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

The importance of non-bonding interactions between and also within molecular systems has come into the focus of many researchers over the last two decades. The important interactions are first order exchange-repulsion, (non-polarized) electrostatic and second order polarization/induction (up to charge-transfer) as well as dispersion interactions. This chapter gives a short review of theoretical basics of non-covalent interactions. It presents an overview of features of non-polar interactions and polar interactions. The chapter discusses the general aspects of non-covalent interactions for molecular modelling methods and semi-empirical quantum mechanical methods. The Grimme ansatz is used for semi-empirical quantum mechanical and density functional tight binding (DFTB) methods as well as periodic DFT calculations in solid-state physics and surface science. The chapter focuses on the treatment of the most complicated interactions, namely dispersion and hydrogen-bond interactions. Two semi-empirical quantum mechanical methods make use of the first-generation hydrogen bond corrections, i.e., PM6-DH and AM1-FS1. Keywords: density functional tight binding method; dispersion interactions; hydrogen-bond interactions; molecular modelling methods; non-covalent interactions; polar interactions; semi-empirical quantum mechanical methods

The 6-Mono- and trans-6,7-di-substituted derivatives of 5,6,7,8-tetrahydrodibenzo[a,c]cyclo-octene exist in solution in two different conformations. The experimental ΔGo values obtained from 1H NMR spectra are compared with the ΔEsteric and ΔG values calculated by molecular mechanics and semiempirical quantum mechanics methods respectively. The experimental ΔGo values are reproduced better by the ΔEsteric values. The semiempirical methods predict the order of stability of the conformers correctly except for two cases in the PM3 and AM1 methods, but the estimated values are far from the experimental ones. The standard deviation between the experimental ΔGo values and those calculated by semiempirical methods is less for AM1 and MNDO and greater for PM3 and MINDO/3. The conformational space of the flexible side chains in monoacetoxy 1d, monohydroxy 1e, trans-diacid 2d, trans-dimethyl ester 2e and trans-bis-hydroxymethyl 2f searched by molecular mechanics is not reproduced completely by semiempirical methods. © 1998 John Wiley & Sons, Ltd.

Semi-empirical calculations including an empirical dispersive correction are used to calculate intermolecular interaction energies and structures for a large database containing 156 biologically relevant molecules (hydrogen-bonded DNA base pairs, interstrand base pairs, stacked base pairs and amino acid base pairs) for which MP2 and CCSD(T) complete basis set (CBS) limit estimates of the interaction energies are available. The dispersion corrected semi-empirical methods are parameterised against a small training set of 22 complexes having a range of biologically important non-covalent interactions. For the full molecule set (156 complexes), compared to the high-level ab initio database, the mean unsigned errors of the interaction energies at the corrected semi-empirical level are 1.1 (AM1-D) and 1.2 (PM3-D) kcal mol(-1), being a significant improvement over existing AM1 and PM3 methods (8.6 and 8.2 kcal mol(-1)). Importantly, the new semi-empirical methods are capable of describing the diverse range of biological interactions, most notably stacking interactions, which are poorly described by both current AM1 and PM3 methods and by many DFT functionals. The new methods require no more computer time than existing semi-empirical methods and therefore represent an important advance in the study of important biological interactions.

The polarizable dipole-dipole interaction model was formulated in our laboratory to rapidly simulate hydrogen bonding in biosystems. In this paper, this model is improved and further parametrized for stacking, T-shaped, and X-H···π interactions by adding the orbital overlap term and fitting to 19 CCSD(T)/CBS interaction energy curves of training dimers. The performance of our model is assessed through its application to more than 100 complexes, including hydrogen-bonded, stacked, T-shaped, and X-H···π complexes. For 124 relatively small testing complexes, our model reproduces benchmark equilibrium intermolecular distances with a root-mean-square deviation (RMSD) of 0.08 Å, and it reproduces benchmark interaction energies with a 0.64 kcal/mol RMSD. For 14 large noncovalent complexes, our model reproduces benchmark equilibrium intermolecular distances with a RMSD of 0.05 Å, and it reproduces benchmark interaction energies with a 0.80 kcal/mol RMSD. Extensive comparisons are made to interaction energies calculated via the M06-2X and M06-2X-D3 methods, via the well-known nonpolarizable AMBER99 force field method, via the popular polarizable AMOEBA force field method, and via semiempirical quantum mechanical (SQM) methods. Our statistical evaluations show that our model outperforms the AMBER99, AMOEBA, and SQM methods and is as accurate as the M06-2X and M06-2X-D3 methods. In summary, the model developed in this work is reasonable, and the newly introduced orbital overlap term is effective in the accurate modeling of the noncovalent interactions. Our testing results also indicate that the polarization interaction term is important in the evaluation of hydrogen bonding, whereas the orbital overlap is important in examining short hydrogen bonding, T-shaped, and X-H···π interactions. Our model may serve as a new tool for modeling biological systems where hydrogen bonding, stacking, T-shaped, and X-H···π interactions are of general importance.

