Optimal control theory for a target state distributed in time: optimizing the probe-pulse signal of a pump-probe-scheme

Optimal control theory (OCT) is formulated for the case of a two-color pump-probe experiment. The approach allows to calculate the pump-pulse shape in such a way that the probe-pulse absorption signal is maximized. Since the latter quantity is given by the time-averaged expectation value of a time dependent operator (the probe-pulse field-strength times the dipole operator) a version of OCT has to be used where the target state is distributed in time. The method is applied to a molecular three-level system with the pump-pulse driving the transition from the electronic ground state into the first-excited electronic state and the probe-pulse connecting the first-excited state with a higher lying electronic state. Depending on the probe-pulse duration, the vibrational wave packet becomes localized or at least highly concentrated in the Franck-Condon window for the transition into the higher-excited state. The dependence on the probe-pulse duration and on the delay time between the optimized pump-pulse and the probe-pulse is discussed in detail. The whole study demonstrates the feasibility of laser pulse induced temporal wave packet localization and the use of spectroscopic quantities as target states in experiments on femtosecond laser pulse control.     

The pure rotational spectrum of the CrS radical in its X 5Π(r) state

The pure rotational spectrum of the CrS radical has been measured in its ground X (5)Π(r) state using gas-phase millimeter/submillimeter direct absorption methods. The molecule was created by the reaction of chromium vapor, sublimed in a Broida-type oven, with hydrogen sulfide. Eleven rotational transitions were recorded for this free radical in the frequency range of 280-405 GHz; in most transitions, all five spin components were observed, and lambda-doubling was resolved in the Ω=0, 1, and 2 ladders. The data were fit with a Hund's case (a) Hamiltonian and rotational, spin-orbit, spin-spin, and lambda-doubling constants were established. Higher order spin and spin-orbit terms were essential in the analysis. The lambda-doubling constants indicate a nearby (5)Σ(+) state at an energy of ～1500-2000?cm(-1). A bond length of 2.0781 A? was derived for CrS from the data, which is larger than the value of 2.0682 A? found for MnS by ～0.01?A?. In contrast, the bond distance for MnO is greater than that of CrO by 0.03 A?, an illustration of the subtle differences between 3d oxide and sulfides. CrS is the second molecule in a (5)Π state that has been studied by rotational spectroscopy.     

Communication: Time-domain measurement of high-pressure N2 and O2 self-broadened linewidths using hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering

The direct measurement of self-broadened linewidths using the time decay of pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps RCARS) signals is demonstrated in gas-phase N(2) and O(2) from 1-20 atm. Using fs pump and Stokes pulses and a spectrally narrowed ps probe pulse, collisional dephasing rates with time constants as short as 2.5 ps are captured with high accuracy for individual rotational transitions. S-branch linewidths of N(2) and O(2) from ~0.06 to 2.2 cm(-1) and the line separation of O(2) triplet states are obtained from the measured dephasing rates and compared with high-resolution, frequency-domain measurements and S-branch approximations using the modified exponential gap model. The accuracy of the current measurements suggests that the fs/ps RCARS approach is well suited for tracking the collisional dynamics of gas-phase mixtures over a wide range of pressures.     

Rotational-translattonal energy exchange in molecule-surface collisions

Reported are calculations of rotational energy transfer in collisions of Cl₂ molecules with a rigid, smooth surface, using both sudden approximations and quasi-classical trajectories. High probabilities are found for very large Δj transitions compared to corresponding gas-phase collisions: thus molecular collisions with walls can be extremely efficient in producing rotational transitions.     

Theory of femtosecond coherent anti-Stokes Raman scattering spectroscopy of gas-phase transitions

