Semiempirical Quantum Mechanical Methods Research Articles

Physicochemical properties of exogenous molecules correlated with their biological efficacy as protectors against carcinogenesis and inflammation

A large number of molecules referred to here as M, several of which are extracted from plants, belong to different chemical classes and exhibit chemoprotective activity against carcinogenesis and inflammation in rodents and in vitro cell culture. The aim of this article is to review and analyse our previous investigations on linear correlations observed between physicochemical parameters of the tested molecules M and their biological efficacies measured in vivo and/or in vitro. The principal physicochemical parameters studied characterise the energy required to oxidise M into M•+, E(M•+/M), namely its first vertical ionisation potential, and the energy liberated by the addition of an electron to M, i.e. its vertical electron affinity. These physicochemical properties were determined experimentally using diverse techniques and theoretically using mainly semiempirical (AM1) and density functional theory (DFT) quantum mechanical methods.

The Semiempirical Quantum Mechanical Scoring Function for In Silico Drug Design.

This Minireview discusses the latest developments in modern quantum mechanics (QM)-based computer-aided drug design, especially using semiempirical QM (SQM) methods. It first tackles biochemical and biophysical quantities and the approaches to their measurements. Protein-ligand affinities are determined mostly by noncovalent interactions. The text thus illustrates how these can be accurately treated with SQM methods. Next, a construction of a modern SQM-based scoring function is presented and its applications listed. In summary, SQM-based scoring is a promising modern efficient strategy to be exploited in computer-aided drug design.

Acceleration of Semiempirical Quantum Mechanical Calculations by Extended Lagrangian Molecular Dynamics Approach.

The implementation and performance of the atom-centered density matrix propagation (ADMP) [J. Chem. Phys. 2001, 114, 9758] and the curvy-steps (CURV) methods [J. Chem. Phys. 2004, 121, 1152] are described. These methods solve the electronic Schrödinger equation approximately by propagating the electronic degrees of freedom using the extended Lagrangian molecular dynamics (ELMD) simulation approach. The ADMP and CURV methods are implemented and parallelized to accelerate semiempirical quantum mechanical (QM) methods (such as the MNDO, AM1, PM3, MNDO/d, and AM1/d methods). Test calculations show that both the ADMP and the CURV methods are 2∼4 times faster than the Born-Oppenheimer molecular dynamics (BOMD) method and conserve the total energy well. The accuracy of the ADMP and CURV simulations is comparable to the BOMD simulations. The parallel implementation accelerates the MD simulation by up to 28 fold for the ADMP method and 25 fold for the CURV method, respectively, relative to the speed of the single core BOMD. In addition, a multiple time scale (MTS) approach is introduced to further speed up the semiempirical QM and QM/MM ELMD simulations. Since a larger integration time step is used for the propagation of the nuclear coordinates than that for the electronic degrees of freedom, the MTS approach allows the ELMD simulation to be carried out with a time step that is larger than the time step accessible by the original ADMP and CURV methods. It renders MD simulation to be carried out about 20 times faster than the BOMD simulation, and yields results that are comparable to the single time scale simulation results. The use of the methods introduced in the present work provides an efficient way to extend the length of the QM and QM/MM molecular dynamics simulations beyond the length accessible by BOMD simulation.

Modelling polymers with side chains: MEH-PPV and P3HT

Modelling polymers with side chains is always a challenge once the degrees of freedom are very high. In this study, we present a successful methodology to model poly[2-methoxy-5-(2′-ethyl-hexyloxy)-p-phenylenevinylene] (MEH-PPV) and poly[3-hexylthiophene] (P3HT) in solutions, taking into account the influence of side chains on the polymer conformation. Molecular dynamics and semi-empirical quantum mechanical methods were used for structure optimisation and evaluation of optical properties. The methodology allows to describe structural and optical characteristics of the polymers in a satisfactory way, as well as to evaluate some usual simplifications adopted for modelling these systems. Effective conjugation lengths of 8-14.6 and 21 monomers were obtained for MEH-PPV and P3HT, respectively, in accordance with experimental findings. In addition, anti/syn conformations of these polymers could be predicted based on intrinsic interactions of the lateral branches.

Does electron-correlation has any role in the quantitative structure–activity relationships?

