Renner-Teller vibronic analysis for a tetra-atomic molecule. I. The effective Hamiltonian and matrix elements

The effective vibronic Hamiltonian for a linear tetra-atomic molecule in a Pi state has been investigated. In addition to the usual vibrational and Renner-Teller coupling terms, the bending mode anharmonicity, spin-orbit coupling, and Fermi resonance interactions have been added to the model. Terms in the Hamiltonian up to the fourth order are given explicitly for molecules of C(infinityupsilon) symmetry and simplifications for symmetric D(infinityh) molecules are discussed. The matrix elements for the HCCS free radical have been obtained and are used to analyze the observed ground-state levels of HCCS and DCCS in a companion paper. The Sears resonance vibronic interaction that couples levels with the selection rules DeltaK=+/-1, DeltaSigma=-/+1, and DeltaP=0 has also been studied and the matrix elements derived. The determinable combinations of signs for the major parameters in the model are discussed.     

Phosphorus hyperfine structure in the electronic spectrum of the HPCl free radical

The 444 nm 2 0 (1) bands of the A 2A'-X 2A" transition of the jet-cooled HP 35Cl and HP 37Cl radicals have been studied at high resolution using the pulsed electric discharge technique with a precursor mixture of PCl3 and H2. Spectra recorded with linewidths of approximately 360 MHz revealed resolved hyperfine structure in both isotopomers arising from the excited state Fermi contact interaction of the unpaired electron with the magnetic moment of the 31P nucleus, with aF'=0.0641(10) cm(-1) and 0.0636(31) cm(-1) for HP 35Cl and HP 37Cl, respectively. No contribution from the ground state, or excited state contributions from the hydrogen or chlorine nuclei were resolved, confirming ab initio predictions that HPCl is a p pi radical in the X state, and an s sigma radical with a substantial contribution from the phosphorus 3s atomic orbital in the A state. The free atom comparison method has been used to estimate that the singly occupied molecular orbital in the excited state has 14% phosphorus 3s character.     

The pure rotational spectrum of HPS (X̃1A'): chemical bonding in second-row elements

The pure rotational spectrum of HPS, as well as its (34)S and D isotopologues, has been recorded at microwave, millimeter, and submillimeter wavelengths, the first observation of this molecule in the gas phase. The data were obtained using a combination of millimeter direct absorption, Fourier transform microwave (FTMW), and microwave-microwave double-resonance techniques, which cover the total frequency range from 15 to 419 GHz. Quantum chemical calculations at the B3LYP and CCSD(T) levels were also performed to aid in spectral identification. HPS was created in the direct absorption experiment from a mixture of elemental phosphorus, H(2)S, and Ar carrier gas; DPS was produced by adding D(2). In the FTMW study, these species were generated in a pulsed discharge nozzle from PH(3) and H(2)S or D(2)S, diluted in neon. The spectra recorded for HPS and its isotopologues exhibit clear asymmetric top patterns indicating bent structures; phosphorus hyperfine splittings were also observed in HPS, but not DPS. Analysis of the data yielded rotation, centrifugal distortion, and phosphorus nuclear spin-rotation parameters for the individual species. The r(m) ((1)) structure for HPS, calculated from the rotational constants, is r(H-P) = 1.438(1) A?, r(P-S) = 1.9320(1) A?, and θ(H-P-S) = 101.85(9)°. Empirically correcting for zero-point vibrational effects yields the geometry r(e)(H-P) = 1.4321(2) A?, r(e)(P-S) = 1.9287(1) A?, and θ(e)(H-P-S) = 101.78(1)°, in close agreement with the r(m) ((1)) structure. A small inertial defect was found for HPS indicating a relatively rigid molecule. Based on these data, the bonding in this species is best represented as H-P=S, similar to the first-row analog HNO, as well as HNS and HPO. Therefore, substitution of phosphorus and sulfur for nitrogen and oxygen does not result in a dramatic structural change.     

The complex spectrum of a "simple" free radical: the Ã-X̃ band system of the jet-cooled boron difluoride free radical

The near-ultraviolet band system of the jet-cooled boron difluoride free radical has been studied by a combination of laser-induced fluorescence and single vibronic level wavelength resolved emission spectroscopies. The radical was produced in a supersonic discharge jet using a precursor mixture of 1%-3% of BF(3) or (10)BF(3) in high pressure argon. A large number of bands were found in the 340-286 nm region and assigned as transitions from the X?(2)A(1) ground state to the lower Renner-Teller component of the A?(2)Π excited state, based on our previous ab initio potential energy surface predictions, matching the emission spectra Franck-Condon profiles of (11)BF(2) and (10)BF(2), and comparison of observed and calculated boron isotope effects. Several bands have been rotationally analyzed providing ground state structural parameters of r(0)(') (BF) = 1.3102(9) ? and θ(0)(') (FBF) = 119.7(6)°. The ground state totally symmetric vibrational energy levels of both boron isotopologues have also been measured and assigned up to energies of more than 8000 cm(-1). Although BF(2) might be considered to be a "simple" free radical, understanding the details of its electronic spectrum remains a major challenge for both theory and experiment.     

Photophysics of the B̃ 1A1 state of thiophosgene

The results of fluorescence lifetime measurements using a dye laser excitation source are combined with other recently published data to present a consistent picture of the photophysics of the B? ¹A₁ state of Cl₂CS.     

Determination of the dipole moment of thioformaldehyde in the a3A2 excited state by laser phosphorescence excitation spectroscopy

Doppler-limited phosphorescence excitation spectra have been recorded at various electric fields for two rotational transitions in the $\text{a}$³A₂-$\text{X}$¹A₁ 0-0 band of H₂CS. Stark splittings were resolved, and were used to determine the dipole moment in the excited electronic state. The value found, 0.57(3) D, is of the order expected by comparison with dipole moments determined for other states of H₂CS, but rather lower than that predicted by ab initio calculations.     

Vectorial Approach to Fast Correlation Attacks

A new, vectorial approach to fast correlation attacks on binary memoryless combiners is proposed. Instead of individual input sequences or their linear combinations, the new attack is targeting subsets of input sequences as a whole thus exploiting the full correlation between the chosen subset and the output sequence. In particular, the set of all the input sequences can be chosen as the target. The attack is based on a novel iterative probabilistic algorithm which is also applicable to general memoryless combiners over finite fields or finite rings. To illustrate the effectiveness of the introduced approach, experimental results obtained for random balanced combining functions are presentedMost of this work was done while he was with Rome CryptoDesign Center, Gemplus, Italy     

On the Motion of a Dynamic System with Minimal Dissipation

The motion of a holonomic scleronomic non-conservative mechanicalsystem with minimal dissipation is considered. As applicationsof the theory several problems are studied in detail.