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In the absence of hydrophobic effects, the driving force for complexation between neutral host and guest molecules (e.g., cryptophane E and halomethanes) is a function of several factors. If size and form are suitable, as in the CHC13 complex 1, complexation is enthalpy driven, and stable supermolecules result (“van der Waals molecules”).

We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.

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We find and analyze the exact time-dependent potential energy surface driving the proton motion for a model of cavity-induced suppression of proton-coupled electron-transfer. We show how, in contrast to the polaritonic surfaces, its features directly correlate to the proton dynamics and discuss cavity-modifications of its structure responsible for the suppression. The results highlight the interplay between non-adiabatic effects from coupling to photons and coupling to electrons, and suggest caution is needed when applying traditional dynamics methods based on polaritonic surfaces. Impressive experimental advances [1][2][3][4][5] have led to a rekindling of interest in cavity quantum electrodynamics. Rapidly expanding applications to molecules and nanostructures require us to go beyond the simplest few-level-single-mode models explored in the early days of quantum mechanics, with the interplay of coupled electronic, nuclear, and photonic excitations revealing a plethora of new phenomena from enhanced conductivity in semiconductors to photochemical suppression of chemical reactions to cavity-enhanced superconductivity to superradiance, see e.g. Refs. [6][7][8][9][10][11][12].There is now the possibility to manipulate real matter with cavity parameters providing tunable dials for photo-chemical control of reactions, replacing shaped laser pulses as photonic reagents [1,13,14]. The hope is attain strong light-matter coupling and control without large power sources, possibly reducing unintended byproducts such as multiphoton absorption and ionization channels.The cavity clearly modifies the potential that the matter evolves in, and various constructs have been put forward to serve in lieu of the Born-Oppenheimer (BO) surfaces that have proved so instrumental for our understanding of cavity-free dynamics. In particular, "polaritonic surfaces" that arise from diagonalizing the electron-photon Hamiltonian parametrized by nuclear coordinates have been instructive in interpreting some of the novel phenomena mentioned above [15][16][17][18][19]. Another construct are the "cavity-BO surfaces" where the photonic displacement-field coordinates are treated on the same footing as the nuclear coordinates [7,20]. A complete dynamical picture of how the electronic and photonic degrees of freedom influence the nuclear dynamics can only be obtained when several of such surfaces in the chosen manifold together with their couplings are considered: quite typically at a given time the nuclear wavepacket locally straddles several surfaces, or distinct parts of the nuclear wavepacket are associated with different surfaces. To go beyond using the surfaces only for qualitative interpretation, and to implement them in dynamics schemes, couplings be-tween the surfaces must be included [8,21], and there is interplay between non-adiabatic effects arising from photon-matter coupling and electron-nuclear coupling. Practical necessity calls for approximations which usually work best when this choice of surfaces in some sense represents a "zeroth o...

The standard description of cavity-modified molecular reactions typically involves a single (resonant) mode, while in reality, the quantum cavity supports a range of photon modes. Here, we demonstrate that as more photon modes are accounted for, physicochemical phenomena can dramatically change, as illustrated by the cavity-induced suppression of the important and ubiquitous process of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfest treatment for the photon-modes, we find that self-polarization effects become essential, and we introduce the concept of self-polarization-modified Born–Oppenheimer surfaces as a new construct to analyze dynamics. As the number of cavity photon modes increases, the increasing deviation of these surfaces from the cavity-free Born–Oppenheimer surfaces, together with the interplay between photon emission and absorption inside the widening bands of these surfaces, leads to enhanced suppression. The present findings are general and will have implications for the description and control of cavity-driven physical processes of molecules, nanostructures, and solids embedded in cavities.

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It was recently shown [Y. Suzuki, L. Lacombe, K. Watanabe, and N. T. Maitra, Phys. Rev. Lett. 119, 263401 (2017)] that peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory are crucial for accurately capturing time-resolved dynamics of electron scattering in a model one-dimensional system. Approximate functionals used today miss these structures and consequently underestimate the scattering probability. The dynamics can vary significantly depending on the choice of the initial Kohn-Sham state, and, with a judicious choice, a recently-proposed non-adiabatic approximation provides extremely accurate dynamics on approach to the target but this ultimately also fails to capture reflection accurately. Here we provide more details, using a model of electron-He + as illustration, in both the inelastic and elastic regimes. In the elastic case, the time-resolved picture is contrasted with the time-independent picture of scattering, where the linear response theory of TDDFT can be used to extract transmission and reflection coefficients. Although the exact functional yields identical scattering probabilities when used in this way as it does in the time-resolved picture, we show that the currently-available approximate functionals do not, even when they have the correct asymptotic behavior.