Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical ...research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.
Highly charged metal ions act as catalytic centers and structural elements in a broad range of chemical complexes. The nonbonded model for metal ions is extensively used in molecular simulations due ...to its simple form, computational speed, and transferability. We have proposed and parametrized a 12-6-4 LJ (Lennard-Jones)-type nonbonded model for divalent metal ions in previous work, which showed a marked improvement over the 12-6 LJ nonbonded model. In the present study, by treating the experimental hydration free energies and ion–oxygen distances of the first solvation shell as targets for our parametrization, we evaluated 12-6 LJ parameters for 18 M(III) and 6 M(IV) metal ions for three widely used water models (TIP3P, SPC/E, and TIP4PEW). As expected, the interaction energy underestimation of the 12-6 LJ nonbonded model increases dramatically for the highly charged metal ions. We then parametrized the 12-6-4 LJ-type nonbonded model for these metal ions with the three water models. The final parameters reproduced the target values with good accuracy, which is consistent with our previous experience using this potential. Finally, tests were performed on a protein system, and the obtained results validate the transferability of these nonbonded model parameters.
MCPB.py, a python based metal center parameter builder, has been developed to build force fields for the simulation of metal complexes employing the bonded model approach. It has an optimized code ...structure, with far fewer required steps than the previous developed MCPB program. It supports various AMBER force fields and more than 80 metal ions. A series of parametrization schemes to derive force constants and charge parameters are available within the program. We give two examples (one metalloprotein example and one organometallic compound example), indicating the program’s ability to build reliable force fields for different metal ion containing complexes. The original version was released with AmberTools15. It is provided via the GNU General Public License v3.0 (GNU_GPL_v3) agreement and is free to download and distribute. MCPB.py provides a bridge between quantum mechanical calculations and molecular dynamics simulation software packages thereby enabling the modeling of metal ion centers. It offers an entry into simulating metal ions in a number of situations by providing an efficient way for researchers to handle the vagaries and difficulties associated with metal ion modeling.
Monovalent ions play significant roles in various biological and material systems. Recently, four new water models (OPC3, OPC, TIP3P-FB, and TIP4P-FB), with significantly improved descriptions of ...condensed phase water, have been developed. The pairwise interaction between the metal ion and water necessitates the development of ion parameters specifically for these water models. Herein, we parameterized the 12-6 and the 12-6-4 nonbonded models for 12 monovalent ions with the respective four new water models. These monovalent ions contain eight cations including alkali metal ions (Li+, Na+, K+, Rb+, Cs+), transition-metal ions (Cu+ and Ag+), and Tl+ from the boron family, along with four halide anions (F–, Cl–, Br–, I–). Our parameters were designed to reproduce the target hydration free energies (the 12-6 hydration free energy (HFE) set), the ion-oxygen distances (the 12-6 ion-oxygen distance (IOD) set), or both of them (the 12-6-4 set). The 12-6-4 parameter set provides highly accurate structural features overcoming the limitations of the routinely used 12-6 nonbonded model for ions. Specifically, we note that the 12-6-4 parameter set is able to reproduce experimental hydration free energies within 1 kcal/mol and experimental ion-oxygen distances within 0.01 Å simultaneously. We further reproduced the experimentally determined activity derivatives for salt solutions, validating the ion parameters for simulations of ion pairs. The improved performance of the present water models over our previous parameter sets for the TIP3P, TIP4P, and SPC/E water models ( Li, P. et al J. Chem. Theory Comput. 2015 11 1645 1657 ) highlights the importance of the choice of water model in conjunction with the metal ion parameter set.
Metal ions play significant roles in biological systems. Accurate molecular dynamics (MD) simulations on these systems require a validated set of parameters. Although there are more detailed ways to ...model metal ions, the nonbonded model, which employs a 12–6 Lennard-Jones (LJ) term plus an electrostatic potential, is still widely used in MD simulations today due to its simple form. However, LJ parameters have limited transferability due to different combining rules, various water models, and diverse simulation methods. Recently, simulations employing a Particle Mesh Ewald (PME) treatment for long-range electrostatics have become more and more popular owing to their speed and accuracy. In the present work, we have systematically designed LJ parameters for 24 +2 metal (M(II)) cations to reproduce different experimental properties appropriate for the Lorentz–Berthelot combining rules and PME simulations. We began by testing the transferability of currently available M(II) ion LJ parameters. The results showed that there are differences between simulations employing Ewald summation with other simulation methods and that it was necessary to design new parameters specific for PME based simulations. Employing the thermodynamic integration (TI) method and performing periodic boundary MD simulations employing PME, allowed for a systematic investigation of the LJ parameter space. Hydration free energies (HFEs), the ion–oxygen distance in the first solvation shell (IOD), and coordination numbers (CNs) were obtained for various combinations of the parameters of the LJ potential for four widely used water models (TIP3P, SPC/E, TIP4P, and TIP4PEW). Results showed that the three simulated properties were highly correlated. Meanwhile, M(II) ions with the same parameters in different water models produce remarkably different HFEs but similar structural properties. It is difficult to reproduce various experimental values simultaneously because the nonbonded model underestimates the interaction between the metal ions and water molecules at short-range. Moreover, the extent of underestimation increases successively for the TIP3P, SPC/E, TIP4PEW, and TIP4P water models. Nonetheless, we fitted a curve to describe the relationship between ε (the well depth) and radius (R min/2) from experimental data on noble gases to facilitate the generation of the best possible compromise models. Hence, by targeting different experimental values, we developed three sets of parameters for M(II) cations for three different water models (TIP3P, SPC/E, and TIP4PEW). These parameters we feel represent the best possible compromise that can be achieved using the nonbonded model for the ions in combination with simple water models. From a computational uncertainty analysis we estimate that the uncertainty in our computed HFEs is on the order of ±1 kcal/mol. Further improvements will require more advanced nonbonded models likely with inclusion of polarization.