Semiempirical quantum mechanical (SEQM) methods offer an attractive middle ground between fully ab initio quantum chemistry and force-field simulations, allowing for a quantum mechanical treatment of the system at a relatively low computational cost. However, SEQM methods have not been frequently utilized in the study of transition metal systems, mostly due to the difficulty in obtaining reliable parameters. This paper examines the accuracy of the PM6 and PM7 semiempirical methods to predict geometries, ionization potentials, and HOMO-LUMO energy gaps of several bare gold clusters (Aun) and thiolate-protected gold nanoclusters (AuSNCs). Contrary to PM6, the PM7 method can predict qualitatively correct geometries and ionization potentials when compared to DFT. PM6 fails to predict the characteristic gold core and gold-sulfur ligand shell (staple motifs) of the AuSNC structures. Both the PM6 and PM7 methods overestimate the HOMO-LUMO gaps. Overall, PM7 provides a more accurate description of bare gold and gold-thiolate nanoclusters than PM6. Nevertheless, refining the gold parameters could help achieve better quantitative accuracy.

Chapter 24 - Improving semiempirical quantum mechanical methods with machine learning

The objective of the present work was to study the quantitative structure-activity relationship (QSAR) of the protective effects of N-p-tolyl/phenyl sulfonyl L-amino acid thiolester derivatives on anoxic damage of rat pheochromocytoma (PC12) cells. Four molecular parameters of seventeen N-p-tolyl/phenyl sulfonyl L-amino acid thiolester derivatives, including heat of formation, dipole moment, the energy of the highest occupied molecular orbital and the energy of the lowest unoccupied molecular orbital, were calculated with two semi-empirical quantum mechanical methods, PM6 and RM1, respectively. The QSAR model based on molecular parameters and protective effects of these compounds on anoxic damage of PC12 cells were studied using the multiple linear regression analysis and principal component analysis. It is found that dipole moment and the energy of the lowest unoccupied molecular orbital are important factors for neurotrophic activities of these N-p-tolyl/phenyl sulfonyl L-amino acid thiolester derivatives. Results from PM6 and RM1 methods were compared, indicating that using PM6 method to calculate these molecular parameters is probably more applicable to the QSAR analysis in this study.

Computational modeling of biological systems is a rapidly evolving field that calls for methods that are able to allow for extensive sampling with systems consisting of thousands of atoms. Semiempirical quantum chemical (SE) methods are a promising tool to aid with this, but the rather bad performance of standard SE methods for noncovalent interactions is clearly a limiting factor. Enhancing SE methods with empirical corrections for dispersion and hydrogen-bonding interactions was found to be a big improvement, but for the hydrogen-bonding corrections the drawback of breaking down in the case of substantial changes to the hydrogen bond, e.g., proton transfer, posed a serious limitation for its general applicability. This work presents a further improved hydrogen-bonding correction that can be generally included in parameter fitting procedures, as it does not suffer from the conceptual flaws of previous approaches: hydrogen bonds are now treated as an interaction term between electronegative acceptor and donor atoms, "weighted" by a function of the position of H atoms between them, and multiplied with a damping function to correct the short- and long-range behavior. The performance of the new approach is evaluated for PM6, AM1, OM3, and SCC-DFTB as well as several force-field (FF) methods for a number of standard benchmark sets with hydrogen-bonded systems. The new approach is found to reach the same accuracy as the second-generation hydrogen-bonding correction with less parameters, while it avoids among other issues the conceptual problem with electronic structure changes. SE methods augmented this way reach the accuracy of DFT-D approaches for a large number of cases investigated, while still being about 3 orders of magnitude faster. Moreover, the new correction scheme is transferable also to FF methods that were shown to have serious problems with hydrogen-bonding interactions.

Theoretical studies on the structure of 1,3-diol systems: Part 1. Monomers, dimers and monohydrates

Major histocompatibility complex class I (MHC-I), a key element of the acquired immune system, plays essential roles in activating CD8+ T cells by recognizing intracellular antigens derived from pa...

