Limiting factors in the accuracy of DFT calculation for redox potentials.

In the present study, we have investigated factors affecting the accuracy of computational chemistry calculation of redox potentials, namely the gas-phase ionization energy (IE) and electron affinity (EA), and the continuum solvation effect. In general, double-hybrid density functional theory methods yield IEs and EAs that are on average within ~0.1 eV of our high-level W3X-L benchmark, with the best performing method being DSD-BLYP/ma-def2-QZVPP. For lower-cost methods, the average errors are ~0.2-0.3 eV, with ωB97X-3c being the most accurate (~0.15 eV). For the solvation component, essentially all methods have an average error of ~0.3 eV, which shows the limitation of the continuum solvation model. Curiously, the directly calculated redox potentials show errors of ~0.3 eV for all methods. These errors are notably smaller than what can be expected from error propagation with the two components (IE and EA, and solvation effect). Such a discrepancy can be attributed to the cancellation of errors, with the lowest-cost GFN2-xTB method benefiting the most, and the most accurate ωB97X-3c method benefiting the least. For organometallic species, the redox potentials show large deviations exceeding ~0.5 eV even for DSD-BLYP. The large errors are attributed to those for the gas-phase IEs and EAs, which represents a major barrier to the accurate calculation of redox potentials for such systems.

The verification of delta SCF and Slater's transition state theory for the calculation of core ionization energy.

The core ionization energies of second- and third-period elements of the molecules C2 H5 NO2 , SiF4 , Si(CH3 )4 , PF3 , POF3 , PSF3 , CS2 , OCS, SO2 , SO2 F2 , CH3 Cl, CFCl3 , SF5 Cl, and Cl3 PS are calculated by using Hartree-Fock (HF), and Kohn-Sham (KS) with BH&HLYP, B3LYP, and LC-BOP functionals. We used ΔSCF, Slater's transition state (STS), and two previously proposed shifted STS (1) and shifted STS (2) methods, which have been developed. The errors of ΔSCF and STS come mainly from the self-interaction errors (SIE) and can be corrected with a shifting scheme. In this study, we used the shifting parameters determined for each atom. The shifted STS (1) reproduces ΔSCF almost perfectly with mean absolute deviations (MAD) of 0.02 eV. While ΔSCF and STS vary significantly depending on the functional used, the variation of shifted STS (2) is small, and all shifted STS (2) values are close to the observed ones. The deviations of the shifted STS (2) from the experiment are 0.24 eV (BH&HLYP), 0.19 eV (B3LYP), and 0.23 eV (LC-BOP). These results further support the use of shifted STS methods for predicting the core ionization energies.

The Bond Energy of the Carbon Skeleton in Polyaromatic Halohydrocarbon Molecules.

We have investigated the thermochemical stability of the carbon skeleton in polycyclic aromatic (halo) hydrocarbons using a systematic collection of molecules (the PAHH343 set). With high-level quantum chemistry methods such as W1X-2, we have obtained chemically accurate (i. e.,±~5 kJ mol-1) "normalized carbon skeleton" bond energies. They are calculated by removing the C-H and C-X (X=F, Cl) bond energies from the total atomization energy, and then normalizing on a per-carbon basis. For species with isomeric halogen-substitution pattern, the energetic variation is generally small, though larger difference can also be seen due to structural distortion from steric repulsion. The skeleton energy becomes smaller with an increasing number of halogen atoms due to the withdrawal of electron density from the bonding orbitals, mainly through the σ-bonds. We have further assessed the performance of some low-cost quantum chemistry methods for the PAHH343 set. The deviations from reference values are largely systematic, and can thus be compensated for, yielding errors that are on average below 10 kJ mol-1. This provides the prospect for the study of an even wider range of PAHH and related systems.

Sorting drug conformers in enzyme active sites: the XTB way.

