Photodissociation of formyl fluoride in rare gas matrixes

Photodissociation of formyl fluoride (HCOF) is studied in Ar, Kr, and Xe matrixes at 248 and 193 nm excitation by following spectral changes in the infrared absorption spectra. In all matrixes, the main photodissociation products are CO/HF species, including CO-HF and OC-HF complexes and thermally unstable CO/HF species (a distorted CO/HF complex or a reaction intermediate), which indicate negligible cage exit of atoms produced via the C-F and C-H bond cleavage channels. However, the observation of traces of H, F, CO, CO(2), F(2)CO, FCO, and HRg(2)(+) (Rg = Kr or Xe) in Kr and Xe matrixes would imply some importance of other reaction channels too. The analysis of the decay curves of the precursor shows that dissociation efficiency of HCOF increases as Ar < Kr < Xe, the difference being the factor of 10 between Ar and Xe. Moreover, HCOF dissociates 20-50 times faster at 193 nm compared to 248 nm. Interestingly, whereas the CO/HF species are stable with respect to photolysis in Ar, they photobleach in Kr and Xe matrixes at 248 and 193 nm, even though the first excited states of CO and HF are not energetically accessible with 193 and 248 nm photons. In krypton matrix, the photodissociation of CO/HF species at 248 nm is observed to be a single photon process. Quantum chemical calculations of electronic excitation energies of CO-HF and OC-HF complexes show that the electronic states of HF and CO mostly retain their diatomic nature in the pair. This clearly demonstrates that photodissociation of CO/HF complexes is promoted by the surrounding rare gas lattice.     

A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains

In this note we investigate the asymptotic behavior of the s-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain Ω with smooth boundary ∂Ω. For this we apply the recently introduced abstract notion of quasi boundary triples and Weyl functions from extension theory of symmetric operators together with Krein type resolvent formulae and well-known eigenvalue asymptotics of the Laplace-Beltrami operator on ∂Ω. It is shown that the resolvent difference of two generalized Robin Laplacians belongs to the Schatten-von Neumann class of any order p for which

     

Schrödinger Operators with δ and δ′-Potentials Supported on Hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity.     

Bounds on Non-Real Eigenvalues of Indefinite Sturm-Liouville Problems

It is known since the early 20th century that regular indefinite Sturm-Liouville problems may possess non-real eigenvalues. However, finding bounds for this set in terms of the coefficients of the differential expression has remained an open problem until recently. In this note we prove a variant of a recent result in [1] on the bounds for the non-real eigenvalues of an indefinite Sturm-Liouville problem with Dirichlet boundary conditions. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Kre?n's formula

Kre?n's formula provides a parametrization of the generalized resolvents and Štraus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Kre?n's formula.     

Sturm-Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions

We consider a class of boundary value problems for Sturm-Liouville operators with indefinite weight functions. The spectral parameter appears nonlinearly in the boundary condition in the form of a function τ which has the property that λ?λτ(λ) is a generalized Nevanlinna function. We construct linearizations of these boundary value problems and study their spectral properties.     

A computational and experimental study of the structures and Raman and 77Se NMR spectra of SeX3+ and SeX2 (X = Cl, Br, I): FT-Raman spectrum of (SeI3)[AsF6

The ability of MP2, B3PW91 and PBE0 methods to produce reliable predictions in structural and spectroscopic properties of small selenium-halogen molecules and cations has been demonstrated by using 6-311G(d) and cc-pVTZ basis sets. Optimized structures and vibrational frequencies agree closely with the experimental information, where available. Raman intensities are also well reproduced at all levels of theory. Calculated GIAO isotropic shielding tensors yield a reasonable linear correlation with the experimental chemical shift data at each level of theory. The largest deviations between calculated and experimental chemical shifts are found for selenium-iodine species. The agreement between observed and calculated chemical shifts for selenium-iodine species can be improved by inclusion of relativistic effects using the ZORA method. The best results are achieved by adding spin-orbit correction terms from ZORA calculations to nonrelativistic GIAO isotropic shielding tensors. The calculated isotropic shielding tensors can be utilized in the spectroscopic assignment of the 77Se chemical shifts of novel selenium-halogen molecules and cations. The experimental FT-Raman spectra of (SeI3)[AsF6] in the solid state and in SO2(l) solution are also reported.     

Experimental and theoretical investigations of structural trends for selenium(IV) imides and oxides: X-ray structure of Se3(NAd)2

The thermal decomposition of Se(NAd)(2) (Ad = 1-adamantyl) in THF was monitored by (77)Se NMR and shown to give the novel cyclic selenium imide Se(3)(NAd)(2) as one of the products. An X-ray structural determination showed that Se(3)(NAd)(2) is a puckered five-membered ring with d(Se-Se) = 2.404(1) A and |d(Se-N)| = 1.873(4) A. On the basis of (77)Se NMR data, other decomposition products include the six-membered ring Se(3)(NAd)(3), and the four-membered rings AdNSe(micro-NAd)(2)SeO and OSe(micro-NAd)(2)SeO. The energies for the cyclodimerization of E(NR)(2) and RNEO (E = S, Se; R = H, Me, (t)Bu, SiMe(3)), and the cycloaddition reactions of RNSeO with E(NR)(2), RNSO(2) with Se(NR)(2), and S(NR)(2) with Se(NR)(2) have been calculated at MP2, CCSD, and CCSD(T) levels of theory using the cc-pVDZ basis sets and B3PW91/6-31G* optimized geometries. Sulfur(IV) and selenium(IV) diimide monomers are predicted to be stable, the sole exception being Se(NSiMe(3))(2) that shows a tendency toward cyclodimerization. The cyclodimerization energy for RNSeO and the cycloaddition reaction energies of RNSeO with Se(NR)(2) as well as that of RNSO(2) with Se(NR)(2) are negative, consistent with the observed formation of OSe(micro-N(t)Bu)(2)SeO, OSe(micro-N(t)Bu)(2)SeN(t)Bu, and O(2)S(micro-N(t)Bu)(2)SeN(t)Bu, respectively. Cycloaddition is unlikely when one of the reactants is a sulfur(IV) diimide.