Accuracy and tractability of a kriging model of intramolecular polarizable multipolar electrostatics and its application to histidine

We propose a generic method to model polarization in the context of high‐rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc‐1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds (“1, 4 and higher” interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom–atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol^?1. © 2013 Wiley Periodicals, Inc.     

Realistic sampling of amino acid geometries for a multipolar polarizable force field

The Quantum Chemical Topological Force Field (QCTFF) uses the machine learning method kriging to map atomic multipole moments to the coordinates of all atoms in the molecular system. It is important that kriging operates on relevant and realistic training sets of molecular geometries. Therefore, we sampled single amino acid geometries directly from protein crystal structures stored in the Protein Databank (PDB). This sampling enhances the conformational realism (in terms of dihedral angles) of the training geometries. However, these geometries can be fraught with inaccurate bond lengths and valence angles due to artefacts of the refinement process of the X‐ray diffraction patterns, combined with experimentally invisible hydrogen atoms. This is why we developed a hybrid PDB/nonstationary normal modes (NM) sampling approach called PDB/NM. This method is superior over standard NM sampling, which captures only geometries optimized from the stationary points of single amino acids in the gas phase. Indeed, PDB/NM combines the sampling of relevant dihedral angles with chemically correct local geometries. Geometries sampled using PDB/NM were used to build kriging models for alanine and lysine, and their prediction accuracy was compared to models built from geometries sampled from three other sampling approaches. Bond length variation, as opposed to variation in dihedral angles, puts pressure on prediction accuracy, potentially lowering it. Hence, the larger coverage of dihedral angles of the PDB/NM method does not deteriorate the predictive accuracy of kriging models, compared to the NM sampling around local energetic minima used so far in the development of QCTFF. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Incorporation of local structure into kriging models for the prediction of atomistic properties in the water decamer

Machine learning algorithms have been demonstrated to predict atomistic properties approaching the accuracy of quantum chemical calculations at significantly less computational cost. Difficulties arise, however, when attempting to apply these techniques to large systems, or systems possessing excessive conformational freedom. In this article, the machine learning method kriging is applied to predict both the intra‐atomic and interatomic energies, as well as the electrostatic multipole moments, of the atoms of a water molecule at the center of a 10 water molecule (decamer) cluster. Unlike previous work, where the properties of small water clusters were predicted using a molecular local frame, and where training set inputs (features) were based on atomic index, a variety of feature definitions and coordinate frames are considered here to increase prediction accuracy. It is shown that, for a water molecule at the center of a decamer, no single method of defining features or coordinate schemes is optimal for every property. However, explicitly accounting for the structure of the first solvation shell in the definition of the features of the kriging training set, and centring the coordinate frame on the atom‐of‐interest will, in general, return better predictions than models that apply the standard methods of feature definition, or a molecular coordinate frame. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Analysis of B3LYP and MP2 conformational population distributions in trans‐nicotine,acetylcholine, and ABT‐594

This work presents an analysis of the equivalence of MP2 and DFT (B3LYP functional) conformational populations. As a test case, we select three cholinergic agents (trans‐nicotine, acetylcholine, and the nicotinic analgesic ABT‐594), where the minima on the conformational energy hypersurfaces expand a large range of energies (～0–30 kJ mol^?1). From energetic and structural data obtained in vacuo at the MP2 and B3LYP/cc‐pVDZ levels, we build conformational partition functions, including the effect of the conformational kinetic energy and the rotovibrational coupling. Our results at a physiological temperature (37°C) show qualitative agreement in all cases. Quantitative agreement, however, is only found for trans‐nicotine and ABT‐594. In the first case, energy minima differ by <0.2 kJ mol^?1. Therefore, the equivalence of structural results translates in the equivalence of the conformational distribution. For ABT‐594, the minima are separated by as much as 8.0 kJ mol^?1, and the conformational energy determines the conformational distribution. In this case, the slight relative variation of conformational energy, between B3LYP and MP2, does not affect the population, since the secondary minima are high in energy and very low in population. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The prediction of atomic kinetic energies from coordinates of surrounding atoms using kriging machine learning

