Ab Initio Quantum Mechanical Charge Field Molecular Dynamics—A Nonparametrized First-Principle Approach to Liquids and Solutions

Characterization of the Coordination and Solvation Dynamics of Solvated Systems─Implications for the Analysis of Molecular Interactions in Solutions and Pure H2O

The characterization of solvation shells of atoms, ions, and molecules in solution is essential to relate solvation properties to chemical phenomena such as complex formation and reactivity. Different definitions of the first-shell coordination sphere from simulation data can lead to potentially conflicting data on the structural properties and associated ligand exchange dynamics. The definition of a solvation shell is typically based on a given threshold distance determined from the respective solute-solvent pair distribution function g(r) (i.e., GC). Alternatively, a nearest neighbor (NN) assignment based on geometric properties of the coordination complex without the need for a predetermined cutoff criterion, such as the relative angular distance (RAD) or the modified Voronoi (MV) tessellation, can be applied. In this study, the effect of different NN algorithms on the coordination number and ligand exchange dynamics evaluated for a series of monatomic ions in aqueous solution, carbon dioxide in aqueous and dichloromethane solutions, and pure liquid water has been investigated. In the case of the monatomic ions, the RAD approach is superior in achieving a well separated definition of the first solvation layer. In contrast, the MV algorithm provides a better separation of the NNs from a molecular point of view, leading to better results in the case of solvated CO2. When analyzing the coordination environment in pure water, the cutoff-based GC framework was found to be the most reliable approach. By comparison of the number of ligand exchange reactions and the associated mean ligand residence times (MRTs) with the properties of the coordination number autocorrelation functions, it is shown that although the average coordination numbers are sensitive to the different definitions of the first solvation shell, highly consistent estimates for the associated MRT of the solvated system are obtained in the majority of cases.

Storage and Diffusion of Carbon Dioxide in the Metal Organic Framework MOF-5─A Semi-empirical Molecular Dynamics Study

Metal-organic frameworks (MOFs) have attracted increasing attention due to their high porosity for exceptional gas storage applications. MOF-5 belongs to the family of isoreticular MOFs (IRMOFs) and consists of Zn4O6+ clusters linked by 1,4-benzenedicarboxylate. Due to the large number of atoms in the unit cell, molecular dynamics simulation based on density functional theory has proved to be too demanding, while force field models are often inadequate to model complex host-guest interactions. To overcome this limitation, an alternative semi-empirical approach using a set of approximations and extensive parametrization of interactions called density functional tight binding (DFTB) was applied in this work to study CO2 in the MOF-5 host. Calculations of pristine MOF-5 yield very good agreement with experimental data in terms of X-ray diffraction patterns as well as mechanical properties, such as the negative thermal expansion coefficient and the bulk modulus. In addition, different loadings of CO2 were introduced, and the associated self-diffusion coefficients and activation energies were investigated. The results show very good agreement with those of other experimental and theoretical investigations. This study provides detailed insights into the capability of semi-empirical DFTB-based molecular dynamics simulations of these challenging guest@host systems. Based on the comparison of the guest-guest pair distributions observed inside the MOF host and the corresponding gas-phase reference, a liquid-like structure of CO2 can be deduced upon storage in the host material.

Deciphering Structural and Dynamical Properties of Hydrated Cobalt Porphyrins via Ab Initio Quantum Mechanical Charge Field Molecular Dynamics Simulation

The present study successfully implemented the ab initio quantum mechanical charge field molecular dynamics (QMCF MD) formalism for the investigation of structural and dynamical properties of hydrated cobalt-porphyrin complexes. Considering the significance of cobalt ions in biological systems (for instance, vitamin B12), which reportedly incorporate cobalt ions in a d6, low spin, +3 state chelated in the corrin ring, an analog of porphyrin, the current study is focused on cobalt in the oxidation states +2 and +3 bound to the parent porphyrin lead structures embedded in an aqueous solution. These cobalt-porphyrin complexes were investigated in terms of their structural and dynamical properties at the quantum chemical level. The structural attributes of these hydrated complexes revealed the contrasting features of the water binding to these solutes, including a detailed evaluation of the associated dynamics. The study also yielded notable findings in regard to the respective electronic configurations vs coordination, which suggested that Co(II)-POR possesses a 5-fold square pyramidal coordination geometry in an aqueous solution containing the metal ion coordinating to four nitrogen atoms of the porphyrin ring and one axial water as the fifth ligand. On the other hand, high-spin Co(III)-POR was hypothesized to be more stable due to the smaller size-to-charge ratio of the cobalt ion, but the high-spin complex demonstrated unstable structural and dynamical behavior. However, the corresponding properties of the hydrated Co(III)_LS-POR revealed a stable structure in an aqueous solution, thus suggesting the Co(III) ion to be in a low-spin state when bound to the porphyrin ring. Moreover, the structural and dynamical data were augmented by computing the free energy of water binding to the cobalt ions and the solvent-accessible surface area, which provide further information on thermochemical properties of the metal-water interaction and the hydrogen bonding potential of the porphyrin ring in these hydrated systems.

