The ORCA quantum chemistry program package

Prediction of Spin Density, Baird-Antiaromaticity, and Singlet-Triplet Energy Gap in Triplet-State Polybenzenoid Systems from Simple Structural Motifs

Triplet-state aromaticity has been recently proposed as a strategy for designing functional organic electronic compounds, many of which are polycyclic aromatic systems. However, in many cases, the aromatic nature of the triplet state cannot be easily predicted. Moreover, it is often unclear how specific structural manipulations affect the electronic properties of the excited-state compounds. Herein, the relationship between the structure of polybenzenoid hydrocarbons (PBHs) and their spin-density distribution and aromatic character in the first triplet excited state is studied. Although a direct link is not immediately visible, classifying the PBHs according to their annulation sequence reveals regularities. Based on these, a set of guidelines is defined to qualitatively predict the location of spin and paratropicity and the singlet-triplet energy gap in larger PBHs, using only their smaller tri- and tetracyclic components, and subsequently tested on larger systems.

Stabilizing a three-center single-electron metal-metal bond in a fullerene cage

Trimetallic carbide clusterfullerenes (TCCFs) encapsulating a quinary M3C2 cluster represent a special family of endohedral fullerenes with an open-shell electronic configuration. Herein, a novel TCCF based on a medium-sized rare earth metal, dysprosium (Dy), is synthesized for the first time. The molecular structure of Dy3C2@I h(7)-C80 determined by single crystal X-ray diffraction shows that the encapsulated Dy3C2 cluster adopts a bat ray configuration, in which the acetylide unit C2 is elevated above the Dy3 plane by ∼1.66 Å, while Dy-Dy distances are ∼3.4 Å. DFT computational analysis of the electronic structure reveals that the endohedral cluster has an unusual formal charge distribution of (Dy3)8+(C2)2-@C80 6- and features an unprecedented three-center single-electron Dy-Dy-Dy bond, which has never been reported for lanthanide compounds. Moreover, this electronic structure is different from that of the analogous Sc3C2@I h(7)-C80 with a (Sc3)9+(C2)3-@C80 6- charge distribution and no metal-metal bonding.

Structure-Property Relationship in Selected Naphtho- and Anthra-Quinone Derivatives on the Basis of Density Functional Theory and Car–Parrinello Molecular Dynamics

Intra- and inter-molecular interactions were studied in 2,3-dichloro-5,8-dihydroxy-1,4-naphthoquinone and 1,4-dihydroxy-anthraquinone to shed more light on the molecular assembly phenomena. The electronic ground and excited states features of the compounds were investigated to find structure-property dependencies. The theoretical study was carried out on the basis of Density Functional Theory (DFT), its Time-Dependent (TD-DFT) extension, and using Car–Parrinello Molecular Dynamics (CPMD). In order to show how the environmental effects modulate the physico-chemical properties, the simulations were performed in vacuo, with the solvent reaction field (Polarizable Continuum Model (PCM) and water as a solvent) and crystalline phase. The intramolecular hydrogen bonds and the bridged proton dynamics were analyzed in detail. The aromatic rings and electronic structure changes were estimated using the Harmonic Oscillator Model of Aromaticity (HOMA) and Atoms in Molecules (AIM) theory. The Symmetry-Adapted Perturbation Theory (SAPT) was employed for interaction energy decomposition in the studied dimers and trimers. It was found that the presence of a polar solvent decreased the energy barrier for the bridged proton transfer. However, it did not significantly affect the aromaticity and electronic structure. The SAPT results showed that the mutual polarization of the monomers in the dimer was weak and that the dispersion was responsible for most of the intermolecular attraction. The intermolecular hydrogen bonds seem to be much weaker than the intramolecular bridges. The TD-DFT results confirmed that the electronic excitations do not play any significant role in the intramolecular proton transfer. The CPMD results indicated that the protons are very labile in the hydrogen bridges. Short proton transfer and proton-sharing events were observed, and a correlation between them in the twin bridges was noticed, especially for the first investigated compound.

Explaining and Fixing DFT Failures for Torsional Barriers

Most torsional barriers are predicted with high accuracies (about 1 kJ/mol) by standard semilocal functionals, but a small subset was found to have much larger errors. We created a database of almost 300 carbon-carbon torsional barriers, including 12 poorly behaved barriers, that stem from the Y═C-X group, where Y is O or S and X is a halide. Functionals with enhanced exchange mixing (about 50%) worked well for all barriers. We found that poor actors have delocalization errors caused by hyperconjugation. These problematic calculations are density-sensitive (i.e., DFT predictions change noticeably with the density), and using HF densities (HF-DFT) fixes these issues. For example, conventional B3LYP performs as accurately as exchange-enhanced functionals if the HF density is used. For long-chain conjugated molecules, HF-DFT can be much better than exchange-enhanced functionals. We suggest that HF-PBE0 has the best overall performance.

