Method and apparatus for creating time-optimal commands for linear systems

A system for and method of determining an input command profile for substantially any dynamic system that can be modeled as a linear system, the input command profile for transitioning an output of the dynamic system from one state to another state. The present invention involves identifying characteristics of the dynamic system, selecting a command profile which defines an input to the dynamic system based on the identified characteristics, wherein the command profile comprises one or more pulses which rise and fall at switch times, imposing a plurality of constraints on the dynamic system, at least one of the constraints being defined in terms of the switch times, and determining the switch times for the input to the dynamic system based on the command profile and the plurality of constraints. The characteristics may be related to poles and zeros of the dynamic system, and the plurality of constraints may include a dynamics cancellation constraint which specifies that the input moves the dynamic system from a first state to a second state such that the dynamic system remains substantially at the second state

Assignment of the vibrations of the S0, S1, and D+0 states of perhydrogenated and perdeuterated isotopologues of chlorobenzene

We report vibrationally resolved spectra of the S1 ← S0 transition of chlorobenzene using resonance-enhanced multiphoton ionization spectroscopy. We study chlorobenzene-h5 as well as its perdeuterated isotopologue, chlorobenzene-d5. Changes in the form of the vibrational modes between the isotopologues and also between the S0 and S1 electronic states are discussed for each species. Vibrational bands are assigned utilizing quantum chemical calculations, previous experimental results, and isotopic shifts, including those between the 35Cl and 37Cl isotopologues. Previous work and assignments of the S1 spectra are discussed. Additionally, the vibrations in the ground state cation, D+0, are considered, since these have also been used by previous workers in assigning the excited neutral state spectra

Theoretical study of Si+(2PJ)-RG complexes and transport of Si+(2PJ) in RG (RG = He – Ar)

We calculate accurate interatomic potentials for the interaction of a singly-charged silicon cation with a rare gas atom of helium, neon or argon. We employ the RCCSD(T) method, and basis sets of quadruple- and quintuple- quality; each point is counterpoise corrected and extrapolated to the basis set limit. We consider the lowest electronic state of the silicon atomic cation, Si+(2P), and calculate the interatomic potentials for the terms that arise from this: 2and 2+. We additionally calculate the interatomic potentials for the respective spin-orbit levels, and examine the effect on the spectroscopic parameters; we also derive effective ionic radii for C+ and Si+. Finally, we employ each set of potentials to calculate transport coefficients, and compare these to available data for Si+ in He

Unravelling overlaps and torsion-facilitated coupling using two-dimensional laser-induced fluorescence

Two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy is employed to identify contributions to fluorescence excitation spectra that arise from both overlapping bands and coupling between zero-order states (ZOSs). Evidence is found for the role of torsional motion in facilitating the coupling between vibrations that particularly involves the lowest-wavenumber out-of-plane vibrational modes. The experiments are carried out on jet-cooled p-fluorotoluene, where the molecules are initially in the lowest two torsional levels. Here we concentrate on the 390–420 cm−1 features in the S1 ← S0 excitation spectrum, assigning the features seen in the 2D-LIF spectrum, aided by separate dispersed fluorescence spectra. The 2D-LIF spectra allow the overlapping contributions to be cleanly separated, including some that arise from vibrational-torsional coupling. Various coupling routes open up because of the different symmetries of the lowest two torsional modes; these combine with the vibrational symmetry to provide new symmetry-allowed vibration-torsion (‘vibtor’) interactions, and the role of the excited m = 1 torsional level is found to be significant

Resonance-enhanced multiphoton ionization (REMPI) spectroscopy of p-chlorofluorobenzene

The S1 ← S0 (A ~ 1B2 ← X~ 1A1) electronic transition of para-chlorofluorobenzene has been investigated using resonance-enhanced multiphoton ionization (REMPI) spectroscopy. Assignment of the vibrational structure has been achieved by comparison with corresponding spectra of related molecules, via quantum chemical calculations, and via shifts in bands between the spectra of the 35Cl and 37Cl isotopologues. In addition, we have also partially reassigned a previously-published spectrum of para-dichlorobenzene

Interaction potentials, spectroscopy and transport properties of C+(2PJ) and C+(4PJ) with helium