A theoretical analysis of coherent anti-Stokes Raman scattering (CARS) spectroscopy of gas-phase resonances using femtosecond lasers is performed. The time-dependent density matrix equations for the femtosecond CARS process are formulated and manipulated into a form suitable for solution by direct numerical integration (DNI). The temporal shapes of the pump, Stokes, and probe laser pulses are specified as an input to the DNI calculations. It is assumed that the laser pulse shapes are 70 fs Gaussians and that the pulses are Fourier-transform limited. A single excited electronic level is defined as an effective intermediate level in the Raman process, and transition strengths are adjusted to match the experimental Raman polarizability. The excitation of the Raman coherence is investigated for different Q-branch rotational transitions in the fundamental 2330 cm(-1) band of diatomic nitrogen, assuming that the pump and Stokes pulses are temporally overlapped. The excitation process is shown to be virtually identical for transitions ranging from Q2 to Q20. The excitation of the Raman coherences is also very efficient; for laser irradiances of 5x10(17) W/m2, corresponding approximately to a 100 microJ, 70 fs pulse focused to 50 microm, approximately 10% of the population of the ground Raman level is pumped to the excited Raman level during the impulsive pump-Stokes excitation, and the magnitude of the induced Raman coherence reaches 40% of its maximum possible value. The theoretical results are compared with the results of experiments where the femtosecond CARS signal is recorded as a function of probe delay with respect to the impulsive pump-Stokes excitation.     

The pure rotational spectrum of NaCH3 ( )

The pure rotational spectrum of NaCH₃ and NaCD₃ in their states has been recorded using millimeter/sub-mm direct absorption techniques in the 300–510 GHz range. This work is the first gas-phase detection of sodium monomethyl, which was created by the reaction of sodium vapor with tetramethyl tin. Ten rotational transitions were measured for NaCH₃ for the K=0 through K=5 components and, in select cases, up to K=10, and four transitions (K=0–7) for NaCD₃. Rotational constants have been accurately determined for both isotopomers, suggesting a sodium–carbon bond length of 2.30 Å and an H–C–H bond angle of 107.3°.     

Rotational spectra and computational analysis of two conformers of leucinamide

Rotational spectra were recorded for two isotopic species of two conformers of the amide derivative of leucine in the range of 10.5-21 GHz and fit to a rigid rotor Hamiltonian. Ab initio calculations at the MP2/6-311++G(d,p) level identified the low energy conformations with different side chain configurations; the rotational spectra were assigned to the two lowest energy ab initio structures. We recorded 16 a- and b-type rotational transitions for conformer 1; the rotational constants of the normal species are A = 2275.6(2), B = 1033.37(2) and C = 911.71(5) MHz. We recorded 23 a- and b-type rotational transitions for conformer 2; the rotational constants of the normal species are A = 2752.775(8), B = 843.502(1) and C = 796.721(1) MHz. The rotational spectra of the (15)N(amide) isotopomer of each conformer were recorded and the atomic coordinates of the amide nitrogen were determined by Kraitchman's method of isotopic substitution. The experimentally observed structures are significantly different from the crystal structures of leucinamide and the gas-phase structures of leucine, and a natural bond orbital analysis revealed the donor-acceptor interactions governing side chain configuration.     

Five isomers of monomeric cytosine and their interconversions induced by tunable UV laser light

Photoisomerization processes involving five isomers of cytosine were induced by narrowband tunable UV irradiation of matrix-isolated monomers of the compound. Irradiation of an argon matrix containing cytosine monomers with UV λ = 313 nm laser light resulted in syn?anti photoisomerizations between the two imino-oxo forms, whereas the substantially more populated amino-hydroxy and amino-oxo forms stayed intact. Subsequent irradiation with shorter-wavelength UV λ = 311 nm laser light led to two concomitant phototautomeric processes consuming the amino-oxo isomer: (i) an oxo → hydroxy hydrogen-atom transfer photoprocess converting the amino-oxo form into the amino-hydroxy tautomer; (ii) amino → imino hydrogen-atom transfer converting the amino-oxo form into the imino-oxo isomers. The UV-induced phototransformations, together with mutual conversions of the two amino-hydroxy conformers induced by irradiation with narrowband NIR light, allowed positive detection and identification of the five isomeric forms of monomeric cytosine. This is the first experimental observation of all five low-energy isomers of cytosine.     

Single-Shot Gas-Phase Thermometry by Time-to-Frequency Mapping of Coherence Dephasing

We demonstrate a single-beam coherent anti-Stokes Raman scattering (CARS) technique for gas-phase thermometry that assesses the species-specific local gas temperature by single-shot time-to-frequency mapping of Raman-coherence dephasing. The proof-of-principle experiments are performed with air in a temperature-controlled gas cell. Impulsive excitation of molecular vibrations by an ultrashort pump/Stokes pulse is followed by multipulse probing of the 2330 cm(-1) Raman transition of N(2). This sequence of colored probe pulses, delayed in time with respect to each other and corresponding to three isolated spectral bands, imprints the coherence dephasing onto the measured CARS spectrum. For calibration purposes, the dephasing rates are recorded at various gas temperatures, and the relationship is fitted to a linear regression. The calibration data are then used to determine the gas temperature and are shown to provide better than 15 K accuracy. The described approach is insensitive to pulse energy fluctuations and can, in principle, gauge the temperature of multiple chemical species in a single laser shot, which is deemed particularly valuable for temperature profiling of reacting flows in gas-turbine combustors.     

