Interaction and protection mechanism between Li@C(60) and nucleic acid bases (NABs): performance of PM6-DH2 on noncovalent interaction of NABs-Li@C60

To discuss the protection mechanism of DNA from radiation as well as assess the performance of PM6-DH2 on noncovalent interactions, the interaction of four nucleic acid bases (NABs) such as adenine (A), cytosine (C), guanine (G), and thymine (T), with Li@C(60) was extensively investigated with the-state-of-art theoretical methods describing noncovalent systems, like M06-2x, PBE-D, and PM6-DH2 methods. In the gas phase, the binding strength of NABs to Li@C(60) from M06-2x decreases in the sequence, G>C>A>T. As dispersion was explicitly included, PBE-D relatively enhances the binding of A and T and corrects the sequence to, G>A>C～T. PM6-DH2 predicted similar binding energies to those from PBE-D within 0.5 kcal/mol and the same binding sequence, suggesting that the PM6-DH2 method is promising for nano-scale systems. In the aqueous solution, binding of NABs-Li@C(60) is considerably decreased, and the M06-2X and PM6-D methods yield a different sequence from the gas phase, G>A>T>C. The encapsulation of Li atom results in a lower IP for Li@C(60) than those of NABs, and the dominant localization of single-occupied molecular orbital on Li@C(60) moiety of the complexes NABs-Li@C(60) further indicates that an electron would be ejected from Li@C(60) upon radiation and Li@C(60) is therefore able to protect DNA bases from radiation. In addition, it was revealed that Li prefers coordination with the hexagonal ring at Li@C(60) , which clarifies the existing controversy in this respect. Finally, Yang's reduced density gradient approach clearly shows that the weak and strong noncovalent interaction regions in the complexes, NABs-Li@C(60) and (NABs-Li@C(60) )(+).     

Transferable scoring function based on semiempirical quantum mechanical PM6-DH2 method: CDK2 with 15 structurally diverse inhibitors

A semiempirical quantum mechanical PM6-DH2 method accurately covering the dispersion interaction and H-bonding was used to score fifteen structurally diverse CDK2 inhibitors. The geometries of all the complexes were taken from the X-ray structures and were reoptimised by the PM6-DH2 method in continuum water. The total scoring function was constructed as an estimate of the binding free energy, i.e., as a sum of the interaction enthalpy, interaction entropy and the corrections for the inhibitor desolvation and deformation energies. The applied scoring function contains a clear thermodynamical terms and does not involve any adjustable empirical parameter. The best correlations with the experimental inhibition constants (ln K _i) were found for bare interaction enthalpy (r ² = 0.87) and interaction enthalpy corrected for ligand desolvation and deformation energies (r ² = 0.77); when the entropic term was considered, however, the correlation becomes worse but still acceptable (r ² = 0.52). The resulting correlation based on the PM6-DH2 scoring function is better than previously published function based on various docking/scoring, SAR studies or advanced QM/MM approach, however, the robustness is limited by number of available experimental data used in the correlation. Since a very similar correlation between the experimental and theoretical results was found also for a different system of the HIV-1 protease, the suggested scoring function based on the PM6-DH2 method seems to be applicable in drug design, even if diverse protein–ligand complexes have to be ranked.     

Prediction of trypsin/molecular fragment binding affinities by free energy decomposition and empirical scores

