Robust Atomistic Modeling of Materials,Organometallic, and Biochemical Systems

Modern chemistry seems to be unlimited in molecular size and elemental composition. Metal-organic frameworks or biological macromolecules involve complex architectures and a large variety of elements. Yet, a general and broadly applicable theoretical method to describe the structures and interactions of molecules beyond the 1000-atom size regime semi-quantitatively is not self-evident. For this purpose, a generic force field named GFN-FF is presented, which is completely newly developed to enable fast structure optimizations and molecular-dynamics simulations for basically any chemical structure consisting of elements up to radon. The freely available computer program requires only starting coordinates and elemental composition as input from which, fully automatically, all potential-energy terms are constructed. GFN-FF outperforms other force fields in terms of generality and accuracy, approaching the performance of much more elaborate quantum-mechanical methods in many cases.     

CHARMM force field and molecular dynamics simulations of protonated polyethylenimine

As a gene delivery vector, polyethylenimine (PEI) shows one of the highest transfection efficiencies, while effectively protecting DNA from enzyme degradation. The distinctive charge pattern of protonated PEI is widely considered responsible for fundamental process such as DNA condensation into PEI/DNA polyplexes (which are able to enter cells via endocytosis), proton sponge effect (which triggers the release of polyplexes from endosome), and release of DNA from polyplexes (to be further processed inside the nucleus). Our investigations are largely motivated by the crucial need for a realistic molecular mechanics force field (FF) for PEI, and, accordingly, we focus on two major issues: (1) development of a new atomistic (CHARMM) FF for PEI in different protonation states, rigorously derived from high‐quality ab initio calculations performed on model polymers, and (2) molecular dynamics investigations of solvated PEI, providing a detailed picture of the dynamic structuring thereof in dependence on their size and protonation state. The modeled PEI chains are essentially described in terms of gyration radius, end‐to‐end distance, persistence length, radial distribution functions, coordination numbers, and diffusion coefficients. They turn out to be more rigid than in other computational studies and we find diffusion coefficients in fair agreement with experimental data. The developed atomistic FF proves adequate for the realistic modeling of the size and protonation behavior of linear PEI, either as individual chains or composing polyplexes. © 2017 Wiley Periodicals, Inc.     

Force field development for organic molecules: Modifying dihedral and 1–n pair interaction parameters

We comprehensively illustrate a general process of fitting all‐atom molecular mechanics force field (FF) parameters based on quantum mechanical calculations and experimental thermodynamic data. For common organic molecules with free dihedral rotations, this FF format is comprised of the usual bond stretching, angle bending, proper and improper dihedral rotation, and 1–4 scaling pair interactions. An extra format of 1–n scaling pair interaction is introduced when a specific intramolecular rotation is strongly hindered. We detail how the preferred order of fitting all intramolecular FF parameters can be determined by systematically generating characteristic configurations. The intermolecular Van der Waals parameters are initially taken from the literature data but adjusted to obtain a better agreement between the molecular dynamics (MD) simulation results and the experimental observations if necessary. By randomly choosing the molecular configurations from MD simulation and comparing their energies computed from FF parameters and quantum mechanics, the FF parameters can be verified self‐consistently. Using an example of a platform chemical 3‐hydroxypropionic acid, we detail the comparison between the new fitting parameters and the existing FF parameters. In particular, the introduced systematic approach has been applied to obtain the dihedral angle potential and 1–n scaling pair interaction parameters for 48 organic molecules with different functionality. We suggest that this procedure might be used to obtain better dihedral and 1–n interaction potentials when they are not available in the current widely used FF. © 2014 Wiley Periodicals, Inc.     

Force field development for cofactors in the photosystem II

We present a set of force field (FF) parameters compatible with the AMBER03 FF to describe five cofactors in photosystem II (PSII) of oxygenic photosynthetic organisms: plastoquinone‐9 (three redox forms), chlorophyll‐a, pheophytin‐a, heme‐b, and β‐carotene. The development of a reliable FF for these cofactors is an essential step for performing molecular dynamics simulations of PSII. Such simulations are important for the calculation of absorption spectrum and the further investigation of the electron and energy transfer processes. We have derived parameters for partial charges, bonds, angles, and dihedral‐angles from solid theoretical models using systematic quantum mechanics (QM) calculations. We have shown that the developed FF parameters are in good agreement with both ab initio QM and experimental structural data in small molecule crystals as well as protein complexes. © 2012 Wiley Periodicals, Inc.     

