Quantum theory of (femtosecond) time-resolved stimulated Raman scattering

We present a complete perturbation theory of stimulated Raman scattering (SRS), which includes the new experimental technique of femtosecond stimulated Raman scattering (FSRS), where a picosecond Raman pump pulse and a femtosecond probe pulse simultaneously act on a stationary or nonstationary vibrational state. It is shown that eight terms in perturbation theory are required to account for SRS, with observation along the probe pulse direction, and they can be grouped into four nonlinear processes which are labeled as stimulated Raman scattering or inverse Raman scattering (IRS): SRS(I), SRS(II), IRS(I), and IRS(II). Previous FSRS theories have used only the SRS(I) process or only the "resonance Raman scattering" term in SRS(I). Each process can be represented by an overlap between a wave packet in the initial electronic state and a wave packet in the excited Raman electronic state. Calculations were performed with Gaussian Raman pump and probe pulses on displaced harmonic potentials to illustrate various features of FSRS, such as high time and frequency resolution; Raman gain for the Stokes line, Raman loss for the anti-Stokes line, and absence of the Rayleigh line in off-resonance FSRS from a stationary or decaying v=0 state; dispersive line shapes in resonance FSRS; and the possibility of observing vibrational wave packet motion with off-resonance FSRS.     

Polarization dependence of vibrational coupling signals in femtosecond stimulated Raman spectroscopy

The polarization dependence of vibrational coupling signals seen in femtosecond stimulated Raman spectroscopy (FSRS) is investigated. Changing the polarization of a pulse used to impulsively excite coherent low frequency chlorine bending motion in CDCl(3) has a dramatic effect on the line shape of vibrational sidebands which arise from the anharmonic coupling of the pumped modes at 262 and 365 cm(-1) with the higher frequency symmetric stretching mode at 652 cm(-1). The asymmetric bend sideband (652+262 cm(-1)) changes sign and magnitude as the impulsive pulse polarization is rotated relative to the Raman pulses, while the symmetric bend sideband (652+365 cm(-1)) is relatively polarization independent. These experiments demonstrate the ability of FSRS to obtain time-resolved information on not only the vibrational coupling strength but also the symmetry of anharmonically coupled modes.     

Wave packet theory of dynamic stimulated Raman spectra in femtosecond pump-probe spectroscopy

The quantum theory for stimulated Raman spectroscopy from a moving wave packet using the third-order density matrix and polarization is derived. The theory applies, in particular, to the new technique of femtosecond broadband stimulated Raman spectroscopy (FSRS). In the general case, a femtosecond actinic pump pulse first prepares a moving wave packet on an excited state surface which is then interrogated with a coupled pair of picosecond Raman pump pulse and a femtosecond Raman probe pulse and the Raman gain in the direction of the probe pulse is measured. It is shown that the third-order polarization in the time domain, whose Fourier transform governs the Raman gain, is given simply by the overlap of a first-order wave packet created by the Raman pump on the upper electronic state with a second-order wave packet on the initial electronic state that is created by the coupling of the Raman pump and probe fields acting on the molecule. Calculations are performed on model potentials to illustrate and interpret the FSRS spectra.     

Probing structural evolution along multidimensional reaction coordinates with femtosecond stimulated Raman spectroscopy

Mapping out multidimensional potential energy surfaces has been a goal of physical chemistry for decades in the quest to both predict and control chemical reactivity. Recently a new spectroscopic approach called Femtosecond Stimulated Raman Spectroscopy or FSRS was introduced that can structurally interrogate multiple dimensions of a reactive potential energy surface. FSRS is an ultrafast laser technique which provides complete time-resolved, background-free Raman spectra in a few laser shots. The FSRS technique provides simultaneous ultrafast time (~50 fs) and spectral (~8 cm(-1)) resolution, thus enabling one to follow reactive structural evolutions as they occur. In this perspective we summarize how FSRS has been used to follow structural dynamics and provide mechanistic detail on three classical chemical reactions: a structural isomerization, an electron transfer reaction, and a proton transfer reaction.     

