Interfacing CRYSTAL/AMBER to Optimize QM/MM Lennard–Jones Parameters for Water and to Study Solvation of TiO2 Nanoparticles

Abstract

Metal oxide nanoparticles (NPs) are regarded as good candidates for many technological applications, where their functional environment is often an aqueous solution. The correct description of metal oxide electronic structure is still a challenge for local and semilocal density functionals, whereas hybrid functional methods provide an improved description, and local atomic function-based codes such as CRYSTAL17 outperform plane wave codes when it comes to hybrid functional calculations. However, the computational cost of hybrids are still prohibitive for systems of real sizes, in a real environment. Therefore, we here present and critically assess the accuracy of our electrostatic embedding quantum mechanical/molecular mechanical (QM/MM) coupling between CRYSTAL17 and AMBER16, and demonstrate some of its capabilities via the case study of TiO2 NPs in water. First, we produced new Lennard–Jones (LJ) parameters that improve the accuracy of water–water interactions in the B3LYP/TIP3P coupling. We found that optimizing LJ parameters based on water tri- to deca-mer clusters provides a less overstructured QM/MM liquid water description than when fitting LJ parameters only based on the water dimer. Then, we applied our QM/MM coupling methodology to describe the interaction of a 1 nm wide multilayer of water surrounding a spherical TiO2 nanoparticle (NP). Optimizing the QM/MM water–water parameters was found to have little to no effect on the local NP properties, which provide insights into the range of influence that can be attributed to the LJ term in the QM/MM coupling. The effect of adding additional water in an MM fashion on the geometry optimized nanoparticle structure is small, but more evident effects are seen in its electronic properties. We also show that there is good transferability of existing QM/MM LJ parameters for organic molecules–water interactions to our QM/MM implementation, even though these parameters were obtained with a different QM code and QM/MM implementation, but with the same functional.

Multiscale electrostatic embedding simulations for modeling structure and dynamics of molecules in solution: A tutorial review

“…[ 16,19,36 ] To evaluate this expression, the MM point charges must be included explicitly in the QM Hamiltonian. This can be achieved through an additional external potential term, [ 66 ] or by using “placeholder atoms” with a single (high‐exponent) s ‐function basis [ 33 ] and their partial charges as nuclear charges, thus again entering into the external potential effectively as point charges. A general form of the additional term in the external potential V ext ( r ) can be obtained by taking the functional derivative of Equation ) with respect to the density: …”

“…This benchmark was carried out by simply using the TIP4P LJ parameters for the QM/MM LJ potential. If one is so inclined, one could continue from here by trying to optimize the QM/MM LJ parameters to decrease the artifacts when using the more accurate basis set, similar to previous work based on dimmers, [ 33,91,92 ] or larger clusters. [ 33 ] The fitting procedures are helped along by the fact that the QM/MM LJ term in Equation ) does not depend on the density, so one can simply perform the electrostatics once, tabulate that part of the energy, and use it in every evaluation of the cost function.…”

“…However, several groups have suggested that the LJ parameters can (and perhaps should) be modified. [33,72,[90][91][92] It seems reasonable, since for the force field method the complete approximation of the noncovalent electronic interactions is parameterized into a Coulomb term between point charges and an LJ term. Thus, if we then effectively exchange the charge description in a region of the system from point charges to a self-consistently optimized charge density by switching from a pure MM to a QM/MM model, it would make sense that the LJ parameters would need adjustment from their original static point-chargecorresponding values.…”

“…If one is so inclined, one could continue from here by trying to optimize the QM/MM LJ parameters to decrease the artifacts when using the more accurate basis set, similar to previous work based on dimmers, [33,91,92] or larger clusters. [33] The fitting procedures are helped along by the fact that the QM/MM LJ term in Equation 2does not depend on the density, so one can simply perform the electrostatics once, tabulate that part of the energy, and use it in every evaluation of the cost function. If the QM/MM LJ potential plays a large role in the overall coupling energy, the effect will be largest for the QM/MM configurations that have the most possible QM/MM LJ coupling terms (ie, five QM molecules for the decamers).…”

“…After the groundbreaking work of Levitt, Warshel, [ 4 ] and Karplus, [ 5 ] the basic idea of combining electronic structure calculations with classical potential functions has undergone a myriad of developments and advancements. [ 5–24 ] This vast landscape of QM/MM models has already been explored extensively within medicine, enzymology and other areas of biology, [ 17,19,25–31 ] enzyme‐based catalysis, materials science and nanotechnology, [ 24,32,33 ] photophysics and photochemistry, [ 34–37 ] and solvation dynamics. [ 38–43 ]…”