Nonfitting protein–ligand interaction scoring function based on first‐principles theoretical chemistry methods: Development and application on kinase inhibitors

Targeted therapy is currently a hot topic in the fields of cancer research and drug design. An important requirement for this approach is the development of potent and selective inhibitors for the identified target protein. However, current ways to estimate inhibitor efficacy rely on empirical protein–ligand interaction scoring functions which, suffering from their heavy parameterizations, often lead to a low accuracy. In this work, we develop a nonfitting scoring function, which consists of three terms: (1) gas‐phase protein‐ligand binding enthalpy obtained by the eXtended ONIOM hybrid method based on an integration of density functional theory (DFT) methods (XYG3 and ωB97X‐D) and the semiempirical PM6 method, (2) solvation free energy based on DFT‐SMD solvation model, and (3) entropy effect estimated by using DFT frequency analysis. The new scoring function is tested on a cyclin‐dependent kinase 2 (CDK2) inhibitor database including 76 CDK2 protein inhibitors and a p21‐activated kinase 1 (PAK1) inhibitor database including 20 organometallic PAK1 protein inhibitors. From the results, good correlations are found between the calculated scores and the experimental inhibitor efficacies with the square of correlation coefficient R² of 0.76–0.88. This suggests a good predictive power of this scoring function. To the best of our knowledge, this is the first high level theory‐based nonfitting scoring function with such a good level of performance. This scoring function is recommended to be used in the final screening of lead structure derivatives. © 2013 Wiley Periodicals, Inc.     

Degree of electron–nuclear entanglement in molecular states

The degree of electron–nuclear entanglement in molecular states is analyzed. This entanglement has, generally, two sources: delocalization of the electronic and nuclear wave functions and vibronic coupling. For a diatomic molecular ground‐state with a single potential energy minimum, it is demonstrated that the entanglement is a function of the product of the vibrational energy and the Born–Huang potential energy correction evaluated at the minimum. In the case of a double‐well potential energy surface, the deviation from maximal entanglement is determined by the overlap of the electronic and nuclear wave functions evaluated at and around the two minima. The adiabatic states of the E⊗ϵ Jahn–Teller model are shown to be maximally entangled and a relation between the degree of entanglement and Ham's reduction factor for this model is derived. Numerical calculations in the E⊗ϵ model demonstrate a nontrivial relation between entanglement and vibronic coupling. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 526–533, 2000     

A Bayesian statistical approach of improving knowledge‐based scoring functions for protein–ligand interactions

Knowledge‐based scoring functions are widely used for assessing putative complexes in protein–ligand and protein–protein docking and for structure prediction. Even with large training sets, knowledge‐based scoring functions face the inevitable problem of sparse data. Here, we have developed a novel approach for handling the sparse data problem that is based on estimating the inaccuracies in knowledge‐based scoring functions. This inaccuracy estimation is used to automatically weight the knowledge‐based scoring function with an alternative, force‐field‐based potential (FFP) that does not rely on training data and can, therefore, provide an improved approximation of the interactions between rare chemical groups. The current version of STScore, a protein–ligand scoring function using our method, achieves a binding mode prediction success rate of 91% on the set of 100 complexes by Wang et al., and a binding affinity correlation of 0.514 with the experimentally determined affinities in PDBbind. The method presented here may be used with other FFPs and other knowledge‐based scoring functions and can also be applied to protein–protein docking and protein structure prediction. © 2014 Wiley Periodicals, Inc.     

Photoconductivity in Metal–Organic Framework (MOF) Thin Films

Photoconductivity is a characteristic property of semi‐conductors. Herein, we present a photo‐conducting crystalline metal–organic framework (MOF) thin film with an on–off photocurrent ratio of two orders of magnitude. These oriented, surface‐mounted MOF thin films (SURMOFs), contain porphyrin in the framework backbone and C₆₀ guests, loaded in the pores using a layer‐by‐layer process. By comparison with results obtained for reference MOF structures and based on DFT calculations, we conclude that donor–acceptor interactions between the porphyrin of the host MOF and the C₆₀ guests give rise to a rapid charge separation. Subsequently, holes and electrons are transported through separate channels formed by porphyrin and by C₆₀, respectively. The ability to tune the properties and energy levels of the porphyrin and fullerene, along with the controlled organization of donor–acceptor pairs in this regular framework offers potential to increase the photoconduction on–off ratio.     

