Hans-Martin Keller

The unimolecular dissociation of HCO: I. Oscillations of pure CO stretching resonance widths

The unimolecular dissociation of the formyl radical HCO in the electronic ground state is investigated using a completely new ab initio potential energy surface. The dynamics calculations are performed in the time‐independent picture by employing a variant of the log‐derivative Kohn variational principle. The full resonance spectrum up to energies more than 2 eV above the vibrational ground state is explored. The three fundamental frequencies (in cm−1) for the H–CO and CO stretches, and the bending mode are 2446 (2435), 1844 (1868), and 1081 (1087), where the numbers in parentheses are the measured values of Sappey and Crosley obtained from dispersed fluorescence excitation spectra [J. Chem. Phys. 93, 7601 (1990)]. In the present work we primarily emphasize the dissociation of the pure CO stretching resonances (0v20) and their decay mechanisms. The excitation energies, dissociation rates, and final vibrational–rotational state distributions of CO agree well with recent experimental data obtained from stim...

THE UNIMOLECULAR DISSOCIATION OF HCO. II. COMPARISON OF CALCULATED RESONANCE ENERGIES AND WIDTHS WITH HIGH-RESOLUTION SPECTROSCOPIC DATA

We present a theoretical study of the unimolecular dissociation resonances of HCO in the electronic ground state, X1A′, using a new ab initio potential energy surface and a modification of the log‐derivative version of the Kohn variational principle for the dynamics calculations. Altogether we have analyzed about 120 resonances up to an energy of ≊2 eV above the H+CO threshold, corresponding to the eleventh overtone in the CO stretching mode (v2=11). The agreement of the resonance energies and widths with recent stimulated emission pumping measurements of Tobiason et al. [J. Chem. Phys. 103, 1448 (1995)] is pleasing. The root‐mean‐square deviation from the experimental energies is only 17 cm−1 over a range of about 20 000 cm−1 and all trends of the resonance widths observed in the experiment are satisfactorily reproduced by the calculations. The assignment of the states is discussed in terms of the resonance wave functions. In addition, we compare the quantum mechanical state‐resolved dissociation rates ...

Theoretical study of the unimolecular dissociation HO2→H+O2. I. Calculation of the bound states of HO2 up to the dissociation threshold and their statistical analysis

This is the first of a series of papers in which we investigate the unimolecular dissociation of hydroperoxyl. Using the DMBE IV potential energy surface [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)], in the present study 726 bound states of HO2(X) up to the H+O2 dissociation threshold are calculated in an attempt to access the extent of the coupling between the modes of the system. The first approach involves an analysis of the nodal structure of the wave functions. While the wave functions for the lowest states are regular and assignable, the degree of mixing and complexity rapidly increases with energy. The wave functions close to the dissociation threshold are mostly irregular without any clear cut nodal structure and fill the entire coordinate space available. Nevertheless, a small number of regular states, that are associated with large excitation in the O2 stretching coordinate and no or only little excitation in the other modes, are found even at high energies. The second approach used to stu...

Theoretical study of the unimolecular dissociation HO2→H+O2. II. Calculation of resonant states, dissociation rates, and O2 product state distributions

Three‐dimensional quantum mechanical calculations have been carried out, using a modification of the log‐derivative version of Kohn’s variational principle, to study the dissociation of HO2 into H and O2. In a previous paper, over 360 bound states were found for each parity, and these are shown to extend into the continuum, forming many resonant states. Analysis of the bound states close to the dissociation threshold have revealed that HO2 is a mainly irregular system and in this paper it is demonstrated how this irregularity persists in the continuum. At low energies above the threshold, these resonances are isolated and have widths that fluctuate strongly over more than two orders of magnitude. At higher energies, the resonances begin to overlap, while the fluctuations in the widths decrease. The fluctuations in the lifetimes and the intensities in an absorption‐type spectrum are compared to the predictions of random matrix theory, and are found to be in fair agreement. The Rampsberger–Rice–Kassel–Marcu...