Tautomerism and microsolvation in 2-hydroxypyridine/2-pyridone

The Fourier transform microwave spectra of the hydrated forms of the tautomeric pair 2-pyridinone/2-hydroxypyridine (2PO/2HP) have been investigated in a supersonic expansion. Three hydrated species, 2PO-H?O, 2HP-H?O, and 2PO-(H?O)?, have been observed in the rotational spectrum. Each molecular complex was confidently identified by the features of the 1?N quadrupole hyperfine structure of the rotational transitions. The presence of water affects the tautomeric equilibrium -N═C(OH)- ? -NH-C(═O)-, which is shifted to the enol form for the bare molecules 2PO/2HP but to the keto tautomer for the hydrated forms.     

The effects of surface temperature on the gas-liquid interfacial reaction dynamics of O(3P)+squalane

OH/OD product state distributions arising from the reaction of gas-phase O(3P) atoms at the surface of the liquid hydrocarbon squalane C30H62/C30D62 have been measured. The O(3P) atoms were generated by 355 nm laser photolysis of NO2 at a low pressure above the continually refreshed liquid. It has been shown unambiguously that the hydroxyl radicals detected by laser-induced fluorescence originate from the squalane surface. The gas-phase OH/OD rotational populations are found to be partially sensitive to the liquid temperature, but do not adapt to it completely. In addition, rotational temperatures for OH/OD(v'=1) are consistently colder (by 34+/-5 K) than those for OH/OD(v'=0). This is reminiscent of, but less pronounced than, a similar effect in the well-studied homogeneous gas-phase reaction of O(3P) with smaller hydrocarbons. We conclude that the rotational distributions are composed of two different components. One originates from a direct abstraction mechanism with product characteristics similar to those in the gas phase. The other is a trapping-desorption process yielding a thermal, Boltzmann-like distribution close to the surface temperature. This conclusion is consistent with that reached previously from independent measurements of OH product velocity distributions in complementary molecular-beam scattering experiments. It is further supported by the temporal profiles of OH/OD laser-induced fluorescence signals as a function of distance from the surface observed in the current experiments. The vibrational branching ratios for (v'=1)/(v'=0) for OH and OD have been found to be (0.07+/-0.02) and (0.30+/-0.10), respectively. The detection of vibrationally excited hydroxyl radicals suggests that secondary and/or tertiary hydrogen atoms may be accessible to the attacking oxygen atoms.     

Vibrational relaxation of methane by oxygen collisions: measurements of the near-resonant energy transfer between CH4 and O2 at low temperature

Vibrational relaxation in methane-oxygen mixtures has been investigated by means of a time-resolved pump-probe technique. Methane molecules are excited into selected rotational levels by tuning the pump laser to 2nu3 lines. The time evolution in population of various vibrational levels after the pumping pulse is monitored by probing, near 3000 cm-1, stretching transitions between various polyads like 2nu3(F2) - nu3, (nu3+2nu4) - 2nu4, and (nu3+nu4) - nu4 transitions. Measurements were performed from room temperature down to 190 K. A numerical kinetic model, taking into account the main collisional processes connecting energy levels up to 6000 cm(-1), has been developed to describe the vibrational relaxation. The model allows us to reproduce the observed signals and to determine rate coefficients of relaxation processes occurring upon CH4-O2 collisions. For the vibrational energy exchange, the rate coefficient of transfer from O2 (v = 1) to CH4 is found equal to (1.32 +/- 0.09) x 10(-12) cm3 molecule-1 s(-1) at 296 K and to (1.50 +/- 0.08) x 10(-12) cm3 molecule(-1) s(-1) at 193 K.     