For developing quantitative structure–activity relationships (QSARs), quantum-mechanical molecular descriptors based on the state-of-the-art quantum-mechanical methods such as Hartree–Fock (HF) method and density-functional theory (DFT), are now routinely employed. The validity of these quantum-mechanical methods, however, rests on the accurate estimation of electron-correlation energy. This work analyses the role of electron-correlation, using correlation energy as a molecular descriptor, in the QSARs. In particular, QSAR models, for the mutagenic activity of a set of nitrated polycyclic aromatic hydrocarbons (nitro-PAHs), are examined for the role of electron-correlation through state-of-the-art external validation parameters such as concordance correlation coefficient and recently proposed predictive squared correlation coefficients, namely, QF12, QF22, and QF32 etc. The electron-correlation contribution to the highest occupied and lowest unoccupied molecular orbital (HOMO/LUMO) energies is also analyzed. QSAR models based on the semi-empirical quantum-mechanical methods like PM6 and RM1 are also compared. It is found that the models, developed using electron-correlation contribution of the quantum-mechanical descriptors, are not only robust but also relatively more predictive than those developed with the HF and DFT descriptors. The latter are found to be even less reliable than PM6 and RM1 descriptors based models, which show comparable robustness and predictivity with those developed using electron correlation based descriptors. The external predictivity of model based on semi-empirical descriptors can be improved if electron-correlation contribution of the quantum-mechanical descriptors is explicitly included in the model. This work reports the first-ever use of electron-correlation energy and its contribution to the HOMO/LUMO energies as molecular descriptors.

Error estimates for (semi-)empirical dispersion terms and large biomacromolecules

The first-principles modeling of biomaterials has made tremendous advances over the last few years with the ongoing growth of computing power and impressive developments in the application of density functional theory (DFT) codes to large systems. One important step forward was the development of dispersion corrections for DFT methods, which account for the otherwise neglected dispersive van der Waals (vdW) interactions. Approaches at different levels of theory exist, with the most often used (semi-)empirical ones based on pair-wise interatomic C6R(-6) terms. Similar terms are now also used in connection with semiempirical QM (SQM) methods and density functional tight binding methods (SCC-DFTB). Their basic structure equals the attractive term in Lennard-Jones potentials, common to most force field approaches, but they usually use some type of cutoff function to make the mixing of the (long-range) dispersion term with the already existing (short-range) dispersion and exchange-repulsion effects from the electronic structure theory methods possible. All these dispersion approximations were found to perform accurately for smaller systems, but error estimates for larger systems are very rare and completely missing for really large biomolecules. We derive such estimates for the dispersion terms of DFT, SQM and MM methods using error statistics for smaller systems and dispersion contribution estimates for the PDBbind database of protein-ligand interactions. We find that dispersion terms will usually not be a limiting factor for reaching chemical accuracy, though some force fields and large ligand sizes are problematic.

Electron inelastic mean free paths in solids: A theoretical approach

In the present paper, the inelastic mean free path (IMFP) of incident electrons is calculated as a function of energy for silicon (Si), oxides of silicon (SiO2), SiO, and Al2O3 in bulk form by employing atomic/molecular inelastic cross sections derived by using a semi-empirical quantum mechanical method developed earlier. A general agreement of the present results is found with most of the available data. It is of great importance that we have been able to estimate the minimum IMFP, which corresponds to the peak of inelastic interactions of incident electrons in each solid investigated. New results are presented for SiO, for which no comparison is available. The present work is important in view of the lack of experimental data on the IMFP in solids.

A Quantitative Structure-Property Relationship Study on Photodegradation of Polybrominated Diphenyl Ethers

Quantitative structure-property relationship (QSPR) models were developed in the present work for photodegradation rate constants (kp) of fifteen individual polybrominated diphenyl ethers (PBDEs) in methanol/water (8:2) by UV light in the sunlight region. The molecular descriptors used in the QSPR models were calculated by the two semi-empirical quantum mechanical methods, RM1 and PM6, respectively. Both multiple linear regression (MLR) and artificialneural network (ANN) were applied in this study. The statistic qualities of the MLR models based on the molecular parameters obtained by RM1 and PM6 calculations were both good with the R values of 0.987 and 0.990, respectively. The QSPR model built by the ANN method with the molecular parameters calculated with PM6 is slightly better than that with RM1.

Fullerene Derivative as Anti-HIV Protease Inhibitor: Molecular Modeling and QSAR Approaches

A Fullerene based system is modified in order to increase its solubility and enhance its ability to carry a protein-like structure. The modified structure, which is proposed to act as HIV-1 protease inhibitor, is [C₆₀-C2H4N-(2,4- XCOCH₂OH)C₆H₄], where the X atom is either O, S or Se. The geometry optimization, vibrational spectra and thermodynamics were performed using semiempirical quantum mechanical PM3 method in order to study the proposed compounds. Furthermore, the quantitative structure activity relationship (QSAR) properties of the compounds are calculated at the same level of theory. Results indicate a possible use of the investigated structures as HIV-1 protease inhibitors. The compounds containing oxygen is more stable as compared to the other two compounds.