Two families of binding affinity estimation methodologies are described which were utilized in the SAMPL3 trypsin/fragment binding affinity challenge. The first is a free energy decomposition scheme based on a thermodynamic cycle, which included separate contributions from enthalpy and entropy of binding as well as a solvent contribution. Enthalpic contributions were estimated with PM6-DH2 semiempirical quantum mechanical interaction energies, which were modified with a statistical error correction procedure. Entropic contributions were estimated with the rigid-rotor harmonic approximation, and solvent contributions to the free energy were estimated with several different methods. The second general methodology is the empirical score LISA, which contains several physics-based terms trained with the large PDBBind database of protein/ligand complexes. Here we also introduce LISA+, an updated version of LISA which, prior to scoring, classifies systems into one of four classes based on a ligand's hydrophobicity and molecular weight. Each version of the two methodologies (a total of 11 methods) was trained against a compiled set of known trypsin binders available in the Protein Data Bank to yield scaling parameters for linear regression models. Both raw and scaled scores were submitted to SAMPL3. Variants of LISA showed relatively low absolute errors but also low correlation with experiment, while the free energy decomposition methods had modest success when scaling factors were included. Nonetheless, re-scaled LISA yielded the best predictions in the challenge in terms of RMS error, and six of these models placed in the top ten best predictions by RMS error. This work highlights some of the difficulties of predicting binding affinities of small molecular fragments to protein receptors as well as the benefit of using training data.     

Blind prediction of SAMPL4 cucurbit[7]uril binding affinities with the mining minima method

Accurate methods for predicting protein–ligand binding affinities are of central interest to computer-aided drug design for hit identification and lead optimization. Here, we used the mining minima (M2) method to predict cucurbit[7]uril binding affinities from the SAMPL4 blind prediction challenge. We tested two different energy models, an empirical classical force field, CHARMm with VCharge charges, and the Poisson–Boltzmann surface area solvation model; and a semiempirical quantum mechanical (QM) Hamiltonian, PM6-DH+, coupled with the COSMO solvation model and a surface area term for nonpolar solvation free energy. Binding affinities based on the classical force field correlated strongly with the experiments with a correlation coefficient (R²) of 0.74. On the other hand, binding affinities based on the QM energy model correlated poorly with experiments (R² = 0.24), due largely to two major outliers. As we used extensive conformational search methods, these results point to possible inaccuracies in the PM6-DH+ energy model or the COSMO solvation model. Furthermore, the different binding free energy components, solute energy, solvation free energy, and configurational entropy showed significant deviations between the classical M2 and quantum M2 calculations. Comparison of different classical M2 free energy components to experiments show that the change in the total energy, i.e. the solute energy plus the solvation free energy, is the key driving force for binding, with a reasonable correlation to experiment (R² = 0.56); however, accounting for configurational entropy further improves the correlation.     

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10–20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4–5.2 kJ/mol and a correlation coefficient (R²) of 0.77–0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD?=?3–8 kJ/mol and R²?=?0.1–0.9), but the results were improved compared to previous studies of this system with similar methods.     

Computational structural determination and energy landscape analysis of the hepatic carcinogen 2-(acetylamino)fluorene

 2-(Acetylamino)fluorene (AAF), a potent mutagen and a prototypical example of the mutagenic aromatic amines, forms covalent adducts to DNA after metabolic activation in the liver. A benchmark study of AAF is presented using a number of the most widely used molecular mechanics and semiempirical computational methods and models. The results are compared to higher-level quantum calculations and to experimentally obtained crystal structures. Hydrogen bonding between AAF molecules in the crystal phase complicates the direct comparison of gas-phase theoretical calculations with experiment, so Hartree–Fock (HF) and Becke–Perdew (BP) density functional theory (DFT) calculations are used as benchmarks for the semiempirical and molecular mechanics results. Systematic conformer searches and dihedral energy landscapes were carried out for AAF using the SYBYL and MMFF94 molecular mechanics force fields; the AM1, PM3 and MNDO semiempirical quantum mechanics methods; HF using the 3-21G*and 6-31G* basis sets; and DFT using the nonlocal BP functional and double numerical polarization basis sets. MMFF94, AM1, HF and DFT calculations all predict the same planar structures, whereas SYBYL, MNDO and PM3 all predict various nonplanar geometries. The AM1 energy landscape is in substantial agreement with HF and DFT predictions; MMFF94 is qualitatively similar to HF and DFT; and the MNDO, PM3 and SYBYL results are qualitatively different from the HF and DFT results and from each other. These results are attributed to deficiencies in MNDO, PM3 and SYBYL. The MNDO, PM3 and SYBYL models may be unreliable for compounds in which an amide group is immediately adjacent to an aromatic ring. Received: 26 May 2002 / Accepted: 12 December 2002 / Published online: 14 February 2003     