High-resolution Fourier transform infrared absorption spectroscopy of the ν6 band of c-C3H2

The gas-phase high-resolution absorption spectrum of the ν(6) band of cyclopropenylidene (c-C(3)H(2)) has been observed using a Fourier transform infrared spectrometer for the first time. The molecule has been produced by microwave discharge in an allene (3.3 Pa) and Ar (4.0 Pa) mixture inside a side arm glass tube. The observed spectrum shows a pattern of c-type ro-vibrational transitions in which the Q-branch lines strongly and distinctly stand out in the spectrum. A combined least-squares analysis of the observed 216 ro-vibrational transitions together with 28 millimeter-wave rotational transitions from the previous study has resulted in an accurate determination of the molecular constants in the ν(6) state. The band center is found to be at 776.11622(13) cm(-1) with one standard deviation in parentheses, which is 2.3% lower than the matrix isolation value. The intensity ratio I(3)(ν(3))/I(6)(ν(6)) obtained from the observed ν(3) and ν(6) bands, 1.90(9), is somewhat lower than the ratio estimated from ab initio (2.4-2.6) and DFT (2.8) calculations.     

Orientation and alignment moments in two-color polarization spectroscopy

A theoretical analysis of two-color polarization spectroscopy (TCPS) is presented as an extension of a previous analysis of one-color PS. Three commonly used schemes in which pump and probe transitions share a common level are considered. Diagrammatic techniques are used to isolate the photon interaction sequences that can contribute to the signal. A perturbation-theory analysis expressing the signal in terms of spherical tensor moments is applied. The analysis emphasises the significance of orientation and alignment tensor moments of rotational angular momentum and their collisional evolution. The assumed context is transitions between single rotational states of gas-phase molecules that subsequently suffer discrete collisions. The time scale of the measurements is assumed to be long relative to the periods of molecular motion, as would typically be the case for signals excited by nanosecond-pulsed lasers from samples at moderate pressures. The Doppler motion of the probed species is included, as is an analytical solution to the integration over the Maxwell-Boltzmann distribution of velocities. The effects of nuclear hyperfine depolarization and velocity-changing collisions are discussed. It is shown that when pump- and probe-laser pulses are separated in time, TCPS creates and probes either orientation or alignment of rotational angular momentum in the common level shared by pump and probe transitions. Example simulations of one- and two-color polarization spectroscopies are included to demonstrate the resulting simplification of the measured signal using TCPS. TCPS is therefore a viable spectroscopic technique for the determination of rotational angular momentum orientation and alignment relaxation rates in molecular gases, of interest because they are sensitive probes of inelastic collisions.     

The far-infrared rotational spectrum of the CF radical

The rotational spectrum of CF in its ground electronic state was studied around 1000 GHz, using a tunable far-infrared source. Seven transitions were observed originating from the ²Π_1/2 and ²Π_3/2 substates. The hyperfine and Λ-type splittings were resolved. The results were combined with gas-phase electron resonance and infrared diode laser spectra to determine all pertinent molecular constants.     

Photoinitiated predissociation of the NO dimer in the region of the second and third NO stretch overtones

Photofragment yield spectra and NO(X(2)Pi(1/2,3/2); v = 1, 2, 3) product vibrational, rotational, and spin-orbit state distributions were measured following NO dimer excitation in the 4000-7400 cm(-1) region in a molecular beam. Photofragment yield spectra were obtained by monitoring NO(X(2)Pi; v = 1, 2, 3) dissociation products via resonance-enhanced multiphoton ionization. New bands that include the symmetric nu(1) and asymmetric nu(5) NO stretch modes were observed and assigned as 3nu(5), 2nu(1) + nu(5), nu(1) + 3nu(5), and 3nu(1) + nu(5). Dissociation occurs primarily via Deltav = -1 processes with vibrational energy confined preferentially to one of the two NO fragments. The vibrationally excited fragments are born with less rotational energy than predicted statistically, and fragments formed via Deltav = -2 processes have a higher rotational temperature than those produced via Deltav = -1 processes. The rotational excitation likely derives from the transformation of low-lying bending and torsional vibrational levels in the dimer into product rotational states. The NO spin-orbit state distribution reveals a slight preference for the ground (2)Pi(1/2) state, and in analogy with previous results, it is suggested that the predominant channel is X(2)Pi(1/2) + X(2)Pi(3/2). It is suggested that the long-range potential in the N-N coordinate is the locus of nonadiabatic transitions to electronic states correlating with excited product spin-orbit states. No evidence of direct excitation to electronic states whose vertical energies lie in the investigated energy region is obtained.     

