Noncovalent Interaction Energies Research Articles

Computation of covalent and noncovalent structural parameters at low computational cost: Efficiency of the DH‐SVPD method

AbstractDH‐SVPD is a tailored atomic basis set originally developed to enhance the domain of applicability of double‐hybrid density functionals to large molecular systems in weak interactions. In combination with any density functional belonging to this approximation, it provides an accurate estimate of noncovalent interaction energies at the cost of a double‐ζ basis set, without adding a posteriori an empirical dispersion correction. Here, we show that the accuracy/cost ratio observed previously for energy properties can be safely extended to the modeling of structural parameters of small‐ and medium‐sized organic molecules. In particular, we demonstrate that, in combination with the nonempirical PBE‐QIDH double hybrid, DH‐SVPD is competitive with very large quadruple‐ζ basis sets when modeling both covalent and noncovalent structural parameters.

Metastasis of cholangiocarcinoma is promoted by extended high-mannose glycans

Membrane-bound oligosaccharides form the interfacial boundary between the cell and its environment, mediating processes such as adhesion and signaling. These structures can undergo dynamic changes in composition and expression based on cell type, external stimuli, and genetic factors. Glycosylation, therefore, is a promising target of therapeutic interventions for presently incurable forms of advanced cancer. Here, we show that cholangiocarcinoma metastasis is characterized by down-regulation of the Golgi α-mannosidase I coding gene MAN1A1, leading to elevation of extended high-mannose glycans with terminating α-1,2-mannose residues. Subsequent reshaping of the glycome by inhibiting α-mannosidase I resulted in significantly higher migratory and invasive capabilities while masking cell surface mannosylation suppressed metastasis-related phenotypes. Exclusive elucidation of differentially expressed membrane glycoproteins and molecular modeling suggested that extended high-mannose glycosylation at the helical domain of transferrin receptor protein 1 promotes conformational changes that improve noncovalent interaction energies and lead to enhancement of cell migration in metastatic cholangiocarcinoma. The results provide support that α-1,2-mannosylated N-glycans present on cancer cell membrane proteins may serve as therapeutic targets for preventing metastasis.

Halogen Bonding Provides Heterooctameric Supramolecular Aggregation of Diaryliodonium Thiocyanate

The crystal structure of the newly synthesized 4-methoxyphenyl(phenyl)iodonium thiocyanate, [PhI(4-C6H4OMe)](SCN), represents the first example of 16-membered cyclic heterooctamer formed by halogen bonding between the iodonium cation and SCN−. Results of density functional theory (DFT) calculations followed by the topological analysis of the electron density distribution within the framework of the quantum theory of atoms in molecules (QTAIM) method at the ωB97XD/DZP-DKH level of theory reveal that energies of attractive intermolecular noncovalent interactions I···S and I···N (responsible for the formation of heterooctameric supramolecular clusters {PhI(4-C6H4OMe)}4·{SCN}4 in the solid state structure of [PhI(4-C6H4OMe)](SCN)) vary from 0.9 to 8.5 kcal/mol.

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules.

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order Mo̷ller-Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFAs), and post-Kohn-Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5 and 10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 0.1% per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed, which uses monomers at full coupling, whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation-dissipation theorem, we obtain a nonperturbative "screened second-order" expression for the dispersion energy in terms of monomer quantities, which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. While the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series for MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete "electrodynamic" screening of the Coulomb interaction due to induced particle-hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust nonperturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.

Toward a less costly but accurate calculation of the CCSD(T)/CBS noncovalent interaction energy

The popular method of calculating the noncovalent interaction energies at the coupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] theory level in the complete basis set (CBS) limit was to add a CCSD(T) correction term to the CBS second-order Møller-Plesset perturbation theory (MP2). The CCSD(T) correction term is the difference between the CCSD(T) and MP2 interaction energies evaluated in a medium basis set. However, the CCSD(T) calculations with the medium basis sets are still very expensive for systems with more than 30 atoms. Comparatively, the domain-based local pair natural orbital coupled-cluster method [DLPNO-CCSD(T)] can be applied to large systems with over 1,000 atoms. Considering both the computational accuracy and efficiency, in this work, we propose a new scheme to calculate the CCSD(T)/CBS interaction energies. In this scheme, the MP2/CBS term keeps intact and the CCSD(T) correction term is replaced by a DLPNO-CCSD(T) correction term which is the difference between the DLPNO-CCSD(T) and DLPNO-MP2 interaction energies evaluated in a medium basis set. The interaction energies of the noncovalent systems in the S22, HSG, HBC6, NBC10, and S66 databases were recalculated employing this new scheme. The consistent and tight settings of the truncation parameters for DLPNO-CCSD(T) and DLPNO-MP2 in this noncanonical CCSD(T)/CBS calculations lead to the maximum absolute deviation and root-mean-square deviation from the canonical CCSD(T)/CBS interaction energies of less than or equal to 0.28 kcal/mol and 0.09 kcal/mol, respectively. The high accuracy and low cost of this new computational scheme make it an excellent candidate for the study of large noncovalent systems.

