MolE8: finding DFT potential energy surface minima values from force-field optimised organic molecules with new machine learning representations

The use of machine learning techniques in computational chemistry has gained significant momentum since large molecular databases are now readily available. Predictions of molecular properties using machine learning have advantages over the traditional quantum mechanics calculations because they can be cheaper computationally without losing the accuracy. We present a new extrapolatable and explainable molecular representation based on bonds, angles and dihedrals that can be used to train machine learning models. The trained models can accurately predict the electronic energy and the free energy of small organic molecules with atom types C, H N and O, with a mean absolute error of 1.2 kcal mol⁻¹. The models can be extrapolated to larger organic molecules with an average error of less than 3.7 kcal mol⁻¹ for 10 or fewer heavy atoms, which represent a chemical space two orders of magnitude larger. The rapid energy predictions of multiple molecules, up to 7 times faster than previous ML models of similar accuracy, has been achieved by sampling geometries around the potential energy surface minima. Therefore, the input geometries do not have to be located precisely on the minima and we show that accurate density functional theory energy predictions can be made from force-field optimised geometries with a mean absolute error 2.5 kcal mol⁻¹.

New representations and machine learning calculate DFT minima from force field geometries.     

A high-spin diradical dianion and its bridged chemically switchable single-molecule magnet

Triplet diradicals have attracted tremendous attention due to their promising application in organic spintronics, organic magnets and spin filters. However, very few examples of triplet diradicals with singlet–triplet energy gaps (ΔE_ST) over 0.59 kcal mol⁻¹ (298 K) have been reported to date. In this work, we first proved that the dianion of 2,7-di-tert-butyl-pyrene-4,5,9,10-tetraone (2,7-tBu₂-PTO) was a triplet ground state diradical in the magnesium complex 1 with a singlet–triplet energy gap ΔE_ST = 0.94 kcal mol⁻¹ (473 K). This is a rare example of stable diradicals with singlet–triplet energy gaps exceeding the thermal energy at room temperature (298 K). Moreover, the iron analog 2 containing the 2,7-tBu₂-PTO diradical dianion was isolated, which was the first single-molecule magnet bridged by a diradical dianion. When 2 was doubly reduced to the dianion salt 2K2, single-molecule magnetism was switched off, highlighting the importance of diradicals in single-molecule magnetism.

We report a triplet diradical dianion in magnesium complex with ΔE_ST = 0.94 kcal mol⁻¹ (473 K). Its iron analog is the first single-molecule magnet bridged by a diradical dianion, and the SMM property is switched off through two-electron reduction.     

Observations of tetrel bonding between sp3-carbon and THF

We report the direct observation of tetrel bonding interactions between sp³-carbons of the supramolecular synthon 3,3-dimethyl-tetracyanocyclopropane (1) and tetrahydrofuran in the gas and crystalline phase. The intermolecular contact is established via σ-holes and is driven mainly by electrostatic forces. The complex manifests distinct binding geometries when captured in the crystalline phase and in the gas phase. We elucidate these binding trends using complementary gas phase quantum chemical calculations and find a total binding energy of −11.2 kcal mol⁻¹ for the adduct. Our observations pave the way for novel strategies to engineer sp³-C centred non-covalent bonding schemes for supramolecular chemistry.

sp³-C⋯THF tetrel bonding was observed in the crystalline state and in the gas phase. Density functional calculations revealed interaction energies up to −11.2 kcal mol⁻¹ and showed that these adducts are held together mainly by electrostatics.     

Facile conversion of ammonia to a nitride in a rhenium system that cleaves dinitrogen

Rhenium complexes with aliphatic PNP pincer ligands have been shown to be capable of reductive N₂ splitting to nitride complexes. However, the conversion of the resulting nitride to ammonia has not been observed. Here, the thermodynamics and mechanism of the hypothetical N–H bond forming steps are evaluated through the reverse reaction, conversion of ammonia to the nitride complex. Depending on the conditions, treatment of a rhenium(iii) precursor with ammonia gives either a bis(amine) complex [(PNP)Re(NH₂)₂Cl]⁺, or results in dehydrohalogenation to the rhenium(iii) amido complex, (PNP)Re(NH₂)Cl. The N–H hydrogen atoms in this amido complex can be abstracted by PCET reagents which implies that they are quite weak. Calorimetric measurements show that the average bond dissociation enthalpy of the two amido N–H bonds is 57 kcal mol⁻¹, while DFT computations indicate a substantially weaker N–H bond of the putative rhenium(iv)-imide intermediate (BDE = 38 kcal mol⁻¹). Our analysis demonstrates that addition of the first H atom to the nitride complex is a thermochemical bottleneck for NH₃ generation.