Protein‐specific force field derived from the fragment molecular orbital method can improve protein–ligand binding interactions

Accurate computational estimate of the protein–ligand binding affinity is of central importance in rational drug design. To improve accuracy of the molecular mechanics (MM) force field (FF) for protein–ligand simulations, we use a protein‐specific FF derived by the fragment molecular orbital (FMO) method and by the restrained electrostatic potential (RESP) method. Applying this FMO‐RESP method to two proteins, dodecin, and lysozyme, we found that protein‐specific partial charges tend to differ more significantly from the standard AMBER charges for isolated charged atoms. We did not see the dependence of partial charges on the secondary structure. Computing the binding affinities of dodecin with five ligands by MM PBSA protocol with the FMO‐RESP charge set as well as with the standard AMBER charges, we found that the former gives better correlation with experimental affinities than the latter. While, for lysozyme with five ligands, both charge sets gave similar and relatively accurate estimates of binding affinities. © 2013 Wiley Periodicals, Inc.     

Bond detectors for molecular dynamics simulations,Part I: Hydrogen bonds

Charge sensitivity analysis in AMBER force‐field resolution has been used in quest for detectors of hydrogen bonds (HBs). The process of HB formation was investigated on ab initio classical trajectories (B3LYP/6‐31G*) of different nucleobase pairs. Several charge sensitivities, namely: electronegativity, hardness, Fukui function (FF), and polarization matrix, were analyzed. The global and constrained equilibria were considered. It was demonstrated that FF indices and polarization matrix elements are good detectors of HB formation. © 2013 Wiley Periodicals, Inc.     

Molecular Simulations of Fatty‐Acid Methyl Esters and Representative Biodiesel Mixtures

Despite the importance of fatty‐acid methyl esters (FAMEs) as key components of various green solvents, detergents, plasticizers, and biodiesels, our understanding of these systems at the molecular level is limited. An enhanced molecular‐level perspective of FAMEs will enable a detailed analysis of the polymorph and crystallization phenomena that adversely impact flow properties at low temperatures. Presented here, is the parameterization and validation of a charge‐modified generalized amber force field (GAFF) for eight common FAMEs and two representative biodiesel mixtures. Our simulations accurately reproduce available experimental data (e.g. densities and self‐diffusivity coefficients) and their trends, with respect to temperature and degree of unsaturation. Structural analyses from our simulations provide a more detailed picture of liquid‐phase molecular ordering in FAMEs and confirm recent experimental hypotheses. This study provides a firm foundation to initiate further studies into the mechanisms that drive crystallization phenomena at the molecular level.     

Polymer characterization by interaction chromatography

Liquid chromatography (LC) is a powerful tool for the characterization of synthetic polymers, that are inherently heterogeneous in molecular weight, chain architecture, chemical composition, and microstructure. Of different versions of the LC methods, size exclusion chromatography (SEC) is most commonly used for the molecular weight distribution analysis. SEC separates the polymer molecules according to the size of a polymer chain, a well‐defined function of molecular weight for linear homopolymers. The same, however, cannot be said of nonlinear polymers or copolymers. Hence, SEC is ill suited for and inefficient in separating the molecules in terms of chemical heterogeneity, such as differences in chemical composition of copolymers, tacticity, and functionality. For these purposes, another chromatographic method called interaction chromatography (IC) is found as a better tool because its separation mechanism is sensitive to the chemical nature of the molecules. The IC separation utilizes the enthalpic interactions to vary adsorption or partition of solute molecules to the stationary phase. Thus, it is used to separate polymers in terms of their chemical composition distribution or functionality. Further, the IC method has been shown to give rise to much higher resolution over SEC in separating polymers by molecular weight. We present here our recent progress in polymer characterization with this method. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1591‐1607, 2005     

New energy terms for reduced protein models implemented in an off‐lattice force field