Divalent metal ions play important roles in biological and materials systems. Molecular dynamics simulation is an efficient tool to investigate these systems at the microscopic level. Recently, four ...new water models (OPC3, OPC, TIP3P-FB, and TIP4P-FB) have been developed and better represent the physical properties of water than previous models. Metal ion parameters are dependent on the water model employed, making it necessary to develop metal ion parameters for select new water models. In the present work, we performed parameter scanning for the 12-6 Lennard-Jones nonbonded model of divalent metal ions in conjunction with the four new water models as well as four previous water models (TIP3P, SPC/E, TIP4P, and TIP4P-Ew). We found that these new three-point and four-point water models provide comparable or significantly improved performance for the simulation of divalent metal ions when compared to previous water models in the same category. Among all eight water models, the OPC3 water model yields the best performance for the simulation of divalent metal ions in the aqueous phase when using the 12-6 model. On the basis of the scanning results, we independently parametrized the 12-6 model for 24 divalent metal ions with each of the four new water models. As noted previously, the 12-6 model still fails to simultaneously reproduce the experimental hydration free energy (HFE) and ion-oxygen distance (IOD) values even with these new water models. To solve this problem, we parametrized the 12-6-4 model for the 16 divalent metal ions for which we have both experimental HFE and IOD values for each of the four new water models. The final parameters are able to reproduce both the experimental HFE and IOD values accurately. To validate the transferability of our parameters, we carried out benchmark calculations to predict the energies and geometries of ion–water clusters as well as the ion diffusivity coefficient of Mg2+. By comparison to quantum chemical calculations and experimental data, these results show that our parameters are well designed and have excellent transferability. The metal ion parameters for the 12-6 and 12-6-4 models reported herein can be employed in simulations of various biological and materials systems when using the OPC3, OPC, TIP3P-FB, or TIP4P-FB water model.
Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays ...accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.
Between Two Worlds—A New World: An amalgamation of quantum mechanics and diffraction experiments is a magnifying lens for the quantum phenomena in molecules and materials. In this Review, the new research domain “quantum crystallography” is debated in the context of current research fields. The perspective of becoming an independent natural science is outlined.
Understanding the energetic landscapes of large molecules is necessary for the study of chemical and biological systems. Recently, deep learning has greatly accelerated the development of models ...based on quantum chemistry, making it possible to build potential energy surfaces and explore chemical space. However, most of this work has focused on organic molecules due to the simplicity of their electronic structures as well as the availability of data sets. In this work, we build a deep learning architecture to model the energetics of zinc organometallic complexes. To achieve this, we have compiled a configurationally and conformationally diverse data set of zinc complexes using metadynamics to overcome the limitations of traditional sampling methods. In terms of the neural network potentials, our results indicate that for zinc complexes, partial charges play an important role in modeling the long-range interactions with a neural network. Our developed model outperforms semiempirical methods in predicting the relative energy of zinc conformers, yielding a mean absolute error (MAE) of 1.32 kcal/mol with reference to the double-hybrid PWPB95 method.
Transition metal complexes are a class of compounds with varied and versatile properties, making them of great technological importance. Their applications cover a wide range of fields, either as ...metallodrugs in medicine or as materials, catalysts, batteries, solar cells, etc. The demand for the novel design of transition metal complexes with new properties remains of great interest. However, the traditional high-throughput screening approach is inherently expensive and laborious since it depends on human expertise. Here, we present LigandDiff, a generative model for the de novo design of novel transition metal complexes. Unlike the existing methods that simply extract and combine ligands with the metal to get new complexes, LigandDiff aims at designing configurationally novel ligands from scratch, which opens new pathways for the discovery of organometallic complexes. Moreover, it overcomes the limitations of current methods, where the diversity of new complexes highly relies on the diversity of available ligands, while LigandDiff can design numerous novel ligands without human intervention. Our results indicate that LigandDiff designs unique and novel ligands under different contexts, and these generated ligands are synthetically accessible. Moreover, LigandDiff shows good transferability by generating successful ligands for any transition metal complex.
Monovalent ions play fundamental roles in many biological processes in organisms. Modeling these ions in molecular simulations continues to be a challenging problem. The 12–6 Lennard-Jones (LJ) ...nonbonded model is widely used to model monovalent ions in classical molecular dynamics simulations. A lot of parameterization efforts have been reported for these ions with a number of experimental end points. However, some reported parameter sets do not have a good balance between the two Lennard-Jones parameters (the van der Waals (VDW) radius and potential well depth), which affects their transferability. In the present work, via the use of a noble gas curve we fitted in former work ( J. Chem. Theory Comput. 2013, 9, 2733 ), we reoptimized the 12–6 LJ parameters for 15 monovalent ions (11 positive and 4 negative ions) for three extensively used water models (TIP3P, SPC/E, and TIP4PEW). Since the 12–6 LJ nonbonded model performs poorly in some instances for these ions, we have also parameterized the 12–6–4 LJ-type nonbonded model ( J. Chem. Theory Comput. 2014, 10, 289 ) using the same three water models. The three derived parameter sets focused on reproducing the hydration free energies (the HFE set) and the ion–oxygen distance (the IOD set) using the 12–6 LJ nonbonded model and the 12–6–4 LJ-type nonbonded model (the 12−6−4 set) overall give improved results. In particular, the final parameter sets showed better agreement with quantum mechanically calculated VDW radii and improved transferability to ion-pair solutions when compared to previous parameter sets.
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