Actinium coordination chemistry: A density functional theory study with monodentate and bidentate ligands

In the current study, the coordination chemistry of nine-coordinate Ac(III) complexes with 35 monodentate and bidentate ligands was investigated using density functional theory (DFT) in terms of their geometries, charges, reaction energies, and bonding interactions. The energy decomposition analysis with naturals orbitals for chemical valence (EDA-NOCV) and the quantum theory of atoms in molecules (QTAIM) were employed as analysis methods. Trivalent Ac exhibits the highest affinities toward hard acids (such as charged oxophilic donors, fluoride), so its classification as a hard acid is justified. Natural population analysis quantified the involvement of 5f orbitals on Ac to be about 30% of total valence electron natural configuration indicating that Ac is a member of the actinide series. Pearson correlation coefficients were used to study the pairwise correlations among the bond lengths, ΔG reaction energies, charges on Ac and donor atoms, and data from EDA-NOCV and QTAIM. Strong correlations and anticorrelations were found between Voronoi charges on donor atoms with ΔG, EDA-NOCV interaction energies and QTAIM bond critical point densities.     

Higher order alchemical derivatives from coupled perturbed self-consistent field theory

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals.     

Electrostatic interactions in molecular mechanics (MM2) calculations via PEOE partial charges I. Haloalkanes

The PEOE (partial equalization of orbital electronegativity) procedure has been modified slightly and reparametrized for haloalkanes to calculate partial atomic charges suitable for evaluation of dipole moments and electrostatic energies in conjunction with molecular mechanics (MM2) calculations. Dipole moments of 66 haloalkanes are calculated with an average absolute deviation of 0.14 D from experimental values. The conformational energies of 40 compounds have been calculated and the agreement with experimental data is generally good and compares well with calculations by the IDME (induced dipole moment and energy) method. In addition, carbon and proton charges correlate well with C-1s core binding energies and ¹H-NMR (nuclear magnetic resonance) shifts for halomethanes. The most striking benefit of treating electrostatics through a set of partial charges compared to the standard MM2 bond dipole approach is demonstrated by calculations on 1,4-disubstituted cyclohexanes, for which standard MM2 fails to predict the most stable conformation.     

X‐ray photoelectron and carbon Kα emission measurements and calculations of O‐, CO‐, N‐, and S‐containing substances

X‐ray fluorescence measurements for O‐containing [polyethylene oxide, polyvinyl alcohol, polyvinyl methyl ether], CO‐containing [polyvinyl methyl ketone, polyethylene terephthalate], N‐containing [poly‐4‐vinylpyridine (P4VP), polyaniline oligomer (PAO)], and S‐containing [polyphenylene sulfide] substances are presented. Carbon Kα X‐ray emission spectra (XES) and X‐ray photoelectron spectra (XPS) are compared with our DFT calculations performed with the Amsterdam density functional (ADF) program. The combined analysis of valence XPS and carbon Kα XES allows us to determine the individual contributions from pσ‐ and pπ‐bonding molecular orbitals of the polymers. The ΔSCF calculations yield the accurate C1s core‐electron binding energies (CEBEs) for all carbon sites of the organic compound. We calculate all CEBEs of the model molecules using the ΔE _KS approach. Our simulated C1s photoelectron and C Kα emission spectra are in good agreement with our measurements. We also obtain WD (work function and the other energies) values for the polymers and PAO from the difference between calculated (gas‐phase) and measured (solid) CEBE values. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 162–172, 2007     

Ab initio calculation of the interaction energy in the P2 binding pocket of HIV‐1 protease

Interactions at the P2 binding pocket of human immunodeficiency virus type 1 (HIV‐1) protease have been studied using calculated interaction energies for model systems that mimic this binding pocket. Models were built for the P2 pocket of HIV‐1 protease in complex with TMC114, nelfinavir, and amprenavir. A two‐step procedure was applied. In the first step, the size of the model system was confined to ～40 atoms, and the interaction energy was calculated at different computational levels. In the second step, the size of the system was increased to 138 atoms, and the calculations were only performed at the HF/6‐31G** level. The interaction energy of the HIV‐1 protease/TMC114 complex was found to be more favorable than the interaction energies of the other complexes because of the additional hydrogen bond interaction this inhibitor is able to make with the HIV‐1 protease backbone. The results of the calculations are supported by stockholder charges and electrostatic potential maps. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Supramolecular binding thermodynamics by dispersion-corrected density functional theory

The equilibrium association free enthalpies ΔG(a) for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG(a) values in the range 0 to -21?kcal?mol(-1) (on average -6?kcal?mol(-1) ) are investigated. The theoretical approach employs a (nondynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to determine structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low-lying vibrational modes are treated by a free-rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60?kcal?mol(-1) (up to 200?% of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG(a) values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG(a) values with errors of only 2?kcal?mol(-1) on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300-400 atoms. The various contributions to binding and enthalpy-entropy compensations are discussed.     