Parameterization and test calculations of a reduced protein model with new energy terms are presented. The new energy terms retain the steric properties and the most significant degrees of freedom of protein side chains in an efficient way using only one to three virtual atoms per amino acid residue. The energy terms are implemented in a force field containing predefined secondary structure elements as constraints, electrostatic interaction terms, and a solvent‐accessible surface area term to include the effect of solvation. In the force field the main‐chain peptide units are modeled as electric dipoles, which have constant directions in α‐helices and β‐sheets and variable conformation‐dependent directions in loops. Protein secondary structures can be readily modeled using these dipole terms. Parameters of the force field were derived using a large set of experimental protein structures and refined by minimizing RMS errors between the experimental structures and structures generated using molecular dynamics simulations. The final average RMS error was 3.7 Å for the main‐chain virtual atoms (C_α atoms) and 4.2 Å for all virtual atoms for a test set of 10 proteins with 58–294 amino acid residues. The force field was further tested with a substantially larger test set of 608 proteins yielding somewhat lower accuracy. The fold recognition capabilities of the force field were also evaluated using a set of 27,814 misfolded decoy structures. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1229–1242, 2001     

Automated and efficient quantum chemical determination and energetic ranking of molecular protonation sites

We present an automated quantum chemical protocol for the determination of preferred protonation sites in organic and organometallic molecules containing up to a few hundred atoms. It is based on the Foster–Boys orbital localization method, whereby we automatically identify lone pairs and π orbitals as possible protonation sites. The method becomes efficient in conjunction with the robust and fast GFN‐xTB semiempirical method proposed recently (Grimme et al ., J. Chem. Theory Comput . 2017, 13 , 1989). The protonated isomers that are found within a few seconds to minutes of computational wall‐time on a standard desktop computer are then energetically refined using density functional theory (DFT), where we use a high‐level double‐hybrid reference method to benchmark GFN‐xTB and low‐cost DFT approaches. The proposed DFT/GFN‐xTB/LMO composite protocol is generally applicable to almost arbitrary molecules including transition metal complexes. Importantly it is found that even in electronically complicated cases, the GFN‐xTB optimized protomer structures are reasonable and can safely be used in single‐point DFT calculations. Corrections from energy to free energy mostly have a small effect on computed protomer populations. The resulting protomer equilibrium is valuable, for example, in the context of electrospray ionization mass spectrometry where it may help identify the ionized species and assist the interpretation of the experiment. © 2017 Wiley Periodicals, Inc.     

Substrate selection for optimum qualitative and quantitative single atmospheric particles analysis using nano-manipulation,sequential thin-window electron probe X-ray microanalysis and micro-Raman spectrometry

Sequential electron probe X-ray microanalysis using thin-window energy dispersive X-ray detection (TW-EDX-EPMA) and micro-Raman spectrometry (MRS) on the same atmospheric particle using nano-manipulation, is demonstrated. The advantageous combination of these two techniques allows information on the morphology, size, elemental and molecular composition, as well as the molecular structure of the same individual particle with a diameter as small as 500 nm. The use of an ultra-thin atmospheric window and a cold stage in EPMA enables qualitative and quantitative analysis of low-Z elements like C, N, and O as well as higher-Z elements. The work illustrates substrate optimisation and subsequent application in the analysis of atmospheric particles. Particle relocation was achieved by manipulative transfer onto transmission electron microscope grids, in an environmental scanning electron microscope, using 100 nm glass tips. A moderate correlation between the elemental composition obtained by TW-EDX-EPMA and the molecular fingerprint obtained by MRS is illustrated and its useful application in the interpretation of indoor air quality is discussed.     

Assessment of performance of the general purpose polarizable force field QMPFF3 in condensed phase

The recently introduced force field (FF) QMPFF3 is thoroughly validated in gas, liquid, and solid phases. For the first time, it is demonstrated that a physically well-grounded general purpose FF fitted exclusively to a comprehensive set of high level vacuum quantum mechanical data applied as it is to simulation of condensed phase provides high transferability for a wide range of chemical compounds. QMPFF3 demonstrates accuracy comparable with that of the FFs explicitly fitted to condensed phase data, but due to high transferability it is expected to be successful in simulating large molecular complexes.     