Comparison of many-particle representations for selected-CI I: A tree based approach

The full configuration interaction (FCI) method is only applicable to small molecules with few electrons in moderate size basis sets. One of the main alternatives to obtain approximate FCI energies for bigger molecules and larger basis sets is selected CI. However, due to: (a) the lack of a well-defined structure in a selected CI Hamiltonian, (b) the potentially large number of electrons together with c) potentially large orbital spaces, a computationally and memory efficient algorithm is difficult to construct. In the present series of papers, we describe our attempts to address these issues by exploring tree-based approaches. At the same time, we devote special attention to the issue of obtaining eigenfunctions of the total spin squared operator since this is of particular importance in tackling magnetic properties of complex open shell systems. Dedicated algorithms are designed to tackle the CI problem in terms of determinant, configuration (CFG) and configuration state function many-particle bases by effective use of the tree representation. In this paper we describe the underlying logic of our algorithm design and discuss the advantages and disadvantages of the different many particle bases. We demonstrate by the use of small examples how the use of the tree simplifies many key algorithms required for the design of an efficient selected CI program. Our selected CI algorithm, called the iterative configuration expansion, is presented in the penultimate part. Finally, we discuss the limitations and scaling characteristics of the present approach.

Predicting lanthanide coordination structures in solution with molecular simulation

The chemical and physical properties of lanthanide coordination complexes can significantly change with small variations in their molecular structure. Further, in solution, coordination structures (e.g., lanthanide-ligand complexes) are dynamic. Resolving solution structures, computationally or experimentally, is challenging because structures in solution have limited spatial restrictions and are responsive to chemical or physical changes in their surroundings. To determine structures of lanthanide-ligand complexes in solution, a molecular simulation approach is presented in this chapter, which concurrently considers chemical reactions and molecular dynamics. Lanthanide ion, ligand, solvent, and anion molecules are explicitly included to identify, in atomic resolution, lanthanide coordination structures in solution. The computational protocol described is applicable to determining the molecular structure of lanthanide-ligand complexes, particularly with ligands known to bind lanthanides but whose structures have not been resolved, as well as with ligands not previously known to bind lanthanide ions. The approach in this chapter is also relevant to elucidating lanthanide coordination in more intricate structures, such as in the active site of enzymes.

Modeling Gas-Phase Unimolecular Dissociation for Bond Dissociation Energies: Comparison of Statistical Rate Models within RRKM Theory

The Rice-Ramsperger-Kassel-Marcus (RRKM) theory provides a simple yet powerful rate theory for calculating microcanonical rate constants. In particular, it has found widespread use in combination with gas-phase kinetic experiments of unimolecular dissociations to extract experimental bond dissociation energies (BDEs). We have previously found several discrepancies between the computed BDE values and the respective experimental ones, obtained with our empirical rate model, named L-CID. To investigate the reliability of our rate model, we conducted a theoretical analysis and comparison of the performance of conventional rate models and L-CID within the RRKM framework. Using the previously published microcanonical rate data as well as reaction cross-section data, we show that the BDE values obtained with the L-CID model agree with the ones from the other rate models within the expected uncertainty bounds. Based on this agreement, we discuss the possible rationalization of the good performance of the L-CID model.

How Can We Predict Accurate Electrochromic Shifts for Biochromophores? A Case Study on the Photosynthetic Reaction Center

Protein-embedded chromophores are responsible for light harvesting, excitation energy transfer, and charge separation in photosynthesis. A critical part of the photosynthetic apparatus are reaction centers (RCs), which comprise groups of (bacterio)chlorophyll and (bacterio)pheophytin molecules that transform the excitation energy derived from light absorption into charge separation. The lowest excitation energies of individual pigments (site energies) are key for understanding photosynthetic systems, and form a prime target for quantum chemistry. A major theoretical challenge is to accurately describe the electrochromic (Stark) shifts in site energies produced by the inhomogeneous electric field of the protein matrix. Here, we present large-scale quantum mechanics/molecular mechanics calculations of electrochromic shifts for the RC chromophores of photosystem II (PSII) using various quantum chemical methods evaluated against the domain-based local pair natural orbital (DLPNO) implementation of the similarity-transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD). We show that certain range-separated density functionals (ωΒ97, ωΒ97X-V, ωΒ2PLYP, and LC-BLYP) correctly reproduce RC site energy shifts with time-dependent density functional theory (TD-DFT). The popular CAM-B3LYP functional underestimates the shifts and is not recommended. Global hybrid functionals are too insensitive to the environment and should be avoided, while nonhybrid functionals are strictly nonapplicable. Among the applicable approximate coupled cluster methods, the canonical versions of CC2 and ADC(2) were found to deviate significantly from the reference results both for the description of the lowest excited state and for the electrochromic shifts. By contrast, their spin-component-scaled (SCS) and particularly the scale-opposite-spin (SOS) variants compare well with the reference DLPNO-STEOM-CCSD and the best range-separated DFT methods. The emergence of RC excitation asymmetry is discussed in terms of intrinsic and protein electrostatic potentials. In addition, we evaluate a minimal structural scaffold of PSII, the D1-D2-CytB559 RC complex often employed in experimental studies, and show that it would have the same site energy distribution of RC chromophores as the full PSII supercomplex, but only under the unlikely conditions that the core protein organization and cofactor arrangement remain identical to those of the intact enzyme.