A novel design of a next-generation force field considers not only the electronic inter-atomic energy but also intra-atomic energy. This strategy promises a faithful mapping between the force field and the quantum mechanics that underpins it. Quantum chemical topology provides an energy partitioning in which atoms have well-defined electronic kinetic energies, and we are interested in capturing how they respond to changes in the positions of surrounding atoms. A machine learning method called kriging successfully creates models from a training set of molecular configurations that can then be used to predict the atomic kinetic energies occurring in previously unseen molecular configurations. We present a proof-of-concept based on four molecules of increasing complexity (methanol, N-methylacetamide, glycine and triglycine). We test how well the atomic kinetic energies can be modelled with respect to training set size, molecule size and elemental composition. For all atoms tested, the mean atomic kinetic energy errors fall below 1.5 kJ mol^?1, and far below this in most cases. This represents errors all under 0.5 % and thus the kinetic energies are well modelled using the kriging method, even when using modest-to-small training set sizes.     

Calculation of molecular geometries,relative conformational energies,dipole moments,and molecular electrostatic potential fitted charges of small organic molecules of biochemical interest by density functional theory

Density functional theory is tested on a large ensemble of model compounds containing a wide variety of functional groups to understand better its ability to reproduce experimental molecular geometries, relative conformational energies, and dipole moments. We find that gradient-corrected density functional methods with triple-ζ plus polarization basis sets reproduce geometries well. Most bonds tend to be approximately 0.015 Å longer than the experimental results. Bond angles are very well reproduced and most often fall within a degree of experiment. Torsions are, on average, within 4 degrees of the experimental values. For relative conformational energies, comparisons with Hartree-Fock calculations and correlated conventional ab initio methods indicate that gradient-corrected density functionals easily surpass the Hartree-Fock approximation and give results which are nearly as accurate as MP2 calculations. For the 35 comparisons of conformational energies for which experimental data was available, the root mean square (rms) deviation for gradient-corrected functionals was approximately 0.5 kcal mol^?1. Without gradient corrections, the rms deviation is 0.8 kcal mol^?1, which is even less accurate than the Hartree-Fock calculations. Calculations with extended basis sets and with gradient corrections incorporated into the self-consistent procedure generate dipole moments with an rms deviation of 5%. Dipole moments from local density functional calculations, with more modest basis sets, can be scaled down to achieve roughly the same accuracy. In this study, all density functional geometries were generated by local density functional self-consistent calculations with gradient corrections added in a perturbative fashion. Such an approach generates results that are almost identical to the self-consistent gradient-corrected calculations, which require significantly more computer time. Timings on scalar and vector architectures indicate that, for moderately sized systems, our density functional implementation requires only slightly less computer resources than established Hartree-Fock programs. However, our density functional calculations scale much better and are significantly faster than their MP2 counterparts, whose results they approach. © 1995 John Wiley & Sons, Inc.     

Low temperature 13C NMR study of 1-(3-pentyloxyphenylcarbamoyloxy)-2-dialkyl- aminocyclohexanes

Cyclohexane and piperidine ring reversal in 1-(3-pentyloxyphenylcarbamoyloxy)-2-dialkylaminocyclohexanes was investigated by ¹³C NMR. An unusually low conformational energy ΔG = 0.59 kJ mol^?1 and activation parameters ΔG^≠₂₁₈ = 43.8 ± 0.4 kJ mol^?1, ΔH^≠ = 48.9 ± 2.5 kJ mol^?1 and ΔS^≠ = 23 ± 9 J mol^?1 K^?1 were found for the diequatorial to diaxial transition of the cyclohexane ring in the trans-pyrrolidinyl derivative. In the trans-piperidinyl derivative, ΔG₂₂₂ = 44.7 ± 0.5 KJ mol^?1, ΔH^≠ = 55.7 ± 6.3 kJ mol^?1 and ΔS^≠ = 51 ± 21 J mol^?1 K^?1 was found for the piperidine ring reversal from the non-equivalence of the α-carbons.     

Atomic multipoles: Electrostatic potential fit,local reference axis systems,and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges. © 2012 Wiley Periodicals, Inc.     