Molecular modeling for Cu(II)‐aminopolycarboxylate complexes: Structures,conformational energies,and ligand binding affinities

A ligand field molecular mechanics (LFMM) force field (FF) has been developed for d⁹ copper(II) complexes of aminopolycarboxylate ligands. Training data were derived from density functional theory (DFT) geometry optimizations of 14 complexes comprising potentially hexadentate N₂O₄, tetrasubstituted ethylenediamine (ed), and propylenediamine cores with various combinations of acetate and propionate side arms. The FF was validated against 13 experimental structures from X‐ray crystallography including hexadentate N₂O₄ donors where the nitrogens donors are forced to be cis and bis‐tridentate ONO ligands which generate complexes with trans nitrogen donors. Stochastic conformational searches for [Cu{ed(acetate)_n (propionate)_4‐n}]^2?, n = 0–4, were carried out and the lowest conformers for each system reoptimized with DFT. In each case, both DFT and LFMM predict the same lowest‐energy conformer and the structures and energies of the higher‐energy conformers are also in satisfactory agreement. The relative interaction energies for n = 0, 2, and 4 computed by molecular mechanics correlate with the experimental log β binding affinities. Adding in the predicted log β values for n = 1 and 3 suggest for this set of complexes a monotonic decrease in log β as the number of propionate arms increases. © 2013 Wiley Periodicals, Inc.     

Simulation of multiphase systems utilizing independent force fields to control intraphase and interphase behavior

Fixed‐charge empirical force fields have been developed and widely used over the past three decades for all‐atom molecular simulations. Most simulation programs providing these methods enable only one set of force field parameters to be used for the entire system. Whereas this is generally suitable for single‐phase systems, the molecular environment at the interface between two phases may be sufficiently different from the individual phases to require a different set of parameters to be used to accurately represent the system. Recently published simulations of peptide adsorption to material surfaces using the CHARMM force field have clearly demonstrated this issue by revealing that calculated values of adsorption free energy substantially differ from experimental results. Whereas nonbonded parameters could be adjusted to correct this problem, this cannot be done without also altering the conformational behavior of the peptide in solution, for which CHARMM has been carefully tuned. We have developed a dual‐force‐field approach (Dual‐FF) to address this problem and implemented it in the CHARMM simulation package. This Dual‐FF method provides the capability to use two separate sets of nonbonded force field parameters within the same simulation: one set to represent intraphase interactions and a separate set to represent interphase interactions. Using this approach, we show that interfacial parameters can be adjusted to correct errors in peptide adsorption free energy without altering peptide conformational behavior in solution. This program thus provides the capability to enable both intraphase and interphase molecular behavior to be accurately and efficiently modeled in the same simulation. © 2012 Wiley Periodicals, Inc.     

Alcohols,ethers, carbohydrates,and related compounds. II. The anomeric effect

The anomeric effect has been studied for a variety of compounds using the MM4 force field, and also using MP2/6-311++G(2d,2p) ab initio calculations and experimental data for reference purposes. Geometries and energies, including conformational, rotational barriers, and heats of formation were examined. Overall, the agreement of MM4 with the experimental and ab initio data is good, and significantly better than the agreement obtained with the MM3 force field. The anomeric effect is represented in MM4 by various explicit terms in the force constant matrix. The bond length changes are accounted for with torsion-stretch elements. The angle changes are accounted for with torsion-bend elements. The energies are taken into account with a number of torsional terms in the usual way. A torsion-torsion interaction is also of some importance. With all of these elements included in the calculation, the MM4 results now appear to be adequately accurate. The heats of formation were examined for a total of 12 anomeric compounds, and the experimental values were fit by MM4 with an RMS error of 0.42 kcal/mol.     