Cu2+ in liquid ammonia-The impact of solvent flexibility and electron correlation in ab initio quantum mechanical charge field molecular dynamics

The impact of solvent flexibility and electron correlation on the simulation results of Cu²⁺ in liquid ammonia has been investigated via an ab initio quantum mechanical charge field molecular dynamics (QMCF MD) simulation approach. To achieve this, three different simulation systems were considered in this study, namely Cu²⁺ in rigid and flexible ammonia at Hartree-Fock (HF) level of theory, as well as resolution of identity second order Møller-Plesset (MP2) perturbation theory in the rigid body case. In all cases, a stable octahedral [Cu(NH₃ )₆ ]²⁺ complex subject to dynamic Jahn-Teller distortions without the occurrence of ligand exchange was observed. The Cu²⁺  - NH₃ distance in the first shell agrees well with the experimental and other theoretical data. In all three cases, the structural data shows that the rigid-body ammonia model in conjunction with the HF level of theory provides accurate data for the first solvation shell, while at the same time, the computational demand and thus the achievable simulation time are much more beneficial. The vibrational analysis of the Cu²⁺  - NH₃ interaction yields similar force constants in the three investigated systems indicating that there is no distinct difference on the dynamical properties of the first solvation shell. In addition to the QMCF MD simulations, a number of natural bond orbital (NBO) analyses were carried out, confirming the strong electrostatic character of the Cu²⁺  - NH₃ interaction.

Hybrid Solvation Model with First Solvation Shell for Calculation of Solvation Free Energy

We present a hybrid solvation model with first solvation shell to calculate solvation free energies. This hybrid model combines the quantum mechanics and molecular mechanics methods with the analytical expression based on the Born solvation model to calculate solvation free energies. Based on calculated free energies of solvation and reaction profiles in gas phase, we set up a unified scheme to predict reaction profiles in solution. The predicted solvation free energies and reaction barriers are compared with experimental results for twenty bimolecular nucleophilic substitution reactions. These comparisons show that our hybrid solvation model can predict reliable solvation free energies and reaction barriers for chemical reactions of small molecules in aqueous solution.

Hydration of Closely Related Manganese and Magnesium Porphyrins in Aqueous Solutions: Ab Initio Quantum Mechanical Charge Field Molecular Dynamics Simulation Study

To the best of our knowledge, the current study based on ab initio quantum mechanical charge field molecular dynamics (QMCF-MD) is the first to explore the difference in the hydration behavior between Mn(II)- and Mg(II)-associated porphyrins (Mn(II)-POR and Mg(II)-POR) in aqueous solution. The simulation study highlights similar and dissimilar characteristics of the structural, dynamical, and thermodynamical properties of these closely related metals bound to porphyrins in aqueous solution. The structural analysis is based on radial and angular distribution functions, coordination number distributions, and angular-radial distributions. Both hydrated systems demonstrate similar pentacoordinated structures formed via the axial coordination of one water molecule to the metal ion in addition to the four nitrogen atoms of the porphyrin ring. However, in the case of Mn(II)-POR, the formation of a distorted square pyramidal geometry was observed. It was envisaged as a weak coordination of the water molecule to the Mn(II) atom and thus higher atomic fluctuation for all atoms in contrast to that for the hydrated Mg(II)-POR. The dynamical data in terms of the mean residence times, velocity autocorrelation function, free energy, and other parameters revealed the difference in the metal binding effect because the Mn(II) atom was observed to inhibit H-bond formation more than the presence of Mg(II) atoms in the core of the porphyrin. The current study thus highlights the significant differences in the structural and dynamical properties of Mn(II)- and Mg(II)-associated porphyrin systems.

