Ultrafast dynamics of halogens in rare gas solids

We perform time resolved pump-probe spectroscopy on small halogen molecules ClF, Cl2, Br2, and I2 embedded in rare gas solids (RGS). We find that dissociation, angular depolarization, and the decoherence of the molecule is strongly influenced by the cage structure. The well ordered crystalline environment facilitates the modelling of the experimental angular distribution of the molecular axis after the collision with the rare gas cage. The observation of many subsequent vibrational wave packet oscillations allows the construction of anharmonic potentials and indicate a long vibrational coherence time. We control the vibrational wave packet revivals, thereby gaining information about the vibrational decoherence. The coherence times are remarkable larger when compared to the liquid or high pressure gas phase. This fact is attributed to the highly symmetric molecular environment of the RGS. The decoherence and energy relaxation data agree well with a perturbative model for moderate vibrational excitation and follow a classical model in the strong excitation limit. Furthermore, a wave packet interferometry scheme is applied to deduce electronic coherence times. The positions of those cage atoms, excited by the molecular electronic transitions are modulated by long living coherent phonons of the RGS, which we can probe via the molecular charge transfer states.     

Wave packet dynamics in triplet states of Na2 attached to helium nanodroplets

The dynamics of vibrational wave packets excited in Na2 dimers in the triplet ground and excited states is investigated by means of helium nanodroplet isolation (HENDI) combined with femtosecond pump-probe spectroscopy. Different pathways in the employed resonant multiphoton ionization scheme are identified. Within the precision of the method, the wave packet dynamics appears to be unperturbed by the helium droplet environment.     

Electronic coherences and vibrational wave-packets in single molecules studied with femtosecond phase-controlled spectroscopy

Employing femtosecond pulse-shaping techniques we investigate ultrafast, coherent and incoherent dynamics in single molecules at room temperature. In first experiments single molecules are excited into their purely electronic 0-0 transition by phase-locked double-pulse sequences with pulse durations of 75 fs and 20 nm spectral band width. Their femtosecond kinetics can then be understood in terms of a 2-level system and modelled with the optical Bloch equations. We find that we observe the coherence decay in single molecules, and the purely electronic dephasing times can be retrieved directly in the time domain. In addition, the Rabi-frequencies and thus the transition dipole moments of single molecules are determined from these data. Upon excitation of single molecules into a vibrational level of the electronically excited state also incoherent intra-molecular vibrational relaxation is recorded. Increasing the spectral band width of the excitation pulses to up to 120 nm (resulting in a transform-limited pulse width of 15 fs) coherent superpositions of excited state vibrational modes, i.e. vibrational wave packets, are excited. The wave-packet oscillations in the excited state potential energy surface are followed in time by a phase-controlled pump-probe scheme, which permits to record wave packet interference, and to determine the energies of vibrational modes and their coupling strengths to the electronic transition.     

A semiclassical study of wave packet dynamics in anharmonic potentials

Classical and semiclassical methods are developed to calculate and invert the wave packet motion measured in pump-probe experiments. With classical propagation of the Wigner distribution of the initial wave packet created by the pump pulse, we predict the approximate probe signal with slightly displaced recurrence peaks, and derive a set of first-order canonical perturbation expressions to relate the temporal features of the signal to the characteristics of the potential surface. A reduced dynamics scheme based on the Gaussian assumption leads to the correct center of mass motion but does not describe the evolution of the shape of the wave packet accurately. To incorporate the quantum interference into classical trajectories, we propose a final-value representation semiclassical method, specifically designed for the purpose of computing pump-probe signals, and demonstrate its efficiency and accuracy with a Morse oscillator and two kinetically coupled Morse oscillators. For the case of one-color pump probe, a simple phase-space quantization scheme is devised to reproduce the temporal profile at the left-turning point without actual wave packet propagation, revealing a quantum mechanical perspective of the nearly classical pump-probe signal.     