Study of interaction energies between the PAMAM dendrimer and nonsteroidal anti-inflammatory drug using a distributed computational strategy and experimental analysis by ESI-MS/MS.

The structure of a dendrimer exhibits a large number of internal and superficial cavities, which can be exploited, to capture and deliver small organic molecules, enabling their use in drug delivery. Structure-based modeling and quantum mechanical studies can be used to accurately understand the interactions between functionalized dendrimers and molecules of pharmaceutical and industrial interest. In this study, we implemented a Metropolis Monte Carlo algorithm to calculate the interaction energy of dendrimer-drug complexes, which can be used for in silico prediction of dendrimer-drug affinity. Initially, a large-scale sampling of different dendrimer-drug conformations was generated using Euler angles. Then, each conformation was distributed on different nodes of a GRID computational system, where its interaction energy was calculated by semiempirical quantum mechanical methods. These energy calculations were performed for four different nonsteroidal anti-inflammatory drugs, each showing different affinities for the PAMAM-G4 dendrimer. The affinities were also characterized experimentally by using Cooks' kinetic method to calculate PAMAM-drug dissociation constants. The quantitative structure-activity relationship between the interaction energies and dissociation constants showed statistical correlations with r(2) > 0.9.

Classification and structure of silicon carbide phases

Molecular-mechanical and semiempirical quantum-mechanical methods have been applied to simulate and calculate a geometrically optimized structure of clusters of polymorphic types of silicon carbide, and their structural parameters and some properties (densities, sublimation energies) have been determined. A classification of silicon carbide phases has been proposed, which shows the possible existence of twenty one SiC phases whose atoms are at crystallographically equivalent sites. The structures of seventeen proposed silicon carbide phases have been described and studied for silicon carbide for the first time.

Prediction of SAMPL3 host-guest binding affinities: evaluating the accuracy of generalized force-fields.

We used the second-generation mining minima method (M2) to compute the binding affinities of the novel host-guest complexes in the SAMPL3 blind prediction challenge. The predictions were in poor agreement with experiment, and we conjectured that much of the error might derive from the force field, CHARMm with Vcharge charges. Repeating the calculations with other generalized force-fields led to no significant improvement, and we observed that the predicted affinities were highly sensitive to the choice of force-field. We therefore embarked on a systematic evaluation of a set of generalized force fields, based upon comparisons with PM6-DH2, a fast yet accurate semi-empirical quantum mechanics method. In particular, we compared gas-phase interaction energies and entropies for the host-guest complexes themselves, as well as for smaller chemical fragments derived from the same molecules. The mean deviations of the force field interaction energies from the quantum results were greater than 3 kcal/mol and 9 kcal/mol, for the fragments and host-guest systems respectively. We further evaluated the accuracy of force-fields for computing the vibrational entropies and found the mean errors to be greater than 4 kcal/mol. Given these errors in energy and entropy, it is not surprising in retrospect that the predicted binding affinities deviated from the experiment by several kcal/mol. These results emphasize the need for improvements in generalized force-fields and also highlight the importance of systematic evaluation of force-field parameters prior to evaluating different free-energy methods.

Calculations on Noncovalent Interactions and Databases of Benchmark Interaction Energies

