Quantum chemical descriptors based on semiempirical methods for large biomolecules.

In this Review, we reviewed the efforts to expand the applications of conceptual density functional theory reactivity descriptors and hard and soft acid and base principles for macromolecules and other strategies that focused on low-level quantum chemistry methods. Currently, recent applications are taking advantage of modifications of these descriptors using semiempirical electronic structures to explain enzymatic catalysis reactions, protein-binding processes, and structural analysis in proteins. We have explored these new solutions along with their implementations in the software PRIMoRDiA, discussing their impact on the field and its perspectives. We show the main issues in the analysis of the electronic structure of macromolecules, which are the application of the same calculation protocols used for small molecules without considering particularities in those large systems' electronic configuration. The major result of our discussions is that the use of semiempirical methods is crucial to obtain such a type of analysis, which can provide a powerful dimension of information and be part of future low-cost predictive tools. We expect semiempirical methods continue playing an important role in the quantum chemistry evaluation of large molecules. As computational resources advance, semiempirical methods might lead us to explore the electronic structure of even larger biological macromolecular entities and sets of structures representing larger timescales.

NAMD goes quantum: an integrative suite for hybrid simulations.

Hybrid methods that combine quantum mechanics (QM) and molecular mechanics (MM) can be applied to studies of reaction mechanisms in locations ranging from active sites of small enzymes to multiple sites in large bioenergetic complexes. By combining the widely used molecular dynamics and visualization programs NAMD and VMD with the quantum chemistry packages ORCA and MOPAC, we created an integrated, comprehensive, customizable, and easy-to-use suite (http://www.ks.uiuc.edu/Research/qmmm). Through the QwikMD interface, setup, execution, visualization, and analysis are streamlined for all levels of expertise.

Efficient algorithm for expanding theoretical electron densities in canterakis-zernike functions.

An algorithm for the efficient computation of Canterakis-Zernike moments of theoretically computed molecular electron densities and rotationally invariant Fingerprint indices derived from them is reported. The algorithm is suitable for any density expressed in terms of Gaussian- or Slater-type functions within the Linear Combination of Atomic Orbitals framework at any level of computation. Electron density is expressed as a one-center expansion of real regular spherical harmonics times radial factors by means of translation techniques, which facilitates the efficient computation of the moments in terms of a single one-dimension numerical integration. The performance of the algorithm is analyzed showing that the computation of radial factors in the quadrature points is responsible for almost all computational time. The procedure is applicable to any density obtained with standard packages for molecular structure calculations. © 2018 Wiley Periodicals, Inc.

Determining the Relative Binding Affinity of Ricin Toxin A Inhibitors by Using Molecular Docking and Nonequilibrium Work.

Ricin is a ribosome-inactivating protein (RIP type 2) consisting of two subunits, ricin toxin A (RTA) and ricin toxin B (RTB). Because of its cytotoxicity, ricin has worried world authorities for its potential use as a chemical weapon; therefore, its inhibition is of great biotechnological interest. RTA is the target for inhibitor synthesis, and pterin derivatives are promising candidates to inhibit it. In this study, we used a combination of the molecular docking approach and fast steered molecular dynamics (SMD) to assess the correlation between nonequilibrium work, ⟨ W⟩, and the IC50 for six RTA inhibitors. The results showed that molecular docking is a powerful tool to predict good bioactive poses of RTA inhibitors, and ⟨ W⟩ presented a strong correlation with IC50 ( R2 = 0.961). Such a profile ranked the RTA inhibitors better than the molecular docking approach. Therefore, the combination of docking and fast SMD simulation was shown to be a promising tool to distinguish RTA-active inhibitors from inactive ones and could be used as postdocking filtering approach.

A higher flexibility at the SARS-CoV-2 main protease active site compared to SARS-CoV and its potentialities for new inhibitor virtual screening targeting multi-conformers.