Origin of negative and dispersive features in anti-Stokes and resonance femtosecond stimulated Raman spectroscopy

Femtosecond stimulated Raman spectroscopy is extended to probe ground state anti-Stokes vibrational features. Off resonance, negative anti-Stokes features are seen that are the mirror image of the positive Stokes side spectra. On resonance, the observed dispersive lineshapes are dramatically dependent on the frequencies of the picosecond pump and femtosecond probe pulses used to generate the stimulated Raman spectra. These observations are explained by the contributions of the inverse Raman and hot luminescence four-wave mixing processes discussed by Sun et al. [J. Chem. Phys. 128, 144114 (2008)], which contribute to the overall femtosecond stimulated Raman signal.     

Photoexcited structural dynamics of an azobenzene analog 4-nitro-4'-dimethylamino-azobenzene from femtosecond stimulated Raman

Azobenzenes are used in many applications because of their robust and reversible light induced trans?cis isomerization about the N=N bond, but the mechanism of this ultrafast reaction has not been conclusively defined. Addressing this problem we have used Femtosecond Stimulated Raman Spectroscopy (FSRS) to determine the structural transients in the trans→cis photoisomerization of the azobenzene derivative, 4-nitro-4'-dimethylamino-azobenzene (NDAB). Key marker modes, such as the 1570/1590 cm(-1) NO(2) stretch and the 1630 cm(-1) C-N(Me)(2) stretch, enable the separation and analysis of distinct trans and cis photoproduct dynamics revealing the 400 fs Frank-Condon relaxation, the 800 fs timescale of the cis product formation and the 2 ps emergence and 8 ps relaxation of the unsuccessful ground state trans species. Based on these observations, we propose a reaction mechanism, including initial dilation of the CNN bend later joined by quick movement along the CCNN, CNNC and NNCC torsional coordinates that constitutes a mixed inversion-rotation mechanism.     

Ionization-detected stimulated Raman spectroscopy

We report a new spectroscopic technique which we call “ionization-detected stimulated Raman spectroscopy” that combines the high sensitivity of resonant laser ionization methods with the high spectral resolution of stimulated Raman spectroscopy. A Q-branch spectrum of NO at 10 mTorr pressure illustrates an improvement in sensitivity of over 1000-fold compared to previous stimulated Raman methods.     

Quantum theory of time-resolved femtosecond stimulated Raman spectroscopy: direct versus cascade processes and application to CDCl3

We present a quantum mechanical wave packet treatment of time-resolved femtosecond stimulated Raman spectroscopy (FSRS), or two-dimensional (2D) FSRS, where a vibrational coherence is initiated with an impulsive Raman pump which is subsequently probed by FSRS. It complements the recent classical treatment by Mehlenbacher et al. [J. Chem. Phys. 131, 244512 (2009)]. In this 2D-FSRS, two processes can occur concurrently but with different intensities: a direct fifth-order process taking place on one molecule, and a cascade process comprising two third-order processes on two different molecules. The cascade process comprises a parallel and a sequential cascade. The theory is applied to the 2D-FSRS of CDCl(3) where calculations showed that: (a) the cascade process is stronger than the direct fifth-order process by one order of magnitude, (b) the sidebands assigned to C-Cl E and A(1) bends, observed on both sides of the Stokes C-D stretch frequency, are not due to anharmonic coupling between the C-D stretch and the C-Cl bends, but are instead due to the coherent anti-Stokes Raman spectroscopy (CARS) and coherent Stokes Raman spectroscopy (CSRS) fields produced in the first step of the cascade process, (c) for each delay time between the femtosecond impulsive pump and FSRS probe pulses, the line shape of the sidebands shows an inversion symmetry about the C-D stretch frequency, and this is due to the 180(°) phase difference between the CARS and CSRS fields that produced the left and right sidebands, and (d) for each sideband, the line shape changes from positive Lorentzian to dispersive to negative Lorentzian, then to negative dispersive and back to positive Lorentzian with the period of the bending vibration, and it is correlated with the momentum of the wave packet prepared on the ground-state surface by the impulsive pump along the sideband normal coordinate.     