Selective Oxidation of 5-Hydroxymethylfurfural to 2,5-Diformylfuran by Visible Light-Driven Photocatalysis over In Situ Substrate-Sensitized Titania

Solar energy-driven processes for biomass valorization are priority for the growing industrialized society. To address this challenge, efficient visible light-active photocatalyst for the selective oxidation of biomass-derived platform chemical is highly desirable. Herein, selective oxidation of 5-hydroxymethylfurfural (HMF) to 2,5-diformylfuran (DFF) was achieved by visible light-driven photocatalysis over titania. Pristine titania is photocatalytically inactive under visible light, so an unconventional approach was employed for the visible light (λ=515 nm) sensitization of titania via a formation of a visible light-absorbing complex of HMF (substrate) on the titania surface. Surface-complexation of HMF on titania mediated ligand-to-metal charge transfer (LMCT) under visible light, which efficiently catalyzed the oxidation of HMF to DFF. A high DFF selectivity of 87 % was achieved with 59 % HMF conversion after 4 h of illumination. The apparent quantum yield obtained for DFF production was calculated to be 6.3 %. It was proposed that the dissociative interaction of hydroxyl groups of HMF and the titania surface is responsible for the surface-complex formation. When the hydroxyl groups of titania were modified via surface-fluorination or calcination the oxidation of HMF was inhibited under visible light, signifying that hydroxyl groups are decisive for photocatalytic activity.

What Types of Chemical Problems Benefit from Density-Corrected DFT? A Probe Using an Extensive and Chemically Diverse Test Suite

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange–correlation (XC) functionals (PBE, BLYP, TPSS, and SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation, HF-DFT is highly beneficial, particularly at low HF exchange percentages. This is especially true for noncovalent interactions where the electrostatic component is dominant, such as hydrogen and halogen bonds: for π-stacking, HF-DFT is detrimental. For subsets with significant nondynamical correlation (i.e., where a Hartree–Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals—consistent with Grimme’s proposal of the PBE38 functional—HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4) as the use of HF orbitals greatly mitigates the error at 25% for barrier heights. Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that for HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree–Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorially optimized empirical range-separated hybrids ωB97X-V and ωB97M-V.

Chlorophyll excitation energies and structural stability of the CP47 antenna of photosystem II: a case study in the first-principles simulation of light-harvesting complexes

Natural photosynthesis relies on light harvesting and excitation energy transfer by specialized pigment-protein complexes. Their structure and the electronic properties of the embedded chromophores define the mechanisms of energy transfer. An important example of a pigment-protein complex is CP47, one of the integral antennae of the oxygen-evolving photosystem II (PSII) that is responsible for efficient excitation energy transfer to the PSII reaction center. The charge-transfer excitation induced among coupled reaction center chromophores resolves into charge separation that initiates the electron transfer cascade driving oxygenic photosynthesis. Mapping the distribution of site energies among the 16 chlorophyll molecules of CP47 is essential for understanding excitation energy transfer and overall antenna function. In this work, we demonstrate a multiscale quantum mechanics/molecular mechanics (QM/MM) approach utilizing full time-dependent density functional theory with modern range-separated functionals to compute for the first time the excitation energies of all CP47 chlorophylls in a complete membrane-embedded cyanobacterial PSII dimer. The results quantify the electrostatic effect of the protein on the site energies of CP47 chlorophylls, providing a high-level quantum chemical excitation profile of CP47 within a complete computational model of "near-native" cyanobacterial PSII. The ranking of site energies and the identity of the most red-shifted chlorophylls (B3, followed by B1) differ from previous hypotheses in the literature and provide an alternative basis for evaluating past approaches and semiempirically fitted sets. Given that a lot of experimental studies on CP47 and other light-harvesting complexes utilize extracted samples, we employ molecular dynamics simulations of isolated CP47 to identify which parts of the polypeptide are most destabilized and which pigments are most perturbed when the antenna complex is extracted from PSII. We demonstrate that large parts of the isolated complex rapidly refold to non-native conformations and that certain pigments (such as chlorophyll B1 and β-carotene h1) are so destabilized that they are probably lost upon extraction of CP47 from PSII. The results suggest that the properties of isolated CP47 are not representative of the native complexed antenna. The insights obtained from CP47 are generalizable, with important implications for the information content of experimental studies on biological light-harvesting antenna systems.