The main-protease (Mpro) catalyzes a crucial step for the SARS-CoV-2 life cycle. The recent SARS-CoV-2 presents the main protease (MCoV2pro) with 12 mutations compared to SARS-CoV (MCoV1pro). Recent studies point out that these subtle differences lead to mobility variances at the active site loops with functional implications. We use metadynamics simulations and a sort of computational analysis to probe the dynamic, pharmacophoric and catalytic environment differences between the monomers of both enzymes. So, we verify how much intrinsic distinctions are preserved in the functional dimer of MCoV2pro, as well as its implications for ligand accessibility and optimized drug screening. We find a significantly higher accessibility to open binding conformers in the MCoV2pro monomer compared to MCoV1pro. A higher hydration propensity for the MCoV2pro S2 loop with the A46S substitution seems to exercise a key role. Quantum calculations suggest that the wider conformations for MCoV2pro are less catalytically active in the monomer. However, the statistics for contacts involving the N-finger suggest higher maintenance of this activity at the dimer. Docking analyses suggest that the ability to vary the active site width can be important to improve the access of the ligand to the active site in different ways. So, we carry out a multiconformational virtual screening with different ligand bases. The results point to the importance of taking into account the protein conformational multiplicity for new promissors anti MCoV2pro ligands. We hope these results will be useful in prospecting, repurposing and/or designing new anti SARS-CoV-2 drugs.Communicated by Ramaswamy H. Sarma.

Repurposing approved drugs as inhibitors of SARS-CoV-2 S-protein from molecular modeling and virtual screening.

Herein, molecular modeling techniques were used with the main goal to obtain candidates from a drug database as potential targets to be used against SARS-CoV-2. This novel coronavirus, responsible by the COVID-19 outbreak since the end of 2019, became a challenge since there is not vaccine for this disease. The first step in this investigation was to solvate the isolated S-protein in water for molecular dynamics (MD) simulation, being observed a transition from "up" to "down" conformation of receptor-binding domain (RBD) of the S-protein with angle of 54.3 and 43.0 degrees, respectively. The RBD region was more exposed to the solvent and to the possible drugs due to its enhanced surface area. From the equilibrated MD structure, virtual screening by docking calculations were performed using a library contained 9091 FDA approved drugs. Among them, 24 best-scored ligands (14 traditional herbal isolate and 10 approved drugs) with the binding energy below -8.1 kcal/mol were selected as potential candidates to inhibit the SARS-CoV-2 S-protein, preventing the human cell infection and their replication. For instance, the ivermectin drug (present in our list of promise candidates) was recently used successful to control viral replication in vitro. MD simulations were performed for the three best ligands@S-protein complexes and the binding energies were calculated using the MM/PBSA approach. Overall, it is highlighted an important strategy, some key residues, and chemical groups which may be considered on clinical trials for COVID-19 outbreak. [Formula: see text]Communicated by Ramaswamy H. Sarma.

3-Hydroxy-2-methylene-3-(4-nitrophenylpropanenitrile): A new highly active compound against epimastigote and trypomastigote form of Trypanosoma cruzi.

We have synthesized the Morita-Baylis-Hillman adduct (MBHA) 3-hydroxy-2-methylene-3-(4-nitrophenyl)-propanenitrile (3) in quantitative yield and evaluated on Trypanosoma cruzi epimastigote and bloodstream trypomastigote forms. Compound 3 strongly inhibited epimastigote growth, with IC(50)/72hof 28.5 microM and also caused intense trypomastigotes lysis, with an IC(50)/24h of 25.5 microM. Ultrastructural analysis showed significant morphological changes on both parasite forms treated with 3, including increase of cell volume and rounding of cell body as well as intense intracellular disorganization. Morphological changes indicative of apoptosis, autophagy or necrosis were observed in most affected cells. Docking calculations of 1, 2 and 3 pointed out the possibility of T. cruzi Farnesyl Pyrophosphate Synthase (TcFPPS) enzyme inhibition in 3 mechanism of action.

Efficient synthesis of 16 aromatic Morita-Baylis-Hillman adducts: Biological evaluation on Leishmania amazonensis and Leishmania chagasi.

Sixteen aromatic Morita-Baylis-Hillman adducts (MBHA) 1-16 were efficiently synthesized in a one step Morita-Baylis-Hillman reaction (MBHR) involving commercial aldehydes with methyl acrylate or acrylonitrile (81-100% yields) without the formation of side products on DABCO catalysis and at low temperature (0°C). The toxicities of these compounds were assessed against promastigote form of Leishmania amazonensis and Leishmania chagasi. The low synthetic cost of these MBHA, green synthetic protocols, easy one-step synthesis from commercially available and cheap reagents as well as the very good antileishmanial activity obtained for 14 and 16 (IC50 values of 6.88µgmL⁻¹ and 11.06µgmL⁻¹ respectively on L. amazonensis; 9.58µgmL⁻¹ and 14.34µgmL⁻¹ respectively on L. chagasi) indicates that these MBHA can be a novel and promising class of anti-parasitic compounds.