Supramolecular frameworks formed via hydrogen bonding and non-covalent interactions and interaction energy calculations of solvent coordinated cis-dioxomolybdenum(VI) complexes derived from ONO donor aroylhydrazone: Cytotoxicity studies

A tridentate ONO donor aroylhydrazone, 3,5-diiodosalicylaldehyde-4-methoxybenzoylhydrazone (H2SMB) and four cis-MoO2 complexes [MoO2(SMB)(DMF)] (1), [MoO2(SMB)(DMSO)] (2), [MoO2(SMB)(py)] (3) and [MoO2(SMB)(3-pic)] (4) which vary the solvents/heterocyclic bases in the sixth coordination position have been synthesised. The compounds were characterized by different physico-chemical methods. The single crystal X-ray diffraction studies unambiguously confirm the molecular structures. In the complexes 1, 2, 3 and 4, the octahedral geometry around the Mo(VI) central atom is satisfied by ONO donor atoms and two oxo oxygens, the sixth coordination site is occupied by oxygen/nitrogen atoms of solvent molecules. The supramolecular architectures generated by various hydrogen bonding and non-bonding interactions were investigated. The interaction energy calculations reveal dominance of dispersion energy component over other components. The aroylhydrazone was screened for antioxidant study using DPPH assay. The in vitro cytotoxicity of Mo(VI) complexes was evaluated against lymphoma ascites cell line as well as against normal cell and compared to hydrazone and cyclophosphamide.

Dual-hybrid direct random phase approximation and second-order screened exchange with nonlocal van der Waals correlations for noncovalent interactions.

We have added the nonlocal van der Waals correlation energy functional of Vydrov and Van Voorhis in 2010 (VV10NL) to the dual-hybrid direct random phase approximation (dRPA75) and second-order screened exchange (SOSEX75) for noncovalent interactions. The obtained methods are denoted as dRPA75-NL and SOSEX75-NL, and the corresponding short-range attenuation parameters are fitted with the large aug-cc-pV5Z basis set against the S66 dataset. Therefore, the dRPA75-NL method overcomes the error cancellation problem of the dRPA75 method with the relatively small aug-cc-pVTZ basis set for noncovalent interactions. Based on our benchmark computations, the dRPA75-NL and SOSEX75-NL methods perform very well on evaluating noncovalent interaction energies. Compared with the double-hybrid density functionals (DHDFs) of DSD-PBEP86-NL and DOD-PBEP86-NL, the dRPA75-NL and SOSEX75-NL methods perform much better on charge transfer interactions. Furthermore, the SOSEX75-NL method also gives insight into the development of computational methods for both closed-shell and open-shell noncovalent interactions. In summary, our computations demonstrate that even the full dRPA and SOSEX correlations still need additional dispersion corrections for noncovalent interactions.

Tetrachloroplatinate(ii) anion as a square-planar tecton for crystal engineering involving halogen bonding

The tetrachloroplatinate(ii) anion behaves as a useful XB-accepting tecton toward sigma-hole-donating organohalide species.

Making many-body interactions nearly pairwise additive: The polarized many-body expansion approach.

The Many-Body Expansion (MBE) is a useful tool to simulate condensed phase chemical systems, often avoiding the steep computational cost of usual electronic structure methods. However, it often requires higher than 2-body terms to achieve quantitative accuracy. In this work, we propose the Polarized MBE (PolBE) method where each MBE energy contribution is treated as an embedding problem. In each energy term, a smaller fragment is embedded into a larger, polarized environment and only a small region is treated at the high-level of theory using embedded mean-field theory. The role of polarized environment was found to be crucial in providing quantitative accuracy at the 2-body level. PolBE accurately predicts noncovalent interaction energies for a number of systems, including CO2, water, and hydrated ion clusters, with a variety of interaction mechanisms, from weak dispersion to strong electrostatics considered in this work. We further demonstrate that the PolBE interaction energy is predominantly pairwise unlike the usual vacuum MBE that requires higher-order terms to achieve similar accuracy. We numerically show that PolBE often performs better than other widely used embedded MBE methods such as the electrostatically embedded MBE. Owing to the lack of expensive diagonalization of Fock matrices and its embarrassingly parallel nature, PolBE is a promising way to access condensed phase systems with hybrid density functionals that are difficult to treat with currently available methods.

