Roberto Di Remigio

Four-Component Relativistic Calculations in Solution with the Polarizable Continuum Model of Solvation : Theory, Implementation, and Application to the Group 16 Dihydrides H2X (X = O, S, Se, Te, Po)

We present a formulation of four-component relativistic self-consistent field (SCF) theory for a molecular solute described within the framework of the polarizable continuum model (PCM) for solvation. The linear response function for a four-component PCM-SCF state is also derived, as well as the explicit form of the additional contributions to the first-order response equations. The implementation of such a four-component PCM-SCF model, as carried out in a development version of the DIRAC program package, is documented. In particular, we present the newly developed application programming interface PCMSolver used in the actual implementation with DIRAC. To demonstrate the applicability of the approach, we present and analyze calculations of solvation effects on the geometries, electric dipole moments, and static electric dipole polarizabilities for the group 16 dihydrides H2X (X = O, S, Se, Te, Po).

A polarizable continuum model for molecules at spherical diffuse interfaces

We present an extension of the Polarizable Continuum Model (PCM) to simulate solvent effects at diffuse interfaces with spherical symmetry, such as nanodroplets and micelles. We derive the form of the Greens function for a spatially varying dielectric permittivity with spherical symmetry and exploit the integral equation formalism of the PCM for general dielectric environments to recast the solvation problem into a continuum solvation framework. This allows the investigation of the solvation of ions and molecules in nonuniform dielectric environments, such as liquid droplets, micelles or membranes, while maintaining the computationally appealing characteristics of continuum solvation models. We describe in detail our implementation, both for the calculation of the Greens function and for its subsequent use in the PCM electrostatic problem. The model is then applied on a few test systems, mainly to analyze the effect of interface curvature on solvation energetics.

Wavelet formulation of the polarizable continuum model. II. Use of piecewise bilinear boundary elements

The simplicity of dielectric continuum models has made them a standard tool in almost any Quantum Chemistry (QC) package. Despite being intuitive from a physical point of view, the actual electrostatic problem at the cavity boundary is challenging: the underlying boundary integral equations depend on singular, long-range operators. The parametrization of the cavity boundary should be molecular-shaped, smooth and differentiable. Even the most advanced implementations, based on the integral equation formulation (IEF) of the polarizable continuum model (PCM), generally lead to working equations which do not guarantee convergence to the exact solution and/or might become numerically unstable in the limit of large refinement of the molecular cavity (small tesserae). This is because they generally make use of a surface parametrization with cusps (interlocking spheres) and employ collocation methods for the discretization (point charges). Wavelets on a smooth cavity are an attractive alternative to consider: for the operators involved, they lead to highly sparse matrices and precise error control. Moreover, by making use of a bilinear basis for the representation of operators and functions on the cavity boundary, all equations can be differentiated to enable the computation of geometrical derivatives. In this contribution, we present our implementation of the IEFPCM with bilinear wavelets on a smooth cavity boundary. The implementation has been carried out in our module PCMSolver and interfaced with LSDalton, demonstrating the accuracy of the method both for the electrostatic solvation energy and for linear response properties. In addition, the implementation in a module makes our framework readily available to any QC software with minimal effort.

Four-component relativistic density functional theory with the polarisable continuum model: application to EPR parameters and paramagnetic NMR shifts

ABSTRACT The description of chemical phenomena in solution is as challenging as it is important for the accurate calculation of molecular properties. Here, we present the implementation of the polarisable continuum model (PCM) in the four-component Dirac–Kohn–Sham density functional theory framework, offering a cost-effective way to concurrently model solvent and relativistic effects. The implementation is based on the matrix representation of the Dirac–Coulomb Hamiltonian in the basis of restricted kinetically balanced Gaussian-type functions, exploiting a non-collinear Kramers unrestricted formalism implemented in the program ReSpect, and the integral equation formalism of the PCM available through the stand-alone library PCMSolver. Calculations of electron paramagnetic resonance parameters (g-tensors and hyperfine coupling A-tensors), as well as of the temperature-dependent contribution to paramagnetic nuclear magnetic resonance (pNMR) shifts, are presented to validate the model and to demonstrate the importance of taking both relativistic and solvent effects into account for magnetic properties. As shown for selected Ru and Os complexes, the solvent shifts may amount to as much as 25% of the gas-phase values for g-tensor components and even more for pNMR shifts in some extreme cases.

Combining frozen-density embedding with the conductor-like screening model using Lagrangian techniques for response properties

We present the explicit derivation of an approach to the multiscale description of molecules in complex environments that combines frozen‐density embedding (FDE) with continuum solvation models, in particular the conductor‐like screening model (COSMO). FDE provides an explicit atomistic description of molecule‐environment interactions at reduced computational cost, while the outer continuum layer accounts for the effect of long‐range isotropic electrostatic interactions. Our treatment is based on a variational Lagrangian framework, enabling rigorous derivations of ground‐ and excited‐state response properties. As an example of the flexibility of the theoretical framework, we derive and discuss FDE + COSMO analytical molecular gradients for excited states within the Tamm–Dancoff approximation (TDA) and for ground states within second‐order Møller–Plesset perturbation theory (MP2) and a second‐order approximate coupled cluster with singles and doubles (CC2). It is shown how this method can be used to describe vertical electronic excitation (VEE) energies and Stokes shifts for uracil in water and carbostyril in dimethyl sulfoxide (DMSO), respectively. In addition, VEEs for some simplified protein models are computed, illustrating the performance of this method when applied to larger systems. The interaction terms between the FDE subsystem densities and the continuum can influence excitation energies up to 0.3 eV and, thus, cannot be neglected for general applications. We find that the net influence of the continuum in presence of the first FDE shell on the excitation energy amounts to about 0.05 eV for the cases investigated. The present work is an important step toward rigorously derived ab initio multilayer and multiscale modeling approaches.

PCMSolver: An open-source library for solvation modeling: DI REMIGIO et al.

This is the peer reviewed version of the following article: Di Remigio, R., Steindal, A.H., Mozgawa, K., Weijo, V., Cao, H. & Frediani, L. (2018). PCMSolver: an Open-Source Library for Solvation Modeling. International Journal of Quantum Chemistry, 119(1), which has been published in final form at https://doi.org/10.1002/qua.25685 . This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.