In the present study, we have used the MEI196 set of interaction energies to investigate low-cost computational chemistry approaches for the calculation of binding between a molecule and its environment. Density functional theory (DFT) methods, when used with the vDZP basis set, yield good agreement with the reference energies. On the other hand, semi-empirical methods are less accurate as expected. By examining different groups of systems within MEI196 that contain species of a similar nature, we find that chemical similarity leads to cancellation of errors in the calculation of relative binding energies. Importantly, the semi-empirical method GFN1-xTB (XTB1) yields reasonable results for this purpose. We have thus further assessed the performance of XTB1 for calculating relative energies of docking poses of substrates in enzyme active sites represented by cluster models or within the ONIOM protocol. The results support the observations on error cancellation. This paves the way for the use of XTB1 in parts of large-scale virtual screening workflows to accelerate the drug discovery process.

The Paradox of Global Multireference Diagnostics.

Modern computational chemistry methods are a useful tool for modeling many chemical systems, but they are challenged by multireference species (e.g., transition metals). A variety of diagnostics have been formulated to identify such cases. They are typically developed by analyzing multireference characters of small molecules, and many provide an average picture of the entire system. We caution the use of such diagnostics for large systems because large systems may include parts with varying degrees of multireference characters. Specifically, a small but highly multireference component may yield a large error in absolute terms, which may be masked in an average value over the entire molecule. As the calculation of molecular relative energies often concerns errors in absolute terms, such a false sense of safety may be detrimental. A prospective means to tackle this challenge is to use fractional occupation density to identify potentially problematic components in a system and then examine this moiety with higher-level computations on appropriately constructed smaller models.

Exploiting the Correlation between the 1s, 2s, and 2p Energies for the Prediction of Core-Level Binding Energies of Si, P, S, and Cl species.

The binding energies (BEs) of the 1s, 2s, and 2p core electrons of third-period elements (Si, P, S, Cl) were calculated using Hartree-Fock (HF) and B3LYP, BH&HLYP, and LC-BOP ΔSCF, and the shifted KS ΔSCF methods. Linear relationships between two BEs were derived and compared with the Auger parameter. The derived lines are essentially parallel, with only the intercepts differing. The difference in intercepts is due to the lack of electron correlation effects in HF and the self-interaction errors (SIEs) of the functional. The slope is the slope of the linear relationship between the chemical shifts. The straight lines between the 2s and 2p BEs also coincided with the Auger parameter lines, which have a slope of 1 by definition and an intercept being the difference between the 2s and 2p BEs. The shifted KS ΔSCF scheme compensates for SIEs, yielding equations that are approximately invariant. The calculated average gaps for the 2s and 2p BEs are 51.21 eV for Si, 57.48 eV for P, 63.85 eV for S, and 70.48 eV for Cl. The straight lines representing the relationships between the BEs of the 1s and 2s and 1s and 2p electrons are also parallel to each other in ΔSCF and converge into a single line in the shifted ΔSCF scheme. However, these lines are steeper than the Auger parameter line. The derived relationships can be used to predict unknown BEs, which we have applied to many molecules. The results are highly accurate, with mean absolute errors (MAEs) of less than 0.2 eV compared to experimental values.

Methide Affinity Scale: Key Thermodynamic Data Underpinning Catalysis, Organic Synthesis, and Organometallic and Polymer Chemistry.

Methide transfer reactions play important roles in many areas of chemistry, including the Grignard reaction, in the transmetalation steps of metal-catalyzed cross-coupling reactions, and in the generation of cationic metal polymerization catalysts. Methide affinities (MAs) are the key thermodynamic quantity that underpin such reactions, and yet comprehensive methide affinity scales are poorly developed. Here, B3LYP-D3BJ/def2-TZVP calculations are used to calculate the energy changes (MAs) for cations (MeZ → Z+ + Me-), neutrals (MeY- → Y + Me-), and anions (MeX2- → X- + Me-) derived from permethyl species of all group s and p elements. The MAs range from 2525.8 for the singlet cation F+ to -820.4 kJ/mol for the tetramethylborate anion, Me4B-. The cations show the clearest trends: the MAs in all cases decrease going down the group, while moving across a period, the MAs increase from group 1 to group 2 and then decrease for group 3, remaining about the same or with a modest increase moving to group 4, and then continue to increase across a period to a maximum for the halogens (group 17). The anions and dianions are sensitive to hypervalency; those elements that cannot expand the octet have very unfavorable MAs (e.g., MA of Me4C requires the formation of Me5C- and of Me4B- requires the formation of Me5B2-). To address whether the anion MeY- and dianion MeZ2- are stable, the vertical detachment energies of the anions and dianions were calculated. All of the anions are thermodynamically stable with respect to electron loss, except for Me4N-, while the dianions are all thermodynamically unstable with respect to electron loss. The kinetic stability of the dianions with respect to methide and electron loss was also evaluated for the lowest MAs. The only dianions that might be kinetically stable and observable in the gas phase are Me4Ca2-, Me4Sr2-, and Me4Ba2-. The dianion CF3CaF32- is predicted to be both thermodynamically and kinetically stable in the gas phase.