Cluster-in-Molecule Local Correlation Method with an Accurate Distant Pair Correction for Large Systems

The cluster-in-molecule (CIM) local correlation approach with an accurate distant pair correlation energy correction is presented. For large systems, the inclusion of distant pair correlation energies is essential for the accurate prediction of absolute correlation energies and relative energies. Here, we propose a simple and efficient scheme for evaluating the distant pair correlation energy correction for the CIM approaches. The corrections can be readily extracted from electron correlation calculations of clusters with almost no additional effort. Benchmark calculations show that the improved CIM approach can recover more than 99.94% of the correlation energy calculated by the parent method. By combining the CIM approach with the domain-based local pair natural orbital (DLPNO) local correlation approach, we have provided accurate binding energies at the CIM-DLPNO-CCSD(T) level for a test set consisting of eight weakly bound complexes ranging in size from 200 to 1027 atoms. With these results as the reference data, the accuracy and applicability of other electron correlation methods and a few density functional methods for large systems have been assessed.

Optoelectronic properties of diketopyrrolopyrrole homopolymers compared to donor-acceptor copolymers

Diketopyrrolopyrrole (DPP) is a component of a large number of materials used for optoelectronic applications. As it is exclusively used in combination with aromatic donors, the properties of its homopolymers are unknown. Because donor-acceptor character has been shown for other systems to reduce bandwidths, DPP homopolymers should have even larger conduction bands and better n-type conductivity than the thiophene-flanked systems, which have exceptional n-type conductivity and ambipolar character. Therefore, a theoretical study was carried out to elucidate the properties of the unknown DPP homopolymer. Calculations were done with density functional theory and with the complete active space self-consistent field method plus n-electron valence state perturbation theory for the dynamic correlation. Poly-DPP is predicted to have radical character and an extremely wide low-lying conduction band. If it were possible to produce this material, it should have unprecedented n-type conductivity and might be a synthetic metal. A comparison with various unknown donor-acceptor systems containing vinyl groups and thienyl rings with a higher concentration of DPP than the known copolymers reveals how donor-acceptor substitution reduces bandwidths and decreases electron affinities.

Role of Dopants on the Local Electronic Structure of Polymeric Carbon Nitride Photocatalysts

Polymeric carbon nitride (PCN) is a promising class of materials for solar-to-chemical energy conversion. The increase of the photocatalytic activity of PCN is often achieved by the incorporation of heteroatoms, whose impact on the electronic structure of PCN remains poorly explored. This work reveals that the local electronic structure of PCN is strongly altered by doping with sulfur and iron using X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS). From XAS at the carbon and nitrogen K-edges, sulfur atoms are found to mostly affect carbon atoms, in contrast to iron doping mostly altering nitrogen sites. In RIXS at the nitrogen K-edge, a vibrational progression, affected by iron doping, is evidenced, which is attributed to a vibronic coupling between excited electrons in nitrogen atoms and C-N stretching modes in PCN heterocycling rings. This work opens new perspectives for the characterization of vibronic coupling in polymeric photocatalysts.

Planar Iron Hydride Nanoclusters: Combined Spectroscopic and Theoretical Insights into Structures and Building Principles

The controlled assembly of well-defined planar nanoclusters from molecular precursors is synthetically challenging and often plagued by the predominant formation of 3D-structures and nanoparticles. Herein, we report planar iron hydride nanoclusters from reactions of main group element hydrides with iron(II) bis(hexamethyldisilazide). The structures and properties of isolated Fe4 , Fe6 , and Fe7 nanoplatelets and calculated intermediates enable an unprecedented insight into the underlying building principle and growth mechanism of iron clusters, metal monolayers, and nanoparticles.

Investigating the Nonradiative Decay Pathway in the Excited State of Silepin Derivatives: A Study with Second-Order Multireference Perturbation Wavefunction Theory

The fluorescence quantum yield for fluorescent organic molecules is an important molecular property, and tuning it up is desired for various applications. For the computational estimation of the fluorescence quantum yield, the theoretical prediction of the nonradiative decay rate constant has become an attractive subject of study. The rate constant of thermally activated nonradiative decay is related to the activation energy in the photoreaction; thus, the accuracy and reliability of the excited-state potential energies in the quantum chemical computation are critical. In this study, we employed a second-order multireference perturbation wavefunction theory for studying the thermally activated decay via conical intersection (CI) of 1,1-dimethyldibenzo[b,f]silepin derivatives. The correlation between the computed activation energy to reach the CI geometry in the S₁ state and the experimentally determined fluorescence quantum yield implied that silepins nonradiatively decay via the CI triggered by the twisting of the central C-C bond. Geometry optimization of the transition state using multireference perturbation theory drastically reduced the estimated activation energy. Our computation gave reasonable predictions of the activation free energies of photoexcited 1,1-dimethyldibenzo[b,f]silepin. The energy profiles and geometry optimizations using proper quantum chemical methods played a critical role in reliable estimation of the rate constant and fluorescence quantum yield.

Multicomponent crystals of clotrimazole: a combined theoretical and experimental study

Compared with clotrimazole, some multicomponent crystals showed an improvement in solubility and dissolution rate.

How the magnetic field impacts the chiroptical activities of helical copper enantiomers

A pair of enantiomers {[Cu(l-pro)(l-tyr)]·2H2O}n (L-1) and {[Cu(d-pro)(d-tyr)]·2H2O}n (D-1) based on the chiral ligands l/d-proline and l/d-tyrosine were synthesized and investigated using single-crystal X-ray structure analysis, IR, thermogravimetric analysis, solid-state UV-Vis spectroscopy, circular dichroism, magnetic studies, and DFT calculations.