CORE BINDING ENERGIES OF SOME METAL β-DIKETONATES AND β-DIKETONES IN THE VAPOR PHASE

Abstract

The vapor-phase core binding energies of some tris β-diketonates of A1(III), V(III), Cr(III), and Fe(III) and of two β-diketones have been measured. The rather large shifts observed for the A1 2p energies are believed to be caused mainly by changes in the electrostatic potential at the A1 atom due to changes in the charges of the ligand atoms. Considerable resonance relaxation energy is associated with the core ionization of the carbonyl carbon atoms and the CH carbon atoms. The data for the metal hexafluoroacetylacetonates show that the metal d orbitals are not significantly involved in the bonding and suggest that there is no strong ligand → metal donor bonding.     

Koopmans-like approximation in the Kohn-Sham method and the impact of the frozen core approximation on the computation of the reactivity parameters of the density functional theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.     

Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods

With dispersion-corrected density functional theory (DFT-D3) intermolecular interaction energies for a diverse set of noncovalently bound protein-ligand complexes from the Protein Data Bank are calculated. The focus is on major contacts occurring between the drug molecule and the binding site. Generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are used. DFT-D3 interaction energies are benchmarked against the best available wave function based results that are provided by the estimated complete basis set (CBS) limit of the local pair natural orbital coupled-electron pair approximation (LPNO-CEPA/1) and compared to MP2 and semiempirical data. The size of the complexes and their interaction energies (ΔE(PL)) varies between 50 and 300 atoms and from -1 to -65 kcal/mol, respectively. Basis set effects are considered by applying extended sets of triple- to quadruple-ζ quality. Computed total ΔE(PL) values show a good correlation with the dispersion contribution despite the fact that the protein-ligand complexes contain many hydrogen bonds. It is concluded that an adequate, for example, asymptotically correct, treatment of dispersion interactions is necessary for the realistic modeling of protein-ligand binding. Inclusion of the dispersion correction drastically reduces the dependence of the computed interaction energies on the density functional compared to uncorrected DFT results. DFT-D3 methods provide results that are consistent with LPNO-CEPA/1 and MP2, the differences of about 1-2 kcal/mol on average (<5% of ΔE(PL)) being on the order of their accuracy, while dispersion-corrected semiempirical AM1 and PM3 approaches show a deviating behavior. The DFT-D3 results are found to depend insignificantly on the choice of the short-range damping model. We propose to use DFT-D3 as an essential ingredient in a QM/MM approach for advanced virtual screening approaches of protein-ligand interactions to be combined with similarly "first-principle" accounts for the estimation of solvation and entropic effects.     

pH-induced protonation of lysine in aqueous solution causes chemical shifts in X-ray photoelectron spectroscopy

We demonstrate the applicability of X-ray photoelectron spectroscopy to obtain charge- and site-specific electronic structural information of biomolecules in aqueous solution. Changing the pH of an aqueous solution of lysine from basic to acidic results in nitrogen 1s and carbon 1s chemical shifts to higher binding energies. These shifts are associated with the sequential protonation of the two amino groups, which affects both charge state and hydrogen bonding to the surrounding water molecules. The N1s chemical shift is 2.2 eV, and for carbon atoms directly neighboring a nitrogen the shift for C1s is approximately 0.4 eV. The experimental binding energies agree reasonably with our calculated energies of lysine(aq) for different pH values.     