Computational insights into the singlet-triplet energy gaps, ionization energies, and electron affinities for a diverse set of 812 small fullerenes (C20-C50).

In the present study, we have investigated the energy differences between the lowest-energy singlet and triplet states of a large set of small fullerenes with density functional theory (DFT), and the related quantities of ionization energy (IE) and electron affinity (EA). The DFT methods generally show consistent qualitative observations. For the full set of 812 fullerene isomers, ∼80-90% have a singlet ground state, with the rest being ground-state triplets; some of them may complement existing singlet-fission materials to improve the efficiency for light harvesting. The triplet-singlet energy difference correlates well with the IE-EA differences, which are indicators for charge-transfer capabilities. We have surveyed larger fullerenes in search of candidates with superior charge-transfer properties, with the results suggesting that optimally shaped medium-sized fullerenes may be the most promising.

Compilation of Ionic Clusters with the Rock Salt Structure: Accurate Benchmark Thermochemical Data, Assessment of Quantum Chemistry Methods, and the Convergence Behavior of Lattice Energies.

In the present study, computational quantum chemistry is used to obtain lattice energies (LEs) for a range of ionic clusters with the NaCl structure. Specifically, the compounds include NaF, NaCl, MgO, MgS, KF, CaO, and CaS clusters, (MX)n, with n = 1, 2, 4, 6, 8, 12, 16, 24, 32, 40, 50, 60, 75, 90, and 108. The highest-level W2 and W1X-2 methods are applied to the small clusters with n = 1 to 8 (the MX35 data set). The assessment with MX35 shows that, for the calculation of geometries and vibrational frequencies, the PBE0-D3(BJ) and PBE-D3(BJ) DFT methods are reasonable, but the calculation of atomization energies is more challenging. This is a result of different systematic deviations for clusters of different species. Thus, species-specific adjustments are applied for larger clusters, which are calculated with the DuT-D3 double-hybrid DFT method, the MN15 DFT method, and the PM7 semi-empirical method. They yield smoothly converging LEs to the bulk values. It is also found that, for the alkali-metal species, the LEs for a single molecule are ∼70% of the bulk values, while for the alkali-earth species, they are ∼80%. This has enabled a straightforward means to the first-principles estimation of LEs for similarly structured ionic compounds.

Simple Composite Approach to Efficiently Estimate Basis Set Limit CCSD(T) Harmonic Frequencies and Reaction Thermochemistry.

We introduce a simple strategy that combines the G3(MP2) composite method and explicitly correlated coupled cluster CCSD(T)-F12 method to efficiently estimate complete basis set CCSD(T) molecular geometries and harmonic vibrational frequencies at the cost of a double-ζ basis set calculation. Based on a large test set of 61 neutral, ionic, and open-shell molecules, and additionally 31 molecules in the HFREQ2014 data set, we demonstrate that this composite strategy has an average accuracy of 2 cm-1 or better relative to complete basis set CCSD(T) values. Using this approach, we estimated 696 CCSD(T)/CBS reaction energies of small to medium-sized systems containing up to 6 heavy atoms and confirmed existing approximations that use small basis set density functional theory methods [e.g., M06-2X/6-31+G(d)] to calculate thermal contributions to reaction enthalpies and Gibbs free energies that are accurate to within 0.2 kcal mol-1 on average.

Core-Level 2s and 2p Binding Energies of Third-Period Elements (P, S, and Cl) Calculated by Hartree-Fock and Kohn-Sham ΔSCF Theory.

