometries, main-group, and metalorganic thermochemistry at 26 comprehensive benchmark sets. These include the extensive GMTKN55 database, ROST61, and IONPI19 sets. It is shown that a moderate admixture of HFX leads to relative improvements of the mean absolute deviations for thermochemistry of 11% (r2SCANh-D4), 16% (r2SCAN0-D4), and 1% (r2SCAN50-D4) compared to the parental semi-local meta-GGA. For organometallic reaction energies and barriers, r2SCAN0-D4 yields an even larger mean improvement of 35%. The computation of structural parameters (geometry optimization) does not systematically profit from the HFX admixture. Overall, the best variant r2SCAN0-D4 performs well for both main-group and organometallic thermochemistry and is better or on par with well-established global hybrid functionals, such as PW6B95-D4 or PBE0-D4. Regarding systems prone to self-interaction errors (SIE4x4), r2SCAN0-D4 shows reasonable performance, reaching the quality of the range-separated ωB97X-V functional. Accordingly, r2SCAN0-D4 in combination with a sufficiently converged basis set [def2-QZVP(P)] represents a robust and reliable choice for general use in the calculation of thermochemical properties of both main-group and organometallic chemistry.

Assessing Density Functional Theory for Chemically Relevant Open-Shell Transition Metal Reactions.

Due to the principle lack of systematic improvement possibilities of density functional theory, careful assessment of the performance of density functional approximations (DFAs) on well-designed benchmark sets, for example, for reaction energies and barrier heights, is crucial. While main-group chemistry is well covered by several available sets, benchmark data for transition metal chemistry is sparse. This is especially the case for larger, chemically relevant molecules. Addressing this issue, we recently introduced the MOR41 benchmark which covers chemically relevant reactions of closed-shell complexes. In this work, we extend these efforts to single-reference open-shell systems and introduce the "reactions of open-shell single-reference transition metal complexes" (ROST61) benchmark set. ROST61 includes accurate coupled-cluster reference values for 61 reaction energies with a mean reaction energy of -42.8 kcal mol-1. Complexes with 13-93 atoms covering 20 d-block elements are included, but due to the restriction to single-reference open-shell systems, important elements such as iron or platinum could not be taken into account, or only to a small extent. We assess the performance of 31 DFAs in combination with three London dispersion (LD) correction schemes. Further, DFT-based composite methods, MP2, and a few semiempirical quantum chemical methods are evaluated. Consistent with the results for the MOR41 closed-shell benchmark, we find that the ordering of DFAs according to Jacob's ladder is preserved and that adding an LD correction is crucial, clearly improving almost all tested methods. The recently introduced r2SCAN-3c composite method stands out with a remarkable mean absolute deviation (MAD) of only 2.9 kcal mol-1, which is surpassed only by hybrid DFAs with low amounts of Fock exchange (e.g., 2.3 kcal mol-1 for TPSS0-D4/def2-QZVPP) and double-hybrid (DH) DFAs but at a significantly higher computational cost. The lowest MAD of only 1.6 kcal mol-1 is obtained with the DH DFA PWPB95-D4 in the def2-QZVPP basis set approaching the estimated accuracy of the reference method. Overall, the ROST61 set adds important reference data to a sparsely sampled but practically relevant area of chemistry. At this point, it provides valuable orientation for the application and development of new DFAs and electronic structure methods in general.

First-principles study of benzene and its homologues upon graphene-metal surfaces: Comparison of London dispersion corrections

We perform a comparative theoretical study of benzene and its homologues (toluene, para-xylene, and mesitylene) adsorbed on Cu/Al/Pd(111)-supported graphene using density functional theory (DFT). The long-range attraction is handled by semiempirical dispersion correction method (PBE-D3) and ab initio van der Waals density functionals (vdW-DF2, optB86b-vdW, optB88-vdW, and SCAN-rVV10). Our results show a systematic increase in the adsorption energy of organic molecules on graphene in the presence of underlaying metal substrates. In the case of strong metal-graphene contact, such as Pd(111)-graphene, the adsorption energy of benzene even increases 0.44 eV, which presents suitable platform for filtering harmful molecules such as benzene. Besides, we find out that the dispersion-corrected functionals play a fundamental role in the structure and adsorption energy. Furthermore, the adsorption energy increases linearly with the number of methyl groups on the benzene ring.

Is the Electrophilicity of the Metal Nitrene the Sole Predictor of Metal-Mediated Nitrene Transfer to Olefins? Secondary Contributing Factors as Revealed by a Library of High-Spin Co(II) Reagents.