Although covalent interactions determine the primary structure of a molecule, the noncovalent interactions are responsible for the tertiary and quaternary structure of a molecule and create the fascinating world of the 3D architectures of biomacromolecules. For example, the double helical structure of DNA is of fundamental importance for the function of DNA: it allows it to store and transfer genetic information. To fulfill this role, the structure is rigid to maintain the double helix with a proper positioning of the complementary base, and floppy to allow for its opening. Very strong covalent interactions cannot fulfill both of these criteria, but noncovalent interactions, which are about 2 orders of magnitude weaker, can. This Account highlights the recent advances in the field of the design of novel wave function theory (WFT) methods applicable to noncovalent complexes ranging in size from less than 100 atoms, for which highly accurate ab initio methods are available, up to extended ones (several thousands atoms), which are the domain of semiempirical QM (SQM) methods. Accurate interaction energies for noncovalent complexes are generated by the coupled-cluster technique, taking single- and double-electron excitations iteratively and triple-electron excitation perturbatively with a complete basis set description (CCSD(T)/CBS). The procedure provides interaction energies with high accuracy (error less than 1 kcal/mol). Because the method is computationally demanding, its application is limited to complexes smaller than 30 atoms. But researchers would also like to use computational methods to determine these interaction energies accurately for larger biological and nanoscale structures. Standard QM methods such as MP2, MP3, CCSD, or DFT fail to describe various types of noncovalent systems (H-bonded, stacked, dispersion-controlled, etc.) with comparable accuracy. Therefore, novel methods are needed that have been parametrized toward noncovalent interactions, and existing benchmark data sets represent an important tool for the development of new methods providing reliable characteristics of noncovalent clusters. Our laboratory developed the first suitable data set of CCSD(T)/CBS interaction energies and geometries of various noncovalent complexes, called S22. Since its publication in 2006, it has frequently been applied in parametrization and/or verification of various wave function and density functional techniques. During the intense use of this data set, several inconsistencies emerged, such as the insufficient accuracy of the CCSD(T) correction term or its unbalanced character, which has triggered the introduction of a new, broader, and more accurate data set called the S66 data set. It contains not only 66 CCSD(T)/CBS interaction energies determined in the equilibrium geometries but also 1056 interaction energies calculated at the same level for nonequilibrium geometries. The S22 and S66 data sets have been used for the verification of various WFT methods, and the lowest RMSE (S66, in kcal/mol) was found for the recently introduced SCS-MI-CCSD/CBS (0.08), MP2.5/CBS (0.16), MP2.X/6-31G* (0.27), and SCS-MI-MP2/CBS (0.38) methods. Because of their computational economy, the MP2.5 and MP2.X/6-31G* methods can be recommended for highly accurate calculations of large complexes with up to 100 atoms. The evaluation of SQM methods was based only on the S22 data set, and because some of these methods have been parametrized toward the same data set, the respective results should be taken with caution. For really extended complexes such as protein-ligand systems, only the SMQ methods are applicable. After adding the corrections to the dispersion energy and H-bonding, several methods exhibit surprisingly low RMSE (even below 0.5 kcal/mol). Among the various SMQ methods, the PM6-DH2 can be recommended because of its computational efficiency and it can be used for optimization (which is not the case for other SQM methods). The PM6-DH2 is the base of our novel scoring function used in in silico drug design.

Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations

Lately, there has been great interest in performing free-energy perturbation (FEP) at the combined quantum mechanics and molecular mechanics (QM/MM) level, e.g. for enzyme reactions. Such calculations require extensive sampling of phase space, which typically is prohibitive with density-functional theory or ab initio methods. Therefore, such calculations have mostly been performed with semiempirical QM (SQM) methods, or by using a thermodynamic cycle involving sampling at the MM level and perturbations between the MM and QM/MM levels of theory. However, the latter perturbations typically have convergence problems, unless the QM system is kept fixed during the simulations, because the MM and QM/MM descriptions of the internal degrees of freedom inside the QM system are too dissimilar. We have studied whether the convergence of the MM → QM/MM perturbation can be improved by using a thoroughly parameterised force field or by using SQM/MM methods. As a test case we use the first half-reaction of haloalkane dehalogenase and the QM calculations are performed with the PBE, B3LYP, and TPSSH density-functional methods. We show that the convergence can be improved with a tailored force field, but only locally around the parameterised state. Simulations based on SQM/MM methods using the MNDO, AM1, PM3, RM1, PDDG-MNDO, and PDDG-PM3 Hamiltonians have slightly better convergence properties, but very long simulations are still needed (~10 ns) and convergence is obtained only if electrostatic interactions between the QM system and the surroundings are ignored. This casts some doubts on the common practice to base QM/MM FEPs on semiempirical simulations without any reweighting of the trajectories.

Advanced Corrections of Hydrogen Bonding and Dispersion for Semiempirical Quantum Mechanical Methods.

Semiempirical quantum mechanical methods with corrections for noncovalent interactions, namely dispersion and hydrogen bonds, reach an accuracy comparable to much more expensive methods while being applicable to very large systems (up to 10 000 atoms). These corrections have been successfully applied in computer-assisted drug design, where they significantly improve the correlation with the experimental data. Despite these successes, there are still several unresolved issues that limit the applicability of these methods. We introduce a new generation of both hydrogen-bonding and dispersion corrections that address these problems, make the method more robust, and improve its accuracy. The hydrogen-bonding correction has been completely redesigned and for the first time can be used for geometry optimization and molecular-dynamics simulations without any limitations, as it and its derivatives have a smooth potential energy surface. The form of this correction is simpler than its predecessors, while the accuracy has been improved. For the dispersion correction, we adopt the latest developments in DFT-D, using the D3 formalism by Grimme. The new corrections have been parametrized on a large set of benchmark data including nonequilibrium geometries, the S66x8 data set. As a result, the newly developed D3H4 correction can accurately describe a wider range of interactions. We have parametrized this correction for the PM6, RM1, OM3, PM3, AM1, and SCC-DFTB methods.