Conformational analysis—XXI : H NMR Conformational Study of Alkyl-Substituted 2-Oxo-1,3,2-Dioxathianes

2-Oxo-1,3,2-dioxathiane and all methyl- and several alkyl-substituted 2-oxo-1,3,2-dioxathianes were prepared for a ¹H NMR conformational study. The conformational energy of the axial SO group in CCl₄, - ΔG^θ_SO = 14.8±0.3kJ mol^?1, was determined by chemical equilibration of the epimeric cis-4,6-dimethyl derivatives and it was found to decrease with the increasing solvent polarity. The conformational equilibria of alkyl-substituted derivatives were solved and the proportions of the conformers estimated using ¹H NMR chemical shifts, vicinal coupling constants and in three cases also dipole moments. The configurational interactions in the C₄C₅C₆ moiety are close to the corresponding values of 1,3-dioxanes.     

Theoretical study of the structure and unimolecular decomposition pathways of ethyloxonium, [CH3CH2OH2]+

Ab initio molecular orbital calculations with split-valence plus polarization basis sets and incorporating valence-electron correlation have been performed to determine the equilibrium structure of ethyloxonium ([CH₃CH₂OH₂]⁺) and examine its modes of unimolecular dissociation. An asymmetric structure (1) is predicted to be the most stable form of ethyloxonium, but a second conformational isomer of C_s symmetry lies only 1.4 kJ mol^?1 higher in energy than 1. Four unimolecular decomposition pathways for 1 have been examined involving loss of H₂, CH₄, H₂O or C₂H₄. The most stable fragmentation products, lying 65 kJ mol^?1 above 1, are associated with the H₂ elimination reaction. However, large barriers of 257 and 223 kJ mol^?1 have to be surmounted for H₂ and CH₄ loss, respectively. On the other hand, elimination of either C₂H₄ or H₂O from ethyloxonium can proceed without a barrier to the reverse associations and, with total endothermicities of 130 and 160 kJ mol^?1, respectively, these reactions are expected to dominate at lower energies. A second important equilibrium structure on the surface is a hydrogen-bridged complex, lying 53 kJ mol^?1 above 1. This complex is involved in the C₂H₄ elimination reaction, acts as an intermediate in the proton-transfer reaction connecting [C₂H₅]⁺ +H₂O and C₂H₄ + [H₃O]⁺ and plays an important role in the isotopic scrambling that has been observed experimentally in the elimination of either H₂O or C₂H₄ from ethyloxonium. The proton affinity of ethanol was calculated as 799 kJ mol^?1, in close agreement with the experimental value of 794 kJ mol^?1.     

O2 Binding to Heme is Strongly Facilitated by Near‐Degeneracy of Electronic States

This paper reports the computed O₂ binding to heme, which for the first time explains experimental enthalpies for this process of central importance to bioinorganic chemistry. All four spin states along the relaxed Fe? O₂‐binding curves were optimized using the full heme system with dispersion, thermodynamic, and scalar‐relativistic corrections, applying several density functionals. When including all these physical terms, the experimental enthalpy of O₂ binding (?59 kJ mol^?1) is closely reproduced by TPSSh‐D3 (?66 kJ mol^?1). Dispersion changes the potential energy surfaces and leads to the correct electronic singlet and heptet states for bound and dissociated O₂. The experimental activation enthalpy of dissociation (～82 kJ mol^?1) was also accurately computed (～75 kJ mol^?1) with an actual barrier height of ～60 kJ mol^?1 plus a vibrational component of ～10 and ～5 kJ mol^?1 due to the spin‐forbidden nature of the process, explaining the experimentally observed difference of ～20 kJ mol^?1 in enthalpies of binding and activation. Most importantly, the work shows how the nearly degenerate singlet and triplet states increase crossover probability up to ～0.5 and accelerate binding by ～100 times, explaining why the spin‐forbidden binding of O₂ to heme, so fundamental to higher life forms, is fast and reversible.     

Temperature‐Dependent Prediction of the Liquid Entropy of Ionic Liquids

Modeling of the temperature‐dependent liquid entropy of ionic liquids (ILs) with great accuracy using COSMO‐RS is demonstrated. The minimum structures of eight IL ion pairs are investigated and the entropy, calculated from ion pairs, is found to differ on average only 2 % from the available experimental values (119 data points). For calculations with single ions, the average error amounts to 2.6 % and stronger‐coordinating ions tend to give higher deviations. Additionally, the first parameterization of the standard liquid entropy for ILs is presented in the context of traditional volume‐based thermodynamics (S_l⁰=1.585 kJ mol^?1 K^?1 nm^?3?r_m³+14.09 J mol^?1 K^?1), which sheds light on the statistical treatment of ionic interactions. The findings provide the first direct access to accurate predictions of liquid entropies of ILs, which are tedious and time‐consuming to measure.     