We calculate accurate interatomic potentials for the interaction of a singly-charged carbon cation with a helium atom. We employ the RCCSD(T) method, and basis sets of quadruple-zeta and quintuple-zeta quality; each point is counterpoise corrected and extrapolated to the basis set limit. We consider the two lowest C+(2P) and C+(4P) electronic states of the carbon cation, and calculate the interatomic potentials for the terms that arise from these: 2-PI and 2-SIG+, and 4-PI and 4-SIG- , respectively. We additionally calculate the interatomic potentials for the respective spin-orbit levels, and examine the effect on the spectroscopic parameters. Finally, we employ each set of potentials to calculate transport coefficients, and compare these to available data. Critical comments are made in the cases where there are discrepancies between the calculated values and measured data

Vibrations of the S1 state of fluorobenzene-h5 and fluorobenzene-d5 via resonance-enhanced multiphoton ionization (REMPI) spectroscopy

We report resonance-enhanced multiphoton ionization spectra of the isotopologues fluorobenzeneh5 and fluorobenzene-d5. By making use of quantum chemical calculations, the changes in the wavenumber of the vibrational modes upon deuteration are examined. Additionally, the mixing of vibrational modes both between isotopologues and also between the two electronic states is discussed. The isotopic shifts lead to dramatic changes in the appearance of the spectrum as vibrations shift in and out of Fermi resonance. Assignments of the majority of the fluorobenzene-d5 observed bands are provided, aided by previous results on fluorobenzene-h5

Direct observation of vibrational energy dispersal via methyl torsions

Explicit evidence for the role of methyl rotor levels in promoting energy dispersal is reported. A set of coupled zero-order vibration/vibration-torsion (vibtor) levels in the S1 state of para-fluorotoluene (pFT) are investigated. Two-dimensional laser-induced fluorescence (2D-LIF) and two-dimensional zero-kinetic-energy (2D-ZEKE) spectra are reported, and the assignment of the main features in both sets of spectra reveals that the methyl torsion is instrumental in providing a route for coupling between vibrational levels of different symmetry classes. We find that there is very localized, and selective, dissipation of energy via doorway states, and that, in addition to an increase in the density of states, a critical role of the methyl group is a relaxation of symmetry constraints compared to direct vibrational coupling

Vibration and vibration-torsion levels of the S1 state of para-fluorotoluene in the 580–830 cm-1 range: interactions and coincidences

A study of the vibration and vibration-torsion levels of para-fluorotoluene (pFT) in the 580–830 cm-1 region is presented, where a number of features are located whose identity is complicated by interactions and overlap. We examine this region with a view to ascertaining the assignments of the bands; in particular, identifying those that arise from interactions involving various zero-order states (ZOSs) involving both vibrations and torsions. Resonance-enhanced multiphoton ionization (REMPI) is employed to identify the wavenumbers of the relevant transitions and subsequently zero-kinetic-energy (ZEKE) spectra are recorded to assign the various eigenstates. In some cases, a set of ZEKE spectra are recorded across the wavenumber range of a REMPI feature, and we construct what we term a two-dimensional ZEKE (2D-ZEKE) spectrum, which allows the changing ZOS contributions to the eigenstates to be ascertained. Assignment of the observed bands is aided by quantum chemical calculations and all b1 and a2 symmetry vibrational wavenumbers are now determined in the S1 state and cation, as well as those of the D10 vibration. We also compare with the activity seen in the corresponding S1 ←S0 spectrum of para-difluorobenzene

Molecular symmetry group analysis of the low-wavenumber torsions and vibration-torsions in the S1 state and ground state cation of p-xylene: an investigation using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy

For the first time, a molecular symmetry group (MSG) analysis has been undertaken in the investigation of the electronic spectroscopy of p-xylene (p-dimethylbenzene). Torsional and vibration-torsional (vibtor) levels in the S1 state and ground state of the cation of p-xylene (p-dimethylbenzene) are investigated using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy. In the present work, we concentrate on the 0–350 cm 1 region, where there are a number of torsional and vibtor bands and we discuss the assignment of this region. In an accompanying paper [Tuttle et al. J. Chem. Phys. XXX, xxxxxx (2016)], we examine the 350–600 cm 1 region where vibtor levels are observed as part of a Fermi resonance. The similarity of much of the observed spectral activity to that in the related substituted benzenes, toluene and para-fluorotoluene, is striking, despite the different symmetries. The discussion necessitates a consideration of the MSG of p-xylene, which has been designated G72, but we shall also designate [3,3]D2h and we include the symmetry operations, character table and direct product table for this. We also discuss the symmetries of the internal rotor (torsional) levels and the selection rules for the particular electronic transition of p-xylene investigated here