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Controlling molecular reactivity by shaped laser pulses is a long-standing goal in chemistry. Here, we suggest a direct optimal control approach that combines external pulse optimization with other control parameters arising in the upcoming field of vibro-polaritonic chemistry for enhanced controllability. The direct optimal control approach is characterized by a simultaneous simulation and optimization paradigm, meaning that the equations of motion are discretized and converted into a set of holonomic constraints for a nonlinear optimization problem given by the control functional. Compared with indirect optimal control, this procedure offers great flexibility, such as final time or Hamiltonian parameter optimization. A simultaneous direct optimal control theory will be applied to a model system describing H-atom transfer in a lossy Fabry-Pérot cavity under vibrational strong coupling conditions. Specifically, optimization of the cavity coupling strength and, thus, of the control landscape will be demonstrated., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

We present a quantum-mechanical tier model for vibrational relaxation of low-lying excited states of an adsorbate vibrational mode (system), coupled to surface phonons (bath), at zero temperature. The tier model, widely used in studies of intramolecular vibrational energy redistribution in polyatomics, is adapted here to adsorbate-surface systems with the help of an embedded cluster approach, using orthogonal coordinates for the system and bath modes, and a phononic expansion of their interaction. The key idea of the model is to organize the system-bath zeroth-order vibrational space into a hierarchical structure of vibrational tiers and keep therein only vibrational states that are sequentially generated from the system-bath initial vibrational state. Each tier is generated from the previous one by means of a successor operator, derived from the system-bath interaction Hamiltonian. This sequential procedure leads to a drastic reduction of the dimension of the system-bath vibrational space. We notably show that for harmonic vibrational motion of the system and linear system-bath couplings in the system coordinate, the dimension of the tier-model vibrational basis scales as ∼N l×υ . Here, N is the number of bath modes, l is the highest-order of the phononic expansion, and υ is the size of the system vibrational basis. This polynomial scaling is computationally far superior to the exponential scaling of the original zeroth-order vibrational basis, ∼M N , with M being the number of basis functions per bath mode. In addition, since each tier is coupled only to its adjacent neighbors, the matrix representation of the system-bath Hamiltonian in this new vibrational basis has a symmetric block-tridiagonal form, with each block being very sparse. This favors the combination of the tier-model with iterative Krylov techniques, such as the Lanczos algorithm, to solve the time-dependent Schrödinger equation for the full Hamiltonian. To illustrate the method, we study vibrational relaxation of a D-Si bending mode, coupled via two- and (mainly) one-phonon interactions to a fully D-covered Si(100)-(2 × 1) surface, using a recent first-principles system-bath Hamiltonian. The results of the tier model are compared with those obtained by the Lindblad formalism of the reduced density matrix. We find that the tier model provides much more information and insight into mechanisms of vibration-phonon couplings at surfaces, and gives more reliable estimates of the adsorbate vibrational lifetimes. Moreover, the tier model might also serve as a benchmark for other approximate quantum-dynamics methods, such as multiconfiguration wavefunction approaches.

Based on a concise review of the experimental data, a theory of the structural, kinetic, and dynamic features of the Fischer cluster is put forward. This theory is based on the idea of heterophase fluctuations of glass-forming liquids. According to these ideas in a one-component liquid the solidlike and fluidlike transient associations of molecules (fluctuons) are formed. The fluctuons differ in the short-range order and, consequently, in the free energy. They form a random free energy landscape. The random field free energy functional of the Ginzburg-Landau type, which accounts for the free energy landscape, is deduced. Based on this, the phase equilibrium, critical behavior, and ordering phenomena of the heterophase liquid are considered. It is shown that in the critical region an effective attractive interaction of the fluctuons results in their gravitation and formation of correlated fractal aggregations. The aggregation consists of the fluctuons of similar short-range order. The fractal aggregation formation is a special structural state of the liquid above the glass transition temperature. The condition at which the aggregations are formed is formulated. Thus it is shown that the Fischer cluster is an array of fractal aggregations of fluctuons. The growth kinetics and dynamics of the Fischer cluster are described. The experimental data are analyzed and discussed using the theory that is put forward., ((c) 2004 American Institute of Physics.)