Comparison of Force Fields on the Basis of Various Model Approaches—How To Design the Best Model for the [CnMIM][NTf2] Family of Ionic Liquids

In this contribution, we present two new united‐atom force fields (UA‐FFs) for 1‐alkyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide [C_nMIM][NTf₂] (n=1, 2, 4, 6, 8) ionic liquids (ILs). One is parametrized manually, and the other is developed with the gradient‐based optimization workflow (GROW). By doing so, we wanted to perform a hard test to determine how researchers could benefit from semiautomated optimization procedures. As with our already published all‐atom force field (AA‐FF) for [C_nMIM][NTf₂] (T. Köddermann, D. Paschek, R. Ludwig, ChemPhysChem­ 2007, 8, 2464 ), the new force fields were derived to fit experimental densities, self‐diffusion coefficients, and NMR rotational correlation times for the IL cation and for water molecules dissolved in [C₂MIM][NTf₂]. In the manual force field, the alkyl chains of the cation and the CF₃ groups of the anion were treated as united atoms. In the GROW force field, only the alkyl chains of the cation were united. All other parts of the structures of the ions remained unchanged to prevent any loss of physical information. Structural, dynamic, and thermodynamic properties such as viscosity, cation rotational correlation times, and heats of vaporization calculated with the new force fields were compared with values simulated with the previous AA‐FF and the experimental data. All simulated properties were in excellent agreement with the experimental values. Altogether, the UA‐FFs are slightly superior for speed‐up reasons. The UA‐FF speeds up the simulation by about 100 % and reduces the demanded disk space by about 78 %. More importantly, real time and efforts to generate force fields could be significantly reduced by utilizing GROW. The real time for the GROW parametrization in this work was 2 months. Manual parametrization, in contrast, may take up to 12 months, and this is, therefore, a significant increase in speed, though it is difficult to estimate the duration of manual parametrization.     

An automated approach for the parameterization of accurate intermolecular force‐fields: Pyridine as a case study

An automated protocol is proposed and validated, which integrates accurate quantum mechanical calculations with classical numerical simulations. Intermolecular force fields, (FF) suitable for molecular dynamics (MD) and Monte Carlo simulations, are parameterized through a novel iterative approach, fully based on quantum mechanical data, which has been automated and coded into the PICKY software, here presented. The whole procedure is tested and validated for pyridine, whose bulk phase, described through MD simulations performed with the specifically parameterized FF, is characterized by computing several of its thermodynamic, structural, and transport properties, comparing them with their experimental counterparts. © 2011 Wiley Periodicals, Inc.     

CHARMM36 all‐atom additive protein force field: Validation based on comparison to NMR data

Protein structure and dynamics can be characterized on the atomistic level with both nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations. Here, we quantify the ability of the recently presented CHARMM36 (C36) force field (FF) to reproduce various NMR observables using MD simulations. The studied NMR properties include backbone scalar couplings across hydrogen bonds, residual dipolar couplings (RDCs) and relaxation order parameter, as well as scalar couplings, RDCs, and order parameters for side‐chain amino‐ and methyl‐containing groups. It is shown that the C36 FF leads to better correlation with experimental data compared to the CHARMM22/CMAP FF and suggest using C36 in protein simulations. Although both CHARMM FFs contains the same nonbond parameters, our results show how the changes in the internal parameters associated with the peptide backbone via CMAP and the χ₁ and χ₂ dihedral parameters leads to improved treatment of the analyzed nonbond interactions. This highlights the importance of proper treatment of the internal covalent components in modeling nonbond interactions with molecular mechanics FFs. © 2013 Wiley Periodicals, Inc.     

Partial hessian fitting for determining force constant parameters in molecular mechanics

We present a new protocol for deriving force constant parameters that are used in molecular mechanics (MM) force fields to describe the bond‐stretching, angle‐bending, and dihedral terms. A 3 × 3 partial matrix is chosen from the MM Hessian matrix in Cartesian coordinates according to a simple rule and made as close as possible to the corresponding partial Hessian matrix computed using quantum mechanics (QM). This partial Hessian fitting (PHF) is done analytically and thus rapidly in a least‐squares sense, yielding force constant parameters as the output. We herein apply this approach to derive force constant parameters for the AMBER‐type energy expression. Test calculations on several different molecules show good performance of the PHF parameter sets in terms of how well they can reproduce QM‐calculated frequencies. When soft bonds are involved in the target molecule as in the case of secondary building units of metal‐organic frameworks, the MM‐optimized geometry sometimes deviates significantly from the QM‐optimized one. We show that this problem is rectified effectively by use of a simple procedure called Katachi that modifies the equilibrium bond distances and angles in bond‐stretching and angle‐bending terms. © 2016 Wiley Periodicals, Inc.