Semiempirical calculations of binding enthalpy for protein–ligand complexes

A systematic semiempirical quantum mechanical study of the interactions between proteins and ligands has been performed to determine the ability of this approach for the accurate estimation of the enthalpic contribution to the binding free energy of the protein–ligand systems. This approach has been applied for eight test protein–ligand complexes with experimentally known binding enthalpies. The calculations were performed using the semiempirical PM3 approach incorporated in the MOPAC 97, ZAVA originally elaborated in Algodign, and MOPAC 2002 with MOZYME facility packages. Special attention was paid to take into account structural water molecules, which were located in the protein–ligand binding site. It was shown that the results of binding enthalpy calculations fit experimental data within ～2 kcal/mol in the presented approach. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Theoretical studies on the heats of formation and the interactions among the difluoroamino groups in polydifluoroaminocubanes

The heats of formation (HOFs) were calculated for a series of polydifluoroaminocubanes by using density functional theory (DFT), Hartree-Fock, and MP2 method with 6-31G basis set as well as semiempirical methods. The cubane skeleton was not broken in the process of designing isodesmic reactions; i.e., the cubane skeleton was chosen for a reference compound. The contribution of difluoroamino group to the heat of formation deviates from group additivity. The semiempirical MO (MNDO, AM1, and PM3) methods did not produce accurate and reliable results for the HOFs of the title compounds. The relationship between HOFs and molecular structures was discussed. It was found that the HOFs decreased dramatically initially and then gradually with each difluoroamino group attached to the cubane skeleton. The distance between difluoroamino groups influences the values of HOFs. The interacting energies of polydifluoroaminocubanes are in the range 14-20 kJ/mol. The interaction of neighbor difluoroamino groups discords with the group additivity. The average interaction energy between the nearest-neighbor NF(2) group in the most stable conformer of octadifluoroaminocubane is 13.94 kJ/mol at the B3LYP/6-31G level. The NF(2) group can rotate freely around the C-N bond. The relative stability of the title compounds was accessed on the basis of the calculated HOFs, the energy gaps between the frontier orbitals, and the bond order of C-NF(2). These results provide basic information for the molecular design of novel high energetic density materials.     

Activation Energy and Transition State Determination of the Olefin Insertion Process of Metallocene Catalysts Using a Semiempirical Molecular Orbital Calculation

The transition state of the olefin insertion process of metallocene catalysts can be determined by adopting the semiempirical PM3 model. In computational chemistry, the computational methods most employed are the ab initio method and density functional theory, which are very time consuming. The semiempirical molecular orbital method requires much less computational resources than the above methods. However, the accuracy and reliability of the semiempirical molecular orbital method remains to be determined. The PM3 model is the most recently developed the semiempirical molecular orbital method and can also be applied to transition metal calculations. This study is intended to investigate the reliability of computational results determined using semiempirical PM3 model on metallocene catalysts through comparison with published results on the density functional theory (DFT). The saddle point finding procedure is adopted to find the transition state of the ethylene insertion process of metallocene catalysts. Results on the geometry and energy trends of the ethylene insertion process of metallocene catalysts determined using the PM3 model are in good agreement with the DFT results. In addition, the saddle point of the potential energy surface of ethylene insertion is verified in accordance with the eigenvalue of the vibrational frequency spectrum. Correct eigenvalues indicate that the correct saddle point of the potential energy surface of ethylene insertion has been successfully located. Hence, the eigenvalue of the vibrational frequency spectrum is a valuable reference in terms of saddle point justification. Computational results and vibrational frequency spectrum analysis demonstrate that the PM3 model can be used to locate the correct saddle point of the potential energy surface. The results obtained using the PM3 model confirm that the eigenvalue of the transition state lies nearly on the vibrational frequency spectrum. The eigenvalues are also analyzed, providing a valuable reference for further studies of the transition state of olefin insertion of metallocene catalysts. The activation energies for the olefin insertion reaction are also studied for evaluation of the catalyst.     