Rhenium–PNP complexes split N₂ to nitrides, but the nitrides do not give ammonia. Here, the thermodynamics of the hypothetical N–H bond forming steps are evaluated through the reverse reaction, showing that the first H addition is the bottleneck.     

Synthesis,characterization and computational evaluation of bicyclooctadienes towards molecular solar thermal energy storage

Molecular solar-thermal energy storage (MOST) systems are based on photoswitches that reversibly convert solar energy into chemical energy. In this context, bicyclooctadienes (BODs) undergo a photoinduced transformation to the corresponding higher energy tetracyclooctanes (TCOs), but the photoswitch system has not until now been evaluated for MOST application, due to the short half-life of the TCO form and limited available synthetic methods. The BOD system degrades at higher temperature via a retro-Diels–Alder reaction, which complicates the synthesis of the compounds. We here report a cross-coupling reaction strategy that enables an efficient synthesis of a series of 4 new BOD compounds. We show that the BODs were able to switch to the corresponding tetracyclooctanes (TCOs) in a reversible way and can be cycled 645 times with only 0.01% degradation. Half-lives of the TCOs were measured, and we illustrate how the half-life could be engineered from seconds to minutes by molecular structure design. A density functional theory (DFT) based modelling framework was developed to access absorption spectra, thermal half-lives, and storage energies which were calculated to be 143–153 kJ mol⁻¹ (0.47–0.51 MJ kg⁻¹), up to 76% higher than for the corresponding norbornadiene. The combined computational and experimental findings provide a reliable way of designing future BOD/TCO systems with tailored properties.

Molecular solar-thermal energy storage (MOST) systems are based on photoswitches that reversibly convert solar energy into chemical energy.     

Intramitochondrial co-assembly between ATP and nucleopeptides induces cancer cell apoptosis

Mitochondria are essential intracellular organelles involved in many cellular processes, especially adenosine triphosphate (ATP) production. Since cancer cells require high ATP levels for proliferation, ATP elimination can be a unique target for cancer growth inhibition. We describe a newly developed mitochondria-targeting nucleopeptide (MNP) that sequesters ATP by self-assembling with ATP inside mitochondria. MNP interacts strongly with ATP through electrostatic and hydrogen bonding interactions. MNP exhibits higher binding affinity for ATP (−637.5 kJ mol⁻¹) than for adenosine diphosphate (ADP) (−578.2 kJ mol⁻¹). To improve anticancer efficacy, the small-sized MNP/ADP complex formed large assemblies with ATP inside cancer cell mitochondria. ATP sequestration and formation of large assemblies of the MNP/ADP–ATP complex inside mitochondria caused physical stress by large structures and metabolic disorders in cancer cells, leading to apoptosis. This work illustrates a facile approach to developing cancer therapeutics that relies on molecular assemblies.

Mitochondria-targeting nucleopeptide (MNP) can sequester ATP by self-assembling with ATP. A small nanosized MNP/ADP complex forms a large assembly with ATP. Thus, intramitochondrial co-assembly causes stress by large structures and apoptosis.     