The Jahn-Teller effect in mixed aqueous solution: the solvation of Cu2+ in 18.6% aqueous ammonia obtained from ab initio quantum mechanical charge field molecular dynamics

The solvation structure and dynamics of Cu2+ in 18.6 % aqueous ammonia have been investigated using an ab initio quantum mechanical charge field molecular dynamics (QMCF MD) simulation approach at the Hartree–Fock (HF) level of theory applying the LANL2DZ ECP and Dunning DZP basis sets for Cu2+, ammonia and water, respectively. During a simulation time of 20 ps, only NH3 molecules are observed within the first solvation shell of Cu2+, resulting in the formation of an octahedral [Cu(NH3)6]2+ complex. While no exchange of these ligands with the second solvation shell are observed along the simulation, the monitoring of the associated N-Ntrans distances highlight the dynamics of the associated Jahn-Teller distortions, showing on average 2 elongated axial (2.19 Å) and 4 equatorial Cu–N bonds (2.39 Å). The observed structural properties are found in excellent agreement with experimental studies. In addition, an NBO analysis was carried out, confirming the strong electrostatic character of the Cu2+–NH3 interaction.

Structure, Dynamics, and Hydration Free Energy of Carbon Dioxide in Aqueous Solution: A Quantum Mechanical/Molecular Mechanics Molecular Dynamics Thermodynamic Integration (QM/MM MD TI) Simulation Study

The solvation of carbon dioxide in solution represents a key step for the capture and fixation CO₂ in nature, which may be further influenced by the formation of (bi)carbonate species and/or the formation of CO₂ clusters in solution. The latter processes are strongly dependent on the exact environment of the liquid state (e.g., pH value, solvated ions, etc.) and may interfere with the experimental determination of structural, dynamical, and thermodynamic properties. In this work a hybrid quantum mechanical/molecular mechanical (QM/MM) simulation approach at correlated ab initio level of theory resolution-of-identity second-order Møller-Plesset Perturbation Theory (RI-MP2) has been applied in the framework of thermodynamic integration (TI) to study structure, dynamics, and the hydration free energy of a single carbon dioxide molecule in aqueous solution. A detailed analysis of the individual QM/MM potential energy contributions demonstrate that the overall potential remains highly consistent over the entire sampling phase and that no artificial contributions are influencing the determination of the hydration free energy. The latter value of 0.01 ± 0.92 kcal/mol was found in very good agreement with the values of 0.06 and 0.24 kcal/mol obtained via quasi-chemical theory and experimental measurements, respectively. In order to obtain detailed information about the C- and O _C-water interaction, conically restricted regions with respect to the main axis of the CO₂ molecule have been employed in structural analysis. The presented data not only provide detailed information about the hydration properties of CO₂ but act as a critical validation of the simulation technique, which will be beneficial in the study of nonaqueous solvents such as pure and aqueous NH₃ solutions, which have been suggested as potential candidates to capture CO₂ from anthropogenic sources.

Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δ_s G_M⁺,wat^◦ of the Li⁺ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χ_wat^◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol^-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol^-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li⁺ are also compared to those for Na⁺ and K⁺ from a previous study in terms of relative hydration free energies ΔΔ_s G_M⁺,wat^◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔ_s G_M⁺,wat^• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li⁺ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

Towards a dissociative SPC-like water model II. The impact of Lennard-Jones and Buckingham non-coulombic forces

The dissociative water potential by Garofalini and coworkers has been re-formulated in the framework of the widely employed Lennard-Jones and Buckingham potentials, enhancing the transferability of the model to third party simulation programs.

Square planar or octahedral after all? The indistinct solvation of platinum(ii)

The solvation structures of Pd(ii) and Pt(ii) are typically reduced to the well-known square-planar structural motif, although it has been shown, in both experimental and theoretical investigations, that these solutes demonstrate the affinity to bind ligand molecules at elongated distance in axial coordination sites.

Hydration of iron-porphyrins: ab initio quantum mechanical charge field molecular dynamics simulation study

The ab initio quantum mechanical charge field molecular dynamics (QMCF-MD) simulation approach was successfully applied to Fe²⁺-P and Fe³⁺-P in water to evaluate their structural, dynamical and energetic properties. Based on the structural data, it was found that Fe²⁺-P accommodates one water molecule in the first coordination sphere of the Fe²⁺ ion including the four nitrogen atoms of the porphyrin system coordinating with central metal species. On the other hand, two water molecules were coordinated to Fe³⁺-P, thus forming a hexa-coordinated species. Comparison of dynamical properties such as the vibrational power spectrum and ligand mean residence times to other metal-free porphyrin systems demonstrate the ions' influence on the hydration structure, enabling a characterisation of the strong interaction of the ions which greatly reduces the hydrogen bonding potential of the complex. The association of water molecules with the metal ions in both solutes was quantified by computing the free energy of binding obtained via the potential of mean force. This further confirmed the strong association of water to the metal ions which was conversely weak as inferred from the energetic data for the Fe²⁺-P system.