Reducing the Many-Electron Self-Interaction Error in the Second-Order Screened Exchange Method.

Preserving the beneficial properties of the second-order screened exchange (SOSEX) method, such as its freedom from one-body self-correlation error, and its seamless treatment of long-range dispersion interaction, we construct new nonlocal functionals by down-scaling the higher-order terms in the SOSEX series to reduce the many-body self-correlation error in molecular systems. Our down-scaled SOSEX (dsSOSEX) and scaled equation SOSEX (seSOSEX) approaches deliver considerably more accurate noncovalent interaction energies, reaction energies, and barrier heights than the original SOSEX method. The dsSOSEX approach improves on the description of medium- and long-range correlation, for example, in isogyric processes, while the seSOSEX approach improves on the description of processes with short- and medium-range rearrangement in the electronic structure, such as atomization. The He2+ potential energy curve shows that the many-body self-correlation error is slightly smaller in the dsSOSEX method than in the seSOSEX approach. Furthermore, the H2 potential energy curve reveals that the static correlation error can also be reduced at medium range by the dsSOSEX and seSOSEX schemes. As our dsSOSEX method provides a better description of medium- and long-range correlation, it generally leads to more accurate energetics than the seSOSEX method; hence it should be preferred over the latter. We compare our results to other empirical and nonempirical direct random phase approximation (dRPA) and beyond-dRPA methods and also discuss the possibilities for further development.

Unraveling the Structure-Property Relationship of Molecular Hole-Transporting Materials for Perovskite Solar Cells.

Clarifying the structural basis and microscopic mechanism lying behind electronic properties of molecular semiconductors is of paramount importance in further material design to enhance the performance of perovskite solar cells. In this paper, three conjugated quasilinear segments of 9,9-dimethyl-9H-fluorene, 9,9-dimethyl-2,7-diphenyl-9H-fluorene, and 2,6-diphenyldithieno[3,2-b:2',3'-d]thiophene are end-capped with two bis(4-methoxyphenyl)amino groups for structurally simple molecular semiconductors Z1, Z2, and Z3, which crystallize in the monoclinic P21/n, triclinic P1̅, and monoclinic C2/c space groups, respectively. The modes and energies of intermolecular noncovalent interactions in various closely packed dimers extracted from single crystals are computed based on the quantum theory of atoms in molecules and energy decomposition analysis. Transfer integrals, reorganization energies, and center-of-mass distances in these dimers as well as band structures of single crystals are also calculated to define the theoretical limit of hole transport and microscopic transport pictures. Joint X-ray diffraction and space-charge-limiting current measurements on solution-deposited films suggest the dominant role of crystallinity in thin-film hole mobility. Photoelectron spectroscopy and photoluminescence measurements show that an enhanced interfacial interaction between the perovskite and Z3 could attenuate the adverse impact of reducing the energetic driving force of hole extraction. Our comparative studies show that the molecular semiconductor Z3 with a properly aligned highest occupied molecular orbital energy level and a high thin-film mobility can be employed for efficient perovskite solar cells, achieving a good power conversion efficiency of 20.84%, which is even higher than that of 20.42% for the spiro-OMeTAD control.

HFLD: A Nonempirical London Dispersion-Corrected Hartree-Fock Method for the Quantification and Analysis of Noncovalent Interaction Energies of Large Molecular Systems †.