Optical control of excited-state vibrational coherences of a molecule in solution: The influence of the excitation pulse spectrum and phase in LD690

Spectral and phase shaping of femtosecond laser pulses is used to selectively excite vibrational wave packets on the ground (S0) and excited (S1) electronic states in the laser dye LD690. The transient absorption signals observed following excitation near the peak of the ground-state absorption spectrum are characterized by a dominant 586 cm(-1) vibrational mode. This vibration is assigned to a wave packet on the S0 potential energy surface. When the excitation pulse is tuned to the blue wing of the absorption spectrum, a lower frequency 568 cm(-1) vibration dominates the response. This lower frequency mode is assigned to a vibrational wave packet on the S1 electronic state. The spectrum and phase of the excitation pulse also influence both the dephasing of the vibrational wave packet and the amplitude profiles of the oscillations as a function of probe wavelength. Excitation by blue-tuned, positively chirped pulses slows the apparent dephasing of the vibrational coherences compared with a transform-limited pulse having the same spectrum. Blue-tuned negatively chirped excitation pulses suppress the observation of coherent oscillations in the ground state.     

Theoretical treatments of ultrafast electron transfer from adsorbed dye molecule to semiconductor nanocrystalline surface

In studying ultrafast electron transfer from a dye molecule to a nanosized semiconductor particle, pump-probe experiments are commonly used. In this system the electron transfer (ET) rate is faster than vibrational relaxation so that the ET rate should be described by a single-level rate constant and the probing signal (often in the form of time-resolved spectra) contains the contribution from the dynamics of both population and coherence (i.e., wave packet). In this paper, we shall present the theoretical treatments for femtosecond time-resolved pump-probe experiment and the dynamics of population and coherence by the density matrix method, and the calculation of single-level ET rate constant involved in a pump-probe experiment. As an application, we show the theoretical results using parameters extracted from experiments on a specific dye/semiconductor system.     

The principles of infrared-x-ray pump-probe spectroscopy. Applications on proton transfer in core-ionized water dimers

In this paper we derive the basic physics underlying infrared-x-ray pump-probe spectroscopy (IR, infrared). Particular features of the spectroscopy are highlighted and discussed, such as dependence on phase of the infrared pulse, duration and delay time of the x-ray pulse, and molecular orientation. Numerical applications are carried out for the water dimer using wave packet techniques. It is shown that core ionization of the donor oxygen of the water dimer results in a drastic change of the potential with the global minimum placed in the proton transfer region. The results of the modeling indicate that IR-x-ray pump-probe spectroscopy can be used to study the dynamics of proton transfer in this core-ionized state, and that, contrary to conventional core level photoelectron spectroscopy, x-ray core-ionization driven by an IR field is a proper method to explore the proton transfer in a system like the water dimer. We observe that the trajectory of the nuclear wave packet in the ground state potential well is strongly affected by the absolute phase of the IR pulse.     

Femtosecond spectroscopy of the (2)1Σ u + double minimum state of Na2: time domain and frequency spectroscopy

Femtosecond time resolved pump-probe experiments studying wave packet dynamics in the (2)¹Σ _u ⁺ double minimum state of Na₂ are reported. The experiments were performed in a molecular beam with ion Time of Flight (TOF) detection. By Fast Fourier Transformation (FFT) of the observed time domain data the energy spacings of the coherently coupled vibrational levels in the (2)¹Σ _u ⁺ potential are obtained with an accuracy of 0.02 cm^?1, although an ultrafast laser source with its inherent spectral width was used in the experiment. The wavelengths of the pump and probe laser pulses are chosen such that in this two color experiment we can control ionisation versus ionisation induced fragmentation. In order to study the influence of the potential barrier on a vibrational wave packet motion we performed simulations based on time dependent quantum calculations.     

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.     