Recent research has highlighted the key role played by the electron affinity of the active metal-nitrene/imido oxidant as the driving force in nitrene additions to olefins to afford valuable aziridines. The present work showcases a library of Co(II) reagents that, unlike the previously examined Mn(II) and Fe(II) analogues, demonstrate reactivity trends in olefin aziridinations that cannot be solely explained by the electron affinity criterion. A family of Co(II) catalysts (17 members) has been synthesized with the assistance of a trisphenylamido-amine scaffold decorated by various alkyl, aryl, and acyl groups attached to the equatorial amidos. Single-crystal X-ray diffraction analysis, cyclic voltammetry and EPR data reveal that the high-spin Co(II) sites (S = 3/2) feature a minimal [N3N] coordination and span a range of 1.4 V in redox potentials. Surprisingly, the Co(II)-mediated aziridination of styrene demonstrates reactivity patterns that deviate from those anticipated by the relevant electrophilicities of the putative metal nitrenes. The representative L4Co catalyst (-COCMe3 arm) is operating faster than the L8Co analogue (-COCF3 arm), in spite of diminished metal-nitrene electrophilicity. Mechanistic data (Hammett plots, KIE, stereocontrol studies) reveal that although both reagents follow a two-step reactivity path (turnover-limiting metal-nitrene addition to the C b atom of styrene, followed by product-determining ring-closure), the L4Co catalyst is associated with lower energy barriers in both steps. DFT calculations indicate that the putative [L4Co]NTs and [L8Co]NTs species are electronically distinct, inasmuch as the former exhibits a single-electron oxidized ligand arm. In addition, DFT calculations suggest that including London dispersion corrections for L4Co (due to the polarizability of the tert-Bu substituent) can provide significant stabilization of the turnover-limiting transition state. This study highlights how small ligand modifications can generate stereoelectronic variants that in certain cases are even capable of overriding the preponderance of the metal-nitrene electrophilicity as a driving force.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

R2SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications.

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r2SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal-organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

The significance of long-range correction to the hydroperoxyl radical-scavenging reaction of trans-resveratrol and gnetin C.

Density functional theory has been gaining popularity for studying the radical scavenging activity of antioxidants. However, only a few studies investigate the importance of calculation methods on the radical-scavenging reactions. In this study, we examined the significance of (i) the long-range correction on the coulombic interaction and (ii) the London dispersion correction to the hydroperoxyl radical-scavenging reaction of trans-resveratrol and gnetin C. We employed B3LYP, CAM-B3LYP, M06-2X exchange-correlation functionals and B3LYP with the D3 version of Grimme’s dispersion in the calculations. The results showed that long-range correction on the coulombic interaction had a significant effect on the increase of reaction and activation energies. The increase was in line with the change of hydroperoxyl radical’s orientation in the transition state structure. Meanwhile, the London dispersion correction only had a minor effect on the transition state structure, reaction energy and activation energy. Overall, long-range correction on the coulombic interaction had a significant impact on the radical-scavenging reaction.

London Dispersion Corrections to Density Functional Theory for Transition Metals Based on Fitting to Experimental Temperature-Programmed Desorption of Benzene Monolayers.

Standard implementations of generalized gradient approximation (GGA)-based density functional theory (DFT) describe well strongly bound molecules and solids but fail to describe long-range London dispersion or van der Waals (vdW) attraction interactions that are important in molecular crystals and two-dimensional solids. To provide accurate values for the vdW distance and energies for the metals Cu, Ag, Au, Ni, Pd, and Pt, we determined empirical vdW corrections to Perdew, Burke, and Ernzerhof (PBE) DFT by fitting the experimental adsorption enthalpies measured by temperature-programmed desorption (TPD) from benzene monolayers by Campbell and co-workers ( J. Phys. Chem. C 2016, 120, 25161-25172). Benzene physisorbed to these metals without chemical reaction; therefore, we consider the bonding to be vdW. We use the low gradient form for the vdW corrections, EvdW-LG = -C6LG/[R6 + RvdwLG6] with just two parameters per atom (C6LG and RvdwLG). This LG form leads to negligible changes in bond distances and angles, so adjusting the parameters should not sacrifice accuracy for the bonding interactions. We demonstrate that the parameters fitted to benzene also describe well the physisorption enthalpies for other hydrocarbons (naphthalene, cyclohexane, methane, ethane, and propane) on Pt. We also report low gradient vdW correction parameters for the noble gases that fit the equilibrium lattice parameter and heat of vaporization of the crystals.

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.

Ab Initio Molecular Dynamics Simulation and Energetics of the Ribulose-1,5-biphosphate Carboxylation Reaction Catalyzed by Rubisco: Toward Elucidating the Stereospecific Protonation Mechanism.