The Binding Mode of the Sonic Hedgehog Inhibitor Robotnikinin, a Combined Docking and QM/MM MD Study

Erroneous activation of the Hedgehog pathway has been linked to a great amount of cancerous diseases and therefore a large number of studies aiming at its inhibition have been carried out. One leverage point for novel therapeutic strategies targeting the proteins involved, is the prevention of complex formation between the extracellular signaling protein Sonic Hedgehog and the transmembrane protein Patched 1. In 2009 robotnikinin, a small molecule capable of binding to and inhibiting the activity of Sonic Hedgehog has been identified, however in the absence of X-ray structures of the Sonic Hedgehog-robotnikinin complex, the binding mode of this inhibitor remains unknown. In order to aid with the identification of novel Sonic Hedgehog inhibitors, the presented investigation elucidates the binding mode of robotnikinin by performing an extensive docking study, including subsequent molecular mechanical as well as quantum mechanical/molecular mechanical molecular dynamics simulations. The attained configurations enabled the identification of a number of key protein-ligand interactions, aiding complex formation and providing stabilizing contributions to the binding of the ligand. The predicted structure of the Sonic Hedgehog-robotnikinin complex is provided via a PDB file as Supplementary Material and can be used for further reference.

Zinc- and copper-porphyrins in aqueous solution - two similar complexes with strongly contrasting hydration

We present detailed analysis of the hydration behavior of zinc and copper bound porphyrins treated via ab initio quantum mechanical charge field molecular dynamics which agrees well with available experimental data. The computed metal-water coordination in the case of zinc bound porphyrin demonstrates a strong association of water with zinc compared to the copper-water interaction which correlates well with the calculated free energy of binding. The H-bond dynamics in these hydrated systems yield weaker H-bond interactions as compared to that observed in the case of metal-free porphyrin; nevertheless, the effect of metal association with porphyrin resulted in shifts in the vibrational frequencies. These characteristic data suggest a contrasting behavior between these metalloporphyrins in solution which could also serve to correlate with the properties of biological systems.

Palladium(ii) in liquid ammonia: an investigation of structural and dynamical properties by applying quantum mechanical charge field molecular dynamics (QMCF-MD)

The structural and dynamical properties of Pd²⁺ in liquid ammonia have been investigated via quantum mechanical charge field molecular dynamics.

Towards a dissociative SPC-like water model – probing the impact of intramolecular Coulombic contributions

A modification of the dissociative Garofalini water model towards an SPC-like Coulombic formulation proved to enhance accuracy and transferability of this successful force field approach.

A Comparative Study of [CaEDTA](2-) and [MgEDTA](2-): Structural and Dynamical Insights from Quantum Mechanical Charge Field Molecular Dynamics

Structure and dynamics of [MgEDTA](2-) and [CaEDTA](2-) complexes in aqueous solution have been investigated via quantum mechanical/molecular mechanical (QM/MM) simulations. While for the first a 6-fold octahedral complex has been observed, the presence of an additional coordinating water ligand has been observed in the latter case. Because of rapidly exchanging water molecules, this 7-fold coordination complex was found to form pentagonal bipyramidal as well as capped trigonal prismatic configurations along the simulation interchanging on the picosecond time scale. Also in the case of [MgEDTA](2-) a trigonal prismatic configuration has been observed for a very short time period of approximately 1 ps. This work reports for the first time the presence of trigonal prismatic structures observed in the coordination sphere of [MgEDTA](2-) and [CaEDTA](2-) complexes in aqueous solution. In addition to the detailed characterization of structure and dynamics of the systems, the prediction of the associated infrared spectra indicates that the ion-water vibrational mode found at approximately 250 cm(-1) provides a distinctive measure to experimentally detect the presence of the coordinating water molecule via low-frequency IR setups.

Remarkable conformational flexibility of aqueous 18-crown-6 and its strontium(II) complex-ab initio molecular dynamics simulations

Ab initio QMCF-MD simulations of aqueous 18-crown-6 (18C6) and strontium(II)-18-crown-6 (18C6-Sr) were performed to gather insight into their hydration properties. Strongly different characteristics were found for the two solutes in terms of structure and dynamics such as H-bonding. They, however, have in common that their backbone shows high flexibility in aqueous medium, adopting structures significantly differing from idealized gas phase geometries. In particular, planar oxyethylene units stable in the picosecond range occurred in 18C6, while the strontium complex readily exhibits a bent structure. Detailed analysis of this high flexibility was done via two dimensional root mean square deviation plots as well as the evolution of dihedral angles and angles within the simulation trajectory. The vibrational spectra obtained from the QMCF-MD simulations are in excellent agreement with experimental data and show a pronounced blueshift upon complexation of the strontium(II) ion in 18C6.