Carbon 1s excitation spectroscopy of propyne, trifluoropropyne, and propargyl alcohol

The C 1s excitation spectra of propyne (HC2CH3), 3,3,3-trifluoropropyne (HC2CF3), and propargyl alcohol (HC3CH3OH) have been studied using synchrotron radiation and ion time-of-flight mass spectrometry. Discrete peaks below the carbon 1s ionization thresholds are compared and assigned, aided in part by ab-initio calculations incorporating an explicit C 1s hole. Calculated C 1s ionization potentials are in good agreement with previously reported experimental values. Calculated absolute excitation energies consistently underestimate the transition term values, but calculated relative excitation energies and intensities are in good agreement with the experimental results. The spectra are dominated by intense C 1s --> pi transitions. In the case of propyne, C 1s excitations from each of the three chemically inequivalent carbon atoms are observed. The effect of electronegative substitution is found to be different for the C 1s --> Rydberg transitions than for transitions to unoccupied valence levels, with Rydberg transition energies shifting with changes in the C 1s ionization potentials but valence transition energies showing only small changes with electronegative substitution. The C 1s (3a1,4a1) --> pi (6e) transitions of trifluoropropyne are shifted to lower energy relative to propyne even though the electronegative fluorine atoms cause a significant shift to higher energy in the corresponding C 1s IPs.     

Localized exchange-correlation potential from second-order self-energy for accurate Kohn-Sham energy gap

A local Kohn-Sham (KS) exchange-correlation potential is derived by localizing the second-order self-energy operator, using approximations to the linear response Sham-Schlüter equation. Thanks to the use of the resolution-of-identity technique for the calculation of the self-energy matrix elements, the method is very efficient and can be applied to large systems. The authors investigate the KS energy gaps and lowest excitation energies of atoms and small- and medium-size molecules. Reference KS energy gaps (from accurate densities) of atoms and small molecules can be reproduced with great accuracy. For larger systems they found that the KS energy gap is smaller than the one obtained from the local-density approximation, showing the importance of an ab initio correlation in the Kohn-Sham potential.     

Physical quantity of residue electrostatic energy in flavin mononucleotide binding protein dimer

The electrostatic (ES) energy of each residue was for the first time quantitatively evaluated in a flavin mononucleotide binding protein (FBP). A residue electrostatic energy (RES) was obtained as the sum of the ES energies between atoms in each residue and all other atoms in the FBP dimer using atomic coordinates obtained by a molecular dynamics (MD) simulation. ES is one of the most important energies among the interaction energies in a protein. It is determined from the RES, the residues which mainly contribute to stabilize the structure of each subunit, and the binding energy between two subunits can be estimated. The RES of all residues in subunit A (Sub A) and subunit B (Sub B) were attractive forces, even though the residues contain net negative or positive charges. This reveals that the ES energies of any of the residues can contribute to stabilize the protein structure. The total binding ES energy over all residues among the subunits was distributed between −0.2 to −1.2 eV (mean = −0.67 eV) from the MD simulation time.     

Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.     

The correlation of core replacement energies with nonbonding s electron density

Core replacement energies are calculated for nitrogen and oxygen in various gaseous cations from accurate core binding energies and thermodynamic data. The values for a given element differ in some cases by much more than the experimental errors. These chemical shifts in core replacement energy can be rationalized by recognizing that they are equal to the shifts in the energy of transfering an electron from a core level to a nucleus. As expected, relatively endothermic core replacement energies are found for atoms which have a high density of nonbonding valence s electrons.     

Effect of the Solute Cavity on the Solvation Energy and its Derivatives within the Framework of the Gaussian Charge Scheme

The treatment of the solvation charges using Gaussian functions in the polarizable continuum model results in a smooth potential energy surface. These charges are placed on top of the surface of the solute cavity. In this article, we study the effect of the solute cavity (van der Waals-type or solvent-excluded surface-type) using the Gaussian charge scheme within the framework of the conductor-like polarizable continuum model on (a) the accuracy and computational cost of the self-consistent field (SCF) energy and its gradient and on (b) the calculation of free energies of solvation. For that purpose, we have considered a large set of systems ranging from few atoms to more than 200 atoms in different solvents. Our results at the DFT level using the B3LYP functional and the def2-TZVP basis set show that the choice of the solute cavity does neither affect the accuracy nor the cost of calculations for small systems (< 100 atoms). For larger systems, the use of a vdW-type cavity is recommended, as it prevents small oscillations in the gradient (present when using a SES-type cavity), which affect the convergence of the SCF energy gradient. Regarding the free energies of solvation, we consider a solvent-dependent probe sphere to construct the solvent-accessible surface area required to calculate the nonelectrostatic contribution to the free energy of solvation. For this part, our results for a large set of organic molecules in different solvents agree with available experimental data with an accuracy lower than 1 kcal/mol for both polar and nonpolar solvents.     