Parameters for the RM1 Quantum Chemical Calculation of Complexes of the Trications of Thulium, Ytterbium and Lutetium.

The RM1 quantum chemical model for the calculation of complexes of Tm(III), Yb(III) and Lu(III) is advanced. Subsequently, we tested the models by fully optimizing the geometries of 126 complexes. We then compared the optimized structures with known crystallographic ones from the Cambridge Structural Database. Results indicate that, for thulium complexes, the accuracy in terms of the distances between the lanthanide ion and its directly coordinated atoms is about 2%. Corresponding results for ytterbium and lutetium are both 3%, levels of accuracy useful for the design of lanthanide complexes, targeting their countless applications.

RM1 Semiempirical Quantum Chemistry: Parameters for Trivalent Lanthanum, Cerium and Praseodymium.

The RM1 model for the lanthanides is parameterized for complexes of the trications of lanthanum, cerium, and praseodymium. The semiempirical quantum chemical model core stands for the [Xe]4fn electronic configuration, with n =0,1,2 for La(III), Ce(III), and Pr(III), respectively. In addition, the valence shell is described by three electrons in a set of 5d, 6s, and 6p orbitals. Results indicate that the present model is more accurate than the previous sparkle models, although these are still very good methods provided the ligands only possess oxygen or nitrogen atoms directly coordinated to the lanthanide ion. For all other different types of coordination, the present RM1 model for the lanthanides is much superior and must definitely be used. Overall, the accuracy of the model is of the order of 0.07Å for La(III) and Pr(III), and 0.08Å for Ce(III) for lanthanide-ligand atom distances which lie mostly around the 2.3Å to 2.6Å interval, implying an error around 3% only.

Semiempirical quantum chemistry model for the lanthanides: RM1 (Recife Model 1) parameters for dysprosium, holmium and erbium.

Complexes of dysprosium, holmium, and erbium find many applications as single-molecule magnets, as contrast agents for magnetic resonance imaging, as anti-cancer agents, in optical telecommunications, etc. Therefore, the development of tools that can be proven helpful to complex design is presently an active area of research. In this article, we advance a major improvement to the semiempirical description of lanthanide complexes: the Recife Model 1, RM1, model for the lanthanides, parameterized for the trications of Dy, Ho, and Er. By representing such lanthanide in the RM1 calculation as a three-electron atom with a set of 5 d, 6 s, and 6 p semiempirical orbitals, the accuracy of the previous sparkle models, mainly concentrated on lanthanide-oxygen and lanthanide-nitrogen distances, is extended to other types of bonds in the trication complexes' coordination polyhedra, such as lanthanide-carbon, lanthanide-chlorine, etc. This is even more important as, for example, lanthanide-carbon atom distances in the coordination polyhedra of the complexes comprise about 30% of all distances for all complexes of Dy, Ho, and Er considered. Our results indicate that the average unsigned mean error for the lanthanide-carbon distances dropped from an average of 0.30 Å, for the sparkle models, to 0.04 Å for the RM1 model for the lanthanides; for a total of 509 such distances for the set of all Dy, Ho, and Er complexes considered. A similar behavior took place for the other distances as well, such as lanthanide-chlorine, lanthanide-bromine, lanthanide, phosphorus and lanthanide-sulfur. Thus, the RM1 model for the lanthanides, being advanced in this article, broadens the range of application of semiempirical models to lanthanide complexes by including comprehensively many other types of bonds not adequately described by the previous models.

RM1 Model for the Prediction of Geometries of Complexes of the Trications of Eu, Gd, and Tb.