In the present study, we investigate the use of the ΔSCF method and Slater's transition state (STS) theory to calculate the binding energies of the 2s and 2p electrons of third-period elements (P, S, and Cl). Both the Hartree-Fock (HF) and Kohn-Sham (KS) approximations are examined. The STS approximation performs well in reproducing the ΔSCF values. However, for the ΔSCF method itself, while the binding energy of the 2p electrons is accurately predicted, the results for 2s are fairly sensitive to the functional, exhibiting significant variations due to self-interaction errors (SIE). Nonetheless, the variations in chemical shifts between different species remain relatively small, and the values agree with experiments due to the cancellation of SIE. A notable observation is that the chemical shifts of the 2s and 2p electrons are similar, indicating a perturbation caused by the valence electrons. The error in the absolute binding energy of KS ΔSCF against the experiment is nearly constant for the same element in different molecules, and it depends largely on the functional owing to SIE. A shifting scheme previously developed can be employed to reproduce the experimental 2s and 2p binding energies, with dependence on the functional and atom but not on the molecule even for 2s KS ΔSCF binding energies. Upon obtaining the corrected binding energies, we find that the gap between 2s and 2p binding energy is nearly independent of chemical environment for a given element: 57.5, 63.9, and 70.9 eV for the elements P, S, and Cl, respectively.

The core ionization energies calculated by delta SCF and Slater's transition state theory.

The core ionization energies of the second-period and third-period elements are studied by ΔSCF and Slater's transition state (STS) theory by using Hartree-Fock (HF) and Kohn-Sham (KS) approximations. Electron correlation increases the estimated core ionization energies, while the self-interaction error (SIE) decreases them, especially for the third-period elements and is a more significant factor. As a result, while HF lacks electron correlation, it is free of SIE and reasonably predicts the core ionization energies. The core ionization energies calculated by HF STS are very close to those calculated by HF ΔSCF, showing that STS reasonably describes the relaxation of the core hole. The core ionization energies calculated by KS are particularly sensitive to the SIE of the functional used, with functionals having less SIE yielding more accurate ΔSCF core ionization energies. Consequently, BH&HLYP gives better results than B3LYP and LC-BOP since BH&HLYP is the hybrid functional with high proportion of the exact HF exchange. Although the core ionization energies are underestimated by ΔSCF due to SIE, STS gives larger core ionization energies than ΔSCF due to a concave behavior of the error curves of STS, which is also related to SIE. The mean absolute deviations of STS relative to ΔSCF, and relative to the experiment, are almost constant regardless of the nuclei among the element in the second period, and likewise among those in the third period. The systematic nature suggests that shifting the STS core ionization energies may be useful. We propose the shifted STS (1) for reproducing ΔSCF values, and the shifted STS (2) to reproduce the observed ones for KS calculations. Both schemes work quite well. The calculated results of KS ΔSCF and STS vary depending on the functional. However, the variation of each species' shifted STS (2) is very small, and all shifted STS (2) values are close to the observed ones. As the shifted STS require only one SCF calculation, they are simple and practical for predicting the core ionization energies.

Assessment of DLPNO-CCSD(T)-F12 and its use for the formulation of the low-cost and reliable L-W1X composite method.

In the present study, we have investigated the performance of RIJCOSX DLPNO-CCSD(T)-F12 methods for a wide range of systems. Calculations with a high-accuracy option ["DefGrid3 RIJCOSX DLPNO-CCSD(T1 )-F12"] extrapolated to the complete-basis-set limit using the maug-cc-pV[D+d,T+d]Z basis sets provides fairly good agreements with the canonical CCSD(T)/CBS reference for a diverse set of thermochemical and kinetic properties [with mean absolute deviations (MADs) of ~1-2 kJ mol-1 except for atomization energies]. On the other hand, the low-cost "RIJCOSX DLPNO-CCSD(T)-F12D" option leads to substantial deviations for certain properties, notably atomization energies (MADs of up to tens of kJ mol-1 ). With the high-accuracy CBS approach, we have formulated the L-W1X method, which further includes a low-cost core-valence plus scalar-relativistic term. It shows generally good accuracy. For improved accuracies in specific cases, we advise replacing maug-cc-pV(n+d)Z with jun-cc-pV(n+d)Z for the calculation of electron affinities, and using well-constructed isodesmic-type reactions to obtain atomization energies. For medium-sized systems, DefGrid3 RIJCOSX DLPNO-CCSD(T1 )-F12 calculations are several times faster than the corresponding canonical computation; the use of the local approximations (RIJCOSX and DLPNO) leads to a better scaling than that for the canonical calculation (from ~6-7 down to ~2-4 for our test systems). Thus, the DefGrid3 RIJCOSX DLPNO-CCSD(T1 )-F12 method, and the L-W1X protocol that based on it, represent a useful means for obtaining accurate thermochemical quantities for larger systems.