QTAIM charge-charge flux-dipole flux interpretation of electronegativity and potential models of the fluorochloromethane mean dipole moment derivatives

Infrared fundamental vibrational intensities and quantum theory atoms in molecules (QTAIM) charge-charge flux-dipole flux (CCFDF) contributions to the polar tensors of the fluorochloromethanes have been calculated at the QCISD/cc-pVTZ level. A root-mean-square error of 20.0 km mol(-1) has been found compared to an experimental error estimate of 14.4 and 21.1 km mol(-1) for MP2/6-311++G(3d,3p) results. The errors in the QCISD polar tensor elements and mean dipole moment derivatives are 0.059 e when compared with the experimental values. Both theoretical levels provide results showing that the dynamical charge and dipole fluxes provide significant contributions to the mean dipole moment derivatives and tend to be of opposite signs canceling one another. Although the experimental mean dipole moment derivative values suggest that all the fluorochloromethane molecules have electronic structures consistent with a simple electronegativity model with transferable atomic charges for their terminal atoms, the QTAIM/CCFDF models confirm this only for the fluoromethanes. Whereas the fluorine atom does not suffer a saturation effect in its capacity to drain electronic charge from carbon atoms that are attached to other fluorine and chlorine atoms, the zero flux electronic charge of the chlorine atom depends on the number and kind of the other substituent atoms. Both the QTAIM carbon charges (r = 0.990) and mean dipole moment derivatives (r = 0.996) are found to obey Siegbahn's potential model for carbon 1s electron ionization energies at the QCISD/cc-pVTZ level. The latter is a consequence of the carbon mean derivatives obeying the electronegativity model and not necessarily to their similarities with atomic charges. Atomic dipole contributions to the neighboring atom electrostatic potentials of the fluorochloromethanes are found to be of comparable size to the atomic charge contributions and increase the accuracy of Siegbahn's model for the QTAIM charge model results. Substitution effects of the hydrogen, fluorine, and chlorine atoms on the charge and dipole flux QTAIM contributions are found to be additive for the mean dipole derivatives of the fluorochloromethanes.     

Supramolecular Binding Thermodynamics by Dispersion‐Corrected Density Functional Theory

The equilibrium association free enthalpies ΔG_a for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG_a values in the range 0 to ?21 kcal mol^?1 (on average ?6 kcal mol^?1) are investigated. The theoretical approach employs a (nondynamic) single‐structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT‐D3) with extended basis sets (triple‐ζ and quadruple‐ζ quality) is used to determine structures and gas‐phase interaction energies (ΔE), the COSMO‐RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro‐vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low‐lying vibrational modes are treated by a free‐rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range ?5 to ?60 kcal mol^?1 (up to 200 % of ΔE). Inclusion of three‐body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG_a values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG_a values with errors of only 2 kcal mol^?1 on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300–400 atoms. The various contributions to binding and enthalpy–entropy compensations are discussed.     

Partition coefficients of methylated DNA bases obtained from free energy calculations with molecular electron density derived atomic charges

Partition coefficients serve in various areas as pharmacology and environmental sciences to predict the hydrophobicity of different substances. Recently, they have also been used to address the accuracy of force fields for various organic compounds and specifically the methylated DNA bases. In this study, atomic charges were derived by different partitioning methods (Hirshfeld and Minimal Basis Iterative Stockholder) directly from the electron density obtained by electronic structure calculations in a vacuum, with an implicit solvation model or with explicit solvation taking the dynamics of the solute and the solvent into account. To test the ability of these charges to describe electrostatic interactions in force fields for condensed phases, the original atomic charges of the AMBER99 force field were replaced with the new atomic charges and combined with different solvent models to obtain the hydration and chloroform solvation free energies by molecular dynamics simulations. Chloroform–water partition coefficients derived from the obtained free energies were compared to experimental and previously reported values obtained with the GAFF or the AMBER‐99 force field. The results show that good agreement with experimental data is obtained when the polarization of the electron density by the solvent has been taken into account, and when the energy needed to polarize the electron density of the solute has been considered in the transfer free energy. These results were further confirmed by hydration free energies of polar and aromatic amino acid side chain analogs. Comparison of the two partitioning methods, Hirshfeld‐I and Minimal Basis Iterative Stockholder (MBIS), revealed some deficiencies in the Hirshfeld‐I method related to the unstable isolated anionic nitrogen pro‐atom used in the method. Hydration free energies and partitioning coefficients obtained with atomic charges from the MBIS partitioning method accounting for polarization by the implicit solvation model are in good agreement with the experimental values. © 2018 Wiley Periodicals, Inc.