All versions of our previous Sparkle Model were very accurate in predicting lanthanide-lanthanide distances in complexes where the two lanthanide ions directly face each other, and mainly lanthanide-oxygen, and lanthanide-nitrogen distances, which are by far the most common ones in lanthanide complexes. In this article, we are advancing for the first time the RM1 model for lanthanides. Designed to be a much more general NDDO model, the RM1 model for lanthanides is capable of predicting geometries of lanthanide complexes for the cases when the central lanthanide trication is directly coordinated to any other atoms, not only oxygen or nitrogen. The RM1 model for lanthanides is defined by three important attributes: (a) the orbitals, the lanthanide ion has now three electrons and a NDDO basis set made of 5d, 6s, and 6p functions; (b) the parametrization, via cluster analysis and an adequate sampling; and (c), the statistical validation of the parameters to make sure the errors behave as random around a mean. All three aspects are described in detail in the article. Results indicate that the RM1 model does extend the accuracy of the previous Sparkle Models to types of coordinating bonds other than Ln-O and Ln-N; the most common ones for Eu, Gd, and Tb, being Ln-C, Ln-S, Ln-Cl, and Ln-Br. Overall, these other coordinating bonds are now predicted within 0.06 Å of their correct values. Therefore, the RM1 model here presented is capable of predicting geometries of lanthanide complexes, materials, metal-organic frameworks, etc., with useful accuracy.

Performance assessment of semiempirical molecular orbital methods in the structural prediction of Sb(III) and Bi(III) complexes.

In this paper we carried out a systematic study in order to assess the quality of some semiempirical methods (AM1, PM3 and PM6), comparing predicted structural properties of many Sb(III) and Bi(III) complexes with the corresponding experimental data, indicating which one is more appropriate to describe the structure of such compounds. Root-mean squared deviation (RMSD) and unsigned mean error (UME) were used to evaluate the accuracy of the semiempirical methods to predict the ground state geometries of complexes with many ligand types. Our results have shown that, in general, PM3 predicts more accurately the geometry of Sb(III) complexes, being considered by us as the method of choice to study Sb(III) complexes with a great variety of ligands. PM6 is indicated as the method of choice to study Bi(III) complexes with many types of ligands and also to study Sb(III) thiocompounds, even though PM6 showed an inability to reproduce Sb-N bonds for complexes with flexible ligands, presenting an average deviation of 71.5 % compared the X-ray data.

Sparse Projected-Gradient Method As a Linear-Scaling Low-Memory Alternative to Diagonalization in Self-Consistent Field Electronic Structure Calculations.

Large-scale electronic structure calculations usually involve huge nonlinear eigenvalue problems. A method for solving these problems without employing expensive eigenvalue decompositions of the Fock matrix is presented in this work. The sparsity of the input and output matrices is preserved at every iteration, and the memory required by the algorithm scales linearly with the number of atoms of the system. The algorithm is based on a projected gradient iteration applied to the constraint fulfillment problem. The computer time required by the algorithm also scales approximately linearly with the number of atoms (or non-null elements of the matrices), and the algorithm is faster than standard implementations of modern eigenvalue decomposition methods for sparse matrices containing more than 50 000 non-null elements. The new method reproduces the sequence of semiempirical SCF iterations obtained by standard eigenvalue decomposition algorithms to good precision.

Sparkle/PM7 Lanthanide Parameters for the Modeling of Complexes and Materials.

The recently published Parametric Method number 7, PM7, is the first semiempirical method to be successfully tested by modeling crystal structures and heats of formation of solids. PM7 is thus also capable of producing results of useful accuracy for materials science, and constitutes a great improvement over its predecessor, PM6. In this article, we present Sparkle Model parameters to be used with PM7 that allow the prediction of geometries of metal complexes and materials which contain lanthanide trications. Accordingly, we considered the geometries of 224 high-quality crystallographic structures of complexes for the parameterization set and 395 more for the validation of the parameterization for the whole lanthanide series, from La(III) to Lu(III). The average unsigned error for Sparkle/PM7 for the distances between the metal ion and its coordinating atoms is 0.063Å for all lanthanides, ranging from a minimum of 0.052Å for Tb(III) to 0.088Å for Ce(III), comparable to the equivalent errors in the distances predicted by PM7 for other metals. These distance deviations follow a gamma distribution within a 95% level of confidence, signifying that they appear to be random around a mean, confirming that Sparkle/PM7 is a well-tempered method. We conclude by carrying out a Sparkle/PM7 full geometry optimization of two spatial groups of the same thulium-containing metal organic framework, with unit cells accommodating 376 atoms, of which 16 are Tm(III) cations; the optimized geometries were in good agreement with the crystallographic ones. These results emphasize the capability of the use of the Sparkle Model for the prediction of geometries of compounds containing lanthanide trications within the PM7 semiempirical model, as well as the usefulness of such semiempirical calculations for materials modeling. Sparkle/PM7 is available in the software package MOPAC2012, at no cost for academics and can be obtained from http://openmopac.net.