An Exceptionally Close,Non‐Bonded Hydrogen–Hydrogen Contact with Strong Through‐Space Spin–Spin Coupling

Condensation of 1,8,13‐tris(mercaptomethyl)triptycene and tris(bromomethyl)methane yields an in,in‐cyclophane with two inwardly directed methine groups. Based on X‐ray analysis and DFT and MP2 calculations, the hydrogen–hydrogen non‐bonded contact distance is estimated to be 1.50–1.53 Å. Furthermore, the two in‐hydrogen atoms show obvious spin–spin coupling with J=2.0 Hz.     

An Exceptionally Close,Non‐Bonded Hydrogen–Hydrogen Contact with Strong Through‐Space Spin–Spin Coupling

Condensation of 1,8,13‐tris(mercaptomethyl)triptycene and tris(bromomethyl)methane yields an in,in‐cyclophane with two inwardly directed methine groups. Based on X‐ray analysis and DFT and MP2 calculations, the hydrogen–hydrogen non‐bonded contact distance is estimated to be 1.50–1.53 Å. Furthermore, the two in‐hydrogen atoms show obvious spin–spin coupling with J=2.0 Hz.     

Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.     

Attractive electron–electron interactions within robust local fitting approximations

An analysis of Dunlap's robust fitting approach reveals that the resulting two‐electron integral matrix is not manifestly positive semidefinite when local fitting domains or non‐Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four‐center two‐electron integrals based on the resolution‐of‐the‐identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair‐atomic resolution‐of‐the‐identity (PARI) approach, atomic‐orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree–Fock and Kohn–Sham calculations, the indefinite integral matrix causes nonconvergence in the self‐consistent‐field iterations. In these cases, the two‐electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb‐metric RI method. The speed‐up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple‐zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky‐decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. © 2013 Wiley Periodicals, Inc.     

The Nature of Activated Non‐classical Hydrogen Bonds: A Case Study on Acetylcholinesterase–Ligand Complexes

Molecular recognition events in biological systems are driven by non‐covalent interactions between interacting species. Here, we have studied hydrogen bonds of the CH???Y type involving electron‐deficient CH donors using dispersion‐corrected density functional theory (DFT) calculations applied to acetylcholinesterase–ligand complexes. The strengths of CH???Y interactions activated by a proximal cation were considerably strong; comparable to or greater than those of classical hydrogen bonds. Significant differences in the energetic components compared to classical hydrogen bonds and non‐activated CH???Y interactions were observed. Comparison between DFT and molecular mechanics calculations showed that common force fields could not reproduce the interaction energy values of the studied hydrogen bonds. The presented results highlight the importance of considering CH???Y interactions when analysing protein–ligand complexes, call for a review of current force fields, and opens up possibilities for the development of improved design tools for drug discovery.     

An analytic potential energy function for the amide–amide and amide–water intermolecular hydrogen bonds in peptides

An analytic potential energy function is proposed and applied to evaluate the amide–amide and amide–water hydrogen‐bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen‐bonded training dimers. The analytic potential energy function is then employed to calculate the N? H…O?C, C? H…O?C, N? H…OH₂, and C?O…HOH hydrogen‐bonding interaction energies in amide–amide and amide–water dimers containing N‐methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N‐methylformamide, N‐methylpropanamide, N‐ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O…H) and the hydrogen‐bonding energies. The function is also applied to calculate the binding energies in models of β‐sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen‐bonding interaction energies in peptides quickly and accurately. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Probing Absolute Electronic Energy Levels in Hg‐Doped CdTe Semiconductor Nanocrystals by Electrochemistry and Density Functional Theory

