Martin Quack

Theory of unimolecular reactions induced by monochromatic infrared radiation

A theory of unimolecular reactions induced by coherent, monochromatic infrared radiation (URIMIR) in the absence of collisions is presented. It is shown that the set of first order linear differential equations for the amplitudes of molecular states (Schrodinger equation) can be reduced, under specified conditions, to a much smaller set of first order linear differential equations for the coarse grained populations of levels for polyatomic molecules (master equation). Four limiting situations are identified in which such linear rate equations provide a reasonable approximation. Rate coefficients are obtained as a function of spectroscopic parameters (energy levels and transition moments). Solutions for the master equations are given as a function of time and at steady‐state. Simple limiting cases (Strong Field Limit, Weak Field Limit, Reaction Threshold Bottleneck, etc.) are identified and very simple rate expressions are obtained for these cases. A complete statistical mechanical theory of URIMIR is form...

Tridiagonal Fermi resonance structure in the IR spectrum of the excited CH chromophore in CF3H

The absorption spectrum of trifluoromethane has been recorded between 900 and 14 000 cm−1 with resolutions between 0.004 and 0.5 cm−1 (pressure broadened). 22 bands were assigned as arising from the interacting CH stretching and bending manifolds, which account for most of the absorption in the overtone region. The results can be understood quantitatively with an effective, tridiagonal many‐level Fermi resonance Hamiltonian. The experimental and theoretical results are summarized in Table II. The Hamiltonian is given in Table III and shows a very large stretching–bending interaction constant ‖ksbb‖=106 cm−1, which is even larger than the diagonal anharmonic constant for the stretching vibration ‖x′ss‖=62 cm−1. This leads to extensive vibrational redistribution between stretching and bending motions at high levels of excitation. The time dependent redistribution is calculated with the spectroscopic Hamiltonian. A rotational analysis is presented for some of the bands involved in the Fermi resonance. The ef...

Potential energy surfaces, quasiadiabatic channels, rovibrational spectra, and intramolecular dynamics of (HF)2 and its isotopomers from quantum Monte Carlo calculations

We report analytical representations of the six‐dimensional potential energy hypersurface for (HF)2, the parameters of which are closely adjusted to low energy experimental properties such as hydrogen bond dissociation energy (D0=1062 cm−1 ) and vibrational–rotational spectra in the far and mid infrared. We present a detailed analysis of properties of the hypersurface in terms of its stationary points, harmonic normal mode amplitudes, and frequencies for the Cs minimum and C2h saddle point and effective Morse parameters and anharmonic overtone vibrational structure for the hydrogen bond and the HF stretching vibrations. The comparison between experimental data and the potential energy surface is carried out by means of accurate solutions of the rotational–vibrational Schrodinger equation with quantum Monte Carlo techniques, which include anharmonic interactions between all modes for the highly flexible dimer. Two extensions of the quantum Monte Carlo technique are presented, which are based on the clamped...

Detailed symmetry selection rules for reactive collisions

A simple general method for obtaining selection rules for the ro-vibronic states of reactant and product molecules connected in a reactive collision is discussed. Neglecting only the coupling with nuclear spin, rather stringent restrictions are found to occur in systems involving three and more identical nuclei. Several radical and ion molecule reactions of current interest are used to illustrate this finding. Even more restrictive selection rules are found when assuming weak coupling (‘ incomplete exchange of identical nuclei ’) in the intermediate reaction complex. These include the well-known selection rules for inelastic collisions of molecules with several identical nuclei, but less trivial examples with chemical reaction are also presented. The symmetry corrections and nuclear spin statistics in statistical theories of scattering (including the prior distributions for the information-theoretic approach) are derived. Further applications are discussed briefly.

Anchoring the water dimer potential energy surface with explicitly correlated computations and focal point analyses

Ten stationary points on the water dimer potential energy surface have been characterized with the coupled-cluster technique which includes all single and double excitations as well as a perturbative approximation of triple excitations [CCSD(T)]. Using a triple-ζ basis set with two sets of polarization functions augmented with higher angular momentum and diffuse functions [TZ2P(f,d)+dif], the fully optimized geometries and harmonic vibrational frequencies of these ten stationary points were determined at the CCSD(T) theoretical level. In agreement with other ab initio investigations, only one of these ten stationary points is a true minimum. Of the other nine structures, three are transition structures, and the remaining are higher order saddle points. These high-level ab initio results indicate that the lowest lying transition state involved in hydrogen interchange is chiral, of C1 symmetry rather than Cs as suggested by recently developed 6D potential energy surfaces. The one- and n-particle limits of t...

