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## Density- and response density-based models for Intermolecular Interactions in Molecular Assemblies and in Solids

#### Nancy

#### Organisers

**State of the art **

Models for the intermolecular interaction energy are usually much more powerful and versatile than the usually computationally expensive ab initio methods on which they are based. Accurate models for intermolecular interactions are conventionally based on a decomposition of the interaction energy into physical terms such as the electrostatic, dispersion and short-range repulsive effects [SAPT]. These terms are usually included in standard atom-atom pair potential models, however, a number of contributions to the interaction energy which originate from the quantum mechanical nature of the interaction, cannot be accurately described, or indeed, may be impossible within the atom-atom framework. These involve the polarization, charge-transfer, charge penetration, and more generally, subtle anisotropic effects. Moreover, since typical atom-atom pair potential models are unable to take into account the electronic structure of the interacting systems, they fail to describe interactions of molecules which are not in their equilibrium structure (internal flexibility) or if one or both of the systems are in an excited state.

Better success can be obtained with models based on the electronic density rather than the nuclear coordinates only. The successes of the SIBFA density-based force field Ref [SIBFA] and 'many-body' dispersion (MBD) Ref[MBD] methods are two good examples of density and density-reponse based models. In principle density-based models can account for the electrostatic interaction exactly and the exchange-repulsion fairly accurately, additionally, by extensions to include density responses, they can also be used to construct plausibly accurate models for quantities that involve excited states such as polarizabilities and dispersion coefficients Refs[XH-Disp] [XDM] [MBD].

Response-based models have recently seen a significant success in systems where van der Waals (dispersion) interactions are significant.These interactions are important in the modeling of several problems in materials science, including the study of the stability of molecular crystals or the adsorption of molecules on surfaces. The poor description of this kind of interactions by traditional approximations employed in density functional theory (DFT) has long limited the applicability of this methodology to systems where vdW forces play an important role. This problem has been to a certain extent overcome by empirically adding pairwise corrections to include van der Waals (vdW) interactions in DFT Ref[TS] [Grimme], however, arguably the biggest improvement was obtained by the inclusion of both density and response effects in the MBD model which was successfully used to calculate the correct ordering of the relative stability of the different polymorphs of glycine Ref[Glycine].

It becomes timely to extend such new methodologies to other interactions than dispersion.

**Focus of the workshop**

Thus far the emphasis of density and density response models has been largely on the dispersion energy, with only the SIBFA model attempting to model interaction energy components like the electrostatic, exchange and charge-transfer energies. And even in this case, the charge-transfer model remains the least well-understood. There is a real need to extend these models to this and other effects (many-body polarization), to test the models in challenging applications involving heavy atoms (for which they are rarely parameterised) and excited states (a new and important area pertinent to our current energy applications), and finally, to benchmark these against accurate and reliable ab initio data. This needs to be done both in molecular systems and in the solid state: the two areas are complementary. These are the broad areas of focus of this meeting, and below we list specific examples of questions that will be addressed during the meeting:

* Charge-transfer: Intermolecular charge transfer is a density response property that arises at second and higher orders of perturbation theory and can be understood as a charge delocalisation through tunneling. While there exist for the intermolecular CT, it is unclear just how reliable they are, particularly as, even now, there are debates about how we should define the intermolecular charge-transfer energy. Methods like symmetry-adapted perturbation theory (SAPT) and supermolecular energy decomposition analysis (EDA) techniques like Pauli-Blockade DFT do not uniquely define the CT energy. There are EDA schemes that attempt to do so using localized basis sets but these inevitably breakdown at short-range. Consequently issues that need addressing include the very definition of the intermolecular CT energy, the creation of new density response-based models, their assessment, and investigations into the many-body nature of the CT.

* Interactions involving heavy atoms and excited states: Since most models are tested/parameterised using systems containing light atoms in their ground state, their applicability to systems outside this important but limited ares remains an open question. A specific question that needs to be addressed is whether we obtain sensible polarizabilities and dispersion coefficients for these systems.

* Dielectric screening plays an important role in determining the properties of a system. Indeed, from a quantum mechanical point of view the knowledge of the exact response functions leads to the exact ground state energy and the exact excited state properties of a system. The possibility of approximating the total screening of a complex system starting from the linear response on each constituting component could lead to the development of new models with improved accuracy. As an example, the dielectric screening of water or ice could be approximated using response functions localized on single molecules. This idea, requiring the decomposition of the response functions into local components, has the potential to add a new level of sophistication to the modeling of intermolecular interactions and it will be the subject of discussions during the meeting

## References

**France**

Janos Ángyán (CNRS and Université de Lorraine) - Organiser

**Germany**

Andreas Hesselmann (University of Erlangen) - Organiser

**United Kingdom**

Alston J. Misquitta (Queen Mary University of London) - Organiser & speaker

**United States**

Dario Rocca (QC Ware Corp.) - Organiser & speaker