Calculation of absolute molecular entropies and heat capacities made simple

We propose a fully-automated composite scheme for the accurate and numerically stable calculation of molecular entropies by efficiently combining density-functional theory (DFT), semi-empirical methods (SQM), and force-field (FF) approximations. The scheme is systematically expandable and can be integrated seamlessly with continuum-solvation models. Anharmonic effects are included through the modified rigid-rotor-harmonic-oscillator (msRRHO) approximation and the Gibbs–Shannon formula for extensive conformer ensembles (CEs), which are generated by a metadynamics search algorithm and are extrapolated to completeness. For the first time, variations of the ro-vibrational entropy over the CE are consistently accounted-for through a Boltzmann-population average. Extensive tests of the protocol with the two standard DFT approaches B97-3c and B3LYP-D3 reveal an unprecedented accuracy with mean deviations <1 cal mol⁻¹ K⁻¹ (about <1–2%) for the total gas phase molecular entropy of medium-sized molecules. Even for the hardship case of extremely flexible linear alkanes (C₁₄H₃₀–C₁₆H₃₄), errors are only about 3 cal mol⁻¹ K⁻¹. Comprehensive tests indicate a relatively strong variation of the conformational entropy on the underlying level of theory for typical drug molecules, inferring the complex potential energy surfaces as the main source of error. Furthermore, we show some application examples for the calculation of free energy differences in typical chemical reactions.

A novel scheme for the automated calculation of the conformational entropy together with a modified thermostatistical treatment provides entropies with unprecedented accuracy even for large, complicated molecules.     

Combining metal–metal cooperativity,metal–ligand cooperativity and chemical non-innocence in diiron carbonyl complexes

Several metalloenzymes, including [FeFe]-hydrogenase, employ cofactors wherein multiple metal atoms work together with surrounding ligands that mediate heterolytic and concerted proton–electron transfer (CPET) bond activation steps. Herein, we report a new dinucleating PNNP expanded pincer ligand, which can bind two low-valent iron atoms in close proximity to enable metal–metal cooperativity (MMC). In addition, reversible partial dearomatization of the ligand''s naphthyridine core enables both heterolytic metal–ligand cooperativity (MLC) and chemical non-innocence through CPET steps. Thermochemical and computational studies show how a change in ligand binding mode can lower the bond dissociation free energy of ligand C(sp³)–H bonds by ∼25 kcal mol⁻¹. H-atom abstraction enabled trapping of an unstable intermediate, which undergoes facile loss of two carbonyl ligands to form an unusual paramagnetic (S = ) complex containing a mixed-valent iron(0)–iron(i) core bound within a partially dearomatized PNNP ligand. Finally, cyclic voltammetry experiments showed that these diiron complexes show catalytic activity for the electrochemical hydrogen evolution reaction. This work presents the first example of a ligand system that enables MMC, heterolytic MLC and chemical non-innocence, thereby providing important insights and opportunities for the development of bimetallic systems that exploit these features to enable new (catalytic) reactivity.

The PNNP expanded pincer ligand can bind two iron centers in close proximity and display heterolytic and homolytic metal–ligand cooperativity.     

Thermal isomerization of acetylnitrene: a quantum-chemical study

The electronic structure and pathways of thermal isomerization of formylnitrene and acetylnitrene were studied by the B3LYP/6-311G(d,p) density functional method and ab initio G2(MP2,SVP) computational procedure using the geometries obtained from B3LYP calculations. According to G2 calculations, both nitrenes have singlet ground states while the energies of the corresponding triplet states are 2.8 and 5.7 kcal mol^–1 higher. For acetylnitrene, the activation barrier to the nitrene isocyanate isomerization was estimated at 28.9 kcal mol^–1 (G2). Calculations revealed no pathway for single-step isomerization of nitrene into cyanate in both systems. The formation of methyl cyanate from isocyanate is thermodynamically unfavorable (E = 26.5 kcal mol^–1) and requires a high activation barrier (89.4 kcal mol^–1) should be overcome. Based on the results obtained, the pathways of transformation of nitrene formed in thermal decomposition of acetyl azide (Curtius rearrangement) were analyzed.     

MCSCF reaction-path energetics and thermal rate-constants for the reaction of3NH with H2

Summary The intrinsic reaction-path, reactants, transition state and products for the reaction of NH (^3–)+H₂ (¹ _g ⁺ ) NH₂ (²B₁)+H (²S) involving the lowest triplet electronic state of NH₃ were calculated using multi-configuration (MC) SCF methods. The calculated change of internal energy for the reaction of 11.0 kcal mol^–1 agrees with the experimental value within 2 kcal mol^–1. The barrier to reaction is 23.4 kcal mol^–1 high. The harmonic MCSCF reaction-path potential was calculated and canonical variational transition state theory calculations of the rate constants performed over a temperature range from 400 to 2500 K. The computed rate constants are generally two orders of magnitude smaller than those of the comparable reaction of OH with H₂, whereas those of the reverse reaction are by a factor of 20 larger than those of OH₂ with H.     