A nonempirical quantum mechanical method for the efficient and accurate quantification and analysis of intermolecular interactions is presented and tested on existing benchmark sets. The leading idea here is to focus on the intermolecular part of the correlation energy that contains the all-important London dispersion (LD) interaction. To keep the cost of the method low, essentially at the level of a Hartree-Fock (HF) calculation, the intramolecular part of the correlation energy is neglected. We also neglect the nondispersive parts of the intermolecular correlation energy. This scheme that we denote as Hartree-Fock plus London dispersion (HFLD) can be readily realized on the basis of the recently reported multilevel implementation of the domain-based local pair natural orbital coupled-cluster (DLPNO-CC) theory in conjunction with the well-established local energy decomposition (LED) analysis. The accuracy and efficiency of the HFLD method are evaluated on rare gas dimers, on the S66 and L7 benchmark sets of noncovalent interactions, and on an additional set (LP14) consisting of bulky Lewis pairs held together by intermolecular interactions of various strengths, with interaction energies ranging from -8 to -107 kcal/mol. It is first shown that the LD energy calculated with this approach is essentially identical to that obtained from the full DLPNO-CCSD(T)/LED calculation, with a mean absolute error of 0.2 kcal/mol on the S66 benchmark set. Moreover, in terms of the overall interaction energies, the HFLD method shows an efficiency that is comparable to that of the HF method, while retaining an accuracy between that of the DLPNO-CCSD and DLPNO-CCSD(T) schemes. Since the underlying DLPNO-CCSD method is linear scaling with respect to the system size, the HFLD approach also does not lead to new bottlenecks for large systems. As an illustrative example of its efficiency, the HFLD scheme was applied to the interaction between the substrate and the residues in the active site of the cyclohexanone monooxygenase enzyme. The excellent cost/performance ratio indicates that the HFLD method opens new avenues for the accurate calculation and analysis of noncovalent interaction energies in large molecular systems.

Explicitly Correlated Dispersion and Exchange Dispersion Energies in Symmetry-Adapted Perturbation Theory.

The individual interaction energy terms in symmetry-adapted perturbation theory (SAPT) not only have different physical interpretations but also converge to their complete basis set (CBS) limit values at quite different rates. Dispersion energy is notoriously the slowest converging interaction energy contribution, and exchange dispersion energy, while smaller in absolute value, converges just as poorly in relative terms. To speed up the basis set convergence of the lowest-order SAPT dispersion and exchange dispersion energies, we borrow the techniques from explicitly correlated (F12) electronic structure theory and develop practical expressions for the closed-shell Edisp(20)-F12 and Eexch-disp(20)-F12 contributions. While the latter term has been derived and implemented for the first time, the former correction was recently proposed by Przybytek [ J. Chem. Theory Comput. 2018 , 14 , 5105 - 5117 ] using an Ansatz with a full optimization of the explicitly correlated amplitudes. In addition to reimplementing the fully optimized variant of Edisp(20)-F12, we propose three approximate Ansätze that substantially improve the scaling of the method and at the same time avoid the numerical instabilities of the unrestricted optimization. The performance of all four resulting flavors of Edisp(20)-F12 and Eexch-disp(20)-F12 is first tested on helium, neon, argon, water, and methane dimers, with orbital and auxiliary basis sets up to aug-cc-pV5Z and aug-cc-pV5Z-RI, respectively. The double- and triple-ζ basis set calculations are then extended to the entire A24 database of noncovalent interaction energies and compared with CBS estimates for Edisp(20) and Eexch-disp(20) computed using conventional SAPT with basis sets up to aug-cc-pV6Z with midbond functions. It is shown that the F12 treatment is highly successful in improving the basis set convergence of the SAPT terms, with the F12 calculations in an X-tuple ζ basis about as accurate as conventional calculations in bases with cardinal numbers (X + 2) for Edisp(20) and either (X + 1) or (X + 2) for Eexch-disp(20). While the full amplitude optimization affords the highest accuracy for both corrections, the much simpler and numerically stable optimized diagonal Ansatz is a very close second. We have also tested the performance of the simple F12 correction based on the second-order Møller-Plesset perturbation theory, SAPT-F12(MP2) [ Frey , J. A. ; Chem. Rev. 2016 , 116 , 5614 - 5641 ] and observed that it is also quite successful in speeding up the basis set convergence of conventional Edisp(20) + Eexch-disp(20), albeit with some outliers.

Crystal structure and evaluating C[sbnd]H⋯π (aryl/chelate) interactions in bis(2-{[(2-hydroxyethyl)imino]-methyl}-4,6-diiodophenolato)-palladium(II) Schiff base complex derived from (E)-2-(((2-hydroxyethyl)imino)methyl)-4,6-diiodophenol

A novel PdII complex [bis(2-{[(2-hydroxyethyl)imino]methyl}-4,6-diiodophenolato)-Palladium(II), (Pd(L1))] has been synthesized using a N,O-donor Schiff base ligand, (E)-2-(((2-hydroxyethyl)imino)methyl)-4,6-diiodophenol (L1). The structure of Pd(L1) has been confirmed by single crystal X-ray diffraction analysis. Pd(L1) shows unusual CH⋯π (chelate) interaction beside with the usual CH⋯π (aryl) interactions in the solid-state. A comprehensive analysis of Hirshfeld surfaces and fingerprint plots are useful to measure the interactions within the crystal structure. The CH⋯π (chelate/aryl) interactions and the binding energies of noncovalent interactions observed in the crystal structure were analyzed using theoretical DFT calculations. Besides, the interactions have been exemplified by using both Bader’s theory of AIM analysis and the noncovalent interaction plot. The topological analysis of the electron density was carried out to analyze the bonding nature in the complex.