Pt(ii)-Chiral diene-catalyzed enantioselective formal [4 + 2] cycloaddition initiated by C–C bond cleavage and elucidation of a Pt(ii)/(iv) cycle by DFT calculations

A Pt(ii)-chiral diene complex demonstrates a high catalytic activity in the enantioselective formal [4 + 2] cycloaddition along with C–C bond cleavage of biphenylene at room temp. DFT calculations elucidated that the present catalysis involves a rare Pt(ii)/Pt(iv) cycle.

Screening RAFT agents and photocatalysts to mediate PET-RAFT polymerization using a high throughput approach

We report a high throughput approach for the screening of RAFT agents and photocatalysts to mediate photoinduced electron/energy transfer-reversible addition–fragmentation chain transfer (PET-RAFT) polymerization.

Valence electrons in lanthanide-based single-atom magnets: a paradigm shift in 4f-magnetism modeling and design

Impact of valence electrons on the magnetic properties of lanthanide-based monatomic magnetic systems on surfaces and in molecules. And FV-magnetism - as a crucial bit in the further understanding and design of a new generation of atomic magnets.

Successes, challenges, and opportunities for quantum chemistry in understanding metalloenzymes for solar fuels research

Overview of the rich and diverse contributions of quantum chemistry to understanding the structure and function of the biological archetypes for solar fuel research, photosystem II and hydrogenases.

Solution structure of a europium–nicotianamine complex supports that phytosiderophores bind lanthanides

The structures of europium–EDTA (known lanthanide chelator) and europium–nicotianamine (biochemical precursor of phytosiderophores) complexes are resolved, in solution, with ab initio molecular dynamics as well as excitation and emission spectroscopy.

An unexpected in-solution instability of diiodido analogue of picoplatin complicates its biological characterization

Complex cis-[PtI2(NH3)(pic)] (1; pic = 2-methylpyridine), a diiodido analogue of clinically studied picoplatin (2), is unstable in solution, which is intriguingly connected with the release of its pic ligand. This observation complicates the biological testing of e.g. cytotoxicity in human cancer cells for 1.

Photochemical conversion of CO2 to CO by a Re complex: theoretical insights into the formation of CO and HCO3− from an experimentally detected monoalkyl carbonate complex

Triethanolamine (TEOA) has been used for the photocatalytic reduction of CO₂, and the experimental studies have demonstrated that the TEOA increases the catalytic efficiency. In addition, the formation of a carbonate complex has been confirmed in the Re photocatalytic system where DMF and TEOA are used as solvents. In this study, we survey the reaction pathways of the photocatalytic conversions of CO₂ to CO + H₂O and CO₂ to CO + HCO₃⁻ by fac-Re(bpy)(CO)₃Br in the presence of TEOA using density functional theory (DFT) and domain-based local pair natural orbital coupled cluster approach, DLPNO-CCSD(T). Under light irradiation, the solvent-coordinated Re complex is first reduced to form a monoalkyl carbonate complex in the doublet pathway. This doublet pathway is kinetically advantageous over the singlet pathway. To reduce carbon dioxide, the Re complex needs to be reduced by two electrons. The second electron reduction occurs after the monoalkyl carbonate complex is protonated. The second reduction involves the dissociation of the monoalkyl carbonate ligand, and the dissociated ligand recombines the Re center via carbon to generate Re–COOH species, which further reacts with CO₂ to generate tetracarbonyl complex and HCO₃⁻. The two-electron reduced ligand-free Re complex converts CO₂ to CO and H₂O. The pathways leading to H₂O formation have lower barriers than the pathways leading to HCO₃⁻ formation, but their portion of formation must depend on proton concentration.

DFT and DLPNO-CCSD(T) calculations proposed a pathway for the conversion of the experimentally detected monoarkyl carbonate complex to tetracarbonyl complex.

Estimates of electron correlation based on density expansions

Two methods for estimating the correlation energy of molecules and other electronic systems are discussed based on the assumption that the correlation energy can be partitioned between atomic regions. In the first method, the electron density is expanded in terms of atomic contributions using rigorous electron repulsion bounds, and in the second method, correlation contributions are associated with basis function pairs. These methods do not consider the detailed nature of localized excitations but instead define a correlation energy per electron factor that is unique to a specific atom. The correlation factors are basis function dependent and are determined by configuration interaction (CI) calculations on diatomic and hydride molecules. The correlation energy estimates are compared with the results of high-level CI calculations for a test set of 27 molecules representing a wide range of bonding environments (average error of 2.6%). An extension based on truncated CI calculations in which d-type and hydrogen p-type functions are eliminated from the virtual space combined with estimates of dynamical correlation contributions using atomic correlation factors is discussed and applied to the dissociation of several molecules.

