Atomistic Polarizable Embeddings: Energy, Dynamics, Spectroscopy, and Reactivity.

The computational modeling of realistic extended systems, relevant in, e.g., Chemistry and Biophysics, is a fundamental problem of paramount importance in contemporary research. Enzymatic catalysis and photoinduced processes in pigment-protein complexes are typical problems targeted by computer-aided approaches, to complement experiments as interpretative tools at a molecular scale. The daunting complexity of this task lies in between the opposite stringent requirements of results' reliability for structural/dynamical properties and related intermolecular interactions, and a mandatory principle of realism in the modeling strategy. Therefore, in practice, a truly realistic computational model of a biologically relevant system can easily fail to meet the accuracy requirement, in order to balance the excessive computational cost necessary to reach the desired precision.To address such an "accuracy vs reality" dualistic requirement, mixed quantum mechanics/classical mechanics approaches within Atomistic (i.e., preserving the discrete particle configuration) Polarizable Embeddings (QM/APEs) methods have been proposed over the years. In this Account, we review recent developments in the design and application of general QM/APE methods, targeting situations where a local intrinsically quantum behavior is coupled to a large molecular system (i.e., an environment), often involving processes with different dynamical time scales, in order to avoid brute-force, unpractical quantum chemistry calculations on the complete system.In the first place, our interest is devoted to the available APEs models presently implemented in computational software, highlighting the quantum chemistry methods that can be used to treat the QM subsystem. We review the coupling strategy between the QM subsystem and the APE, which requires to examine the way the QM/MM mutual interactions are accounted for and how the polarization of the classical environment is considered with respect to (wrt) the quantum variables. Because of the need of reliable molecular and macromolecular structures, a pivotal aspect to address here is the handling of the system dynamics (i.e., gradients wrt nuclear positions are required), especially for large molecular assemblies composed by an overwhelming number of atoms, exploring many conformations on a complex energy landscape.Alongside, we highlight our views on the necessary steps to take toward more accurate general-purposes and transferable explicit embeddings. The main objective to achieve here is to design a more physically grounded multiscale approach. To do so, one should apply advanced new generation classical models to account for refined induction effects that are able to (i) improve the quality of QM/MM interaction energies; (ii) enhance transferability by avoiding the compulsory partial (or total) reparameterization of the classical model. Moreover, the extension of recent developments originating from the field of advanced classical molecular dynamics (MD) to the realm of QM/APE methods is a key direction to improve both speed and efficiency for the phase space exploration of systems of growing size and complexity.Lastly, we point out specific research topics where an advanced QM/APE dynamics can certainly shed some light. For example, we discuss chemical reactions in "harsh" environments and the case of spectroscopic theoretical modeling where the inclusion of refined environment effects is often mandatory.