Internally amplified stimulated Raman spectroscopy

Internally amplified stimulated Raman scattering is developed as a novel approach to study concentrational thresholds in stimulated Raman scattering (SRS). In the proposed physical model, amplifier molecules are used to bridge the spatial gaps among analyte molecules distributed distantly from each other throughout a dilute solution. As a result, Stokes photons can more effectively reach the next target molecules down the pump light path to sustain and amplify the desirable SRS process. The model has been verified by experimental results which give a better understanding of the threshold phenomenon in SRS. The technique of internal amplification is practically useful to lower concentrational thresholds, leading to improved detection limits in analytical SRS measurements.     

A microcomputer for the simultaneous data processing of different automatic elemental analysers

Summary A microcomputer has been developed for automated data processing of different automatic elemental analysers. The microcomputer allows users, already in possession of multimeters or integrators, an electronic microbalance and elemental analysers, to combine their equipment into an automated system. Depending on the elemental analysers available, it is possible with this system to determine simultaneously the elements C-H-N and O, C-H-N and S, or O and S, or it is also possible to determine these elements in duplicate. The microcomputer system is flexible and can easily be adapted for other applications by changing the software. After the analysers have been started, this system processes all data and calculates the blanks, calibration factors and percentages successively. The modes of operation of the principal parts of the microcomputer are described.

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Ein Mikrocomputer zur gleichzeitigen Datenverarbeitung verschiedener automatischer Elementaranalysengeräte

Zusammenfassung Ein Mikrocomputer zur automatischen Datenverarbeitung verschiedener automatischer Elementaranalysengeräte wurde entwickelt. Dieser ermöglicht, Vielfachmeßgeräte oder Zählgeräte, eine elektronische Mikrowaage und Analysengeräte zu einem automatischen System zusammenzuschließen. Je nach dem vorhandenen Analysator lassen sich damit C-H-N und O, C-H-N und S oder O und S gleichzeitig bestimmen oder man kann Doppelbestimmungen dieser Elemente durchführen. Das Mikrocomputer-System ist flexibel und kann durch Austausch der Soft-ware leicht für andere Zwecke adaptiert werden. Nach dem Start der Analysatoren verarbeitet dieses System alle Daten und berechnet die Leer werte, die Berechnungsfaktoren und die Prozentgehalte der Reihe nach. Die Arbeitsweise der Hauptteile des Mikrocomputers wurde beschrieben.

     

Induced changes in stimulated Raman scattering intensities

The stimulated Raman scattering (SRS) intensity of neat liquids and of binary liquid mixtures was measured as a function of the power of the pump field and of an additional radiation field at the Stokes frequency. In neat p-xylene SRS intensity transfer, form one vibrational mode to another, was observed. In benzene/nitrobenzene mixtures it was found possible, at various concentrations, to selectively generate SRS from one component in the mixture, including the minor one. Implications of the results for the selective excitation by the SRS process of a single species in a mixture are discussed.     

Morphology-dependent stimulated Raman scattering (MDSRS)

A novel non-linear Raman spectroscopic technique, which can be used to characterize the chemical composition of the interface region of volatile aerosol particles, is described. The technique is morphology-dependent stimulated Raman scattering (MDSRS). We discuss the phenomenology behind this new optical probe, and present experimental results which show that this technique can be used as quantitative spectroscopic tool. We outline the potential application of MDSRS to in situ gas—aerosol kinetics and dynamics studies.     

