The Jahn-Teller effect of the TiIII ion in aqueous solution: extended ab initio QM/MM molecular dynamics simulations.

Combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations, including only the first and the first and second hydration shells in the QM region, were performed for TiIII in aqueous solution. The hydration structure of TiIII is discussed in terms of radial distribution functions, coordination-number distributions and several angle distributions. Dynamical properties, such as librational and vibrational motions and TiIII-O vibrations, were evaluated. A fast dynamical Jahn-Teller effect of TiIII(aq) was observed in the QM/MM simulations, in particular when the second hydration shell was included into the QM region. The results justify the computational effort required for the inclusion of the second hydration shell into the QM region and show the importance of this effort for obtaining accurate hydration-shell geometries, dynamical properties, and details of the Jahn-Teller effect.     

Dynamical properties of the water molecules in the hydration shells of Fe(II) and Fe(III) ions: ab initio QM/MM molecular dynamics simulations

Dynamical properties, librational and vibrational motions of water molecules in the first and second hydration shells of the Fe(II) and Fe(III) ion were evaluated by means of velocity autocorrelation functions obtained by combined quantum mechanical/molecular mechanical molecular dynamics (QM/MM-MD) simulations. The frequencies of rotation around three principal axes and the frequencies of intramolecular vibration of the water molecules in the first hydration shells obtained from the simulations are blue-shifted for both ions compared to those observed experimentally for liquid water. The intramolecular geometry of water molecules in the quantum mechanically treated region (ion plus first hydration shell) shows shorter O–H bonds and wider H–O–H angles than the bulk solvent.     

Be(II) in aqueous solution--an extended ab initio QM/MM MD study

An ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulation at double-zeta restricted Hartree-Fock (RHF) level was performed at 293.15 K, including first and second hydration shell in the QM region to study the structural and dynamical properties of the Be(II)-hydrate in aqueous solution. The first tetrahedrally arranged hydration shell, with the four water molecules located at a mean Be-O distance of 1.61 A, is highly inert with respect to ligand exchange processes. The second shell, however, consisting in average of approximately 9.2 water ligands at a mean Be-O distance of 3.7 A and the third shell at a mean Be-O distance of 5.4 A with approximately 19 ligands rapidly exchange water molecules between them and with the bulk, respectively. Other structural parameters such as radial and angular distribution functions (RDF and ADF) and tilt- and theta-angle distributions were also evaluated. The dynamics of the hydrate were studied in terms of ligand mean residence times (MRTs) and librational and vibrational frequencies. The mean residence times for second shell and third shell ligands were determined as 4.8 and 3.2 ps, respectively. The Be-O stretching frequency of 658 cm(-1), associated with a force constant of 147 N m(-1) could be overestimated but it certainly reflects the exceptional stability of the ion-ligand bond in the first hydration shell.     

Ab initio QM/MM simulation of Ag+ in 18.6% aqueous ammonia solution: structure and dynamics investigations

Structure and dynamics investigations of Ag(+) in 18.6% aqueous ammonia solution have been carried out by means of the ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulation method. The most important region, the first solvation shell, was treated by ab initio quantum mechanics at the Restricted Hartree-Fock (RHF) level using double-zeta plus polarization basis sets for ammonia and plus ECP for Ag(+). For the remaining region in the system, newly constructed three-body corrected potential functions were used. The average composition of the first solvation shell was found to be [Ag(NH(3))(2)(H(2)O)(2.8)](+). No ammonia exchange process was observed for the first solvation shell, whereas ligand exchange processes occurred with a very short mean residence time of 1.1 ps for the water ligands. No distinct second solvation shell was observed in this simulation.     

Structure and dynamics of the CrIII ion in aqueous solution: Ab initio QM/MM molecular dynamics simulation

Structural and dynamical properties of the Cr(III) ion in aqueous solution have been investigated using a combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation. The hydration structure of Cr(III) was determined in terms of radial distribution functions, coordination numbers, and angular distributions. The QM/MM simulation gives coordination numbers of 6 and 15.4 for the first and second hydration shell, respectively. The first hydration shell is kinetically very inert but by no means rigid and variations of the first hydration shell geometry lead to distinct splitting in the vibrational spectra of Cr(H(2)O)(6) (3+). A mean residence time of 22 ps was obtained for water ligands residing in the second hydration shell, which is remarkably shorter than the experimentally estimated value. The hydration energy of -1108 +/- 7 kcal/mol, obtained from the QM/MM simulation, corresponds well to the experimental hydration enthalpy value.     

