Resonance calculation

Moiseyev N 1998 Quantum theory of resonances calculating energies, widths and cross-sections by complex scaling Rhys. Rep. 302 212... 

Consider any risers that may be installed in the piping system. In considering risers, use resonant calculations for a closed tube (C/L) and investigate the open-end tube (C/2L). 

In Table 7-9 there are given values for carbon-carbon bond lengths for single-bond double-bond resonance, calculated by Equation 7-3 with D = 1.504 A (as corrected for the adjacent-bent-bond effect) and Dt = 1.334 A. These values are for application to conjugated and aromatic systems of single bonds and double bonds, as illustrated in the following section and in later chapter. ... 

For H20, the fundamental frequencies vx and vy are fairly close together and one might expect Fermi resonance between the (100) and (001) levels however, these levels have different symmetry species (Section 6.3) and cannot interact. The levels (200) and (002) both have symmetry species Ax and do interact. A little thought shows that only H20 vibrational levels with both t and t>3 less than 2 do not undergo Fermi resonance. (Details of the Fermi-resonance calculations for H20 and C02 are given in Herz-berg, Infrared and Raman Spectra, pp. 216-219.)... 

In actual resonance calculations, explicit decomposition of the Hamiltonian is not always needed. The whole Schrodinger equation (1) is often solved somehow without explicit use of HQ or H. General methods for analyzing results from such a treatment are the main subject of this article. A comprehensive review of computational methods or computational results is outside of its scope. 

G.D. Doolen, J. Nuttal, R.W. Stagat, Electron-hydrogen resonance calculation by the coordinate-rotation method, Phys. Rev. A 10 (5) (1974) 1612. 

Unlikely though it may seem, a stable Dewar benzene was synthesized in 1963. But all five forms of benzene contribute to produce a truly symmetrical benzene molecule the resonance calculations are very complicated. 

Figure 1 Differences in positions and widths for HN2 resonance calculated from doubled and undoubled Chebyshev correlation functions.

Specific Approaches In Direct Variational Resonance Calculations... 

FIGURE 4.2.5 a) NEXAFS spectra of a 50-nm thick evaporated pentacene film collected at a PEY bias of -50 V. These spectra are postedge normalized to the intensity at 330 eV to account for changing spot size, b) The intensity of the n resonances calculated by integrating the spectra from 282 to 286.5 eV, displayed versus the squared sine of incident angle. The standard experimental uncertainty of PEY and its integrated intensity are <2%. 

The illustrative results on scattering and resonance calculation using the stabilization method for the collinear H + H2 -> H2 + H exchange reaction had been presented in Ref. 32. This model calculation showed that the method requires a relatively modest amount of computational effort and can be used for the general case of the multichannel (arrangement) problem. In the next section we show an illustrative calculation of resonances for the 3D (J = 0) HCO formyl radical using Eq. (55). 

B. C. Garrett and D. G. Truhlar, WKB approximation for the reaction-path Hamiltonian Application to variational transition state theory, vibrationally adiabatic excited-state barrier heights, and resonance calculations,/. Chem. Phys. 81 309 (1984). 

If the condition 0 < ( 7 — jS) < tt is fulfilled, the second exponential factor in the last form of exp [iknR] goes to zero as p = R — oo. The channel function then behaves as that of a bound state. It is also important to note that this complex transformation of the coordinate does not affect the decreasing asymptotic behavior and the square integrability of a bound sfafe wavefunc-tion. This means that any method available for bound sfafe calculafions can be used for resonance calculations. A variant of the complex rotation method consists in transforming the reaction coordinate only after some value, say Rq. The form given to the coordinate is then Rq + [R — Ro)exp(k). This procedure is called exterior scaling [42,43]. 

N. Moiseyev, Quantum theory of resonances Calculating energies widths ans cross-sections by complex scaling, Phys. Rep. 302 (1998) 212. 

Y, H-Y, H-MOR, H-ZSM-5) and correlated especially the shift, Av (OH), of the (high-frequency) OH stretching bands to the acid strength (Sanderson s charge on the H atom). The shifted OH bands appeared as broad signals between 3025 (AN H-X) and 2540 cm (AN - H-ZSM-5) for the neutral complexes. Also, the in-plane, 6(OH) and out-of-plane, y(OH), bending vibrations were measured and compared with the results of Fermi resonance calculations. Interaction of di-acetonitrile with NH4-, H, Na-, H-, and Co-Beta led to the detection of Brqnsted and Lewis sites through the appearance of bands at 2297 and 2325 cm", respectively. Na+ and Co + were identified by bands at 2284 and 2308 cm, respectively. 

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