GPU Linear Algebra Libraries and GPGPU Programming for Accelerating MOPAC Semiempirical Quantum Chemistry Calculations.

In this study, we present some modifications in the semiempirical quantum chemistry MOPAC2009 code that accelerate single-point energy calculations (1SCF) of medium-size (up to 2500 atoms) molecular systems using GPU coprocessors and multithreaded shared-memory CPUs. Our modifications consisted of using a combination of highly optimized linear algebra libraries for both CPU (LAPACK and BLAS from Intel MKL) and GPU (MAGMA and CUBLAS) to hasten time-consuming parts of MOPAC such as the pseudodiagonalization, full diagonalization, and density matrix assembling. We have shown that it is possible to obtain large speedups just by using CPU serial linear algebra libraries in the MOPAC code. As a special case, we show a speedup of up to 14 times for a methanol simulation box containing 2400 atoms and 4800 basis functions, with even greater gains in performance when using multithreaded CPUs (2.1 times in relation to the single-threaded CPU code using linear algebra libraries) and GPUs (3.8 times). This degree of acceleration opens new perspectives for modeling larger structures which appear in inorganic chemistry (such as zeolites and MOFs), biochemistry (such as polysaccharides, small proteins, and DNA fragments), and materials science (such as nanotubes and fullerenes). In addition, we believe that this parallel (GPU-GPU) MOPAC code will make it feasible to use semiempirical methods in lengthy molecular simulations using both hybrid QM/MM and QM/QM potentials.

Sparkle/PM3 Parameters for the Modeling of Neodymium(III), Promethium(III), and Samarium(III) Complexes.

The Sparkle/PM3 model is extended to neodymium(III), promethium(III), and samarium(III) complexes. The unsigned mean error, for all Sparkle/PM3 interatomic distances between the trivalent lanthanide ion and the ligand atoms of the first sphere of coordination, is 0.074 Å for Nd(III); 0.057 Å for Pm(III); and 0.075 Å for Sm(III). These figures are similar to the Sparkle/AM1 ones of 0.076 Å, 0.059 Å, and 0.075 Å, respectively, indicating they are all comparable models. Moreover, their accuracy is similar to what can be obtained by present-day ab initio effective potential calculations on such lanthanide complexes. Hence, the choice of which model to utilize will depend on the assessment of the effect of either AM1 or PM3 on the quantum chemical description of the organic ligands. Finally, we present a preliminary attempt to verify the geometry prediction consistency of Sparkle/PM3. Since lanthanide complexes are usually flexible, we randomly generated 200 different input geometries for the samarium complex QIPQOV which were then fully optimized by Sparkle/PM3. A trend appeared in that, on average, the lower the total energy of the local minima found, the lower the unsigned mean errors, and the higher the accuracy of the model. These preliminary results do indicate that attempting to find, with Sparkle/PM3, a global minimum for the geometry of a given complex, with the understanding that it will tend to be closer to the experimental geometry, appears to be warranted. Therefore, the sparkle model is seemingly a trustworthy semiempirical quantum chemical model for the prediction of lanthanide complexes geometries.

Structure modeling of trivalent lanthanum and lutetium complexes: Sparkle/PM3.

The recently defined Sparkle model for the quantum chemical prediction of geometries of lanthanum(III) and lutetium(III) complexes within AM1 (J. Phys. Chem. A 2006, 110, 5897) has been extended to PM3. As training sets, we used the same two groups, one for each lanthanide, of 15 high-crystallographic-quality (R factor < 0.05 A) complexes as was previously chosen to parametrize Sparkle/AM1. Likewise, in the validation procedure, we used the same Sparkle/AM1 validation sets of 60 additional La(III) and 15 additional Lu(III) complexes. The Sparkle/PM3 unsigned mean errors for all interatomic distances between the metal ions and the ligand atoms of the first sphere of coordination proved to be random around the means of 0.068 A for lanthanum(III) and 0.076 A for lutetium(III), thus being comparable to the respective Sparkle/AM1 values of 0.078 and 0.075 A. Furthermore, effective-core-potential ab initio calculations on smaller subsets of such complexes led to similar accuracies. Sparkle/PM3 and Sparkle/AM1 are therefore made available to the researcher who must decide which of the models to use based on considerations of the impact of either PM3 or AM1 on the description of the ligands and the consequence of such a choice on the properties of interest.

