Franck-Condon Mechanism Research Articles

Two-photon excitation spectra of the lowest electronic states of 2,2′-bipyridine

The two-photon absorption spectra of 2,2′-bipyridine single crystal at 77 K and solution Li the region 30000–38500 cm −1 and 32000–38500 cm −1, respectively, have been measured. The lowest (n,π*) and (π,π*) electronic systems have been observed and discussed in terms of two-photon allowed and vibronicauy induced transitions. Proportionality factors for two-photon intensities in the crystal were calculated in the oriented gas model approximation and used to assign the observed bands to the proper tensor under the C 2h molecular symmetry. In the (n, π*) absorption region of the crystal the (0-0) 1Bg(n,π*) ← 1Ag, not active in one-photon experiments, has been found at ≈30075 cm −1. The 1Bg(n, π*) −1Au(n, π*) energy gap amounts to ≲800 cm −1. The observed vibronic structure is assigned to totally symmetric vibrational modes through a Franck—Condon mechanism. The (π, π*) absorption region is discussed on the basis of both the crystal and solution spectrum. McClain's polarization rules for the solution and polarized crystal intensities show that the (π, π*) two-photon absorption region begins at ≈34300 cm −1. Transitions to B u × b u × ag states are responsible of the band pattern up to about 37000 cm −1 The relative two-photon cross section of 2.2′-bipyridine in solution at 34780 cm −1 has been estimated to be of the order of 6 × 10 −2 that of benzend's 1B 2u × b 2u (ν 14). The one-photon absorption spectrum of the solution reran here has revealed a shoulder on the red of the well-known maximum at ≌2835 A and it has been assigned to the (0-0) 1 Bu(π, π*).

Formation ofN2+BΣu+2andN2CΠu3in collisions ofH+and H withN2

The 200-500-nm radiation excited by collisions of beams of 1-25-keV ${\mathrm{H}}^{+}$, ${\mathrm{D}}^{+}$, H, and D with ${\mathrm{N}}_{2}$ has been studied under thin-target conditions with a viewing geometry chosen to minimize polarization effects. For both ion and neutral impact, the $\mathrm{N}_{2}^{}{}_{}{}^{+}$ ($B^{2}\ensuremath{\Sigma}_{u}^{+}\ensuremath{-}X^{2}\ensuremath{\Sigma}_{g}^{+}$) first negative ($1n$) bands are the most intense spectral features in this wavelength range. As expected from consideration of electron-spin conservation, the probability of excitation of the ${\mathrm{N}}_{2}C^{3}\ensuremath{\Pi}_{u}\ensuremath{-}B^{3}\ensuremath{\Pi}_{g}$ second positive ($2p$) bands by H or D impact greatly exceeds that for ${\mathrm{H}}^{+}$ or ${\mathrm{D}}^{+}$ bombardment. Relative emission cross sections for the (0,0) bands of the $1n$ system at 391.4 nm and the $2p$ system at 337.1 nm were determined and made absolute via normalization to measurements reported at higher energies by previous workers. The relative vibrational population $P({v}^{\ensuremath{'}})$ for ${\mathrm{N}}_{2}C^{3}\ensuremath{\Pi}_{u}$ formed in 3-25-keV H and D impact is in good agreement with the prediction of a simple, Franck-Condon excitation mechanism; however, for $\mathrm{N}_{2}^{}{}_{}{}^{+}B^{2}\ensuremath{\Sigma}_{u}^{+}$ formed in collisions with 4-25-keV H and D, a dramatic enhancement in $P({v}^{\ensuremath{'}})$ for ${v}^{\ensuremath{'}}>0$ over the Franck-Condon values is observed at low projectile velocities. The higher-velocity onset and greater magnitude of this effect for H and D in comparison with that observed for ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ are in disagreement with the predictions of a modified Franck-Condon mechanism that allows for polarization of ${\mathrm{N}}_{2}$ by the incident projectile. The measured values of $P({v}^{\ensuremath{'}})$ were used in conjunction with the (0,0) band cross sections to derive total cross sections for formation of $\mathrm{N}_{2}^{}{}_{}{}^{+}B^{2}\ensuremath{\Sigma}_{u}^{+}$ and ${\mathrm{N}}_{2}C^{3}\ensuremath{\Pi}_{u}$. A maximum in the cross section for formation of $\mathrm{N}_{2}^{}{}_{}{}^{+}B^{2}\ensuremath{\Sigma}_{u}^{+}$ of 1.12\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ at 10 keV was found for ${\mathrm{H}}^{+}$ impact, while for H, the cross section for formation of this state rises steadily with increasing collision energy until reaching a nearly constant value of 3.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ in the 15-25-keV range. The fraction of the total $\mathrm{N}_{2}^{}{}_{}{}^{+}$ yield that is formed in the $B$ state increases from about 0.03 to 0.08 in the energy range studied. For formation of ${\mathrm{N}}_{2}C^{3}\ensuremath{\Pi}_{u}$ the cross section has a maximum value of 2.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 5 keV. At H-atom energies below 7 keV, exchange excitation of ${\mathrm{N}}_{2}$ to the $C^{3}\ensuremath{\Pi}_{u}$ state is more probable than ionization to yield $\mathrm{N}_{2}^{}{}_{}{}^{+}$ in the $B$ state while, at higher energies, ionization to yield the $B$ state is the more probable process. Comparison of our results with values calculated via the application of recently developed, semiempirical scaling relationships to electron impact cross-section data indicates that the latter approach yields a good prediction of the energy dependence and an acceptable prediction of the magnitude of the $C^{3}\ensuremath{\Pi}_{u}$ cross section for 1-100-keV H impact. The semiempirical approach also makes a good prediction of the cross section for formation of $\mathrm{N}_{2}^{}{}_{}{}^{+}B^{2}\ensuremath{\Sigma}_{u}^{+}$ in ${\mathrm{H}}^{+}$ or H impact above 10 keV; however, primarily because of the lack of experimental data at lower energies, previous semiempirical predictions have overestimated the ionization contribution to the over-all $\mathrm{N}_{2}^{}{}_{}{}^{+}B^{2}\ensuremath{\Sigma}_{u}^{+}$ cross section.

The Effect of Isotopic Substitution on Mass Spectra of Molecules

A general method for calculating the effect of isotopic substitution on mass spectra is presented. The calculation is based on the notion that the various fragment ions, formed by electron impact on a molecule, are produced by a Franck-Condon mechanism. It is assumed that those bonds will break which possess more potential energy than bond energy at the instant of ionization. The mass spectral data for a molecule are used in conjunction with the ground-state vibrational wave function to evaluate critical bond distances (distances for which the potential energy equals the bond energy). Then the mass spectral pattern for isotopic molecules can be predicted from a knowledge of the ground-state vibrational wave function of the isotopic molecule. The method is applied to the diatomic molecules N14N14, N14N15, N15N15, and C12O16, C13O16. The predicted values compare favorably with previously observed results, however, experimental errors obscure a sharp test of the predictions for these cases. New experimental values are presented for the ratios C13+/C13O216+ and C12+/C12O216+ from carbon dioxide and compared with predictions. Good agreement is found between ratios extrapolated to high ion accelerating voltage and predicted ones.