Compact broadband vibrational sum-frequency generation spectrometer with nonresonant suppression

A compact broadband vibrational sum-frequency spectroscopy (SFG) apparatus is described to study molecules at surfaces and interfaces. Using an étalon as the frequency narrowing device, the visible pulse has a time-asymmetric profile that allows the user to deeply suppress nonresonant background signals that hinder detection of molecular vibrational resonances. Several features of the spectrometer that, in aggregate, improve signal-to-noise ratios by a large factor are described. The spectrometer features a series of interchangeable prealigned sample holders for different applications. Examples of applications are presented where nonresonant suppression greatly improves the ability to study adsorbates on single-crystal surfaces as a function of rotation about the azimuth, and where the rapid data acquisition abilities of the spectrometer are used to study electrochemical transformations on single-crystal electrodes.     

Experimental and theoretical study of the OH vibrational spectra and overtone chemistry of gas-phase vinylacetic acid

In this study we present the gas-phase vibrational spectrum of vinylacetic acid with a focus on the nu = 1-5 vibrational states of the OH stretching transitions. Cross sections for nu = 1, 2, 4 and 5 of the OH stretching vibrational transitions are derived on the basis of the vapor pressure data obtained for vinylacetic acid. Ab initio calculations are used to assist in the band assignments of the experimental spectra, and to determine the threshold for the decarboxylation of vinylacetic acid. When compared to the theoretical energy barrier to decarboxylation, it is found that the nu OH = 4 transition with thermal excitation of low frequency modes or rotational motion and nu OH = 5 transitions have sufficient energy for the reaction to proceed following overtone excitation.     

Laser-induced alignment and anti-alignment of rotationally excited molecules

We numerically investigate the post-pulse alignment of rotationally excited diatomic molecules upon nonresonant interaction with a linearly polarized laser pulse. In addition to the simulations, we develop a simple model which qualitatively describes the shape and amplitude of post-pulse alignment induced by a laser pulse of moderate power density. In our treatment we take into account that molecules in rotationally excited states can interact with a laser pulse not only by absorbing energy but also by stimulated emission. The extent to which these processes are present in the interaction depends, on the one hand, on the directionality of the molecular angular momentum (given by the M quantum number), and on the other hand on the ratio of transition frequencies and pulse duration (determined by the J number). A rotational wave packet created by a strong pulse from an initially pure state contains a broad range of rotational levels, over which the character of the interaction can change from non-adiabatic to adiabatic. Depending on the laser pulse duration and amplitude, the transition from the non-adiabatic to the adiabatic limit proceeds through a region with dominant rotational heating, or alignment, for short pulses and a large region with rotational cooling, and correspondingly preferred anti-alignment, for longer pulses.     

Rotational and vibrational relaxation of methane excited to 2nu3 in CH4/H2 and CH4/He mixtures at 296 and 193 K from double-resonance measurements

A series of time-resolved IR-IR double-resonance experiments have been conducted where methane molecules are excited into a selected rovibrational level of the 2nu3(F2) vibrational substate of the tetradecad and where the time evolution of the population of the various energy levels is probed by a tunable continuous wave laser. The rotational relaxation and vibrational energy transfer processes occurring in methane upon inelastic CH4-H2 and CH4-He collisions have been investigated by this technique at room temperature and at 193 K. By probing transitions in which either the lower or the upper level is the laser-excited level, rotational depopulation rates in the 2nu3(F2) substate were measured. The rate constants for CH4-H2 collisions were found to be 17.7 +/- 2.0 and 18.9 +/- 2.0 micros(-1) Torr(-1) at 296 and 193 K, respectively, and for CH(4)-He collisions they are 12.1 +/- 1.5 and 16.0 +/- 2.0 micros(-1) Torr(-1) at the same temperatures. The vibrational relaxation was investigated by probing other stretching transitions such as 2nu3(F2) - nu3, nu3 + 2nu4 - 2nu4, and nu3 + nu4 - nu4. A kinetic model, taking into account the main collisional processes connecting energy levels up to 6000 cm(-1), that has been developed to describe the various relaxation pathways allowed us to calculate the temporal evolution of populations in these levels and to simulate double-resonance signals. The different rate coefficients of the vibrational relaxation processes involved in these mixtures were determined by fitting simulated signals to the observed signals corresponding to assigned transitions. For vibration to translation energy transfer processes, hydrogen is a much more efficient collision partner than helium, nitrogen, or methane itself at 193 K as well as at room temperature.