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Biased enhanced sampling methods utilizing collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to high intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While methods like temperature-accelerated molecular dynamics (TAMD) can adopt many CVs in a simulation, unbiasing the simulation requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We test the score-based diffusion unbiasing method on TAMD simulations. The results demonstrate that this unbiasing approach significantly outperforms traditional unbiasing methods, and can generate accurate unbiased conformational ensembles for simulations with a number of CVs higher than usual ranges.

Molecular polaritons arise when molecules interact so strongly with light that they become entangled with each other. This light-matter hybridization alters the chemical and physical properties of the molecular system and allows chemical reactions to be controlled without the use of external fields. We investigate the impact of strong light-matter coupling on the electronic structure using perturbative approaches and demonstrate that Rayleigh-Schr\"odinger perturbation theory can reproduce the ground state energies in optical cavities to comparable accuracy as ab initio cavity quantum electrodynamics methodologies for currently relevant coupling strengths. The method is effective in both low and high cavity frequency regimes and straightforward to implement via response functions. Furthermore, we establish simple relations between cavity-induced intermolecular forces and van der Waals forces. These findings provide valuable insight into the manipulation of ground-state polaritonic energy landscapes, shedding light on the systems and conditions in which modifications can be achieved., Comment: 11 pages, 3 Figures

Intermolecular van der Waals interactions are central to chemical and physical phenomena ranging from biomolecule binding to soft-matter phase transitions. However, there are currently very limited approaches to manipulate van der Waals interactions. In this work, we demonstrate that strong light-matter coupling can be used to tune van der Waals interactions, and, thus, control the thermodynamic properties of many-molecule systems. Our analyses reveal orientation dependent single molecule energies and interaction energies for van der Waals molecules (for example, H$_{2}$). For example, we find intermolecular interactions that depend on the distance between the molecules $R$ as $R^{-3}$ and $R^{0}$. Moreover, we employ non-perturbative \textit{ab initio} cavity quantum electrodynamics calculations to develop machine learning-based interaction potentials for molecules inside optical cavities. By simulating systems ranging from $12$ H$_2$ to $144$ H$_2$ molecules, we demonstrate that strong light-matter coupling can tune the structural and thermodynamic properties of molecular fluids. In particular, we observe varying degrees of orientational order as a consequence of cavity-modified interactions, and we explain how quantum nuclear effects, light-matter coupling strengths, number of cavity modes, molecular anisotropies, and system size all impact the extent of orientational order. These simulations and analyses demonstrate both local and collective effects induced by strong light-matter coupling and open new paths for controlling the properties of molecular clusters., Comment: 7 pages and 3 figures in main text - 16 pages and 13 figures supplemental material

Enhanced sampling methods are indispensable in computational physics and chemistry, where atomistic simulations cannot exhaustively sample the high-dimensional configuration space of dynamical systems due to the sampling problem. A class of such enhanced sampling methods works by identifying a few slow degrees of freedom, termed collective variables (CVs), and enhancing the sampling along these CVs. Selecting CVs to analyze and drive the sampling is not trivial and often relies on physical and chemical intuition. Despite routinely circumventing this issue using manifold learning to estimate CVs directly from standard simulations, such methods cannot provide mappings to a low-dimensional manifold from enhanced sampling simulations as the geometry and density of the learned manifold are biased. Here, we address this crucial issue and provide a general reweighting framework based on anisotropic diffusion maps for manifold learning that takes into account that the learning data set is sampled from a biased probability distribution. We consider manifold learning methods based on constructing a Markov chain describing transition probabilities between high-dimensional samples. We show that our framework reverts the biasing effect yielding CVs that correctly describe the equilibrium density. This advancement enables the construction of low-dimensional CVs using manifold learning directly from data generated by enhanced sampling simulations. We call our framework reweighted manifold learning. We show that it can be used in many manifold learning techniques on data from both standard and enhanced sampling simulations., Comment: Published version

Qualitatively incorrect results are obtained for the Mn dimer in density functional theory calculations using the generalized gradient approximation (GGA) and similar results are obtained from local density and meta-GGA functionals. The coupling is predicted to be ferromagnetic rather than antiferromagnetic and the bond between the atoms is predicted to be an order of magnitude too strong and about an {\AA}ngstr{\o}m too short. Explicit, self-interaction correction (SIC) applied to a commonly used GGA energy functional, however, provides close agreement with both experimental data and high-level, multi-reference wave function calculations. These results show that the failure is not due to strong correlation but rather the single electron self-interaction that is necessarily introduced in estimates of the classical Coulomb and exchange-correlation energy when only the total electron density is used as input. The corrected functional depends explicitly on the orbital densities and can, therefore, avoid the introduction of self-Coulomb interaction. The error arises because of over-stabilization of bonding $d$-states in the minority spin channel resulting from an overestimate of the $d$-electron self-interaction in the semi-local exchange-correlation functionals. Since the computational effort in the self-interaction corrected calculations scales with system size in the same way as for regular semi-local functional calculations, this approach provides a way to calculate properties of Mn nanoclusters as well as biomolecules and extended solids where Mn dimers and larger cluster are present, while multi-reference wave function calculations can only be applied to small systems., Comment: 20 pages, 4 figures

Bistable shells can reversibly change between two stable configurations with very little energetic input. Understanding what governs the shape and snap-through criteria of these structures is crucial for designing devices that utilize instability for functionality. Bistable cylindrical shells fabricated by stretching and bonding multiple layers of elastic plates will contain residual stress that will impact the shell's shape and the magnitude of stimulus necessary to induce snapping. Using the framework of non-Euclidean shell theory, we first predict the mean curvature of a nearly cylindrical shell formed by arbitrarily prestretching one layer of a bilayer plate with respect to another. Then, beginning with a residually stressed cylinder, we determine the amount of the stimuli needed to trigger the snapping between two configurations through a combination of numerical simulations and theory. We demonstrate the role of prestress on the snap-through criteria, and highlight the important role that the Gaussian curvature in the boundary layer of the shell plays in dictating shell stability., Comment: 8 pages, 8 figures