Platinum, gold, and silver standards of intermolecular interaction energy calculations

High-accuracy noncovalent interaction energies are indispensable as data points for potential energy surfaces and as benchmark values for improving and testing more approximate approaches. The preferred algorithm (the gold standard) for computing these energies has been the coupled-cluster method with singles, doubles, and perturbative triples [CCSD(T)] converged to the complete basis set (CBS) limit. However, gold-standard calculations are expensive as correlated interaction energies converge slowly with the basis set size, and establishing the CBS limit to better than 0.05 kcal/mol typically requires a CCSD(T) calculation in a basis set of at least triple-zeta quality. If an even higher accuracy is required (for example, for the assignment of complicated high-resolution spectra), establishing a superior platinum standard requires both a precisely converged CCSD(T)/CBS limit and the corrections for the core correlation, relativistic effects, and higher-order coupled-cluster terms at least through the perturbative quadruple excitations. On the other hand, if a triple-zeta CCSD(T) calculation is not feasible but a double-zeta one is, it is worthwhile to look for a silver standard that provides the most accurate and consistent approximation to the gold standard at a reduced computational cost. We review the recent developments aimed at (i) increasing the breadth and diversity of the available collection of gold-standard benchmark interaction energies, (ii) evaluating the best computational strategies for platinum-standard calculations and producing beyond-CCSD(T) potential energy surfaces for spectroscopic and scattering applications of the highest precision, and (iii) improving the accuracy of the silver-standard, double-zeta-level CCSD(T)/CBS estimates through the use of explicit correlation and midbond basis functions. We also outline the remaining challenges in the accurate ab initio calculations of noncovalent interaction energies.

Interaction of rat α9α10 nicotinic acetylcholine receptor with α-conotoxin RgIA and Vc1.1: Insights from docking, molecular dynamics and binding free energy contributions

The α9α10 nicotinic acetylcholine receptor (nAChR) is an effective therapeutic target for neuropathic pain. α-Conotoxin RgIA and Vc1.1 are two well-known peptides blocking α9α10 nAChR potently and selectively, which have been extensively investigated as drug candidates. Several key residues were established in previous experimental research. However, the mechanism of the specific interaction still needs to be elucidated in more detail. In this work, we explored the interaction mechanism between RgIA/Vc1.1 and rat α9α10 nAChR using docking and molecular dynamics (MD) simulations. Energy and network analysis programs were used to reveal key residues responsible for their interaction. Our results indicated that the most critical residues were in accord with previous studies. Importantly, several novel residues, including Tyr95, Trp151 in α9 (+)α10 (−) interface as well as Tyr196, Arg59in α10 (+)α9 (−) interface, were found in our models. Furthermore, we analyzed noncovalent interaction energies between RgIA/Vc1.1 and rat α9α10 nAChR. The results showed that three negatively charged residues (Glu197 in α10 subunit, Asp168 in α9 subunit and Asp205 in α10 subunit) were involved in the interaction between RgIA and rat α9α10 nAChR. In contrast, the interaction between Vc1.1 and rat α9α10 nAChR was mediated by the positively charged residues Arg59, Arg81 in α9 (−) subunit. These findings provided further insights into the molecular mechanisms of interaction between RgIA and Vc1.1 and rat α9α10 nAChR.

Minimally Empirical Double-Hybrid Functionals Trained against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4.