The inversion of tetrahedral p-block element compounds: general trends and the relation to the second-order Jahn–Teller effect

The tetrahedron is the primary structural motif among the p-block elements and determines the architecture of our bio- and geosphere. However, a broad understanding of the configurational inversion of tetrahedral compounds is missing. Here, we report over 250 energies (DLPNO-CCSD(T)) for square planar inversion of third- and fourth-period element species of groups 13, 14, and 15. Surprisingly low inversion barriers are identified for compounds of industrial relevance (e.g., ≈100 kJ mol⁻¹ for Al(OH)₄⁻). More fundamentally, the second-order Jahn–Teller theorem is disclosed as suitable to rationalize substituent and central element effects. Bond analysis tools give further insights into the preference of eight valence electron systems with four substituents to be tetrahedral. Hence, this study develops a model to understand, memorize, and predict the angular flexibility of tetrahedral species. Perceiving the tetrahedron not as forcingly rigid but as a dynamic structural entity might leverage new approaches and visions for adaptive matter.

The tetrahedron is the primary structural motif among the p-block elements and determines the architecture of our bio- and geosphere. This study sheds light on its stereochemical inversion process.     

Universal dynamical onset in water at distinct material interfaces

Interfacial water remains liquid and mobile much below 0 °C, imparting flexibility to the encapsulated materials to ensure their diverse functions at subzero temperatures. However, a united picture that can describe the dynamical differences of interfacial water on different materials and its role in imparting system-specific flexibility to distinct materials is lacking. By combining neutron spectroscopy and isotope labeling, we explored the dynamics of water and the underlying substrates independently below 0 °C across a broad range of materials. Surprisingly, while the function-related anharmonic dynamical onset in the materials exhibits diverse activation temperatures, the surface water presents a universal onset at a common temperature. Further analysis of the neutron experiment and simulation results revealed that the universal onset of water results from an intrinsic surface-independent relaxation: switching of hydrogen bonds between neighboring water molecules with a common energy barrier of ∼35 kJ mol⁻¹.

We demonstrated that the dynamical onset of interfacial water is an intrinsic property of water itself, resulting from a surface independent relaxation process in water with an approximately universal energy barrier of ∼35 kJ mol⁻¹.     

Ab initio MP2 calculations of the products of acetylene addition to HgCl2

Gas-phase reaction of acetylene with HgCl₂ resulting in -chlorovinylmercury derivatives and their interaction with Cl^– and I^– anions and KI molecule was studied by the ab initio MP2 method with the Dunning—Hay double zeta basis set and LanL pseudopotential for Hg, K, and I atoms. The reaction was shown to proceed via a -complex of acetylene and HgCl₂ (the calculated enthalpy of formation is –6.5 kcal mol^–1). According to calculations, the activation energy of formation of cis--chlorovinylmercury chloride from acetylene and HgCl₂ is 31 kcal mol^–1. Chloride and iodide anions and KI molecule are readily added to both cis- and trans-isomer of -chlorovinylmercury chloride to give stable species.     

Uncovering an oxide ion substitution for the OH− + CH3F reaction

Theoretical investigations on chemical reactions allow us to understand the dynamics of the possible pathways and identify new unexpected routes. Here, we develop a global analytical potential energy surface (PES) for the OH⁻ + CH₃F reaction in order to perform high-level dynamics simulations. Besides bimolecular nucleophilic substitution (S_N2) and proton abstraction, our quasi-classical trajectory computations reveal a novel oxide ion substitution leading to the HF + CH₃O⁻ products. This exothermic reaction pathway occurs via the CH₃OH⋯F⁻ deep potential well of the S_N2 product channel as a result of a proton abstraction from the hydroxyl group by the fluoride ion. The present detailed dynamics study of the OH⁻ + CH₃F reaction focusing on the surprising oxide ion substitution demonstrates how incomplete our knowledge is of fundamental chemical reactions.