Structure and dynamics of high-spin Ru in aqueous solution: Ab initio QM/MM molecular dynamics simulation

The structural and dynamical properties of high-spin Ru²⁺ in aqueous solution have been theoretically studied using molecular dynamics (MD) simulations. The conventional MD simulation based on pair potentials gives the overestimated average first shell coordination number of 9, whereas the value of 5.9 was observed when the three-body corrected function was included. A combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation has been performed to take into account the many-body effects on the hydration shell structure of Ru²⁺. The most important region, the first hydration shell, was treated by ab initio quantum mechanics at UHF level using the SBKJC VDZ ECP basis set for Ru²⁺ and the 6-31G^∗ basis sets for water. An exact coordination number of 6 for the first hydration shell was obtained from the QM/MM simulation. The QM/MM simulation predicts the average Ru²⁺–O distance of 2.42 Å for the first hydration shell, whereas the values of 2.34 and 2.46 Å are resulted from the pair potentials without and with the three-body corrected simulations, respectively. Several other structural properties representing position and orientation of the solvate molecules were evaluated for describing the hydration shell structure of the Ru²⁺ ion in dilute aqueous solution. A mean residence time of 7.1 ps was obtained for water ligands residing in the second hydration shell.     

Characterization of structure and dynamics of an aqueous scandium(iii) ion by an extended ab initio QM/MM molecular dynamics simulation

Hydration structure and dynamics of an aqueous Sc(iii) solution were characterized by means of an extended ab initio quantum mechanical/molecular dynamical (QM/MM) molecular dynamics simulation at Hartree-Fock level. A monocapped trigonal prismatic structure composed of seven water molecules surrounding scandium(iii) ion was proposed by the QM/MM simulation including the quantum mechanical effects for the first and second hydration shells. The mean Sc(iii)-O bond length of 2.14 ? was identified for six prism water molecules with one capping water located at around 2.26 ?, reproducing well the X-ray diffraction data. The Sc(iii)-O stretching frequency of 432 cm(-1) corresponding to a force constant of 130 N m(-1), evaluated from the enlarged QM/MM simulation, is in good agreement with the experimentally determined value of 430 cm(-1) (128 N m(-1)). Various water exchange processes in the second hydration shell of the hydrated Sc(iii) ion predict a mean ligand residence time of 7.3 ps.     

Quantum mechanical/molecular mechanical simulations of the Tl(III) ion in water

Classical molecular dynamics (MD) and combined quantum mechanical/molecular mechanical (QM/MM) MD simulations have been performed to investigate the structural and dynamical properties of the Tl(III) ion in water. A six-coordinate hydration structure with a maximum probability of the Tl-O distance at 2.21 A was observed, which is in good agreement with X-ray data. The librational and vibrational spectra of water molecules in the first hydration shell are blue-shifted compared with those of pure liquid water, and the Tl-O stretching force constant was evaluated as 148 Nm(-1). Both structural and dynamical properties show a distortion of the first solvation shell structure. The second shell ligands' mean residence time was determined as 12.8 ps. The Tl(III) ion can be classified as "structure forming" ion; the calculated hydration energy of -986 +/- 9 kcal mol agrees well with the experimental value of -986 kcal mol.     

Structure and dynamics of hydrated NH(4) (+): an ab initio QM/MM molecular dynamics simulation

A combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation has been performed to investigate solvation structure and dynamics of NH(4) (+) in water. The most interesting region, the sphere includes an ammonium ion and its first hydration shell, was treated at the Hartree-Fock level using DZV basis set, while the rest of the system was described by classical pair potentials. On the basis of detailed QM/MM simulation results, the solvation structure of NH(4) (+) is rather flexible, in which many water molecules are cooperatively involved in the solvation shell of the ion. Of particular interest, the QM/MM results show fast translation and rotation of NH(4) (+) in water. This phenomenon has resulted from multiple coordination, which drives the NH(4) (+) to translate and rotate quite freely within its surrounding water molecules. In addition, a "structure-breaking" behavior of the NH(4) (+) is well reflected by the detailed analysis on the water exchange process and the mean residence times of water molecules surrounding the ion.     