Exploring Free Energy Profiles of Enantioselective Organocatalytic Aldol Reactions under Full Solvent Influence

We present a computational study on the enantioselectivity of organocatalytic proline-catalyzed aldol reactions between aldehydes in dimethylformamide (DMF). To explore the free energy surface of the reaction, we apply two-dimensional metadynamics on top of ab initio molecular dynamics (AIMD) simulations with explicit solvent description on the DFT level of theory. We avoid unwanted side reactions by utilizing our newly developed hybrid AIMD (HyAIMD) simulation scheme, which adds a simple force field to the AIMD simulation to prevent unwanted bond breaking and formation. Our condensed phase simulation results are able to nicely reproduce the experimental findings, including the main stereoisomer that is formed, and give a correct qualitative prediction of the change in syn:anti product ratio with different substituents. Furthermore, we give a microscopic explanation for the selectivity. We show that both the explicit description of the solvent and the inclusion of entropic effects are vital to a good outcome-metadynamics simulations in vacuum and static nudged elastic band (NEB) calculations yield significantly worse predictions when compared to the experiment. The approach described here can be applied to a plethora of other enantioselective or organocatalytic reactions, enabling us to tune the catalyst or determine the solvent with the highest stereoselectivity.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

Gas-Phase Thermochemistry of MX3 and M2X6 (M = Sc, Y; X = F, Cl, Br, I) from a Composite Reaction-Based Approach: Homolytic versus Heterolytic Cleavage

A domain-based local-pair natural-orbital coupled-cluster approach with single, double, and improved linear-scaling perturbative triple correction via an iterative algorithm, DLPNO-CCSD(T₁), was applied within the framework of the Feller-Peterson-Dixon approach to derive gas-phase heats of formation of scandium and yttrium trihalides and their dimers via a set of homolytic and heterolytic dissociation reactions. All predicted heats of formation moderately depend on the reaction type with the most and least negative values obtained for homolytic and heterolytic dissociation, respectively. The basis set size dependence, as well as the influence of static correlation effects not covered by the standard (DLPNO-)CCSD(T) approach, suggests that exploitation of the heterolytic dissociation reactions with the formation of M³⁺ and X^- ions leads to the most robust heats of formation. The gas-phase formation enthalpies ΔH_f°(0 K)/ΔH_f°(298.15 K) and absolute entropies S°(298.15 K) were obtained for the first time for the Sc₂F₆, Sc₂Br₆, and Sc₂I₆ species. For ScBr₃, ScI₃, Sc₂Cl₆, and Y₂Cl₆, we suggest a reexamination of the experimental heats of formation available in the literature. For other compounds, the predicted values were found to be in good agreement with the experimental estimates. Extracted MX₃ (M = Sc, Y; X = F, Cl, Br, and I) 0 K atomization enthalpies indicate weaker bonding when moving from fluorine to iodine and from yttrium to scandium. Likewise, the stability of yttrium trihalide dimers degrades when going from fluorine to iodine. Respective scandium trihalide dimers are less stable, with 0 K dimer dissociation energy decreasing in the row fluorine - chlorine - bromine ≈ iodine. Correlation of the (n - 1)s²p⁶ electrons on bromine and iodine, inclusion of zero-point energy, relativistic effects, and the effective-core-potential correction as well as amelioration of the DLPNO localization inaccuracy are shown to be of similar magnitude, which is critical if accurate heats of formation are a goal.

57Fe Mössbauer parameters from domain based local pair-natural orbital coupled-cluster theory

We report on applications of the domain based local pair-natural orbital (PNO) coupled-cluster method within the singles and doubles approximation (DLPNO-CCSD) to the calculation of ⁵⁷Fe isomer shifts and quadrupole splittings in a small training set of iron complexes consisting of large molecular ligands and iron atoms in varying charge, spin, and oxidation states. The electron densities and electric field gradients needed for these calculations were obtained within the recently implemented analytic derivative scheme. A method for the direct treatment of scalar relativistic effects in the calculation of effective electron densities is described by using the first-order Douglas-Kroll-Hess Hamiltonian and a Gaussian charge distribution model for the nucleus. The performance of DLPNO-CCSD is compared with four modern-day density functionals, namely, RPBE, TPSS, B3LYP, and B2PLYP, as well as with the second-order Møller-Plesset perturbation theory. An excellent correlation between the calculated electron densities and the experimental isomer shifts is attained with the DLPNO-CCSD method. The correlation constant a obtained from the slope of the linear correlation plot is found to be ≈-0.31 a.u.³ mm s^-1, which agrees very well with the experimental calibration constant α = -0.31 ± 0.04 a.u.³ mm s^-1. This value of a is obtained consistently using both nonrelativistic and scalar relativistic DLPNO-CCSD electron densities. While the B3LYP and B2PLYP functionals achieve equally good correlation between theory and experiment, the correlation constant a is found to deviate from the experimental value. Similar trends are observed also for quadrupole splittings. The value of the nuclear quadrupole moment for ⁵⁷Fe is estimated to be 0.15 b at the DLPNO-CCSD level. This is consistent with previous results and is here supported by a higher level of theory. The DLPNO-CCSD results are found to be insensitive to the intrinsic approximations in the method, in particular the PNO occupation number truncation error, while the results obtained with density functional theory (DFT) are found to depend on the choice of the functional. In a statistical sense, i.e., on the basis of the linear regression analysis, however, the accuracies of the DFT and DLPNO-CCSD results can be considered comparable.