Vibrational spectrum and potential energy surface of the CH chromophore in CHD3

The rovibrational spectrum of trideutero‐methane has been measured at resolutions mostly close to the Doppler limit on an interferometric Fourier transform spectrometer from the lowest fundamental vibration to high overtones of the CH stretching vibration (wave numbers from 900 to 12 000 cm−1). The CH chromophore spectrum is fully assigned and interpreted by means of the tridiagonal Fermi resonance Hamiltonian for the coupled CH stretching and bending vibrations. The Hamiltonian predicts and also fits the visible spectrum up to 19 000 cm−1 measured by Scherer et al., Perry et al., and Campargue et al. The effective tridiagonal Hamiltonian is derived ab initio by means of MRD‐CI and full CI calculations of the potential surface of methane, a variational vibrational calculation in a normal coordinate subspace of the coupled CH stretching and bending motions and an approximate similarity transformation to tridiagonal form. Fits of the experimental results by the tridiagonal and the variational Hamiltonian le...

A new six-dimensional analytical potential up to chemically significant energies for the electronic ground state of hydrogen peroxide

We report calculations of the electronic ground state potential energy surface (PES) of hydrogen peroxide covering, in an almost global fashion, all six internal degrees of freedom by two different ab initio techniques. Density functional theory (DFT) calculations using the Becke 3 parameter Lee–Yang–Parr (B3LYP) hybrid functional and multiconfigurational second order perturbation theory (CASPT2) calculations, both using large basis sets, are performed for a wide range of geometries (8145 DFT and 5310 CASPT2 single-point energies). We use a combined data set of mostly DFT with additional CASPT2 ab initio points and the complete CASPT2 surface to fit a total of four different 6D analytical representations. The resulting potentials contain 70–76 freely adjusted parameters and represent the ground state PES up to 40000 cm−1 above the equilibrium energy with a standard deviation of 100–107 cm−1 without any important artifacts. One of the model surfaces is further empirically refined to match the bond dissocia...

On the measurement of the parity violating energy difference between enantiomers

Abstract An experiment is outlined for measuring the small energy difference between two enantiomers due to the parity-violating weak neutral current perturbation. The method is based on the violation of the selection rules for the time evolution of states of well defined initial parity in isolated molecules. It could confirm or reject recent quantitative theoretical estimates of parity-violating energy differences.

Resonance fluorescence of aniline vapour

Abstract Resonance fluorescence spectra in the vapor have been recorded for C 6 H 5 NH 2 , C 6 H 5 ND 2 , C 6 D 5 NH 2 , and C 6 D 5 ND 2 . Twenty-five different spectra have been obtained by irradiation with narrow bandwidth light into various absorption bands of the 2900 A system ( 1 B 2 - 1 A 1 ). A detailed vibrational analysis has been carried out. Assignments and wavenumbers for parts of the spectra are given in tables, the rest is available on request.—The activity of totally symmetric vibrations is in accordance with expectations for monosubstituted benzene derivatives. A special feature of the spectra is the occurrence of intense bands which are due to the strongly anharmonic inversion vibration (“umbrella mode”) of the NH 2 group. From the spectroscopic data a one-dimensional double-minimum potential function for this coordinate has been determined. A barrier height of about 450 cm −1 was derived from this potential function. The equilibrium angle between NH 2 and the ring plane is then 42°.

Structure and dynamics of the excited CH–chromophore in (CF3)3CH

The absorption spectra of gaseous (CF3) 3CH (1,1,1,3,3,3‐hexafluoro, 2‐trifluoromethyl propane) were recorded in the IR between 800 and 12 000 cm−1 by high resolution interferometric Fourier transform techniques and in the visible from 12 000 to 17 000 cm−1 by laser photoacoustic spectroscopy. Instead of single bands in the CH overtone region, complex multiplet structures were observed. Thirty‐nine bands were assigned as arising from the interacting CH‐stretching and CH‐bending manifolds, which account for most of the absorption in the overtone region. The results can be understood quantitatively with an effective, tridiagonal many‐level Fermi resonance Hamiltonian. Close agreement is obtained for the positions and intensities of the observed spectral features using only seven spectroscopic parameters. The experimental and theoretical results are summarized in Tables II, III, and IV. The Hamiltonian can be used to calculate and understand the time‐dependent redistribution of vibrational energy between the...