The Jahn-Teller effect of the Cr(2+) ion in aqueous solution: Ab initio QM/MM molecular dynamics simulations

The hydration structure of Cr(2+) has been studied using molecular dynamics (MD) simulations including three-body corrections and combined ab initio quantum mechanical/molecular mechanical (QM/MM) MD simulations at the Hartree-Fock level. The structural properties are determined in terms of radial distribution functions, coordination numbers, and several angle distributions. The mean residence time was evaluated for describing ligand exchange processes in the second hydration shell. The Jahn-Teller distorted octahedral [Cr(H(2)O)(6)](2+) complex was pronounced in the QM/MM MD simulation. The first-shell distances of Cr(2+) are in the range of 1.9-2.8 A, which are slightly larger than those observed in the cases of Cu(2+) and Ti(3+). No first-shell water exchange occurred during the simulation time of 35 ps. Several water-exchange processes were observed in the second hydration shell with a mean residence time of 7.3 ps.     

Hydration shell structure and dynamics of curium(III) in aqueous solution: first principles and empirical studies

Results of ab initio molecular dynamics (AIMD), quantum mechanics/molecular mechanics (QM/MM), and classical molecular dynamics (CMD) simulations of Cm(3+) in liquid water at a temperature of 300 K are reported. The AIMD simulation was based on the Car-Parrinello MD scheme and GGA-PBE formulation of density functional theory. Two QM/MM simulations were performed by treating Cm(3+) and the water molecules in the first shell quantum mechanically using the PBE (QM/MM-PBE) and the hybrid PBE0 density functionals (QM/MM-PBE0). Two CMD simulations were carried out using ab initio derived pair plus three-body potentials (CMD-3B) and empirical Lennard-Jones pair potential (CMD-LJ). The AIMD and QM/MM-PBE simulations predict average first shell hydration numbers of 8, both of which disagree with recent experimental EXAFS and TRLFS value of 9. On the other hand, the average first shell hydration numbers obtained in the QM/MM-PBE0 and CMD simulations was 9, which agrees with experiment. All the simulations predicted an average first shell and second shell Cm-O bond distance of 2.49-2.53 ? and 4.67-4.75 ? respectively, both of which are in fair agreement with corresponding experimental values of 2.45-2.48 and 4.65 ?. The geometric arrangement of the 8-fold and 9-fold coordinated first shell structures corresponded to the square antiprism and tricapped trigonal prisms, respectively. The second shell hydration number for AIMD QM/MM-PBE, QM/MM-PBE0, CMD-3B, and CMD-LJ, were 15.8, 17.2, 17.7, 17.4, and 16.4 respectively, which indicates second hydration shell overcoordination compared to a recent EXAFS experimental value of 13. Save the EXAFS spectra CMD-LJ simulation, all the computed EXAFS spectra agree fairly well with experiment and a clear distinction could not be made between configurations with 8-fold and 9-fold coordinated first shells. The mechanisms responsible for the first shell associative and dissociative ligand exchange in the classical simulations have been analyzed. The first shell mean residence time was predicted to be on the nanosecond time scale. The computed diffusion constants of Cm(3+) and water are in good agreement with experimental data.     

Structure-breaking effects of solvated Rb(I) in dilute aqueous solution--an ab initio QM/MM MD approach

Structural properties of the hydrated Rb(I) ion have been investigated by ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations at the double-zeta HF quantum mechanical level. The first shell coordination number was found to be 7.1, and several other structural parameters such as angular distribution functions, radial distribution functions and tilt- and theta-angle distributions allowed the full characterization of the hydration structure of the Rb(I) ion in dilute aqueous solution. Velocity autocorrelation functions were used to calculate librational and vibrational motions, ion-ligand motions, as well as reorientation times. Different dynamical parameters such as water reorientation, mean ligand residence time, the number of ligand exchange processes, and rate constants were also analyzed. The mean ligand residence time for the first shell was determined as tau = 2.0 ps.     

Structure and dynamics of the [Zn(NH3)(H2O)5]2+ complex in aqueous solution obtained by an ab initio QM/MM molecular dynamics study

A model complex of the hexahydrated zinc(ii) cation with one water substituted by ammonia in aqueous solution has been studied by hybrid ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) at the double-zeta Hartree-Fock (HF) quantum mechanical level. The first solvation shell, consisting of 5 + 1 ligand(s) at mean distances of 2.2 and 2.1 A, respectively, from the Zn(ii) ion, was found to remain stable with respect to exchange processes within the simulation time. The labile second shell consists on average of approximately 19 water molecules. For structural elucidation of the pentaaquozinc(ii) amine complex in aqueous solution several data sets such as radial distribution functions (RDF), coordination number distributions (CND) and different angular distributions (ADF, tilt and theta angle) were employed. Dynamics were characterised by the ligands' mean residence time (MRT), ion-ligand stretching frequencies and the vibrational and librational motions of water ligands. The labile second shell's MRT value decreases upon introduction of one NH(3) ligand to 7.2 ps from the 10.5 ps observed for the hexaaquozinc(ii) complex.     

