William F. Polik

Stark level‐crossing spectroscopy of S0 formaldehyde eigenstates at the dissociation threshold

Spectra of S0 D2CO rovibrational eigenstates with 28 300 cm−1 of vibrational excitation are measured by Stark level‐crossing spectroscopy. In this new method, the lifetime of a single J, K, M‐resolved S1 state is monitored as a function of electric field. Enhanced nonradiative decay causes the S1 lifetime to decrease as S0 states are Stark tuned into resonance. Analysis of the resulting resonance lineshapes yields complete distributions of S0 decay rates (linewidths) and S1‐S0 coupling matrix elements. The S0 decay rates represent the first measurements of unimolecular dissociation rates of a polyatomic molecule at the eigenstate‐resolved level. S0 decay widths vary from 6.4×10−5 to 3.8×10−3 cm−1 and S1‐S0 coupling matrix elements vary from 3.5×10−7 to 4.7×10−5 cm−1, demonstrating that chemical properties of neighboring eigenstates fluctuate by over two orders of magnitude. The observed density of S0 vibrational states is ∼400 per cm−1, six times greater than an estimate including first‐order anharmonic c...

A transition state theory‐based statistical distribution of unimolecular decay rates with application to unimolecular decomposition of formaldehyde

A statistical distribution of state‐specific unimolecular decay rates is derived (within the framework of random matrix theory) that is determined completely by the transition state properties of the potential energy surface. It includes the standard χ‐square distributions as a special case. Model calculations are presented to show the extent to which it can differ from the χ‐square distribution, and specific application is made to the state‐specific unimolecular decay rate data for D2CO→D2+CO.

Eigenstate‐resolved unimolecular reaction dynamics: Ergodic character of S0 formaldehyde at the dissociation threshold

The Stark level‐crossing spectra of S0 D2CO are analyzed for evidence of energy level correlations and quantum ergodicity. The analysis for short and long range level correlations gives an apparent energy level spacing distribution which lies between the Poisson and GOE limits. However, the Stark level‐crossing method diminishes any existing correlations. The true level spacing distribution must be closer to the Gaussian orthogonal ensemble (GOE) than to the Poisson limit. Complete distributions of S1−S0 coupling matrix elements and S0 dissociation rates are reported and subjected to statistical tests for ergodicity. The distribution of S1−S0 coupling matrix elements indicates that the dynamics of intramolecular vibrational redistribution of energy (IVR) is very nearly quantum ergodic. There is strong coupling and free flow of energy among vibrational degrees of freedom in this molecule above its dissociation threshold. The average S0 decay rate can be accounted for by RRKM theory with tunneling correctio...

Pure vibrational spectroscopy of S0 formaldehyde by dispersed fluorescence

Dispersed fluorescence spectra from the 000 rotational level of 40, 41, 51, and 3141 S1 formaldehyde (H2CO) have been recorded. From these spectra, 198 new vibrational states have been assigned with energies up to 12 500 cm−1, and their positions have been determined to within an uncertainty of 1 cm−1. The assignment of vibrational lines to specific vibrational states becomes increasingly difficult at the higher energy regions of the spectra (≳9000 cm−1) due to extensive state mixing. Harmonic and first‐order anharmonic vibrational constants were extracted from fits to these vibrational states. For states with highest zero‐order coefficient squared greater than 35%, the standard deviation of the spectroscopic fit is 6.9 cm−1. For states which are lower energy (<9500 cm−1) and relatively pure (zero‐order coefficient squared greater than 0.75 or largest in a given normal mode combination), the standard deviation is 1.7 cm−1. Good agreement with ab initio vibrational constants calculated by Martin et al. [J....

Dissociation rates for individual eigenstates of S0 formaldehyde: Fluctuations and barrier height

Spectra of S0 D2CO rovibronic states near the dissociation threshold have been taken with a new method by monitoring S1 lifetime while Stark shifting an S1 level through the S0 manifold. An order of magnitude variation in the unimolecular dissociation rate and in the S1–S0 vibronic coupling matrix element is observed among S0 levels within a 0.2 cm−1 energy range. These individual molecular eigenstates exhibit distinctive chemical properties. Dissociation rates averaged over an energy range of a few cm−1 vary smoothly with energy and give a barrier height of 78.0–81.1 kcal/mol for H2CO→H2+CO.