Vibrational structure of the S(2) (1B(u)) excited state of diphenyloctatetraene observed by femtosecond stimulated Raman spectroscopy

Femtosecond time-resolved stimulated Raman spectroscopy (FSRS) is used to study the vibrational structure and dynamics of the S(2) state of diphenyloctatetraene. Strong vibrational features at 1184, 1259 and 1578 cm(-1) whose linewidths are determined by the S(2) electronic lifetime are observed at early times after photoexcitation at 397 nm. Kinetic analysis of the integrated Raman intensities as well as the transient absorption reveals an exponential decay of the S(2) state on the order of 100 fs. These results demonstrate the ability of FSRS to study the vibrational structure of excited state and chemical reaction dynamics on the femtosecond timescale.     

Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory

Optimal control theory is used to tailor laser pulses which enhance a femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) spectrum in a certain frequency range. For this aim the optimal control theory has to be applied to a target state distributed in time. Explicit control mechanisms are given for shaping either the Stokes or the probe pulse in the four-wave mixing process. A simple molecule for which highly accurate potential energy surfaces are available, namely molecular iodine, is used to test the procedure. This approach of controlling vibrational motion and delivering higher intensities to certain frequency ranges might also be important for the improvement of CARS microscopy.     

High-accuracy structure of cyclobutane by femtosecond rotational Raman four-wave mixing

The femtosecond degenerate four-wave mixing (fs-DFWM) technique is applied for the measurement of accurate rotational constants of cyclobutane (C4H8). The vibrational levels of C4H8 exhibit tunneling splitting due to the ring-puckering interconversion between the symmetry-equivalent D2d minima via a planar D4h barrier. For the v = 0 ground state, the fs-DFWM method yields a rotational constant B + 0 = 10663.452(18) MHz. The ring-puckering tunneling leads to slightly different rotational constants for the 0+ and 0- levels, B + 0 - B -0 = 33 +/- 2 kHz. This difference increases by a factor of approximately 90 in the v = 1+/1- ring-puckering states to B +1 - B -1 = -3059 +/- 4 kHz. Combining the experimental rotational constants with the structure parameters and rotational constants calculated by high-level ab initio calculations allows us to determine accurate equilibrium and vibrationally averaged structure parameters for cyclobutane, for example, re(C-C) = 1.5474 A, re(C-Haxial) = 1.0830 A, re(C-Hequatorial) = 1.0810 A, and ring puckering angle theta e = 29.8 degrees .     

Transient stimulated vibrational Raman scattering in small molecule liquids

Transient stimulated vibrational Raman scattering in liquid HCl, HBr, Cl₂, CO₂, N₂O, CH₃F, CH₃Cl and SF₆ has been observed using a mode-locked ruby laser. Efficient conversions to Stokes wavelengths (up to 10%) are observed resulting in large excitation of the vibrational population.     

Femtosecond stimulated Raman study of excited-state evolution in bacteriorhodopsin

Femtosecond time-resolved stimulated Raman spectroscopy (FSRS) is used to examine the photoisomerization dynamics in the excited state of bacteriorhodopsin. Near-IR stimulated emission is observed in the FSRS probe window that decays with a 400-600-fs time constant. Additionally, dispersive vibrational lines appear at the locations of the ground-state vibrational frequencies and decay with a 260-fs time constant. The dispersive line shapes are caused by a nonlinear effect we term Raman initiated by nonlinear emission (RINE) that generates vibrational coherence on the ground-state surface. Theoretical expressions for the RINE line shapes are developed and used to fit the spectral and temporal evolution of the spectra. The rapid 260-fs decay of the RINE peak intensity, compared to the slower evolution of the stimulated emission, indicates that the excited-state population moves in approximately 260 fs to a region on the potential energy surface where the RINE signal is attenuated. This loss of RINE signal is best explained by structural evolution of the excited-state population along multiple low-frequency modes that carry the molecule out of the harmonic photochemically inactive Franck-Condon region and into the photochemically active geometry.