Lanthanide complex coordination polyhedron geometry prediction accuracies of ab initio effective core potential calculations.

lanthanide coordination compounds efficiently and accurately is central for the design of new ligands capable of forming stable and highly luminescent complexes. Accordingly, we present in this paper a report on the capability of various ab initio effective core potential calculations in reproducing the coordination polyhedron geometries of lanthanide complexes. Starting with all combinations of HF, B3LYP and MP2(Full) with STO-3G, 3-21G, 6-31G, 6-31G* and 6-31+G basis sets for [Eu(H2O)9]3+ and closing with more manageable calculations for the larger complexes, we computed the fully predicted ab initio geometries for a total of 80 calculations on 52 complexes of Sm(III), Eu(III), Gd(III), Tb(III), Dy(III), Ho(III), Er(III) and Tm(III), the largest containing 164 atoms. Our results indicate that RHF/STO-3G/ECP appears to be the most efficient model chemistry in terms of coordination polyhedron crystallographic geometry predictions from isolated lanthanide complex ion calculations. Moreover, both augmenting the basis set and/or including electron correlation generally enlarged the deviations and aggravated the quality of the predicted coordination polyhedron crystallographic geometry. Our results further indicate that Cosentino et al.'s suggestion of using RHF/3-21G/ECP geometries appears to be indeed a more robust, but not necessarily, more accurate recommendation to be adopted for the general lanthanide complex case. [Figure: see text].

RM1: a reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I.

Twenty years ago, the landmark AM1 was introduced, and has since had an increasingly wide following among chemists due to its consistently good results and time-tested reliability--being presently available in countless computational quantum chemistry programs. However, semiempirical molecular orbital models still are of limited accuracy and need to be improved if the full potential of new linear scaling techniques, such as MOZYME and LocalSCF, is to be realized. Accordingly, in this article we present RM1 (Recife Model 1): a reparameterization of AM1. As before, the properties used in the parameterization procedure were: heats of formation, dipole moments, ionization potentials and geometric variables (bond lengths and angles). Considering that the vast majority of molecules of importance to life can be assembled by using only six elements: C, H, N, O, P, and S, and that by adding the halogens we can now build most molecules of importance to pharmaceutical research, our training set consisted of 1736 molecules, representative of organic and biochemistry, containing C, H, N, O, P, S, F, Cl, Br, and I atoms. Unlike AM1, and similar to PM3, all RM1 parameters have been optimized. For enthalpies of formation, dipole moments, ionization potentials, and interatomic distances, the average errors in RM1, for the 1736 molecules, are less than those for AM1, PM3, and PM5. Indeed, the average errors in kcal x mol(-1) of the enthalpies of formation for AM1, PM3, and PM5 are 11.15, 7.98, and 6.03, whereas for RM1 this value is 5.77. The errors, in Debye, of the dipole moments for AM1, PM3, PM5, and RM1 are, respectively, 0.37, 0.38, 0.50, and 0.34. Likewise, the respective errors for the ionization potentials, in eV, are 0.60, 0.55, 0.48, and 0.45, and the respective errors, in angstroms, for the interatomic distances are 0.036, 0.029, 0.037, and 0.027. The RM1 average error in bond angles of 6.82 degrees is only slightly higher than the AM1 figure of 5.88 degrees, and both are much smaller than the PM3 and PM5 figures of 6.98 degrees and 9.83 degrees, respectively. Moreover, a known error in PM3 nitrogen charges is corrected in RM1. Therefore, RM1 represents an improvement over AM1 and its similar successor PM3, and is probably very competitive with PM5, which is a somewhat different model, and not fully disclosed. RM1 possesses the same analytical construct and the same number of parameters for each atom as AM1, and, therefore, can be easily implemented in any software that already has AM1, not requiring any change in any line of code, with the sole exception of the values of the parameters themselves.