Quantum interference among competing unimolecular decay channels: Asymmetric S0 D2CO decay profiles

The dynamics of a state undergoing decay to a manifold of states coupled to a dissociative continuum is investigated in the weak coupling limit. The decay rate is found to be composed of terms symmetric and asymmetric in the relative energy difference between the initial state and the states in the manifold. The well‐known symmetric terms arise from resonantly enhanced decay of the initial state through each state in the manifold to the continuum. The newly identified asymmetric terms arise from interfering couplings of the initial state to the continuum through different states in the manifold, i.e., from off‐diagonal elements of the width matrix Γkk’ of the effective Hamiltonian describing dissociation of the states in the manifold. The general line shape derived here is used to fit asymmetric features in Stark level‐crossing spectra of D2CO. Statistical properties of the width matrix are summarized, and the relation between diagonal and off‐diagonal matrix element magnitudes is derived.

A random matrix/transition state theory for the probability distribution of state‐specific unimolecular decay rates: Generalization to include total angular momentum conservation and other dynamical symmetries

A previously developed random matrix/transition state theory (RM/TST) model for the probability distribution of state‐specific unimolecular decay rates has been generalized to incorporate total angular momentum conservation and other dynamical symmetries. The model is made into a predictive theory by using a semiclassical method to determine the transmission probabilities of a nonseparable rovibrational Hamiltonian at the transition state. The overall theory gives a good description of the state‐specific rates for the D2CO→D2+CO unimolecular decay; in particular, it describes the dependence of the distribution of rates on total angular momentum J. Comparison of the experimental values with results of the RM/TST theory suggests that there is mixing among the rovibrational states.

Vibronic spectroscopy and lifetime of S1 acrolein

The S1 vibronic spectrum of acrolein (CH2CHCHO) was obtained in a supersonic free-jet expansion using cavity ringdown spectroscopy. Comparison of room temperature and free-jet spectra was used to assign vibronic transitions. Computations using the configuration interaction-singles method were used to predict the values of the S1 fundamental vibrational frequencies. The current set of assignments increases the number of identified bands from 27 to 59, corrects 16 misassignments in the previous literature, and identifies two new fundamental bands. A lower limit for the lifetime of the S1 vibronic origin was determined from linewidth measurements to be 1.8–2.1 ps.

Accurate and efficient calculation of excited vibrational states from quartic potential energy surfaces

Vibrational anharmonicity and resonances frequently complicate assignment of vibrational spectra. In order to analyse such spectra, these effects can be calculated from ab initio quartic potential energy surfaces (PESs) using second-order vibrational theory with resonances (VPT2 + K). This study compares the accuracies of using the cc-pVTZ basis set, the aug-cc-pVQZ basis set, and a hybrid approach that uses the cc-pVTZ basis set for the equilibrium geometry and quadratic force constants and the aug-cc-pVQZ basis set for the cubic and quartic force constants. Quartic PESs are computed using these basis sets for H2O, H2CO, HFCO, SCCl2, and their deuterated analogs with the CCSD(T) method. The computed PESs are assessed by comparing experimentally determined and theoretically calculated spectroscopic constants. The average absolute difference (⟨|error|⟩) between theoretical and experimental zero-point energy-corrected harmonic frequencies ( ) decreases by 54.7% when the hybrid approach is used instead of the cc-pVTZ basis, but decreases by only an additional 2.3% when the aug-cc-pVQZ basis is used. The computed PESs are also assessed by comparing predicted and observed vibrational energy states. The weighted average root-mean-square (RMS) difference between predicted and observed vibrational energy levels decreases by 42.3% when the hybrid approach is used instead of cc-pVTZ, but decreases by only an additional 4.0% when aug-cc-pVQZ is used. These results demonstrate that calculations performed using the hybrid basis set approach, which have a substantially lower computational cost, are comparable in accuracy to those performed using the aug-cc-pVQZ basis set.

Dispersed fluorescence spectroscopy of excited rovibrational states in S0 formaldehyde

Dispersed fluorescence (DF) spectroscopy is used to explore the rovibrational structure of highly excited S0 formaldehyde (H2CO). A narrowband laser excites formaldehyde molecules to a single S1 rovibronic quantum state, and the resulting fluorescence is dispersed with a monochromator. DF spectra of ten vibrational levels with excitation in ν2, the carbon–oxygen stretch, and ν4, the out‐of‐plane bend, have been recorded, and the effective A, B, and C rotational constants are extracted. Five of the effective A rotational constants and seven of the effective B and C rotational constants are new to the literature. The dependence of these effective rotational constants on vibrational state are both calculated and discussed with regard to both the present and previous experiments. Particular attention is given to the manner in which that the effective A rotational constant depends on increasing excitation in ν4 due to the strong A‐axis ν4/ν6 Coriolis interaction. For states where v2 is less than two, quantitat...