Nucleophilic Fluorination with KF Catalyzed by 18-Crown-6 and Bulky Diols: A Theoretical and Experimental Study

The activation of potassium fluoride for nucleophilic fluorination of alkyl halides is an important challenge because of the high lattice energy of this salt and its low solubility in many polar aprotic solvents. Crown ethers have been used for increasing the solubilization of KF during several decades. Nevertheless, these macrocycles are not enough to produce a high reaction rate. In this work, theoretical methods were used for designing a synergic combination of bulky diols with crown ethers able to accelerate this kind of reaction. The calculations have predicted that the bulky diol 1,4-Bis(2-hydroxy-2-propyl)benzene, which has distant hydroxyl groups, is able to catalyze nucleophilic fluorination in combination with 18-crown-6 via two hydrogen bonds to the S_N2 transition state. Experimental studies following the theoretical predictions have confirmed the catalytic effect and the estimated kinetic data point out that the bulky diol at 1 mol L^-1 in combination with 18-crown-6 is able to produce an 18-fold increase in the reaction rate in relation to crown ether catalysis only. The reaction produces 46% yield of fluorination after 24 h at moderate temperature of 82 °C, with minimal formation of the side elimination product. Thus, this work presents an improved method for fluorination with KF salt.

Reinterpreting π-stacking

The nature of π-π interactions has long been debated. The term "π-stacking" is considered by some to be a misnomer, in part because overlapping π-electron densities are thought to incur steric repulsion, and the physical origins of the widely-encountered "slip-stacked" motif have variously been attributed to either sterics or electrostatics, in competition with dispersion. Here, we use quantum-mechanical energy decomposition analysis to investigate π-π interactions in supramolecular complexes of polycyclic aromatic hydrocarbons, ranging in size up to realistic models of graphene, and for comparison we perform the same analysis on stacked complexes of polycyclic saturated hydrocarbons, which are cyclohexane-based analogues of graphane. Our results help to explain the short-range structure of liquid hydrocarbons that is inferred from neutron scattering, trends in melting-point data, the interlayer separation of graphene sheets, and finally band gaps and observation of molecular plasmons in graphene nanoribbons. Analysis of intermolecular forces demonstrates that aromatic π-π interactions constitute a unique and fundamentally quantum-mechanical form of non-bonded interaction. Not only do stacked π-π architectures enhance dispersion, but quadrupolar electrostatic interactions that may be repulsive at long range are rendered attractive at the intermolecular distances that characterize π-stacking, as a result of charge penetration effects. The planar geometries of aromatic sp² carbon networks lead to attractive interactions that are "served up on a molecular pizza peel", and adoption of slip-stacked geometries minimizes steric (rather than electrostatic) repulsion. The slip-stacked motif therefore emerges not as a defect induced by electrostatic repulsion but rather as a natural outcome of a conformational landscape that is dominated by van der Waals interactions (dispersion plus Pauli repulsion), and is therefore fundamentally quantum-mechanical in its origins. This reinterpretation of the forces responsible for π-stacking has important implications for the manner in which non-bonded interactions are modeled using classical force fields, and for rationalizing the prevalence of the slip-stacked π-π motif in protein crystal structures.

Comparison of Density Functional and Correlated Wave Function Methods for the Prediction of Cu(II) Hyperfine Coupling Constants

The reliable prediction of Cu(II) hyperfine coupling constants remains a challenge for quantum chemistry. Until recently only density functional theory (DFT) could target this property for systems of realistic size. However, wave function based methods become increasingly applicable. In the present work, we define a large set of Cu(II) complexes with experimentally known hyperfine coupling constants and use it to investigate the performance of modern quantum chemical methods for the prediction of this challenging spectroscopic parameter. DFT methods are evaluated against orbital‐optimized second‐order Møller‐Plesset (OO‐MP2) theory and coupled cluster calculations including singles and doubles excitations, driven by the domain‐based local pair natural orbital approach (DLPNO‐CCSD). Special attention is paid to the definition of a basis set that converges adequately toward the basis set limit for the given property for all methods considered in this study, and a specifically optimized basis set is proposed for this purpose. The results suggest that wave function based methods can supplant but do not outcompete DFT for the calculation of Cu(II) hyperfine coupling constants. Mainstream hybrid functionals such as B3PW91 remain on average the best choice.

