Rapid Calculation of the Structures of Solutions with ab Initio Interaction Potentials

Accelerating the Calculation of Solute-Solvent Interaction Energies through Systematic Molecular Fragmentation

The method of systematic molecular fragmentation by annihilation (SMFA) is modified to apply to the interaction energy between a solute and solvent, where the solute is a pair of reacting molecules. For NH₃ + CH₃Cl as the solute, it is shown that SMFA can estimate (to chemical accuracy) the average binding energy of the solute in large water clusters containing up to 160 water molecules, at an appropriate level of electronic structure theory. The SMFA calculation can be carried out in a computation time that makes it feasible to estimate the solvation contribution to free energies of activation and reaction by ensemble averaging.

Use of Interaction Energies in QM/MM Free Energy Simulations

The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.

Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations

Lately, there has been great interest in performing free-energy perturbation (FEP) at the combined quantum mechanics and molecular mechanics (QM/MM) level, e.g. for enzyme reactions. Such calculations require extensive sampling of phase space, which typically is prohibitive with density-functional theory or ab initio methods. Therefore, such calculations have mostly been performed with semiempirical QM (SQM) methods, or by using a thermodynamic cycle involving sampling at the MM level and perturbations between the MM and QM/MM levels of theory. However, the latter perturbations typically have convergence problems, unless the QM system is kept fixed during the simulations, because the MM and QM/MM descriptions of the internal degrees of freedom inside the QM system are too dissimilar. We have studied whether the convergence of the MM → QM/MM perturbation can be improved by using a thoroughly parameterised force field or by using SQM/MM methods. As a test case we use the first half-reaction of haloalkane dehalogenase and the QM calculations are performed with the PBE, B3LYP, and TPSSH density-functional methods. We show that the convergence can be improved with a tailored force field, but only locally around the parameterised state. Simulations based on SQM/MM methods using the MNDO, AM1, PM3, RM1, PDDG-MNDO, and PDDG-PM3 Hamiltonians have slightly better convergence properties, but very long simulations are still needed (~10 ns) and convergence is obtained only if electrostatic interactions between the QM system and the surroundings are ignored. This casts some doubts on the common practice to base QM/MM FEPs on semiempirical simulations without any reweighting of the trajectories.

Structure of an accurate ab initio model of the aqueous Cl- ion at high temperatures

The structure of an accurate ab initio model of aqueous chloride ion was calculated at two high-temperature state points (573 K, 0.725 g/cm(3) and 723 K, 0.0098 g/cm(3)) by a two-step procedure. First, the structure of an approximate model was calculated from a molecular dynamics simulation of the model. Then the difference between the structure of the ab initio model and the approximate model was calculated by non-Boltzmann weighting of a sample of configurations taken from the approximate model simulation. Radial distribution functions, average coordination numbers, the distribution of coordination numbers, an analysis of orientations of water in the first coordination shell, and the free energy of hydration of the chloride ion are reported for both state points. The most common water structure has one hydrogen close to the chloride ion and one pointing away (46% at 573 K and 57% at 723 K). Waters in the first coordination shell that are not strongly bound to the chloride ions are common. Several variations of the method were tested. Models in which the water-water interaction is calculated with ab initio methods predict only a slightly different structure than models in which water-water interactions are determined from the approximate models. Similarly, using the approximate model for solute-water interactions when the water is far from the chloride ion did not affect the results. Uncertainties due to the limited sample of configurations are estimated and found to be small. The results are in qualitative agreement with X-ray and neutron diffraction experiments and with simulations of approximate models.

Hybrid coupled cluster and molecular dynamics approach: Application to the excitation spectrum of cytosine in the native DNA environment

Evolution of the excited state energies of cytosine base in the native DNA environment was investigated using a hybrid coupled cluster and classical molecular dynamics approach. The time averaged excitation energies obtained with the variant of the completely renormalized equation-of-motion with singles, doubles, and non-iterative triples approach that includes a bulk of the correlation effects for excited states, are compared with the analogous calculations in the gas phase. Significant blue shifts for the two lowest singlet excitation energies can be observed as a result of the interaction of the quantum system with the surrounding environment.