Reaction dynamics simulations on a high-level ab initio analytical potential energy surface reveal a novel oxide ion substitution channel for the OH⁻ + CH₃F reaction.     

Energy transfer (EnT) photocatalysis enabled by gold-N-heterocyclic carbene (NHC) complexes

We present the use of gold sensitizers [Au(SIPr)(Cbz)] (PhotAu 1) and [Au(IPr)(Cbz)] (PhotAu 2) as attractive alternatives to state-of-the-art iridium-based systems. These novel photocatalysts are deployed in [2 + 2] cycloadditions of diallyl ethers and N-tosylamides. The reactions proceed in short reaction times and in environmentally friendly solvents. [Au(SIPr)Cbz] and [Au(IPr)(Cbz)] have higher triplet energy (E_T) values (66.6 and 66.3 kcal mol⁻¹, respectively) compared to commonly used iridium photosensitizers. These E_T values permit the use of these gold complexes as sensitizers enabling energy transfer catalysis involving unprotected indole derivatives, a substrate class previously inaccessible with state-of-the-art Ir photocatalysts. The photosynthesis of unprotected tetracyclic spiroindolines via intramolecular [2 + 2] cycloaddition using our simple mononuclear gold sensitizer is readily achieved. Mechanistic studies support the involvement of triplet–triplet energy transfer (TTEnT) for both [2 + 2] photocycloadditions.

We present the use of gold sensitizers [Au(SIPr)(Cbz)] (PhotAu 1) and [Au(IPr)(Cbz)] (PhotAu 2) as attractive alternatives to state-of-the-art iridium-based systems.     

Preparation,structure and stereodynamics of phosphorus-bridged calixarenes

The pyrolysis of several dialkylphosphate ester derivatives of calix[4]arenes yielded the same phosphorus bridged compound7. Under the pyrolytic conditions the phosphate groups may be cleaved or intermolecularly transferred. X-ray crystallography of the bridged calixarenes7 and8 shows that they exist in a chiral flattened cone (fc) conformation. The bridged calixarenes undergo in solution a dynamic process with a barrier of about 10.1 kcal mol^–1 for7 and8 and 13.1 kcal mol^–1 for10, respectively. The dynamic processes result in enantiomerization of the systems. Pyrolysis of partially phosphorylated calix[6]arenes resulted in the formation of two products (11 and12), each consisting of two subunits of three proximal rings bridged by a phosphate group. The rotational barriers for11 and12 are 14.4 and 8.8 kcal mol^–1, indicating that the bridged calix[6]arene system12 is appreciably more flexible than11. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82169 (51 pages)This paper is dedicated to the commemorative issue on the 50th anniversary of calixarenes.     

Analysis of Kojic Acid Derivatives as Competitive Inhibitors of Tyrosinase: A Molecular Modeling Approach

Tyrosinases belong to the functional copper-containing proteins family, and their structure contains two copper atoms, in the active site, which are coordinated by three histidine residues. The biosynthesis of melanin in melanocytes has two stages depending on the actions of the natural substrates L-DOPA and L-tyrosine. The dysregulation of tyrosinase is involved in skin cancer initiation. In the present study, using molecular modeling tools, we analyzed the inhibition activity of tyrosinase activity using kojic acid (KA) derivatives designed from aromatic aldehydes and malononitrile. All derivatives showed conformational affinity to the enzyme active site, and a favorable distance to chelate the copper ion, which is essential for enzyme function. Molecular dynamics simulations revealed that the derivatives formed promising complexes, presenting stable conformations with deviations between 0.2 and 0.35 Å. In addition, the investigated KA derivatives showed favorable binding free energies. The most stable KA derivatives showed the following binding free energies: −17.65 kcal mol⁻¹ (D6), −18.07 kcal mol⁻¹ (D2), −18.13 (D5) kcal mol⁻¹, and −10.31 kcal mol⁻¹ (D4). Our results suggest that these derivatives could be potent competitive inhibitors of the natural substrates of L-DOPA (−12.84 kcal mol⁻¹) and L-tyrosine (−9.04 kcal mol⁻¹) in melanogenesis.     

