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

Abstract

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. © 2017 Wiley Periodicals, Inc.

Modeling Complex Solvent Effects on the Optical Rotation of Chiral Molecules: A Combined Molecular Dynamics and Density Functional Theory Study

“…For the same solute in CCl 4 , we see a more significant shift on the addition of the implicit solvent toward larger standard deviation values, indicating that the rotation values do not converge even more strongly. These results are in line with results obtained by Schieschke et al on the small effect of adding a continuum solvent model on top of FDE on solvent shifts of the vertical excitation energy.…”

Quantum embedding electronic structure methods

“…[ 51,62,63 ] Interesting combinations of QM/MM or density embedding and continuum models exist where the role of the continuum is to include polarizations from faraway environments. [ 64–66 ]…”

“…[51,62,63] Interesting combinations of QM/MM or density embedding and continuum models exist where the role of the continuum is to include polarizations from faraway environments. [64][65][66] 3 | PRESENT Density embedding: Recent applications have included charge transfer reactions, [67] charge transfer excitation energies and diabatic couplings, [68] van der Waals interactions, [69] spectroscopy of complex systems and solvatochromatic shifts, [70][71][72][73][74][75] and many more. [21,[76][77][78] Numerically accurate (although inadequate in practical calculations) methods can calculate δT Snad /δn(r) for covalent bonds.…”

The KOALA program: Wavefunction frozen‐density embedding

“…[103][104][105][106][107][108][109] The constructions of the matrix representations, as well as differentiated matrix representations, have been implemented in the KOALA program. [110] For the special case of the conductor-like screening model (COSMO), all equations have been explicitly implemented in the KOALA program as well.…”