On the activation free energy of the Cl− + CH3Cl SN2 reaction in solution

Accelerated Quantum Mechanics/Molecular Mechanics Simulations via Neural Networks Incorporated with Mechanical Embedding Scheme

A powerful tool to study the mechanism of reactions in solutions or enzymes is to perform the ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations. However, the computational cost is too high due to the explicit electronic structure calculations at every time step of the simulation. A neural network (NN) method can accelerate the QM/MM-MD simulations, but it has long been a problem to accurately describe the QM/MM electrostatic coupling by NN in the electrostatic embedding (EE) scheme. In this work, we developed a new method to accelerate QM/MM calculations in the mechanic embedding (ME) scheme. The potentials and partial point charges of QM atoms are first learned in vacuo by the embedded atom neural networks (EANN) approach. MD simulations are then performed on this EANN/MM potential energy surface (PES) to obtain free energy (FE) profiles for reactions, in which the QM/MM electrostatic coupling is treated in the mechanic embedding (ME) scheme. Finally, a weighted thermodynamic perturbation (wTP) corrects the FE profiles in the ME scheme to the EE scheme. For two reactions in water and one in methanol, our simulations reproduced the B3LYP/MM free energy profiles within 0.5 kcal/mol with a speed-up of 30-60-fold. The results show that the strategy of combining EANN potential in the ME scheme with the wTP correction is efficient and reliable for chemical reaction simulations in liquid. Another advantage of our method is that the QM PES is independent of the MM subsystem, so it can be applied to various MM environments as demonstrated by an S_N2 reaction studied in water and methanol individually, which used the same EANN PES. The free energy profiles are in excellent accordance with the results obtained from B3LYP/MM-MD simulations. In future, this method will be applied to the reactions of enzymes and their variants.

Combined Electrostatically Embedded Multiconfiguration Molecular Mechanics and Molecular Mechanical Method: Application to Molecular Dynamics Simulation of a Chemical Reaction in Aqueous Solution with Hybrid Density Functional Theory

We here combine the electrostatically embedded multiconfiguration molecular mechanics (EE-MCMM) method for generating global potential energy surfaces in the presence of an electrostatic potential with molecular mechanics (MM). The resulting EE-MCMM/MM method is illustrated by applying it to carry out a molecular dynamics simulation for the symmetric bimolecular reaction Cl(-) + CH3Cl' → ClCH3 + Cl'(-) in aqueous solution with hybrid density functional theory as the quantum mechanical level. The potential of mean force is calculated, and the free energy barrier is found to be 25.3 kcal/mol, which is in good agreement with previous work. The advantage of the combined EE-MCMM and MM method is that the number of quantum mechanical calculations required for the active subsystem is very small compared to straight direct dynamics.

Calculation of Electrochemical Reorganization Energies for Redox Molecules at Self-Assembled Monolayer Modified Electrodes

Electrochemical electron transfer reactions play an important role in energy conversion processes with many technological applications. Electrodes modified by self-assembled monolayers (SAMs) exhibit reduced double layer effects and are used in molecular electronics. An important quantity for calculating the electron transfer rate constant is the reorganization energy, which is associated with changes in the solute geometry and the environment. In this Letter, an approach for calculating the electrochemical reorganization energy for a redox molecule attached to or near a SAM modified electrode is presented. This integral equations formalism polarizable continuum model (IEF-PCM) approach accounts for the detailed electronic structure of the molecule, as well as the contributions from the electrode, SAM, and electronic and inertial solvent responses. The calculated total reorganization energies are in good agreement with experimental data for a series of metal complexes in aqueous solution. This approach will be useful for calculating electron transfer rate constants for molecular electrocatalysts.

Reaction dynamics at liquid interfaces

The liquid interface is a narrow, highly anisotropic region, characterized by rapidly varying density, polarity, and molecular structure. I review several aspects of interfacial solvation and show how these affect reactivity at liquid/liquid interfaces. I specifically consider ion transfer, electron transfer, and SN2 reactions, showing that solvent effects on these reactions can be understood by examining the unique structure and dynamics of the liquid interface region.

Cold chemistry with electronically excited Ca+ Coulomb crystals

Rate constants for chemical reactions of laser-cooled Ca(+) ions and neutral polar molecules (CH(3)F, CH(2)F(2), or CH(3)Cl) have been measured at low collision energies (<E(coll)>/k(B)=5-243 K). Low kinetic energy ensembles of (40)Ca(+) ions are prepared through Doppler laser cooling to form "Coulomb crystals" in which the ions form a latticelike arrangement in the trapping potential. The trapped ions react with translationally cold beams of polar molecules produced by a quadrupole guide velocity selector or with room-temperature gas admitted into the vacuum chamber. Imaging of the Ca(+) ion fluorescence allows the progress of the reaction to be monitored. Product ions are sympathetically cooled into the crystal structure and are unambiguously identified through resonance-excitation mass spectrometry using just two trapped ions. Variations of the laser-cooling parameters are shown to result in different steady-state populations of the electronic states of (40)Ca(+) involved in the laser-cooling cycle, and these are modeled by solving the optical Bloch equations for the eight-level system. Systematic variation of the steady-state populations over a series of reaction experiments allows the extraction of bimolecular rate constants for reactions of the ground state ((2)S(1/2)) and the combined excited states ((2)D(3/2) and (2)P(1/2)) of (40)Ca(+). These results are analyzed in the context of capture theories and ab initio electronic structure calculations of the reaction profiles. In each case, suppression of the ground state rate constant is explained by the presence of a submerged or real barrier on the ground state potential surface. Rate constants for the excited states are generally found to be in line with capture theories.

On the temperature and pressure dependences of cavities in the dielectric continuum picture

Cavity size at equilibrium and its variations with thermodynamic conditions are studied in the dielectric continuum framework of solvents. By employing Gibbs' theory of dividing surfaces, the fluctuating cavity description of Kim [H.J. Kim, J. Chem. Phys. 105, 6818 (1996)] is extended to include effects related to the local solvent density inhomogeneity near the cavity. The resulting theory is applied to study cavity size variations with temperature and pressure in dipolar and nondipolar solvents. Model calculations show that the cavity size tends to increase with temperature along an isobar and decrease with pressure along an isotherm.

A Coupled Reference Interaction Site Model/Molecular Dynamics Study of the Potential of Mean Force Curve of the SN2 Cl- + CH3Cl Reaction in Water

An application of the coupled reference interaction site model (RISM)/simulation methodology to the calculation of the potential of mean force (PMF) curve in aqueous solution for the identity nucleophilic substitution reaction Cl(-) + CH(3)Cl is performed. The free energy of activation is calculated to be 27.1 kcal/mol which compares very well with the experimentally determined barrier height of 26.6 kcal/mol. Furthermore, the calculated PMF is almost superimposed with that previously calculated using the computationally rigorous Monte Carlo with importance sampling method (Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J. Am. Chem. Soc. 1985, 107, 154). Using the calculated PMF, a crude estimate of the solvated kinetic transmission coefficient also compares well with that of previous more accurate simulations. These results indicate that the coupled RISM/simulation method provides a cost-effective methodology for studying reactions in solution.

No-barrier theory: calculating rates of chemical reactions from equilibrium constants and distortion energies

No-barrier theory is a new approach to the calculation of rate constants for reactions in solution, from the corresponding equilibrium constants. It requires relatively small molecular orbital theory calculations, and has been very successful. It is in the spirit of Marcus theory, but does not require an "intrinsic barrier". The approach is explained, with an examination of the way in which the ideas on which it is based were "in the air".