Structure and water exchange dynamics of hydrated oxo halo ions in aqueous solution using QMCF MD simulation, large angle X-ray scattering and EXAFS

Theoretical ab initio quantum mechanical charge field molecular dynamics (QMCF MD) has been applied in conjunction with experimental large angle X-ray scattering (LAXS) and EXAFS measurements to study structure and dynamics of the hydrated oxo chloro anions chlorite, ClO2(-), chlorate, ClO3(-), and perchlorate, ClO4(-). In addition, the structures of the hydrated hypochlorite, ClO(-), bromate, BrO3(-), iodate, IO3(-) and metaperiodate, IO4(-), ions have been determined in aqueous solution by means of LAXS. The structures of the bromate, metaperiodate, and orthoperiodate, H2IO6(3-), ions have been determined by EXAFS as solid sodium salts and in aqueous solution as well. The results show clearly that the only form of periodate present in aqueous solution is metaperiodate. The Cl-O bond distances in the hydrated oxo chloro anions as determined by LAXS and obtained in the QMCF MD simulations are in excellent agreement, being 0.01-0.02 Å longer than in solid anhydrous salts due to hydration through hydrogen bonding to water molecules. The oxo halo anions, all with unit negative charge, have low charge density making them typical structure breakers, thus the hydrogen bonds formed to the hydrating water molecules are weaker and more short-lived than those between water molecules in pure water. The water exchange mechanism of the oxo chloro anions resembles those of the oxo sulfur anions with a direct exchange at the oxygen atoms for perchlorate and sulfate. The water exchange rate for the perchlorate ion is significantly faster, τ0.5 = 1.4 ps, compared to the hydrated sulfate ion and pure water, τ0.5 = 2.6 and 1.7 ps, respectively. The angular radial distribution functions show that the chlorate and sulfite ions have a more complex water exchange mechanism. As the chlorite and chlorate ions are more weakly hydrated than the sulfite ion the spatial occupancy is less well-defined and it is not possible to follow any well-defined migration pattern as it is difficult to distinguish between hydrating water molecules and bulk water in the region close to the ions.

Perspectives for hybrid ab initio/molecular mechanical simulations of solutions: from complex chemistry to proton-transfer reactions and interfaces

As a consequence of the ongoing development of enhanced computational resources, theoretical chemistry has become an increasingly valuable field for the investigation of a variety of chemical systems. Simulations employing a hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) technique have been shown to be a particularly promising approach, whenever ultrafast (i.e., picosecond) dynamical properties are to be studied, which are in many cases difficult to access via experimental techniques. Details of the quantum mechanical charge field (QMCF) ansatz, an advanced QM/MM protocol, are discussed and simulation results for various systems ranging from simple ionic hydrates to solvated organic molecules and coordination complexes in solution are presented. A particularly challenging application is the description of proton-transfer reactions in chemical simulations, which is a prerequisite to study acidified and basic systems. The methodical requirements for a combination of the QMCF methodology with a dissociative potential model for the description of the solvent are discussed. Furthermore, the possible extension of QM/MM approaches to solid/liquid interfaces is outlined.

Structure and water exchange of the hydrated thiosulfate ion in aqueous solution using QMCF MD simulation and large angle X-ray scattering

Experimental and simulation data of the thiosulfate ion show large similarities in hydration structure and mechanism with the sulfate ion but with weaker hydration of the terminal sulfur atom in thiosulfate.

Erbium(III) in aqueous solution: an ab initio molecular dynamics study

Structural and dynamical properties of the erbium(III) ion in water have been obtained by means of ab initio quantum mechanical charge field molecular dynamics (QMCF-MD) simulations for the ground state and an excited state. The quality of the simulations has been monitored by recording UV/vis and Raman spectra of dilute solutions of ErCl3 and Er(NO3)3 in water and by comparison with EXAFS data from literature. Slight deviations between these data can be mainly attributed to relativistic effects, which are not sufficiently considered by the methodological framework. In both simulations, a mixture of coordination numbers eight and nine and a ligand exchange on the picosecond range are observed. The strength of the Er-ligand bond is considerably lower than that of trivalent transition metal ions but higher than that for La(III) and Ce(III) in aqueous solution. The main difference between ground state and excited state is the ligand exchange rate of the first shell. The second hydration shell is stable in both cases but with significantly different properties.