Protein Matrix Control of Reaction Center Excitation in Photosystem II

Photosystem II (PSII) is a multisubunit pigment-protein complex that uses light-induced charge separation to power oxygenic photosynthesis. Its reaction center chromophores, where the charge transfer cascade is initiated, are arranged symmetrically along the D1 and D2 core polypeptides and comprise four chlorophyll (PD1, PD2, ChlD1, ChlD2) and two pheophytin molecules (PheoD1 and PheoD2). Evolution favored productive electron transfer only via the D1 branch, with the precise nature of primary excitation and the factors that control asymmetric charge transfer remaining under investigation. Here we present a detailed atomistic description for both. We combine large-scale simulations of membrane-embedded PSII with high-level quantum-mechanics/molecular-mechanics (QM/MM) calculations of individual and coupled reaction center chromophores to describe reaction center excited states. We employ both range-separated time-dependent density functional theory and the recently developed domain based local pair natural orbital (DLPNO) implementation of the similarity transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD), the first coupled cluster QM/MM calculations of the reaction center. We find that the protein matrix is exclusively responsible for both transverse (chlorophylls versus pheophytins) and lateral (D1 versus D2 branch) excitation asymmetry, making ChlD1 the chromophore with the lowest site energy. Multipigment calculations show that the protein matrix renders the ChlD1 → PheoD1 charge-transfer the lowest energy excitation globally within the reaction center, lower than any pigment-centered local excitation. Remarkably, no low-energy charge transfer states are located within the "special pair" PD1-PD2, which is therefore excluded as the site of initial charge separation in PSII. Finally, molecular dynamics simulations suggest that modulation of the electrostatic environment due to protein conformational flexibility enables direct excitation of low-lying charge transfer states by far-red light.

Accurate prediction of norbornadiene cycle enthalpies by DLPNO-CCSD(T1 )/CBS method

The DLPNO-CCSD(T₁ )/CBS method combined with simple reactions containing small reference species leads to an improvement in the accuracy of theoretically evaluated enthalpies of formation of medium-sized polyalicyclic hydrocarbons when compared with the widely used composite approach. The efficiency of the DLPNO-CCSD(T₁ )/CBS method is most vividly demonstrated by comparing with the results of G4 calculations for adamantane. The most important factor in choosing appropriate working reaction is the same number of species on both sides of the equation. Among these reactions, the reactions with small enthalpy change usually provide a better cancellation of errors. The DLPNO-CCSD(T₁ )/CBS method was used to calculate the enthalpies of formation of compounds belonging to the norbornadiene cycle (norbornadiene, quadricyclane, norbornene, nortricyclane, and norbornane). The most reliable experimental enthalpies of formation are recommended for these compounds by comparing calculated values with conflicting experimental data.

The formyloxyl radical: electrophilicity, C-H bond activation and anti-Markovnikov selectivity in the oxidation of aliphatic alkenes

In the past the formyloxyl radical, HC(O)O˙, had only been rarely experimentally observed, and those studies were theoretical-spectroscopic in the context of electronic structure. The absence of a convenient method for the preparation of the formyloxyl radical has precluded investigations into its reactivity towards organic substrates. Very recently, we discovered that HC(O)O˙ is formed in the anodic electrochemical oxidation of formic acid/lithium formate. Using a [Co^IIIW₁₂O₄₀]⁵⁻ polyanion catalyst, this led to the formation of phenyl formate from benzene. Here, we present our studies into the reactivity of electrochemically in situ generated HC(O)O˙ with organic substrates. Reactions with benzene and a selection of substituted derivatives showed that HC(O)O˙ is mildly electrophilic according to both experimentally and computationally derived Hammett linear free energy relationships. The reactions of HC(O)O˙ with terminal alkenes significantly favor anti-Markovnikov oxidations yielding the corresponding aldehyde as the major product as well as further oxidation products. Analysis of plausible reaction pathways using 1-hexene as a representative substrate favored the likelihood of hydrogen abstraction from the allylic C–H bond forming a hexallyl radical followed by strongly preferred further attack of a second HC(O)O˙ radical at the C1 position. Further oxidation products are surmised to be mostly a result of two consecutive addition reactions of HC(O)O˙ to the C Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> C double bond. An outer-sphere electron transfer between the formyloxyl radical donor and the [Co^IIIW₁₂O₄₀]⁵⁻ polyanion acceptor forming a donor–acceptor [D⁺–A⁻] complex is proposed to induce the observed anti-Markovnikov selectivity. Finally, the overall reactivity of HC(O)O˙ towards hydrogen abstraction was evaluated using additional substrates. Alkanes were only slightly reactive, while the reactions of alkylarenes showed that aromatic substitution on the ring competes with C–H bond activation at the benzylic position. C–H bonds with bond dissociation energies (BDE) ≤ 85 kcal mol⁻¹ are easily attacked by HC(O)O˙ and reactivity appears to be significant for C–H bonds with a BDE of up to 90 kcal mol⁻¹. In summary, this research identifies the reactivity of HC(O)O˙ towards radical electrophilic substitution of arenes, anti-Markovnikov type oxidation of terminal alkenes, and indirectly defines the activity of HC(O)O˙ towards C–H bond activation.

The formyloxyl radical, formed electrochemically, is electrophilic, yields anti-Markovnikov oxidation products from alkenes, and is effective for C–H bond activation.