Ab initio- and density-functional studies of conformational behaviour of N-formylmethionine in gaseous phase

The current work is a study of the conformational space of the non-ionic N-formylmethionine molecule around its seven structurally significant internal backbone torsional angles at B3LYP/6-31++G(d,p) levels of theory in the gaseous phase. The potential energy surface exploration reveals that a total of 432 different conformers would result if all the possible combinations of the internal rotations were to be considered. A set of twelve conformers of the N-formylmethionine molecule are then further analysed in terms of their relative stabilities, theoretically predicted harmonic vibrational frequencies, HOMO-LUMO energy gaps, ESP charges, rotational constants and dipole moments calculated using MP2/6-31++G(d,p) and B3LYP/6-311++G(d,p) levels. The calculated relative energy-range of the conformers at the MP2 level is 11.08 kcal mol^?1 (1 kcal = 4.1868 kJ), whereas the same obtained at the B3LYP level is 10.02 kcal mol^?1. The results of this study provide a good account of the role of four types of intramolecular H-bonds, namely O…H—O, O…H—N, O…H—C and N…H—C, in influencing the energies of the conformers as well as their conformational and vibrational spectroscopic aspects. The relative stability order of the conformers appears to depend on the level of theory used while the vibrational frequencies calculated at the B3LYP level are in better agreement with the experimental values.     

Conformational polymorphs of 22‐cyano‐N‐methyl‐5‐phenylpent‐2‐en‐4‐ynamide

Although the two polymorphic modifications, (I) and (II), of the title compound, C₁₃H₁₀N₂O, crystallize in the same space group (P2₁/c), their asymmetric units have Z′ values of 1 and 2, respectively. These are conformational polymorphs, since the mol­ecules in phases (I) and (II) adopt different rotations of the phenyl ring with respect the central 2‐cyano­carboxy­amino­prop‐2‐enyl fragment. Calculations of crystal packing using Cerius² [Molecular Simulations (1999). 9685 Scranton Road, San Diego, CA 92121, USA] have shown that (I) is more stable than (II), by 1.3 kcal mol^?1 for the crystallographically determined structures and by 1.56 kcal mol^?1 for the optimized structures (1 kcal mol^?1 = 4.184 kJ mol^?1). This difference is mainly attributed to the different strengths of the hydrogen bonding in the two forms.     

Binding Matter with Antimatter: The Covalent Positron Bond

We report sufficient theoretical evidence of the energy stability of the e⁺?H₂^2? molecule, formed by two H^? anions and one positron. Analysis of the electronic and positronic densities of the latter compound undoubtedly points out the formation of a positronic covalent bond between the otherwise repelling hydride anions. The lower limit for the bonding energy of the e⁺?H₂^2? molecule is 74 kJ mol^?1 (0.77 eV), accounting for the zero‐point vibrational correction. The formation of a non electronic covalent bond is fundamentally distinct from positron attachment to stable molecules, as the latter process is characterized by a positron affinity, analogous to the electron affinity.     

Computational study on the mechanism for the gas‐phase reaction of dimethyl disulfide with OH

The mechanisms for the reaction of CH₃SSCH₃ with OH radical are investigated at the QCISD(T)/6‐311++G(d,p)//B3LYP/6‐311++G(d,p) level of theory. Five channels have been obtained and six transition state structures have been located for the title reaction. The initial association between CH₃SSCH₃ and OH, which forms two low‐energy adducts named as CH₃S(OH)SCH₃ (IM1 and IM2), is confirmed to be a barrierless process, The S? S bond rupture and H? S bond formation of IM1 lead to the products P1(CH₃SH + CH₃SO) with a barrier height of 40.00 kJ mol^?1. The reaction energy of Path 1 is ?74.04 kJ mol^?1. P1 is the most abundant in view of both thermodynamics and dynamics. In addition, IMs can lead to the products P2 (CH₃S + CH₃SOH), P3 (H₂O + CH₂S + CH₃S), P4 (CH₃ + CH₃SSOH), and P5 (CH₄ + CH₃SSO) by addition‐elimination or hydrogen abstraction mechanism. All products are thermodynamically favorable except for P4 (CH₃ + CH₃SSOH). The reaction energies of Path 2, Path 3, Path 4, and Path 5 are ?28.42, ?46.90, 28.03, and ?89.47 kJ mol^?1, respectively. Path 5 is the least favorable channel despite its largest exothermicity (?89.47 kJ mol^?1) because this process must undergo two barriers of TS5 (109.0 kJ mol^?1) and TS6 (25.49 kJ mol^?1). Hopefully, the results presented in this study may provide helpful information on deep insight into the reaction mechanism. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Reaction rates for nucleophiles with cyanogen chloride: Comparison with two other digonal carbon compounds