Dynamics of low molecular weight and polymeric glass forming liquids in confined geometries has been studied by means of depolarized dynamic light scattering: photon correlation spectroscopy and Fabry-Perot interferometry. The pore size of the glassy matrix amounted to 2.5, 5.0, and 7.5 nm. The glass transition temperature T(g) of these liquids in confined geometries has been measured using differential scanning calorimetry. A systematic decrease of T(g) (up to 25 K) with decreasing pore size has been observed. The relaxation times of the alpha process at constant temperature were decreasing with decreasing pore size (up to 6 orders of magnitude at T(g)), while the width of their distribution was increasing. The change of the relaxation times can be assigned to the change of T(g) in confined geometries. After correcting the activation plots for the shift of T(g) a master curve was obtained for all pore sizes and the bulk material. The effect of chemical modification of the surface of the porous matrix on the dynamics of ortho-terphenyl has also been studied. These dramatic changes of the T(g) and the relaxation time of confined liquids can be explained by simple thermodynamic arguments. There is no indication that they are related to the change of the correlation length of cooperative dynamics.

A speckle pattern can be observed in the polarized component of light scattered from glass forming liquids far above their glass transition temperature. This speckle pattern fluctuates with characteristic time that corresponds to the relaxation time of the additional ultraslow component in the correlation function and is about seven orders of magnitude longer than the relaxation time of the alpha-process. This slow process is out of the experimental time window when the alpha-process is measured by means of the photon correlation spectroscopy and results in an apparent nonergodicity which can be seen as a baseline offset in the ensemble-averaged correlation function. In contrast, the time-averaged field correlation functions which have been measured in practically all light scattering studies always decay to zero. The slow process contributes a q-dependent excess intensity to the polarized component of scattered light. The values of the nonergodicity parameters obtained from the static and dynamic light scattering experiments are equal. Both the slow component and the excess intensity result from denser regions of fractal character which develop in glass-forming liquids on approaching the glass transition.

A new feature of glass-forming liquids, i.e., long-range density fluctuations of the order of 100 nm, has been extensively characterized by means of static light scattering, photon correlation spectroscopy and Rayleigh-Brillouin spectroscopy in orthoterphenyl (OTP) and 1,1-di(4(')-methoxy-5(')methyl-phenyl)-cyclohexane (BMMPC). These long-range density fluctuations result in the following unusual features observed in a light scattering experiment, which are not described by the existing theories: (i) strong q-dependent isotropic excess Rayleigh intensity, (ii) additional slow component in the polarized photon correlation function, and (iii) high Landau-Placzek ratio. These unusual features are equilibrium properties of the glass-forming liquids and depend only on temperature, provided that the sample has been equilibrated long enough. The temperature-dependent equilibration times were measured for BMMPC and are about 11 orders of magnitude longer than the alpha process. It was found that the glass-forming liquid OTP may occur in two states: with and without long-range density fluctuations ("clusters"). We have characterized the two states by static and dynamic light scattering in the temperature range from T(g) to T(g)+200 K. The relaxation times of the alpha process as well as the parameters of the Brillouin line are identical in both OTP with and without clusters. The alpha process (density fluctuations) in OTP was characterized by measuring either the polarized (VV) or depolarized (VH) correlation function, which are practically identical and q-independent. This feature, which is commonly observed in glass-forming liquids, is not fully explained by the existing theories.

The structure factor of a fragile glass-forming liquid orthoterphenyl was measured in the previously inaccessible intermediate q range between the conventional light scattering (LS) and small-angle x-ray scattering (SAXS) q ranges using the low-angle scattering beam line at the European Synchrotron Radiation Facility. At low q the structure factor exhibits an excess scattering and matches well the LS data. This excess scattering is due to long-range density fluctuations also observed in the isotropic component of scattered light. At high q the structure factor decays to a plateau corresponding to the isothermal compressibility in agreement with the conventional SAXS data. In the intermediate q range, the structure factor exhibits a power law q dependence which indicates that the excess scattering is due to fractal aggregates of denser domains.

The dynamics of the fragile glass-forming liquid diglycidyl ether of bisphenol-A was studied by depolarized Rayleigh-Brillouin light-scattering and photon correlation spectroscopy above the glass transition, in the temperature range from 261 to 473 K and in the frequency range from 1 Hz to 300 GHz. The structural (alpha-) relaxation process was revealed and no signature of the secondary relaxation previously evidenced by dielectric spectroscopy at about 0.1 GHz was observed. The characteristic time of the alpha process differs from that determined by dielectric spectroscopy of an amount, which increases with increasing temperature. The relaxation times were compared with viscosity data to test the predictions of the classic Stokes-Einstein-Debye model. The tau proportional, variant eta behavior was verified for dielectric data, while a fractional power law of viscosity tau proportional, variant eta(0.89) was obtained for light-scattering relaxation times, extending over more than seven decades in viscosity and time. This deviation of light scattering from viscosity data could be interpreted in terms of cooperative motion in the supercooled liquid with a characteristic length xi(a) proportional, variant(T-T0)(-v) where T(0)=229 K is the Vogel temperature and v is close to 2 / 3 which is consistent with the prediction of the fluctuation theory of glass transition.