Unimolecular dissociation dynamics of highly vibrationally excited DCO(X̃ 2A). II. Calculation of resonance energies and widths and comparison with high-resolution spectroscopic data

We present a theoretical study of the unimolecular dissociation of DCO in the electronic ground state, X 1A, using a new ab initio potential energy surface. Altogether we have analyzed about 140 resonances up to an energy of ≈1.4 eV above the D+CO threshold, corresponding to the ninth overtone in the CO stretching mode (v2=9). The agreement of the resonance positions and widths with recent stimulated emission pumping measurements of Stock et al. [J. Chem. Phys. 106, 5333 (1997), the preceding article] is pleasing. The root-mean-square deviation from the experimental energies is only 16 cm−1 over a range of about 16 500 cm−1 and all trends of the resonance widths observed in the experiment are satisfactorily reproduced by the calculations. A strong 1:1:2 stretch–stretch–bend resonance prohibits a unique assignment for the majority of vibrational states.

Highly excited vibrational states of HCP and their analysis in terms of periodic orbits: The genesis of saddle-node states and their spectroscopic signature

We present quantum mechanical bound-state calculations for HCP(X) using an ab initio potential energy surface. The wave functions of the first 700 states, corresponding to energies roughly 23 000 cm−1 above the ground vibrational state, are visually inspected and it is found that the majority can be uniquely assigned by three quantum numbers. The energy spectrum is governed, from the lowest excited states up to very high states, by a pronounced Fermi resonance between the CP stretching and the HCP bending mode leading to a clear polyad structure. At an energy of about 15 000 cm−1 above the origin, the states at the lower end of the polyads rather suddenly change their bending character. While all states below this critical energy avoid the isomerization pathway, the states with the new behaviour develop nodes along the minimum energy path and show large-amplitude motion with H swinging from the C- to the P-end of the diatomic entity. How this structural change can be understood in terms of periodic class...

Normal mode and isomerization bending states in HCP: Periodic orbit assignment and spectroscopic signature

We present exact quantum mechanical bound‐state calculations for HCP using an ab initio potential energy surface. The main result is the existence of two distinct families of bending states: one with normal‐mode‐type behavior and wave functions confined to small bending angles and the other one sampling the isomerization path all the way from H–CP to CP–H. Stable periodic orbits provide a clear‐cut assignment. Possible relations to recent spectroscopic observations are discussed.

Quantum mechanical study of the unimolecular dissociation of HO2: A rigorous test of RRKM theory

Three‐dimensional quantum mechanical calculations are carried out, in a time‐independent scattering approach, to study the unimolecular dissociation HO2→H+O2. The dissociation cross section is governed by narrow resonances with widths that vary over five orders of magnitude. The unimolecular dissociation rates strongly fluctuate about an average which agrees surprisingly well with the Rampsberger–Rice–Kassel–Marcus (RRKM) theory.

The dissociation of HNO. I. Potential energy surfaces for the X̃ 1A′, Ã 1A″, and ã 3A″ states

Three-dimensional potential energy surfaces for the X 1A′, A 1A′′, and a 3A′′ states of HNO have been calculated at the multireference configuration interaction (MRCI) level of ab initio theory. Energy points are calculated at 1728 molecular configurations, predominantly sampling the HNO well and the H+NO product channel regions. Energies between grid points are obtained by interpolation with a three-dimensional cubic spline. The well depths are 2.14, 1.27, and 0.38 eV for X 1A′, a 3A′′, and A 1A′′, respectively. Saddle points to inversion, isomerization, and dissociation are reported and their importance discussed to relevant processes. The HNO(X 1A′) potential energy surface is purely attractive along its minimum energy path to ground-state products, whereas the a 3A′′ and A 1A′′ states have barriers of 0.21 and 0.50 eV, respectively. Vibrational term values and rotational constants for HNO and DNO are reported for the fundamental vibrations for all three electronic states. Where comparison with expe...

THE UNIMOLECULAR DISSOCIATION OF HCO. IV. VARIATIONAL CALCULATION OF SIEGERT STATES

We present a new variational method for calculating complex resonance (Siegert) states in unimolecular dissociation reactions. The approach is based on the log-derivative version of the Kohn variational principle. The basic matrix equations can be formulated in terms of scattering-wave boundary conditions yielding the resonance states as homogeneous solutions for singular energies. Thus, the resonance positions and widths can be calculated directly without employing an artificial absorbing potential. This method is applied to the photodissociation of HCO and DCO and the results are compared to the resonance parameters obtained from absorption-type spectra.