Ab initio and direct quasiclassical-trajectory study of the F+CH4-->HF+CH3 reaction

We present an electronic structure and dynamics study of the F+CH4-->HF+CH3 reaction. CCSD(T)/aug-cc-pVDZ geometry optimizations, harmonic-frequency, and energy calculations indicate that the potential-energy surface is remarkably isotropic near the transition state. In addition, while the saddle-point F-H-C angle is 180 degrees using MP2 methods, CCSD(T) geometry optimizations predict a bent transition state, with a 153 degrees F-H-C angle. We use these high-quality ab initio data to reparametrize the parameter-model 3 (PM3) semiempirical Hamiltonian so that calculations with the improved Hamiltonian and employing restricted open-shell wave functions agree with the higher accuracy data. Using this specific-reaction-parameter PM3 semiempirical Hamiltonian (SRP-PM3), we investigate the reaction dynamics by propagating quasiclassical trajectories. The results of our calculations using the SRP-PM3 Hamiltonian are compared with experiments and with the estimates of two recently reported potential-energy surfaces. The trajectory calculations using the SRP-PM3 Hamiltonian reproduce quantitatively the measured HF vibrational distributions. The calculations also agree with the experimental HF rotational distributions and capture the essential features of the excitation function. The results of the SRP semiempirical Hamiltonian developed here clearly improve over those using the two prior potential-energy surfaces and suggest that reparametrization of semiempirical Hamiltonians is a promising strategy to develop accurate potential-energy surfaces for reaction dynamics studies of polyatomic systems.     

Theoretical study of hydrogen bonding in homodimers and heterodimers of amide, boronic acid, and carboxylic acid, free and in encapsulation complexes

The homodimers and the heterodimers of two amides, two boronic acids, and two carboxylic acids have been calculated in the gas phase and in N,N-dimethylformamide (DMF) and CCl(4) solvents using the DFT (M06-2X and M06-L) and the MP2 methods in conjunction with the 6-31G(d,p) and 6-311+G(d,p) basis sets. Furthermore, their pairwise coencapsulation was studied to examine its effect on the calculated properties of the hydrogen bonds at the ONIOM[M06-2X/6-31G(d,p);PM6], ONIOM[MP2/6-31G(d,p); PM6], and M06-2X/6-31G(d,p) levels of theory. The present work is directed toward the theoretical rationalization and interpretation of recent experimental results on hydrogen bonding in encaptulation complexes [D. Ajami et al. J. Am. Chem. Soc. 2011, 133, 9689-9691]. The calculated dimerization energy (ΔE) values range from 0.74 to 0.35 eV for the different dimers in the gas phase, with the ordering carboxylic homodimers > amide-carboxylic dimers > amide homodimers > boronic-carboxylic dimers > amide-boronic dimers > boronic homodimers. In solvents, generally smaller ΔE values are calculated with only small variations in the ordering. In the capsule, the ΔE values range between 0.67 and 0.33 eV with practically the same ordering as in the gas phase. The calculated % distributions of the encapsulated dimers, taking into account statistical factors, are in agreement with the experimental distribution, where the occurrence of boronic homodimer dominates, even though it is calculated to have the smallest ΔE.     

A sobering assessment of small‐molecule force field methods for low energy conformer predictions

We have carried out a large scale computational investigation to assess the utility of common small‐molecule force fields for computational screening of low energy conformers of typical organic molecules. Using statistical analyses on the energies and relative rankings of up to 250 diverse conformers of 700 different molecular structures, we find that energies from widely used classical force fields (MMFF94, UFF, and GAFF) show unconditionally poor energy and rank correlation with semiempirical (PM7) and Kohn–Sham density functional theory (DFT) energies calculated at PM7 and DFT optimized geometries. In contrast, semiempirical PM7 calculations show significantly better correlation with DFT calculations and generally better geometries. With these results, we make recommendations to more reliably carry out conformer screening.     

