Relativistic Polarizable Embedding

Abstract

Most chemistry, including chemistry where relativistic effects are important, occurs in an environment, and in many cases, this environment has a significant effect on the chemistry. In nonrelativistic quantum chemistry, a lot of progress has been achieved with respect to including environments such as a solvent or protein in the calculations, and now is the time to extend the possibilities for also doing this in relativistic quantum chemistry. The polarizable embedding (PE) model efficiently incorporates electrostatic effects of the environment by describing it as a collection of localized electric multipoles and polarizabilities obtained through quantum chemical calculations. In this article, we present the theory and implementation of four- and exact two-component Hamiltonians within a PE framework. We denote the methods the PE-4c-DFT and PE-X2C-DFT models. The models include a linear response formalism to calculate time-dependent (TD) properties: PE-TD-4c-DFT and PE-TD-X2C-DFT. With this first implementation, we calculate the PE-TD-4c-PBE0 excitation energies of the TcO and ReO ions in an explicit water solvent. This initial investigation focuses on the relative size of relativistic and solvent contributions to the excitation energies. The solvent effect is divided into an indirect solvent effect due to the structural perturbation of the XO ion and a direct electrostatic effect. The relativistic effects as well as both types of solvent effects are found to contribute to a shift in the excitation energies, but they do so to different extents depending on the ion and the electronic transition in question.

Investigating the influence of relativistic effects on absorption spectra for platinum complexes with light-activated activity against cancer cells

“…We plan to investigate the solvent effect in a forthcoming paper, employing a recent extension of the so-called polarizable embedding model. 63 We finally note that although our present results show that it is advantageous to include spin-orbit coupling in investigations of Pt complexes used for PACT, it is probably not necessary to use a 4c framework; we anticipate that various two-component methods will be sufficient.…”

Response properties of embedded molecules through the polarizable embedding model

“…[23] Finally, the PE model has been combined with a number of electronic-structure methods including Hartree-Fock (HF) and Kohn-Sham density functional theory (DFT) [10,11] but also correlated wave-function-based methods such as coupled cluster (CC), [24,25] multiconfigurational self-consistent-field theory, [26] multiconfigurational short-range DFT, [27] the second-order polarization propagator approach [28] and also in a relativistic framework using DFT. [29] For a recent perspective on the PE model, we refer to Reference [30]. The user is thus able to choose among different electronic-structure methods and select the one that is known to perform best from a cost-efficiency point of view for a given property.…”

The DIRAC code for relativistic molecular calculations

“…The current implementation of the PE model in DIRAC can be used in combination with mean-field electronic-structure methods (i.e., HF and DFT) including electric linear response and transition properties where local-field effects, termed effective external field (EEF) 166,167 effects in the PE context, may be included. 168 The model is implemented in the Polarizable Embedding library (PElib) 169 that has been interfaced to DIRAC. 168 The library itself is based on an AO density-matrix-driven formulation, which facilitates a loose-coupling modular implementation in host programs.…”

“…168 The model is implemented in the Polarizable Embedding library (PElib) 169 that has been interfaced to DIRAC. 168 The library itself is based on an AO density-matrix-driven formulation, which facilitates a loose-coupling modular implementation in host programs. The effects from the environment are included by adding an effective one-electron embedding operator to the Fock operator of the embedded quantum subsystem.…”