Computational Design of Molecular Probes for Electronic Preresonance Raman Scattering Microscopy.

Recently developed electronic preresonance stimulated Raman scattering (epr-SRS) microscopy, in which the Raman signal of a dye is significantly boosted by setting the incident laser frequency near the electronic excitation energy, has pushed the sensitivity of SRS microscopy close to that offered by confocal fluorescence microscopy. Prominently, the maintained narrow line-width of epr-SRS also offers high multiplexity that breaks the "color barrier" in optical microscopy. However, detailed understanding of the fundamental mechanism in these epr-SRS dyes still remains elusive. Here, we combine experiments with theoretical modeling to investigate the structure-function relationship, aiming to facilitate the design of new probes and expanding epr-SRS palettes. Our ab initio approach employing the displaced harmonic oscillator (DHO) model provides a consistent agreement between simulated and experimental SRS intensities of various triple-bond bearing epr-SRS probes with distinct scaffolds. We further review two popular approximate expressions for epr-SRS, namely the short-time and Albrecht A-term equations, and compare them to the DHO model. Overall, the theory allows us to illustrate how the observed intensity differences between molecular scaffolds stem from the coupling strength between the electronic excitation and the targeted vibrational mode, leading to a general design strategy for highly sensitive next-generation vibrational imaging probes.

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy.

Two-dimensional Raman and hybrid terahertz-Raman spectroscopic techniques provide invaluable insight into molecular structures and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.

Small Nuclear Quantum Effects in Scattering of H and D from Graphene.

We study nuclear quantum effects in H/D sticking to graphene, comparing scattering experiments at near-zero coverage with classical, quantized, and transition-state calculations. The experiment shows H/D sticking probabilities that are indistinguishable from one another and markedly smaller than those expected from a consideration of zero-point energy shifts of the chemisorption transition state. Inclusion of dynamical effects and vibrational anharmonicity via ring-polymer molecular dynamics (RPMD) yields results that are in good agreement with the experimental results. RPMD also reveals that nuclear quantum effects, while modest, arise primarily from carbon and not from H/D motion, confirming the importance of a C atom rehybridization mechanism associated with H/D sticking on graphene.

Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches.

We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime. This work suggests a general strategy for the extraction of microcanonical dynamical quantities from RPMD (or other approximate thermal) simulations.

Simple Flux-Side Formulation of State-Resolved Thermal Reaction Rates for Ring-Polymer Surface Hopping.

Employing the recently developed isomorphic Hamiltonian framework for including nuclear quantum effects in mixed quantum-classical nonadiabatic dynamics, we present a flux-side formulation of state-resolved thermal reaction rates for ring-polymer surface hopping (iso-RPSH). An appealing aspect of the new approach is that calculation of multiple state-resolved nonadiabatic thermal reaction rates is enabled with only a single free-energy surface calculation, whereas previous nonadiabatic flux-side formulations for surface hopping involve multiple free-energy surface calculations. The method is shown to be robust and straightforwardly implemented, and numerical results reveal that RPSH in the isomorphic Hamiltonian framework leads to better dividing surface independence than alternative RPSH methods due to improved preservation of the path-integral statistics.

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics.

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

Q-factor enhancement in a one-dimensional photonic crystal cavity with embedded planar plasmonic metamaterials.

We report Q-factor enhancement in a one-dimensional (1D) photonic crystal (PC) cavity by embedding electromagnetic-induced-transparency (EIT) planar plasmonic metamaterials in the cavity. Microwave experiments show tenfold Q-factor enhancements, confirming the numerical simulations. More importantly, the Q-factor enhancement is mainly due to both the longitudinal and lateral confinements contributed by the 1D PC cavity and the planar EIT metamaterials, respectively. The combined PC-EIT structure with a prominent cavity figure of merit may find new applications in nonlinear optics, cavity quantum electrodynamics, and low-threshold lasers.