The absolute electronic energy levels in Hg‐doped CdTe semiconductor nanocrystals (CdHgTe NCs) with varying sizes/volumes and Hg contents are determined by using cyclic voltammetry (CV) measurements and density functional theory (DFT) ‐based calculations. The electrochemical measurements demonstrate several distinct characteristic features in the form of oxidation and reduction peaks in the voltammograms, where the peak positions are dependent on the volume of CdHgTe NCs as well as on their composition. The estimated absolute electronic energy levels for three different volumes, namely 22, 119 and 187 nm³ with 2.7±0.3 % of Hg content, show strong volume dependence. The volume‐dependent shift in the characteristic reduction and oxidation peak potential scan can be attributed to the alteration in the energetic band positions owing to the quantum confinement effect. Moreover, the composition (Cd/Hg=98.3/1.7 and 97.0/3.0) ‐dependent alteration in the electronic energy levels of CdHgTe NCs for two different samples with similar volumes (ca. 124±5 nm³) are shown. Thus obtained electronic energy level values of CdHgTe NCs as a function of volume and composition demonstrate good congruence with the corresponding absorption and emission spectral data, as well as with DFT‐based calculations. DFT calculations reveal that incorporation of Hg into CdTe NCs mostly affects the energy levels of conduction band edge, whereas the valence band edge remains almost unaltered.     

High‐Performance K–CO2 Batteries Based on Metal‐Free Carbon Electrocatalysts

Metal–CO₂ batteries have attracted much attention owing to their high energy density and use of greenhouse CO₂ waste as the energy source. However, the increasing cost of lithium and the low discharge potential of Na–CO₂ batteries create obstacles for practical applications of Li/Na–CO₂ batteries. Recently, earth‐abundant potassium ions have attracted considerable interest as fast ionic charge carriers for electrochemical energy storage. Herein, we report the first K–CO₂ battery with a carbon‐based metal‐free electrocatalyst. The battery shows a higher theoretical discharge potential (E^?=2.48 V) than that of Na–CO₂ batteries (E^?=2.35 V) and can operate for more than 250 cycles (1500 h) with a cutoff capacity of 300 mA h g^?1. Combined DFT calculations and experimental observations revealed a reaction mechanism involving the reversible formation and decomposition of P12₁/c1‐type K₂CO₃ at the efficient carbon‐based catalyst.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Enhancing the Reaction Rates of Morita–Baylis–Hillman Reaction in Heterocyclic Aldehydes by Substitutions

The molecular origin of the experimentally observed pronounced difference in the rates of Morita–Baylis–Hillman (MBH) reaction in heterocyclic aldehydes, depending on the position of the formyl group, is investigated herein by using DFT‐based mechanistic studies and free energy computations. These calculations are based on the 1,4‐diazobicyclo[2.2.2]octane (DABCO)‐catalyzed MBH reaction of methyl acrylate with substituted 4‐ and 5‐isoxazolecarbaldehyde, which are slow‐ and fast‐reacting substrates, respectively. As a result of this study, we propose that by tailoring ring substitutions the reactivity of the formyl group for MBH reactions may be enhanced in slow‐reacting heterocyclic aldehydes. This proposition is demonstrated by enhancing the rate of the MBH reaction in 4‐isoxazolecarbaldehyde more than 10⁴‐fold by installing an ester substitution at the C‐3 position. Similarly, the reactivity of the formyl group towards the MBH reaction in substituted 3‐pyrazolecarbaldehyde and pyridinecarbaldehyde is shown to be increased several‐fold by a halo substitution. We also confirm that the reasons for different reactivities of heterocyclic aldehydes and the proposed scheme for improving the reaction rates remains valid for all the three mechanisms proposed for the MBH reaction, namely, Hill–Isaacs, McQuade, and Aggarwal.     

Synergistic Effect between Metal–Nitrogen–Carbon Sheets and NiO Nanoparticles for Enhanced Electrochemical Water‐Oxidation Performance

Identifying effective means to improve the electrochemical performance of oxygen‐evolution catalysts represents a significant challenge in several emerging renewable energy technologies. Herein, we consider metal–nitrogen–carbon sheets which are commonly used for catalyzing the oxygen‐reduction reaction (ORR), as the support to load NiO nanoparticles for the oxygen‐evolution reaction (OER). FeNC sheets, as the advanced supports, synergistically promote the NiO nanocatalysts to exhibit superior performance in alkaline media, which is confirmed by experimental observations and density functional theory (DFT) calculations. Our findings show the advantages in considering the support effect for designing highly active, durable, and cost‐effective OER electrocatalysts.     