Mechanism of covalent binding of ibrutinib to Bruton's tyrosine kinase revealed by QM/MM calculations

Ibrutinib is the first covalent inhibitor of Bruton''s tyrosine kinase (BTK) to be used in the treatment of B-cell cancers. Understanding the mechanism of covalent inhibition will aid in the design of safer and more selective covalent inhibitors that target BTK. The mechanism of covalent inhibition in BTK has been uncertain because there is no appropriate residue nearby that can act as a base to deprotonate the cysteine thiol prior to covalent bond formation. We investigate several mechanisms of covalent modification of C481 in BTK by ibrutinib using combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics reaction simulations. The lowest energy pathway involves direct proton transfer from C481 to the acrylamide warhead in ibrutinib, followed by covalent bond formation to form an enol intermediate. There is a subsequent rate-limiting keto–enol tautomerisation step (ΔG^‡ = 10.5 kcal mol⁻¹) to reach the inactivated BTK/ibrutinib complex. Our results represent the first mechanistic study of BTK inactivation by ibrutinib to consider multiple mechanistic pathways. These findings should aid in the design of covalent drugs that target BTK and other similar targets.

QM/MM simulations show that covalent modification of BTK by ibrutinib proceeds via an intramolecular proton transfer from C481 to the acrylamide warhead of ibrutinib, followed by covalent bond formation and subsequent keto–enol tautomerisation.      

Cavity catalysis: modifying linear free-energy relationship under cooperative vibrational strong coupling

Here, we used an unconventional idea of cooperative vibrational strong coupling of solute and solvent molecules to enhance the rate of an esterification reaction. Different derivatives of p-nitrophenyl benzoate (solute) and isopropyl acetate (solvent) are cooperatively coupled to an infrared Fabry–Perot cavity mode. The apparent rates are increased by more than six times at the ON resonance condition, and the rate enhancement follows the lineshape of the vibrational envelope. Very interestingly, a strongly coupled system doesn''t obey the Hammett relations. Thermodynamics suggests that the reaction mechanism remains intact for cavity and non-cavity conditions. Temperature-dependent experiments show an entropy-driven process for the coupled molecules. Vacuum field coupling decreases the free energy of activation by 2–5 kJ mol⁻¹, supporting a catalysis process. The non-linear rate enhancement can be due to the reshuffling of the energy distribution between the substituents and the reaction center across the aromatic ring. These findings underline the non-equilibrium behavior of cavity catalysis.

Cavity catalysis: vibrational strong coupling of solute and solvent molecules enhanced the rate of an esterification reaction. Hammett relation breaks under strong light-matter coupling conditions suggesting its potential applications in catalysis.     

Quantum chemical study of the structures and dynamic behavior of tricarbonyl complexes of Group 6 metals (Cr,Mo, W) with polyaromatic hydrocarbons using the density functional theory

The quantum chemical study of the mechanism was performed for tricarbonyl η⁶-complexes of coronene I-M and kekulene II-M (M = Cr, Mo, W) by the density functional method. The activation barriers of η⁶,η⁶-interring haptotropic rearrangements (IHR), being the migration of the metaltricarbonyl group M(CO)₃ from one six-membered aromatic ring to another, were determined. The processes of η⁶,η⁶-IHR in the metal tricarbonyl complexes with relatively high polycyclic aromatic hydrocarbons (PAH) I and II occur with close energy barriers (ΔG^≠ ≈ 20—25 kcal mol^–1), which are lower than the barriers (ΔG^≠ ~ 30 kcal mol^–1) of similar transformations measured or calculated earlier for the chromium tricarbonyl complexes of naphthalene and its derivatives and other PAH. For the molybdenum tricarbonyl complexes the activation barriers of η⁶,η⁶-IHR decrease additionally by ~ 5 kcal mol^–1 compared to those for the chromium tricarbonyl complexes, whereas for the tungsten tricarbonyl complexes they increase again and become approximately equal to the activation barriers of similar chromium tricarbonyl complexes. All stationary states on the potential energy surface determining the mechanism of η⁶,η⁶-IHR are characterized by a decrease in hapticity compared to the initial and final complexes.