The hydrolysis kinetics of CICN have been reinvestigated from pH 0.0–10.5 and from 18–40°C. In the pH range from 1–5, the hydrolysis rate is invariant and the activation parameters (ΔH? = 84 kJ mol^?1 and ΔS? = ?84 J mol^?1 K^?1) are consistent with water attack. In basic solution the rate is first order each in CICN and OH^? concentrations with parameters ΔH? and ΔS? equal to 82 kJ mol^?1 and + 54 J mol^?1 K^?1, respectively. The rate constants with 20 other donors have been measured. Nitrogen nucleophiles are more reactive than oxygen donors, and an alpha-effect is seen. The constants follow a pattern indicative of attack at carbon. Cyanate in its acid form reacts with nucleophiles. Further points on the cyanate rate–pH profile have been obtained. A chromate-catalyzed hydrolysis can contribute between pH 5–10. Some studies were made of the reaction of cyanate with hydrogen peroxide. Free energy correlations are presented.     

Sequential segregation of Sn and Sb in a Cu(111) single crystal

The sequential segregation of Sn and Sb to the surface of a Cu(111) single crystal was measured in the temperature range 400–1100 K by Auger electron spectroscopy. It was found that Sn with the higher diffusion coefficient first segregates to the surface and then is replaced by the slower‐segregating Sb. The results were fitted by a ternary segregation model yielding segregation energies (ΔG_Sn = 76.3 kJ mol^?1, ΔG_Sb = 95.9 kJ mol^?1), interaction parameters (Ω_SnCu = 3.8 kJ mol^?1, Ω_SbCu = 16.2 kJ mol^?1, Ω_SnSb = ?5.3 kJ mol^?1) and diffusion coefficients (D_0(Sn) = 1.8 × 10^?5 m² s^?1, E_Sn = 173 kJ mol^?1, D_0(Sb) = 6.0 × 10^?5 m² s^?1, E_Sb = 205 kJ mol^?1) for both species. The validity of the interaction coefficients and segregation energies was verified using the Guttman equations for equilibrium segregation in ternary systems. Copyright © 2003 John Wiley & Sons, Ltd.     

Ene reaction between 4-phenyl-1,2,4-triazoline-3,5-dione and hex-1-ene. The enthalpies,entropies, and volumes of activation and reaction in solution

The rates of an ene reaction between 4-phenyl-1,2,4-triazoline-3,5-dione and hex-1-ene were studied in a temperature range of 15–40 °C and in a pressure range of 1–2013 bar. The enthalpy of reaction in 1,2-dichloroethane (?158.2±1.0 kJ mol^?1), the enthalpy (51.3±0.5 kJ mol^?1), entropy (122±2 J mol^?1 K^?1), and volume of activation (?31.0±1.0 cm3 mol^?1), and the volume of this reaction (?26.6±0.3 cm³ mol^?1) were determined. The high exothermic effect of the reaction suggests its irreversibility.     

PREPARATION OF 1,3-DIPHOSHAALLENE FROM 1,2-DIPHOSPHACYCLOPROPANES: A THEORETICAL INVESTIGATION

Abstract

The ring opening of diphosphacyclopropane (1a), mono- (1b) and di-fluorodiphosphacyclopropane (1c) with methyllithium to give diphosphaallene is examined at the 3-21G(?) and 6-31G? Hartree-Fock level. In the first step, the diphosphacyclopropane opens to give the stable Li⁺/diphosphaallyl anion pair. The next step, formation of the phosphaallene, is endothermic unless an ionic salt (LiF) is produced, which can be further stabilized by solvent. The overall reaction energetics are 148.7 kJ Mol^?1 for 1a, -169.7 kJ mol^?1 for 1b, and - 137.8 kJ mol^?1 for 1c. The calculated ring strain energy for 1a is 61.8 kJ mol^?1.