W. Thomas Pollard

Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments

The large spectral width of ultrashort optical pulses makes it possible to measure the complete time‐resolved absorption spectrum of a sample with a single pulse, offering simultaneously high resolution in both the time and frequency domains. To quantitatively interpret these experiments, we start with the usual perturbative density matrix theory for the third‐order susceptibility of a multilevel system. However, the theory is formulated in terms of four‐time correlation functions which are interpreted as the time‐dependent overlap of bra and ket vibrational wave packets propagating independently on the ground and excited electronic state potential surfaces. This approach captures the critical distinction between electronic population decay and pure dephasing processes, while retaining the intuitive physical picture offered by the time‐dependent wave packet theories of molecular spectroscopy. A useful simplification is achieved by considering the absorption of the probe pulse as the first‐order spectrosco...

Direct observation of the excited‐state cis–trans photoisomerization of bacteriorhodopsin: Multilevel line shape theory for femtosecond dynamic hole burning and its application

A dynamic hole‐burning study of light‐adapted bacteriorhodopsin (BR568) using 6 fs optical pulses has recently been reported [R. A. Mathies, C. H. Brito Cruz, W. T. Pollard, and C. V. Shank, Science 240, 777 (1988)]. The temporal evolution of the excited state absorption and emission spectra after excitation with 60 fs pulses provides a direct observation of the C13=C14 torsional isomerization of the retinal chromophore on the excited state potential surface. Here, we present a more detailed discussion of these spectra. The transient hole line shapes are then calculated by solving the density matrix equations for the third‐order susceptibility of a multilevel system. The resulting equations are written without reference to the individual vibronic transitions by using the absorption correlation function 〈i‖i(t)〉. The calculations show that the sharp features seen at short delays arise from coherence coupling effects which occur when the pump and probe pulses overlap in time. This analysis demonstrates that...

Pseudospectral localized generalized Mo/ller–Plesset methods with a generalized valence bond reference wave function: Theory and calculation of conformational energies

We describe a new multireference perturbation algorithm for ab initio electronic structure calculations, based on a generalized valence bond (GVB) reference system, a local version of second-order Mo/ller–Plesset perturbation theory (LMP2), and pseudospectral (PS) numerical methods. This PS-GVB-LMP2 algorithm is shown to have a computational scaling of approximately N3 with basis set size N, and is readily applicable to medium to large size molecules using workstations with relatively modest memory and disk storage. Furthermore, the PS-GVB-LMP2 method is applicable to an arbitrary molecule in an automated fashion (although specific protocols for resonance interactions must be incorporated) and hence constitutes a well-defined model chemistry, in contrast to some alternative multireference methodologies. A calculation on the alanine dipeptide using the cc-pVTZ(−f) basis set (338 basis functions total) is presented as an example. We then apply the method to the calculation of 36 conformational energy differ...

Classical theory for real‐time femtosecond probing of the NaI* photodissociation

Femtosecond pump‐probe experiments [Rosker et al., Chem. Phys. Lett. 146, 175 (1988)] on the dissociation of NaI* are modelled classically to obtain the absorption transients as a function of the pump and probe wavelengths. The initial ground state, the optically pumped predissociating state, and the third surface that is coupled by the probe pulse are explicitly included. The classical model can almost quantitatively explain all the features of the experimental results. The oscillations in the transients are shown to be due to molecules trapped in the adiabatic well, with most of the intensity coming from the covalent region of the well before the crossing point rx. The rising troughs in the transients are due to successive leaks out of the well into the covalent region after the crossing point rx, leading to dissociation. The difference in the absorption transient between on‐resonance 589 nm probing as compared to off‐resonance 612 nm and 580 nm probing is shown to arise from the difference in Lorentzia...

Quantum theory for transition state absorption

Abstract A time-dependent quantum model involving two wave packets on two excited-state surfaces is presented to describe absorption (or emission) from the transition state of a chemical reaction. The connection between the quantum result and existing classical theories is shown. The model ia applied to the direct dissociation of ICN* and gives results in good agreement with experiment. The dissociation time - the time to half-maximal absorption - is almost invariant with the pulse width but is dependent on the probe wavelength. A lower absorption plateau and a longer dissociation time is predicted for probe energies above the asymptotic resonance energy.

Quasi-classical models of transition state absorption or emission

Abstract By making a short-time approximation to the correlation function in the quantum result for transition state absorption (or emission) we obtain the Lorentzian and reflection results as integrals of simple configuration space functions. These and the time-integrated quantum results are used to derive and unify the following descriptions of transition-state absorption: (a) the classical model of Bersohn and Zewail, (b) the time-dependent wave mechanical description by Agrawal, Mohan and Sathyamurthy, (c) the classical trajectory approach by Polanyi and coworkers and (d) the time-independent quantum-mechanical description by Engel, Bacic, Schinke and Shapiro.