Assessment of Approximations to the Embedding Potential in Frozen-Density Embedding Theory for the Calculation of Electric Field Gradients.

The approximations to the embedding potential in frozen-density embedding theory (FDET) have been assessed for the first time for the calculation of the electric field gradient (EFG) at a nucleus. FDET-based methods using a hierarchy of approximations are applied to evaluate the EFG at the nuclei of an HCl molecule in several noncovalently bound clusters chosen to represent potential liquid or molecular crystal systems. A detailed assessment of such approximations is made for the Hartree-Fock treatment of electron-electron correlation (both in FDET and in the reference calculations for the whole cluster). The emerging choice of the optimal set of approximations is reconfirmed in calculations in which electron-electron calculations are treated at the MP2 level. Our optimized protocol produces average errors in the complexation-induced EFG shift on the order of 25% relative to conventional quantum mechanical calculations for the whole cluster. This protocol is shown to be numerically robust and leads to enormous computational savings compared to a complete quantum mechanical treatment of the embedded species and its environment. For a cluster comprising a Na+ cation and up to 24 water molecules, the computation time is reduced by a factor of 30,000 at the expense of introducing an error in the environment-induced EFG shift of 22%.

Simulations of electric field gradient fluctuations and dynamics around sodium ions in ionic liquids.

The T1 relaxation time measured in nuclear magnetic resonance experiments contains information about electric field gradient (EFG) fluctuations around a nucleus, but computer simulations are typically required to interpret the underlying dynamics. This study uses classical molecular dynamics (MD) simulations and quantum chemical calculations, to investigate EFG fluctuations around a Na+ ion dissolved in the ionic liquid 1-ethyl 3-methylimidazolium tetrafluoroborate, [Im21][BF4], to provide a framework for future interpretation of NMR experiments. Our calculations demonstrate that the Sternheimer approximation holds for Na+ in [Im21][BF4], and the anti-shielding coefficient is comparable to its value in water. EFG correlation functions, CEFG(t), calculated using quantum mechanical methods or from force field charges are roughly equivalent after 200 fs, supporting the use of classical MD for estimating T1 times of monatomic ions in this ionic liquid. The EFG dynamics are strongly bi-modal, with 75%-90% of the de-correlation attributable to inertial solvent motion and the remainder to a highly distributed diffusional processes. Integral relaxation times, ⟨τEFG⟩, were found to deviate from hydrodynamic predictions and were non-linearly coupled to solvent viscosity. Further investigation showed that Na+ is solvated by four tetrahedrally arranged [BF4]- anions and directly coordinated by ∼6 fluorine atoms. Exchange of [BF4]- anions is rare on the 25-50 ns timescale and suggests that motion of solvent-shell [BF4]- is the primary mechanism for the EFG fluctuations. Different couplings of [BF4]- translational and rotational diffusion to viscosity are shown to be the source of the non-hydrodynamic scaling of ⟨τEFG⟩.

Explicit vs. implicit electronic polarisation of environment of an embedded chromophore in frozen-density embedding theory.

Frozen-Density Embedding Theory (FDET) provides a system-independent formal framework for multi-level computational methods. Despite apparent similarity, the interaction energy components commonly used in QM/MM methods do not have their corresponding counterparts in FDET. We show how the effect of the polarisation on the electron distribution in the environment can be (or is) accounted for either explicitly or implicitly within the FDET framework. Numerical examples are provided for vertical excitation energies in four representative cases of embedded chromophores.