Structure of carbinoid nanotubes and carbinofullerenes

Molecular mechanics methods have been used to calculate the geometrically optimized structure of carbinoid layers, carbinoid nanotubes, and carbinofullerenes consisting of carbine chains linked by atoms in sp2 and/or sp3 hybridization states. Energy characteristics of carbinoid nanostructures have been calculated by semi-empirical quantum-mechanical methods. A structural classification of framework carbinoid nanostructures has been proposed. The dependence of specific binding energies of carbinoid nanostructures on the ratio sp2/sp and their geometrical sizes has been determined.

Benchmarking Semiempirical Methods for Thermochemistry, Kinetics, and Noncovalent Interactions: OMx Methods Are Almost As Accurate and Robust As DFT-GGA Methods for Organic Molecules.

Semiempirical quantum mechanical (SQM) methods offer a fast approximate treatment of the electronic structure and the properties of large molecules. Careful benchmarks are required to establish their accuracy. Here, we report a validation of standard SQM methods using a subset of the comprehensive GMTKN24 database for general main group thermochemistry, kinetics, and noncovalent interactions, which has recently been introduced to evaluate density functional theory (DFT) methods ( J. Chem. Theory Comput. 2010 , 6 , 107 ). For all SQM methods considered presently, parameters are available for the elements H, C, N, and O, and consequently, we have extracted from the GMTKN24 database all species containing only these four elements (excluding multireference cases). The resulting GMTKN24-hcno database has 370 entries (derived from 593 energies) compared with 715 entries (derived from 1033 energies) in the original GMTKN24 database. The current benchmark covers established standard SQM methods (AM1, PM6), more recent approaches with orthogonalization corrections (OM1, OM2, OM3), and the self-consistent-charge density functional tight binding method (SCC-DFTB). The results are compared against each other and against DFT results using standard functionals. We find that the OMx methods outperform AM1, PM6, and SCC-DFTB by a significant margin, with a substantial gain in accuracy especially for OM2 and OM3. These latter methods are quite accurate even in comparison with DFT, with an overall mean absolute deviation of 6.6 kcal/mol for PBE and 7.9 kcal/mol for OM3. The OMx methods are also remarkably robust with regard to the unusual bonding situations encountered in the "mindless" MB08-165 test set, for which all other SQM methods fail badly.

Interaction of naproxen with β-cyclodextrin and its derivatives/polymer: experimental and molecular modeling studies

The interaction of naproxen with β-cyclodextrin and its derivatives (hosts) as well as polymer has been studied using UV Visible (UV–Vis), Fourier Transform Infrared (FTIR), Nuclear Magnetic Resonance (NMR) spectroscopy and Scanning electron microscopy (SEM). In this paper, the solid inclusion complexes were prepared by freeze drying method. The formation constants of the complexes were determined by UV–Vis method. The adsorption properties of naproxen with β-Cyclodextrin bonded silica stationary phase (CDS) were studied for an in-depth understanding of the host–guest interaction. The inclusion process involving naproxen and hosts was investigated by using the PM3 quantum–mechanical semiempirical method. The stabilization energy values obtained from the semiempirical calculation showed the same relation with the formation constant values determined by UV–Vis spectroscopy.

Structures of diamond-like phases

The diamond-like phases containing carbon atoms with the same degree of hybridization, which is close to sp 3, are classified. It is found that twenty such phases can exist, and ten of them are described for the first time. Molecular mechanics and semi-empirical quantum-mechanical methods are used to calculate the geometrically optimized structures of diamond-like phase clusters and to determine their structural parameters and properties, such as the density, the bulk modulus, and the sublimation energy. The difference between the properties of the diamond-like phases and those of diamond is found to be determined by the difference between the structures of these phases and diamond.

Semiempirical Quantum Mechanical Method PM6-DH2X Describes the Geometry and Energetics of CK2-Inhibitor Complexes Involving Halogen Bonds Well, While the Empirical Potential Fails

In the present study, we have investigated complexes of CK2 protein kinase with halogenated inhibitors by means of the advanced semiempirical quantum mechanical (SQM) PM6 method (called PM6-DH2X), which describes various types of noncovalent interactions including halogen bonding well. The PM6-DH2X method provides reliable geometries of those CK2 protein kinase-inhibitor complexes involving halogen bonds that agree well with the X-ray crystal structures. When the Amber empirical potential is applied, this agreement becomes considerably worse. Similarly, the binding free energies determined by the PM6-DH2X SQM method are much closer to the experimental inhibition constants than those based on the Amber empirical potential.