High-Level Quantum Chemistry Reference Heats of Formation for a Large Set of C, H, N, and O Species in the NIST Chemistry Webbook and the Identification and Validation of Reliable Protocols for Their Rapid Computation.

A recent study has examined the accuracy of NIST heats of formation for a set of C, H, and O-containing species with a proposed low-cost quantum chemistry approach. In the present study, we have used high-level methods such as W1X-2 to obtain these data more rigorously, which we have then used to assess the NIST and the previously computed values. We find that many of these NIST data that are as suggested to be unreliable by the previous study are indeed inconsistent with our high-level reference values. However, we also find substantial deviations for the previously computed values from our benchmark. Thus, we have assessed the performance of alternative low-cost methods. In our assessment, we have additionally examined C, H, N, and O-containing species for which heats of formation are available from the NIST database. We find the ωB97M-V/ma-def2-TZVP, DSD-PBEP86/ma-def2-TZVP, and CCSD(T)-F12b/aug'-cc-pVDZ methods to be adequate for obtaining heats of formation with the atomization approach, once their atomic energies are optimized with our benchmark. Notably, the low-cost ωB97M-V method yields values that agree to be within 10 kJ mol-1 for more than 90% of the (∼1500) species. A higher 20 kJ mol-1 threshold captures 98% of the data. The outlier species typically contain many electron-withdrawing (nitro) groups. In these cases, the use of isodesmic-type reactions rather than the atomization approach is more reliable. Our assessment has also identified significant outliers from the NIST database, for which experimental re-determination of the heats of formation would be desirable.

Searching for a Reliable Density Functional for Molecule-Environment Interactions, Found B97M-V/def2-mTZVP.

In the present study, we have examined density functional theory methods for the calculation of the interaction energy between a small molecule and its environment. For simple systems such as a neutral solute in a neutral solvent, good accuracy can be attained using low-cost "3c" methods, in particular r2SCAN-3c. When part(s) of the system is charged, the accurate computation of the interactions is more challenging. In these cases, we find the B97M-V/def2-mTZVP method to agree well with reference values; it also shows good accuracy for the more straightforward neutral systems. Thus, B97M-V/def2-mTZVP provides a means for accurate and low-cost computation of interaction energies, notably the binding between a substrate or a drug molecule and an enzyme, which may facilitate rational drug design.

Modeling the Conformational Preference of the Lignocellulose Interface and Its Interaction with Weak Acids.

We have examined the conformational space of model systems for the hydrogen-bonded and covalent linkages between the sugar and lignin components of lignocellulose. Specifically, glucose and paracoumaryl alcohol moieties are used in our models. Multistage screening protocols are used to identify and validate a set of lowest-energy isomers. We found a cost-effective screening process involving an initial screening with DFTB3/3ob using a 20 kJ mol-1 threshold, a refinement with the SCANh/6-31+G(2d,p) method with a 10 kJ mol-1 cutoff, a third step at the DSD-PBEP86/ma-def2-TZVP//MS1-D3/6-31+G(2d,p) level with the same 10 kJ mol-1 threshold, and a last step at the CCSD(T)/CBS//B3LYP/cc-pVTZ level with a tighter 5 kJ mol-1 threshold. The use of machine learning (with the London and Axilrod-Teller-Muto potential) can further accelerate the screening process. In general, all low-energy conformers are characterized by hydrogen bonding between the sugar and lignin moieties. We examined the interactions of covalently bonded sugar-lignin models with weak acids (HSO3-, H2PO3-, HSeO3-, H2citrate-, etc.) and found that they interacted strongly with the oxygen of the sugar-O-lignin linkage. Our results suggest that acids such as dihydrogen citrate may be attractive alternatives to the commonly used HSO3- for lignocellulose processing.