Analysis of wave packet motion in frequency and time domain: oxazine 1

Wave packet motion in the laser dye oxazine 1 in methanol is investigated by spectrally resolved transient absorption spectroscopy. The spectral range of 600-690 nm was accessible by amplified broadband probe pulses covering the overlap region of ground-state bleach and stimulated emission signal. The influence of vibrational wave packets on the optical signal is analyzed in the frequency domain and the time domain. For the analysis in the frequency domain an algorithm is presented that accounts for interference effects of neighbored vibrational modes. By this method amplitude, phase and decay time of vibrational modes are retrieved as a function of probe wavelength and distortions due to neighbored modes are reduced. The analysis of the data in the time domain yields complementary information on the intensity, central wavelength, and spectral width of the optical bleach spectrum due to wave packet motion.     

Theoretical description of femtosecond fluorescence depletion spectrum of molecules in solution

A theoretical model used for calculating the fluorescence depletion spectrum (FDS) of molecules in liquids induced by femtosecond pump-probe laser pulses is proposed based on the reduced density matrix theory. The FDS intensity is obtained by calculating the stimulated emission of the excited electronic state. As an application of the theoretical model, the FDS of oxazine 750 (OX-750) molecule in acetone solution is calculated. The simulated FDS agrees with the experimental result of Liu et al. [J. Y. Liu et al., J. Phys. Chem. A 107, 10857 (2003)]. The calculated vibrational relaxation rate is 2.5 ps(-1) for the OX-750 molecule. Vibrational population dynamics and wave packet evolution in the excited state are described in detail. The effect of the probe pulse parameter on the FDS is also discussed.     

A first principles approach to optimal control

This article shows that by using ab initio or first principle calculations it is possible to obtain reliable ingredients needed to simulate pump-probe and optimal control experiments. Our experimental challenge is to elucidate the reaction mechanism behind an optimal pulse tailored to maximize ionization in the system CpMn(CO)₃, while avoiding CO dissociation. Starting from MRCI/CASSCF potential energy curves calculated along the relevant CO fragmentation channel, we use the resulting MRCI wave function to estimate non-adiabatic couplings, as well as neutral-to-neutral and neutral-to-ionic dipole couplings. The state-of-the-art potentials and couplings serve to perform wave packet propagations which simulate the femtosecond pump-probe spectra that explain the features shown in the experimental optimal pulse.     

Classification of dynamic vibronic couplings in vibrational real-time spectra of a thiophene derivative by few-cycle pulses

Pump-probe spectroscopy was performed with a few cycle pulses of 6.7 fs duration. The electronic transition intensity modulation was induced by molecular vibration in a quinoid thiophene molecule in solution. The real-time vibrational features were analyzed in terms of dependence of vibrational amplitude and phase on probe photon energy. The electronic transition probability is modulated by molecular vibration via vibronic coupling. Changes in the spectral shape and intensity of the time-resolved spectrum were studied by tracking characteristic spectral features including the peak frequency and intensity, spectral bandwidth, and band-integrated intensity. From the analysis the modulation mechanisms were classified into two groups: (1) Condon type and (2) non-Condon type. The features of the wave packet motions were also classified into zeroth-order derivatives due to quasi-pure non-Condon type and first- and second-order derivative types due to the displacement of the potential minimum and the potential curvature change associated with the relevant vibronic transition, respectively.     

Fractional revivals in the rovibrational motion of I2

Motivated by pump-probe experiments of I(2) in a room-temperature sample, the detection of fractional revivals is investigated using full-dimensional quantum wave packet calculations. It is shown that the structures observed in the pump-probe signal depend sensitively on the probe parameters employed and that the observed signal reflects a particular phase effect between fractional revivals.     