Finite‐field method with unbiased polarizable continuum model for evaluation of the second hyperpolarizability of an open‐shell singlet molecule in solvents

The static second hyperpolarizability γ of the complexes composed of open‐shell singlet 1,3‐dipole molecule involving a boron atom and a water molecule in aqueous phase are investigated by the finite‐field (FF) method combined with a standard polarized continuum model (PCM) and with a newly proposed unbiased PCM (UBPCM). On the basis of the comparison with the results calculated by the FF method using the full quantum and the quantum‐mechanical/molecular‐mechanical and molecular‐dynamics (QM/MM‐MD) treatments, the present FF‐UBPCM method is demonstrated to remedy the artificial overestimation of the γ caused by standard FF‐PCM calculations and to well reproduce the FF‐QM/MM‐MD and FF‐full‐QM results with much lower costs. © 2013 Wiley Periodicals, Inc.     

Structure and dynamics of Au+ ion in aqueous solution: ab initio QM/MM MD simulations

Structure and dynamics of hydrated Au(+) have been investigated by means of molecular dynamics simulations based on ab initio quantum mechanical molecular mechanical forces at Hartree-Fock level for the treatment of the first hydration shell. The outer region of the system was described using a newly constructed classical three-body corrected potential. The structure was evaluated in terms of radial and angular distribution functions and coordination number distributions. Water exchange processes between coordination shells and bulk indicate a very labile structure of the first hydration shell whose average coordination number of 4.7 is a mixture of 3-, 4-, 5-, 6-, and 7-coordinated species. Fast water exchange reactions between first and second hydration shell occur, and the second hydration shell is exceptionally large. Therefore, the mean residence time of water molecules in the first hydration shell (5.6 ps/7.5 ps for t*= 0.5 ps/2.0 ps) is shorter than that in the second shell (9.4 ps/21.2 ps for t*= 0.5 ps/2.0 ps), leading to a quite specific picture of a "structure-breaking" effect.     

Computational methods for the study of enzymic reaction mechanisms III: a perturbation plus QM/MM approach for calculating relative free energies of protonation

We describe a coupling parameter, that is, perturbation, approach to effectively create and annihilate atoms in the quantum mechanical Hamiltonian within the closed shell restricted Hartree-Fock formalism. This perturbed quantum mechanical atom (PQA) method is combined with molecular mechanics (MM) methods (PQA/MM) within a molecular dynamics simulation, to model the protein environment (MM region) effects that also make a contribution to the overall free energy change. Using the semiempirical PM3 method to model the QM region, the application of this PQA/MM method is illustrated by calculation of the relative protonation free energy of the conserved OD2 (Asp27) and the N5 (dihydrofolate) proton acceptor sites in the active site of Escherichia coli dihydrofolate reductase (DHFR) with the bound nicotinamide adenine dinucleotide phosphate (NADPH) cofactor. For a number of choices for the QM region, the relative protonation free energy was calculated as the sum of contributions from the QM region and the interaction between the QM and MM regions via the thermodynamic integration (TI) method. The results demonstrate the importance of including the whole substrate molecule in the QM region, and the overall protein (MM) environment in determining the relative stabilities of protonation sites in the enzyme active site. The PQA/MM free energies obtained by TI were also compared with those estimated by a less computationally demanding nonperturbative method based on the linear response approximation (LRA). For some choices of QM region, the total free energies calculated using the LRA method were in very close agreement with the PQA/MM values. However, the QM and QM/MM component free energies were found to differ significantly between the two methods.     

QM/MM study of aqueous solvation of the uranyl fluoride [UO2F4(2-)] complex

The aqueous solvation of the uranylfluoride complex [UO(2)F(4) (2-)] was studied using full quantum mechanical (QM) and hybrid QM/molecular mechanics (MM) methods. Inclusion of a complete first solvation shell was found necessary to reproduce the experimentally observed heptacoordination of uranium. An efficient and accurate computational model is proposed that consists of structure optimization of the coordinated uranium complex as QM region, followed by single-point full QM calculations to compute relative energies. This method is proven feasible for studies of large solvated actinide complexes.