Higher-order transition state approximation.

We generalize Slater's transition state concept by deriving systematic higher-order transition state approximations. Numerical validation is performed by the calculation of transition energies for various excitations, including core, valence, and charge-transfer excitations, at Hartree-Fock and Kohn-Sham density functional theory levels. All higher-order transition state approximations introduced in this study accurately reproduce the results from delta self-consistent-field calculations. In particular, we demonstrate that the third-order generalized transition state (GTS3) approximation is a promising alternative to the original, owing to a good balance between the accuracy and computational cost. We also demonstrate that accurate and reliable results can be obtained with a low computational cost by combining the GTS3 approximation with the transition potential scheme.

Chiral Bifunctional Selenide Catalysts for Asymmetric Iodolactonizations.

1,1'-Bi-2-naphthol (BINOL)-derived chiral bifunctional sulfide and selenide catalysts that possess a hydroxy group are known to be effective catalysts for enantioselective bromolactonizations. When applied to asymmetric iodolactonizations of 4-pentenoic acids, these catalysts yield chiral γ-butyrolactone products that are important compounds in medicinal chemistry. Although chiral bifunctional selenides have shown good catalytic performances in enantioselective iodolactonizations, reactions with BINOL-derived chiral sulfide catalysts unexpectedly gave iodolactonization products in nearly racemic forms. The roles of chalcogenide moieties and hydroxy groups on bifunctional catalysts were investigated, and the importance of both a selenide moiety and a hydroxy group on chiral bifunctional selenide catalysts to achieve enantioselective iodolactonizations was clarified. An optimized chiral bifunctional selenide catalyst was applied to the asymmetric synthesis of chiral γ-butyrolactones and phthalides. Furthermore, the utility of chiral bifunctional selenides was also demonstrated in the catalytic enantioselective desymmetrizing iodolactonization of α,α-diallyl carboxylic acids.

Thermochemical stabilities of giant fullerenes using density functional tight binding theory and isodesmic-type reactions.

We present a systematic assessment of the density functional tight binding (DFTB) method for calculating heats of formation of fullerenes with isodesmic-type reaction schemes. We show that DFTB3-D/3ob can accurately predict Δf H values of the 1812 structural isomers of C60 , reproduce subtle trends in Δf H values for 24 isolated pentagon rule (IPR) isomers of C84 , and predict Δf H values of giant fullerenes that are in effectively exact agreement with benchmark DSD-PBEP86/def2-QZVPP calculations. For fullerenes up to C320 , DFTB Δf H values are within 1.0 kJ mol-1 of DSD-PBEP86/def2-QZVPP values per carbon atom, and on a per carbon atom basis DFTB3-D/3ob yields exactly the same numerical trend of (Δf H [per carbon] = 722n-0.72 + 5.2 kJ mol-1 ). DFTB3-D/3ob is therefore an accurate replacement for high-level DHDFT and composite thermochemical methods in predicting of thermochemical stabilities of giant fullerenes and analogous nanocarbon architectures.

Substituent effects on through-space intervalence charge transfer in cofacial metal-organic frameworks.

Electroactive metal-organic frameworks (MOFs) are an attractive class of materials owing to their multifunctional 3-dimensional structures, the properties of which can be modulated by changing the redox states of the components. In order to realise both fundamental and applied goals for these materials, a deeper understanding of the structure-function relationships that govern the charge transfer mechanisms is required. Chemical or electrochemical reduction of the framework [Zn(BPPFTzTz)(tdc)]·2DMF, hereafter denoted ZnFTzTz (where BPPFTzTz = 2,5-bis(3-fluoro-4-(pyridin-4-yl)phenyl)thiazolo[5,4-d]thiazole), generates mixed-valence states with optical signatures indicative of through-space intervalence charge transfer (IVCT) between the cofacially stacked ligands. Fluorination of the TzTz ligands influences the IVCT band parameters relative to the unsubstituted parent system, as revealed through Marcus-Hush theory analysis and single crystal UV-Vis spectroscopy. Using a combined experimental, theoretical and density functional theory (DFT) analysis, important insights into the effects of structural modifications, such as ligand substitution, on the degree of electronic coupling and rate of electron transfer have been obtained.