We present a family of minimally empirical double-hybrid DFT functionals parametrized against the very large and diverse GMTKN55 benchmark. The very recently proposed ωB97M(2) empirical double hybrid (with 16 adjustable parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, refits of the DSD-BLYP and DSD-PBEP86 spin-component-scaled, dispersion-corrected double hybrids can achieve WTMAD2 values as low as 2.33 with the very recent D4 dispersion correction (2.42 kcal/mol with the D3(BJ) dispersion term) using just a handful of adjustable parameters. If we use full DFT correlation in the initial orbital evaluation, the xrevDSD-PBEP86-D4 functional reaches WTMAD2 = 2.23 kcal/mol, statistically indistinguishable from ωB97M(2) but using just four nonarbitrary adjustable parameters (and three semiarbitrary ones). The changes from the original DSD parametrizations are primarily due to noncovalent interaction energies for large systems, which were undersampled in the original parametrization set. With the new parametrization, same-spin correlation can be eliminated at minimal cost in performance, which permits revDOD-PBEP86-D4 and revDOD-PBE-D4 functionals that scale as N4 or even N3 with the size of the system. Dependence of WTMAD2 for DSD functionals on the percentage of HF exchange is roughly quadratic; it is sufficiently weak that any reasonable value in the 64% to 72% range can be chosen semiarbitrarily. DSD-SCAN and DOD-SCAN double hybrids involving the SCAN nonempirical meta-GGA as the semilocal component have also been considered and offer a good alternative if one wishes to eliminate either the empirical dispersion correction or the same-spin correlation component. noDispSD-SCAN66 achieves WTMAD2 = 3.0 kcal/mol, compared to 2.7 kcal/mol for DOD-SCAN66-D4. However, the best performance without dispersion corrections (WTMAD2 = 2.8 kcal/mol) is reached by revωB97X-2, a slight reparametrization of the Chai–Head-Gordon range-separated double hybrid. Finally, in the context of double-hybrid functionals, the very recent D4 dispersion correction is clearly superior over D3(BJ).

2-[(4-Bromo-phen-yl)sulfan-yl]-2-meth-oxy-1-phenyl-ethan-1-one: crystal structure, Hirshfeld surface analysis and computational chemistry.

The title compound, C15H13BrO2S, comprises three different substituents bound to a central (and chiral) methine-C atom, i.e. (4-bromo-phen-yl)sulfanyl, benzaldehyde and meth-oxy residues: crystal symmetry generates a racemic mixture. A twist in the mol-ecule is evident about the methine-C-C(carbon-yl) bond as evidenced by the O-C-C-O torsion angle of -20.8 (7)°. The dihedral angle between the bromo-benzene and phenyl rings is 43.2 (2)°, with the former disposed to lie over the oxygen atoms. The most prominent feature of the packing is the formation of helical supra-molecular chains as a result of methyl- and methine-C-H⋯O(carbon-yl) inter-actions. The chains assemble into a three-dimensional architecture without directional inter-actions between them. The nature of the weak points of contacts has been probed by a combination of Hirshfeld surface analysis, non-covalent inter-action plots and inter-action energy calculations. These point to the importance of weaker H⋯H and C-H⋯C inter-actions in the consolidation of the structure.

A regression approach to accurate interaction energies using topological descriptors

Machine learning has a wide range of applications in chemistry, encompassing the prediction of the structure and properties of a variety of chemical systems (molecules, macromolecules and solids). The idea of using a self-learning algorithm to explore chemical problems is particularly alluring when facing open challenges in theoretical chemistry, such as non-covalent interactions, which are known to be critical for density functional methods. Additionally, the difficulty of predicting accurate non-covalent interaction (NCI) energies lies in their small absolute values, which make even the slightest absolute error severely affect the quality of the calculated result. In this work, we test the possibility of computing accurate interaction energies (at the golden standard CCSD(T)/CBS level) of small non-covalent complexes starting from a DFTD/DZ energy and using descriptors derived from the promolecular density. Calculations on the S66x8 dataset of molecular complexes show that these local descriptors can reduce to one third the mean absolute error of DFT results at a virtually negligible computational cost.

Small Basis Set Allowing the Recovery of Dispersion Interactions with Double-Hybrid Functionals.

Taking advantage of the compensation between Basis Set Superposition Error and Basis Set Incompleteness Error, a new basis is developed to improve the performances of Double Hybrid (DH) functionals in reproducing interaction energies in weak noncovalent systems. Using a self-consistent formula, containing only energy terms computed for dimers and the corresponding monomers at the same level of theory, the exponents of the more external functions of the Def2-SVPD basis were optimized on three systems extracted from the S22 set. The transferability of the obtained basis set, called DH-SVPD, was then tested on five benchmark sets, and it is assessed by considering six DH functionals, eventually corrected with empirical dispersion corrections (for a total of 16 methods). Our results show that this simple approach is able to provide accurate results for noncovalent interaction energies of all the considered systems, and, in particular, to recover the performances obtained by coupling the DH functionals with empirical dispersion corrections.