Franck-Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: a branch-cut free, numerically stable derivation

Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulae. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck-Condon approximation for the lowest-order anharmonic and Herzberg-Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F$_2$, HOCl, CH$_2$NH, and NO$_2$.Comment: 34 pages, 4 figure

Direct measurements of DOCO isomers in the kinetics of OD+CO

Quantitative and mechanistically-detailed kinetics of the reaction of hydroxyl radical (OH) with carbon monoxide (CO) have been a longstanding goal of contemporary chemical kinetics. This fundamental prototype reaction plays an important role in atmospheric and combustion chemistry, motivating studies for accurate determination of the reaction rate coefficient and its pressure and temperature dependence at thermal reaction conditions. This intricate dependence can be traced directly to details of the underlying dynamics (formation, isomerization, and dissociation) involving the reactive intermediates cis- and trans-HOCO, which can only be observed transiently. Using time-resolved frequency comb spectroscopy, comprehensive mechanistic elucidation of the kinetics of the isotopic analogue deuteroxyl radical (OD) with CO has been realized. By monitoring the concentrations of reactants, intermediates, and products in real-time, the branching and isomerization kinetics and absolute yields of all species in the OD+CO reaction are quantified as a function of pressure and collision partner.Comment: 19 pages, 4 figure

Spectroscopy and theory of cis-trans isomerization in the S₁ state of acetylene

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Chemistry; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 95-99).This thesis consists of parallel experimental and theoretical studies of the rovibrational structure and dynamics of the Si state of acetylene, C2H2 . This small molecule is a prototypical system for the study of cis-trans isomerization, the barrier to which is moderately low in the Si state, presenting the opportunity to achieve a complete understanding of the global rovibrational dynamics of an isomerizing system. Our analysis of the spectra of ungerade vibrational levels in the region 45800-46550 cm-1 extends the complete assignment of trans vibrational levels to 4300 cm-1 above the Si electronic origin. These exhaustive assignments have enabled the identification of two new cis vibrational states. Reduced dimension rovibrational variational calculations have been carried out to aid in the characterization of spectroscopic signatures and patterns associated with the isomerization process. Such effects include the decoupling of the vibrational polyads that involve the low-energy bending modes [nu]4 and [nu]6 and the large cross-anharmonicity of modes [nu]3 and [nu]6, the combination bands of which follow the isomerization path toward the half-linear transition state. Additionally, we focus on predictions for the K-staggering observed in both cis and trans levels caused by tunneling through the isomerization barrier. The detailed patterns of these staggerings make possible a direct empirical distinction between different possible isomerization mechanisms. We also present an empirical model which analyzes the vibrational level structure along the isomerization path. This model enables the direct spectroscopic characterization of the energy of the transition state, the qualitative structure and width of the isomerization barrier, and the curvature of the nuclear potential surface in directions orthogonal to the isomerization path. This type of analysis is generalizable to other systems, potential surfaces of which contain stationary points and thus provides a powerful new tool for studying transition states via frequency domain spectroscopy.by P. Bryan Changala.S.B

Spectroscopic characterization of isomerization transition states

Transition state theory is central to our understanding of chemical reaction dynamics. We demonstrate a method for extracting transition state energies and properties from a characteristic pattern found in frequency-domain spectra of isomerizing systems. This pattern—a dip in the spacings of certain barrier-proximal vibrational levels—can be understood using the concept of effective frequency, ω[superscript]eff. The method is applied to the cis-trans conformational change in the S[subscript 1] state of C[subscript 2]H[Subscript 2] and the bond-breaking HCN-HNC isomerization. In both cases, the barrier heights derived from spectroscopic data agree extremely well with previous ab initio calculations. We also show that it is possible to distinguish between vibrational modes that are actively involved in the isomerization process and those that are passive bystanders.National Science Foundation (U.S.) (NSF Graduate Research Fellowship DGE 1144083)Alexander von Humboldt-Stiftung (Feodor Lynen fellowship)United States. Department of Energy (Grant DE-FG0287ER136

Photodissociation transition states characterized by chirped pulse millimeter wave spectroscopy.

The 193-nm photolysis of CH2CHCN illustrates the capability of chirped-pulse Fourier transform millimeter-wave spectroscopy to characterize transition states. We investigate the HCN, HNC photofragments in highly excited vibrational states using both frequency and intensity information. Measured relative intensities of J = 1-0 rotational transition lines yield vibrational-level population distributions (VPD). These VPDs encode the properties of the parent molecule transition state at which the fragment molecule was born. A Poisson distribution formalism, based on the generalized Franck-Condon principle, is proposed as a framework for extracting information about the transition-state structure from the observed VPD. We employ the isotopologue CH2CDCN to disentangle the unimolecular 3-center DCN elimination mechanism from other pathways to HCN. Our experimental results reveal a previously unknown transition state that we tentatively associate with the HCN eliminated via a secondary, bimolecular reaction

Probing cis-trans isomerization in the S1 state of C2H2 via H-atom action and hot band-pumped IR-UV double resonance spectroscopies

We report novel experimental strategies that should prove instrumental in extending the vibrational and rotational assignments of the S1 state of acetylene, C[subscript 2]H[subscript 2], in the region of the cis-trans isomerization barrier. At present, the assignments are essentially complete up to ∼500 cm[superscript −1] below the barrier. Two difficulties arise when the assignments are continued to higher energies. One is that predissociation into C[subscript 2]H + H sets in roughly 1100 cm[superscript −1] below the barrier; the resulting quenching of laser-induced fluorescence (LIF) reduces its value for recording spectra in this region. The other difficulty is that tunneling through the barrier causes a staggering in the K-rotational structure of isomerizing vibrational levels. The assignment of these levels requires data for K values up to at least 3. Given the rotational selection rule K' − ℓ" = ± 1, such data must be obtained via excited vibrational levels of the ground state with ℓ" > 0. In this paper, high resolution H-atom resonance-enhanced multiphoton ionization spectra are demonstrated to contain predissociated bands which are almost invisible in LIF spectra, while preliminary data using a hyperthermal pulsed nozzle show that ℓ" = 2 states can be selectively populated in a jet, giving access to K' = 3 states in IR-UV double resonance.United States. Department of Energy (Grant No. DE-FG0287ER13671)Chinese Academy of Sciences (Distinguished Visiting Professorship)Natural Sciences and Engineering Research Council of Canada (NSERC

Collision-induced C_60 rovibrational relaxation probed by state-resolved nonlinear spectroscopy

Quantum state-resolved spectroscopy was recently achieved for C60 molecules when cooled by buffer gas collisions and probed with a midinfrared frequency comb. This rovibrational quantum state resolution for the largest molecule on record is facilitated by the remarkable symmetry and rigidity of C60, which also present new opportunities and challenges to explore energy transfer between quantum states in this many-atom system. Here we combine state-specific optical pumping, buffer gas collisions, and ultrasensitive intracavity nonlinear spectroscopy to initiate and probe the rotation-vibration energy transfer and relaxation. This approach provides the first detailed characterization of C60 collisional energy transfer for a variety of collision partners, and determines the rotational and vibrational inelastic collision cross sections. These results compare well with our theoretical modeling of the collisions, and establish a route towards quantum state control of a new class of unprecedentedly large molecules