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Whereas collisions between atoms and molecules are largely understood, collisions between two molecules have proven much harder to study. In both experiment and theory, our ability to determine quantum state-resolved bimolecular cross…
We investigate dynamics and bifurcations in a mathematical model that captures electrochemical experiments on arrays of microelectrodes. In isolation, each individual microelectrode is described by a one-dimensional unit with a bistable…
We formulate the theory for a diatomic molecule in a spatially degenerate electronic state interacting with a non-resonant laser field and investigate its rovibrational structure in the presence of the field. We report on \textit{ab initio}…
Recent progress in two different fronts is reported. First, the concept of bisection of a harmonic oscillator (HO) or hydrogen atom (HA), used in the past in establishing the connection between U(3) and O(4), is generalized into…
The H$_2$+H$_2$ system has long been considered as a benchmark system for ro-vibrational energy transfer in bimolecular collisions. However, most studies thus far have focused on collisions involving H$_2$ molecules in the ground…
While linear molecules in their vibrational ground state cannot carry angular momentum around their symmetry axis, the presence of vibrational excitations can induce deformations away from linearity and therefore also allow angular momentum…
A study is reported of the quantum scattering resonances of dissociating molecules using a semiclassical approach based on periodic-orbit theory. The dynamics takes place on a potential energy surface with an energy barrier separating two…
A variational solution to the rovibrational problem in curvilinear vibrational coordinates has been implemented and used to investigate the nuclear motions in several linear triatomic molecules, like HCN, OCS, and HCP. The dependence of the…
We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled-cluster framework. This new…
We present an analytical description for the collective dynamics of oscillator ensembles with higher-order coupling encoded by simplicial structure, which serves as an illustrative and insightful paradigm for brain function and information…
We present a general theoretical treatment and calculations of the fine and hyperfine structures in the spectra of high-$n$ molecular Rydberg states in static uniform electric fields. The treatment combines (i) multichannel quantum-defect…
The transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo qualitative changes, known as Morse bifurcations, and to exist for a large range of energies, not just immediately above…
We report a quantum mechanical method for calculating the momentum distributions of constituent atoms of polyatomic molecules in rotational-vibrational eigenstates. Application of the present theory to triatomic molecules in the…
A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states.…
Particles whose shapes couple translation to rotation display a rich array of behaviors as they sediment at low Reynolds number. We introduce a unifying perspective in which the possible dynamical regimes and bifurcations between them can…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…
Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models…
We present a complete theory of bicircular high-order-harmonic emission from N-fold rotationally symmetric molecules. Using a rotating frame of reference we predict the complete structure of the high-order-harmonic spectra for arbitrary…
Strong electric fields can be used to align molecules. However, a non-polar molecule such as H$_2$ has no preference for its orientation. There are thus two equivalent configurations with equal energy separated by a potential-energy…
In what has been described as the fourth age of Quantum Chemistry, variational nuclear motion programs are now routinely being used to obtain the vibration-rotation levels and corresponding wavefunctions of small molecules to the sort of…