Comparative study on the vibrational IR spectra of cytosine and thiocytosine by various semi-empirical quantum mechanical methods

The molecular and crystal structure of the title compound, C14H11Cl2NO, has been determined by X-ray single crystal diffraction technique. The compound crystallizes in the orthorhombic, space group Pbca with unit cell dimensions a = 7.5537(10) A, b = 11.5518(13) A, c = 29.760(4) A, M r = 280.14, V = 2596.8(6) A3, Z = 8, R 1 = 0.065 and wR 2 = 0.191. The title compound exists in the enol–imine tautomeric form with a strong intramolecular O–H···N hydrogen bond. The dihedral angle between the two benzene rings is 37.66(15)°. The asymmetric unit in the crystal structure contains only one neutral molecule. Calculational studies were performed by using AM1, PM3, PM6 semi-empirical and DFT methods. Geometry optimizations of compound have been carried out by using three semi-empirical methods and DFT method and bond lengths, bond and torsion angles of title compound have been determined. Dipole moments (Debye) and the energy parameters of compound (kcal/mol) were calculated by using above mentioned calculation methods. Atomic charge distribution has been obtained from AM1, PM3, PM6 and DFT. In order to determine conformational flexibility on the molecule, molecular energy profile of the title compound was obtained with respect to the selected torsion angle T(N1–C7–C1–C2), which is varied from −180° to +180° in every 10 via PM3 semi-empirical method. A new crystal of (E)-2-[(2,4-Dichlorophenylimino) methyl]-p-cresol with orthorhombic space group Pbca [unit cell dimensions a = 7.5537(10) A, b = 11.5518(13) A, c = 29.760(4) A, V = 2596.8(6) A3, Z = 8, R 1 = 0.065] has been determined by single crystal X-ray diffraction study and theoretical calculations were performed by using AM1, PM3, PM6 semi-empirical and DFT methods.

Cyclooxygenase (COX) is one of the concerned targets in the development of anti-inflammatory therapies. Using semiempirical quantum mechanical (SQM) methods with implicit solvation, we investigated the binding free energies and selectivity of natural cannabinoids and their sulfonamide-modified derivatives with the COX and cannabinoid (CB) receptors. Validation against benchmark data sets demonstrated the accuracy of these methods in predicting binding affinities while minimizing false positives and false negatives often associated with conventional docking tools. Our findings indicate that Δ9-THC and its carboxylic acid derivative exhibit strong binding affinities for COX-2 and CB2, suggesting their potential as anti-inflammatory agents, though their significant CB1 affinity suggests psychoactive risks. In contrast, carboxylic acid derivatives such as CBCA, CBNA, CBEA, CBTA, and CBLA demonstrated selective binding to COX-2 and CB2, with low CB1 affinity, supporting their potential as promising anti-inflammatory leads with reduced psychoactive side effects. Sulfonamide-modified analogs further enhanced COX-2 binding affinities and selectivity, displaying favorable drug-like properties, including compliance with Lipinski's rules, noninhibition of cytochromes P450, and oral bioavailability. These results highlight the utility of GFN2-xTB in identifying and optimizing cannabinoid-based therapeutic candidates for anti-inflammatory applications.

Computational methods for the study of enzymic reaction mechanisms. II. An overlapping mechanically embedded method for hybrid semi-empirical-QM/MM calculations

An empirical approach based on the previously developed zinc AMBER force field (ZAFF) is proposed for the determination of the parameters for bonds and angles involving zinc. We call it the extended ZAFF (EZAFF) model because the original ZAFF model was only formulated for four-coordinated systems, while EZAFF additionally can tackle five- and six-coordinated systems. Tests were carried out for six metalloproteins and six organometallic compounds with different coordination spheres. Results validated the reliability of the current model to handle a variety of zinc containing complexes. Meanwhile, benchmark calculations were performed to assess the performance of three bonded molecular mechanics models (EZAFF, Seminario, and Z-matrix models), four nonbonded parameter sets (the HFE, IOD, CM, and 12-6-4 models), and four semiempirical quantum mechanical methods (AM1, PM3, PM6, and SCC-DFTB methods) for simulating zinc containing systems. The obtained results indicate that, even with their increased computational cost, the semiempirical quantum methods only offered slightly better accuracy for the computation of relative energies and only afforded similar molecular geometries, when compared to the investigated molecular mechanics models.