Femtosecond study of Cu(H(2)O) dynamics

The short-time nuclear dynamics of Cu(H(2)O) is investigated using femtosecond photodetachment-photoionization spectroscopy and time-dependent quantum wave packet calculations. The Cu(H(2)O) dynamics is initiated in the electronic ground state of the complex by electron photodetachment from the Cu(-)(H(2)O) complex, where hydrogen atoms are oriented toward Cu. Several time-resolved resonant multiphoton ionization schemes are used to probe the ensuing reorientation and dissociation. Immediately following photodetachment, the neutral complex is far from its minimum energy geometry and possesses an internal energy comparable to the Cu-H(2)O dissociation energy and undergoes both large-amplitude H(2)O motion and dissociation. Dissociation is observed to occur on three distinct time scales: 0.6, 8, and 100 ps. These results are compared to the results of time-dependent J=0 wave packet calculations, propagating the initial anion vibrational wave functions on the ground-state potential of the neutral complex. An excellent agreement is obtained between the experimental results and the ionization signals derived from the calculated probability amplitudes. Related experiments and calculations are carried out on the Cu(D(2)O) complex, with results very similar to those of Cu(H(2)O).     

Dynamics of small,floppy molecules studied by high-resolution spectroscopic techniques

In molecular spectroscopy one of the common interests is how to transform the information obtained by high-resolution spectroscopic techniques into some reliable approximation of the potential energy surface of a particular molecule. Traditionally vibrational spectroscopy has been used. Rotational spectroscopy can only probe, at least at room temperature, molecular transitions arising from excited vibrational states up to approximately 1000 cm^?1. This corresponds roughly to 10% of a typical bond dissociation energy. However, floppy molecules which exhibit a large-amplitude, low-lying vibrational mode can be studied to a large extent by rotational spectroscopy in the microwave, millimeter and submillimeter wave range. Quasilinearity is a special form of large-amplitude motion, which complicates the observed molecular spectra substantially and which presents a real challenge to theoretical spectroscopists. In this lecture the highlights of quasilinear behavior of the molecules HCNO, OCCCO, HNCS and HNCO will be discussed. Another form of large amplitude motion is the inversion exhibited primarily by molecules derived from NH₃. Isocyanamide will be discussed and its special spectroscopic features will be shown. Cyanamide and isocyanamide are potential prebiotic molecules: cyanamide has been detected as a constituent in the interstellar medium. The analysis of the molecular dynamics of these molecules is shown to be necessary for understanding the frequencies and intensities of the observed spectra in the laboratory and in interstellar space.     

Electron affinity of NO

The electron affinity of NO has been measured to be 0.026 eV by laser photodetachment experiments. This low electron affinity (just 2.5 kJ/mol or 210 cm-1) presents a computational challenge that requires careful attention to several aspects of the computational procedure required to predict the electron affinity of NO from first principles. We have used augmented correlation consistent basis sets with several coupled cluster methods to calculate the molecular energies, bond dissociation energies, bond lengths, vibrational frequencies, and potential energy curves for NO and NO-. The electron affinity of NO, EA0, using the CCSD(T) method and extrapolating to the complete basis set limit, is calculated to be 0.028 eV. The calculated bond dissociation energies, D0, for NO and NO- are 622 and 487 kJ/mol, respectively, compared with experimental values of 626.8 and 487.8 kJ/mol. From the calculated potential energy curves for NO and NO- the vibrational wavefunctions were determined. The calculated vibrational wavefunctions predict Franck-Condon factor ratios in good agreement with the values determined in the photodetachment experiment.     

Time-dependent Wave Packet Quantum Scattering Study of Reaction S(3P)+H2→HS+H on a New ab initio Potential Energy Surface 3A'

A new potential energy surface is presented for the triplet state ³A' of the chemical reaction S(³P)+H₂ from a set of accurate ab initio data. The single point energies are computed using highly correlated complete active space self-consistent-field and multi-reference config-uration interaction wave functions with a basis set of aug-cc-pV5Z. We have fitted the full set of energy values using many-body expansion method with an Aguado-Paniagua function. Based on the new potential energy surface, we carry out the time-dependent wave packet scattering calculations over the collision energy range of 0.8～2.2 eV. Both the centrifugal-sudden approximation and Coriolis Coupling cross sections are obtained. In addition, the total reaction probabilities are calculated for the reactant H₂ initially in the vibrational states v=0～3 (j=0). It is found that initial vibrational excitation enhances the title reaction.