PDDG/PM3 and PDDG/MNDO: improved semiempirical methods

Two new semiempirical methods employing a Pairwise Distance Directed Gaussian modification have been developed: PDDG/PM3 and PDDG/MNDO; they are easily implemented in existing software, and yield heats of formation for compounds containing C, H, N, and O atoms with significantly improved accuracy over the standard NDDO schemes, PM5, PM3, AM1, and MNDO. The PDDG/PM3 results for heats of formation also show substantial improvement over density functional theory with large basis sets. The PDDG modifications consist of a single function, which is added to the existing pairwise core repulsion functions within PM3 and MNDO, a reparameterized semiempirical parameter set, and modified computation of the energy of formation of a gaseous atom. The PDDG addition introduces functional group information via pairwise atomic interactions using only atom-based parameters. For 622 diverse molecules containing C, H, N, and O atoms, mean absolute errors in calculated heats of formation are reduced from 4.4 to 3.2 kcal/mol and from 8.4 to 5.2 kcal/mol using the PDDG modified versions of PM3 and MNDO over the standard versions, respectively. Several specific problems are overcome, including the relative stability of hydrocarbon isomers, and energetics of small rings and molecules containing multiple heteroatoms. The internal consistency of PDDG energies is also significantly improved, enabling more reliable analysis of isomerization energies and trends across series of molecules; PDDG isomerization energies show significant improvement over B3LYP/6-31G* results. Comparison of heats of formation, ionization potentials, dipole moments, isomer, and conformer energetics, intermolecular interaction energies, activation energies, and molecular geometries from the PDDG techniques is made to experimental data and values from other semiempirical and ab initio methods.     

Ab initio treatment of the chemical reaction precursor complex Cl(2P)-HF. 1. Three-dimensional diabatic potential energy surfaces

The three adiabatic potential surfaces of the Cl(2P)-HF complex that correlate with the 2P ground state of the Cl atom were calculated with the ab initio RCCSD(T) method (partially spin-restricted coupled cluster theory including single and double excitations and perturbative correction for the triples). With the aid of a geometry-dependent diabatic mixing angle, calculated by the complete active space self-consistent field (CASSCF) and multireference configuration-interaction (MRCI) methods, these adiabatic potential surfaces were converted to a set of four distinct diabatic potential surfaces required to define the full 3 x 3 matrix of diabatic potentials. Each of these diabatic potential surfaces was expanded in terms of the appropriate spherical harmonics in the angle theta between the HF bond axis r and the Cl-HF intermolecular axis R. The dependence of the expansion coefficients on the Cl-HF distance R and the HF bond length r(HF) was fit to an analytic form. The strongest binding occurs for the hydrogen-bonded linear Cl-HF geometry, with D(e) = 676.5 cm(-1) and R(e) = 6.217 a0 when r(HF) = r(e) = 1.7328 a0. This binding energy D(e) depends strongly on r(HF), with larger r(HF) causing stronger binding. An important contribution to the binding energy is provided by the interaction between the quadrupole moment of the Cl(2P) atom and the dipole of HF. In agreement with this electrostatic picture, the ground state of linear Cl-HF is a 2-fold degenerate electronic Pi state. For the linear Cl-FH geometry the states are in opposite order, i.e., the Sigma state is lower in energy than the Pi state. The following paper in this issue describes full three-dimensional computations of the bound states of the Cl-HF complex, based on the ab initio diabatic potentials of this paper.     

Three-body potential energy terms for methane trimers

An SCF LCAO MO calculation on the methane–methane–methane system is presented, in order to analyze the deviation from pairwise additivity of the interaction energy. Three-body terms are shown to be remarkably similar to those of noble gas trimers both in magnitude and in their dependence on the geometrical arrangements of the three molecules.     