On‐Surface Synthesis and Characterization of Triply Fused Porphyrin–Graphene Nanoribbon Hybrids

On‐surface synthesis offers a versatile approach to prepare novel carbon‐based nanostructures that cannot be obtained by conventional solution chemistry. Graphene nanoribbons (GNRs) have potential for a variety of applications. A key issue for their application in molecular electronics is in the fine‐tuning of their electronic properties through structural modifications, such as heteroatom doping or the incorporation of non‐benzenoid rings. In this context, the covalent fusion of GNRs and porphyrins (Pors) is a highly appealing strategy. Herein we present the selective on‐surface synthesis of a Por–GNR hybrid, which consists of two Pors connected by a short GNR segment. The atomically precise structure of the Por–GNR hybrid has been characterized by bond‐resolved scanning tunneling microscopy (STM) and noncontact atomic force microscopy (nc‐AFM). The electronic properties have been investigated by scanning tunneling spectroscopy (STS), in combination with DFT calculations, which reveals a low electronic gap of 0.4 eV.     

Quantum chemical exploration of formaldehyde clusters (H2CO)n (n = 2–4)

Global exploration of equilibrium structures and interconversion pathways on the quantum chemical potential energy surface (PES) is performed for (H₂CO)n (n = 2–4) by using the Scaled Hypersphere Search‐Anharmonic Downward Distortion Following (SHS‐ADDF) method. Density functional theoretical (DFT) calculations with empirical dispersion corrections (D3) yielded comparable results for formaldehyde dimer in comparison with recent detailed studies at CCSD(T) levels. Based on DFT‐D3 calculations, trimer and tetramer structures and their stabilities were studied. For tetramer, a highly symmetrical S₄ structure was found as the most stable form in good accordance with experimentally determined tetramer unit in the formaldehyde crystal. © 2018 Wiley Periodicals, Inc.     

Markovnikov versus anti‐Markovnikov addition and C–H activation: Pd–Cu synergistic catalysis

Copper‐ and palladium‐mediated transmetalation and coupling reactions are the backbone to several synthetic methodologies in organic chemistry for C–C bond formation. Computer‐aided simulations using density functional theory (DFT) (B3LYP‐D3 functional with 6‐31G** and effective core potential (ECP)‐LACVP** for heavy atoms for optimizations and cc‐pVTZ(?f) and ECP‐LACV3P** for single‐point calculations) was used to shed light on the probable mechanism of a novel synergistic Cu/Pd catalysts for the coupling of alkene, (Bpin)2 (where, pin = pinacolate), and vinyl‐ or aryl‐halogenated analogues. Every single conceivable pathway was carefully contemplated, and the base minimum energy pathway was found effectively. The copper‐catalyzed nucleophilic generation yields anti‐Markovnikov product using styrene as an alkene. This study affirms quantitatively and accurately how the reaction proceeds and at which steps of the synergistic catalysis the demand of the transmetalation and nucleophile formation for the C–C coupling using phosphine ligands arise. We conclude that the E and Z selectivity depends on the stereochemistry of the substrates used.     

Fragment‐based quantum mechanical calculation of protein–protein binding affinities

The electrostatically embedded generalized molecular fractionation with conjugate caps (EE‐GMFCC) method has been successfully utilized for efficient linear‐scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE‐GMFCC method for calculation of binding affinity of Endonuclease colicin–immunity protein complex. The binding free energy changes between the wild‐type and mutants of the complex calculated by EE‐GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6‐31G*‐D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson–Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein–protein binding affinities. Moreover, the self‐consistent calculation of PB solvation energy is required for accurate calculations of protein–protein binding free energies. This study demonstrates that the EE‐GMFCC method is capable of providing reliable prediction of relative binding affinities for protein–protein complexes. © 2018 Wiley Periodicals, Inc.     

Supramolecular Water Oxidation with Ru–bda‐Based Catalysts

Extremely slow and extremely fast new water oxidation catalysts based on the Ru–bda (bda=2,2′‐bipyridine‐6,6′‐dicarboxylate) systems are reported with turnover frequencies in the range of 1 and 900 cycles s^?1, respectively. Detailed analyses of the main factors involved in the water oxidation reaction have been carried out and are based on a combination of reactivity tests, electrochemical experiments, and DFT calculations. These analyses give a convergent interpretation that generates a solid understanding of the main factors involved in the water oxidation reaction, which in turn allows the design of catalysts with very low energy barriers in all the steps involved in the water oxidation catalytic cycle. We show that for this type of system π‐stacking interactions are the key factors that influence reactivity and by adequately controlling them we can generate exceptionally fast water oxidation catalysts.