In the carboxylation reaction catalyzed by ribulose 1,5-bisphosphate (RuBP) carboxylase-oxygenase (Rubisco), which is fundamental to photosynthesis, scission of a C-C bond in the six-carbon gemdiolate intermediate forms a carbanion that must be protonated stereospecifically to form product. It is thought that a conserved lysine side chain (LYS175 in spinach Rubisco), in the immediate vicinity of the carbanion, provides the necessary proton. Here, we endeavor to determine from the electronic-structure calculations whether protonation via this route is energetically possible. The two-dimensional energy surface was mapped to determine the minimum energy path (MEP) using density functional theory (B3LYP) and incorporating basis set superposition and classical (London) dispersion corrections. The potential of mean force (free energy) was then calculated from ab initio molecular dynamics simulations with umbrella sampling in the vicinity of the MEP on the scission-protonation reaction coordinate. MEP calculations were also carried out to evaluate the possibility of an active-site water near the phosphate (P1) of RuBP, with an excess proton positioned at P1, as an alternative facilitator of stereospecific protonation via a classical Grotthuss mechanism. In both cases, the C-C bond scission in the six-carbon intermediate and proton transfer from the donor was found to be concerted and highly asynchronous, without a stable carbanion intermediate. However, the free energy change was unfavorable for direct protonation by the LYS175 side chain. In contrast, the Grotthuss mechanism yielded stable products and an activation energy in good agreement with experiment. It also provides a plausible mechanism for alternative product formed in enzyme mutations at the LYS175 position and is consistent with the observed deuterium isotope effects.

A Comprehensive Assessment of the Effectiveness of Orbital Optimization in Double-Hybrid Density Functionals in the Treatment of Thermochemistry, Kinetics, and Noncovalent Interactions.

Orbital optimization (OO) has been suggested as a way to solve some shortcomings of second-order Møller-Plesset (MP2) variants and double-hybrid density functionals (DHDFs). A closer inspection of the literature, however, shows that the only two studies on OO-DHDFs were limited to three nonempirical PBE-based functionals, which are known to be of only mediocre accuracy. Herein, we provide a more in-depth analysis of OO-DHDFs with the main focus being on main-group thermochemistry, kinetics, and noncovalent interactions. We reanalyze two PBE-based OO-DHDFs and present four new OO-DHDF variants, two of which make use of the spin-component-scaling idea in their nonlocal correlation part. We also provide a more thorough analysis of three OO-MP2 variants. After assessing more than 621 reference points, we come to the conclusion that the benefits of OO are not as straightforward as previously thought. Results heavily depend on the underlying parent method. While OO-SCS/SOS-MP2 usually provide improved results-including for noncovalently bound systems-the opposite is true for OO-MP2. OO-DHDFs, like their nonoptimized counterparts, still require London-dispersion corrections. Among the DHDFs, the largest effect of OO on thermochemical properties is seen for PBE0-2 and the smallest for PBE0-DH. However, results can both worsen and improve with OO. If the latter is the case, the resulting OO-DHDF is still outperformed by the currently most accurate conventional DHDFs, namely DSD-BLYP and DSD-PBEP86. We therefore recommend the OO technique only to be used in specialized cases. For the general method user we re-emphasize using conventional dispersion-corrected DHDFs for robust, reliable results. Our findings also indicate that entirely different strategies seem to be required in order to obtain a substantial improvement over the currently best DHDFs.

Comprehensive Thermochemical Benchmark Set of Realistic Closed-Shell Metal Organic Reactions.

We introduce the new MOR41 benchmark set consisting of 41 closed-shell organometallic reactions resembling many important chemical transformations commonly used in transition metal chemistry and catalysis. It includes significantly larger molecules than presented in other transition metal test sets and covers a broad range of bonding motifs. Recent progress in linear-scaling coupled cluster theory allowed for the calculation of accurate DLPNO-CCSD(T)/CBS(def2-TZVPP/def2-QZVPP) reference energies for 3d,4d,5d-transition metal compounds with up to 120 atoms. Furthermore, 41 density functionals, including seven GGAs, three meta-GGAs, 14 hybrid functionals, and 17 double-hybrid functionals combined with two different London dispersion corrections, are benchmarked with respect to their performance for the newly compiled MOR41 reaction energies. A few wave function-based post-HF methods as, e.g., MP2 or RPA with similar computational demands are also tested and in total, 90 methods were considered. The double-hybrid functional PWPB95-D3(BJ) outperformed all other assessed methods with an MAD of 1.9 kcal/mol, followed by the hybrids ωB97X-V (2.2 kcal/mol) and mPW1B95-D3(BJ) (2.4 kcal/mol). The popular PBE0-D3(BJ) hybrid also performs well (2.8 kcal/mol). Within the meta-GGA class, the recently published SCAN-D3(BJ) functional as well as TPSS-D3(BJ) perform best (MAD of 3.2 and 3.3 kcal/mol, respectively). Many popular methods like BP86-D3(BJ) (4.9 kcal/mol) or B3LYP-D3(BJ) (4.9 kcal/mol) provide significantly worse reaction energies and are not recommended for organometallic thermochemistry considering the availability of better methods with the same computational cost. The results regarding the performance of different functional approximations are consistent with conclusions from previous main-group thermochemistry benchmark studies.