Influence of calculation level and effect of methylation on axial/equatorial equilibria in piperidines

A detailed conformational analysis was performed on the chair forms of piperidine, N-methylpiperidine, and some methylated derivatives using Hartree–Fock (HF) and MP2 ab initio methods with several basis sets (from 3–21G to 6–311++G**), and the most widely used semiempirical approaches (MNDO, AM1, and PM3). It was found that the use of polarized basis sets at the HF level is adequate enough for the prediction of conformational preferences in the axial/equatorial equilibrium of the N-R group in piperidines. On the other hand, the inclusion of electron correlation becomes necessary for predicting the axial/equatorial energy differences of the equilibria of the methyl group. Semiempirical methods are not recommended, because AM1 and PM3 predict opposite stabilities to those obtained experimentally and MNDO ring geometries are systematically too flat. The origin of the conformational stabilities was interpreted in terms of the natural bond orbital analysis of the HF/6–31G** wave functions. The equatorial preferences in the N-H equilibria is mainly due to lower Lewis energies, although delocalization of the nitrogen lone pair is favored in N-H axial forms. N-Methylation increases the equatorial M-Me preferences, because the Lewis energy of axial N-Me forms increases due to larger 1,3-diaxial interactions. Geometrical trends associated with the delocalization of the nitrogen lone pair and with interactions between the introduced N-R and C-Me groups were discussed and related to the degree of planarity of the six-membered ring by means of the puckering coordinates defined by Pople and Cremer. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 961–976, 1998     

Theoretical study of C24N4 molecule

Both ab initio 6-31G, 3-21G and STO-3G basis sets and semiempirical PM3 and AM1 molecular orbital calculations are carried out on the C₂₄N₄ molecule of the T_d symmetry group. Results on the fully optimized structure which constrained T_d symmetry, molecular orbitals and vibrational frequency were obtained by both ab initio and semiempirical methods. The binding energy and various thermodynamic properties were also calculated via the PM3 and AM1 semiempirical methods. All the evidence of this work proves that the C₂₄N₄ molecule is stable and that its four six-membered rings with a remarkable delocalized C…C bond are similar to the related rings in the C₆₀ buckminsterfullerene structure.     

Calculation of Host-Guest Binding Affinities Using a Quantum-Mechanical Energy Model

The prediction of protein-ligand binding affinities is of central interest in computer-aided drug discovery, but it is still difficult to achieve a high degree of accuracy. Recent studies suggesting that available force fields may be a key source of error motivate the present study, which reports the first mining minima (M2) binding affinity calculations based on a quantum mechanical energy model, rather than an empirical force field. We apply a semi-empirical quantum-mechanical energy function, PM6-DH+, coupled with the COSMO solvation model, to 29 host-guest systems with a wide range of measured binding affinities. After correction for a systematic error, which appears to derive from the treatment of polar solvation, the computed absolute binding affinities agree well with experimental measurements, with a mean error 1.6 kcal/mol and a correlation coefficient of 0.91. These calculations also delineate the contributions of various energy components, including solute energy, configurational entropy, and solvation free energy, to the binding free energies of these host-guest complexes. Comparison with our previous calculations, which used empirical force fields, point to significant differences in both the energetic and entropic components of the binding free energy. The present study demonstrates successful combination of a quantum mechanical Hamiltonian with the M2 affinity method.     

Correlation between MO eigenvectors and enthalpies of formation for alkanes

A new model for the calculation of enthalpies of formation of alkanes (up to C₈) is presented. An additive bond energy scheme, using the experimental methane and diamond values for the CH and CC bond energies, respectively, is supplemented by correction for the CC π antibonding character of the highest occupied molecular orbitals (HOMOs), effectively adjusting the CC bond energies. The effect is calculated by the summation of products of appropriate eigenvectors from semiempirical PM3 or HF/STO-3G calculations, after orthogonal transformation. The enthalpy of formation can then be expressed in terms of only one adjustable parameter. With HF/STO-3G eigenvectors, the mean discrepancy between experimental and calculated enthalpies of formation, after a one-parameter correction for 1,4 steric interactions, is 2.2 kJ mol⁻¹, comparable with more highly parameterized models. The results using PM3 eigenvectors are less satisfactory, probably on account of the neglect of overlap in the semiempirical scheme.