Keiichi Tanaka

Transitions to the internal rotation second excited state (j = 2) and the intermolecular stretching first excited state (vs = 1) of He–HCN, located close to the dissociation limit (by 0.2633 and 0.1759 cm−1 lower than the limit, respectively), were observed by millimeter-wave spectroscopy using the supersonic jet technique. The observed transition frequencies were fitted, together with those of the internal rotation fundamental band (j = 1 − 0), to the effective Hamiltonian with the intermolecular potential V(R, θ) expanded with the asymptotic long-range potential coefficients cn,l. The potential energy surface has a global minimum at the linear configuration (He⋯H–C–N) with a depth (De) of 30.150 cm−1 and a saddle point at the anti-linear configuration (He⋯N–C–H) located 9.014 cm−1 higher than the global minimum. The predissociation lifetimes of the quasi-bound states (τ = 0.16–0.29 μs) were derived from the line broadening of the observed transitions and agreed well with the calculated results with the radial probability density outside the centrifugal barrier.

The tunneling-rotation transitions of malonaldehyde, consisting of more than 200 a-type Q-branch lines along with 50 R- and P-branch lines, were observed in the submillimeter-wave region of 590–760 GHz. The proton tunneling splitting in the ground state, ΔE0 = 647 046.1640(40) MHz [21.583 208 818(133) cm−1], and the tunneling-rotation interaction constant, F0 = 45.8004(24) MHz, were determined. In addition, the rotational and centrifugal distortion constants were determined for both the 0+ and 0− tunneling sublevels. The proton tunneling dynamics of malonaldehyde were studied using a linear trajectory model to explain the observed molecular constants, and the potential barrier height hb was determined to be 2196 cm−1.

Fourier-transform microwave spectroscopy has been applied for the 13C/18O-substituted tropolone to observe tunneling-rotation transitions as well as pure rotational transitions. The tunneling-rotation transitions were observed between the 13C-4 and -6 forms as well as between 13C-3 and -7, between 13C-1 and -2, and between 18O-8 and -9 (we denote these tunneling pairs as 13C-46, etc., below) although they have an asymmetric tunneling potential due to the difference in the zero point energy (ZPE). From the observed tunneling splittings ΔEij (0.9800–1.6824 cm−1), the differences in ZPE Δij for the 13C-46, -37, -12, and 18O-89 species are derived to be −0.1104, 0.5652, −1.3682, and 1.3897 cm−1 to agree well with the DFT calculation. The state mixing ratio of the tunneling states decreases drastically from (44%:56%) to (8.7%:91.3%) for 13C-46 and 18O-89 with an increase in the asymmetry Δij of the tunneling potential function. The observed tunneling-rotation interaction constants Fij decrease from 16.001 to 9.224 cm−1 as the differences in ZPE Δij increase, while the diagonal tunneling-rotation interaction constants Fu increase from 1.767 to 13.70 cm−1, explained well by the mixing ratio of the tunneling states.

This study examines whether an alternative calculation approach exists for the asymptotic expansion of the probability density function of risky asset prices. We focus on the partial differential equation by using an eigenfunction expansion related to Hermite polynomials. We show that the expansion coefficients can be obtained by solving ordinary differential equations recursively and which order of Hermite polynomials appear in asymptotic expansion explicitly.

Rotational transitions of the mono(β)-deuterated vinyl radical, HDC=CH, produced in a supersonic jet expansion by the ArF excimer laser photolysis, were observed by millimeter-wave spectroscopy. The b-type rotational transitions together with the weak a-type transitions were observed only for the lower component of the tunneling doublet, and no tunneling-rotation transitions connecting the lower and upper components were observed, suggesting that state mixing between the two components is negligibly small. The derived molecular constants such as the A rotational constant, Fermi contact interaction constants, and magnetic dipolar interaction constants indicate that the carrier of the observed spectrum is the trans-form of HDC=CH isomers, where the α-proton is located on the opposite side of the β-deuteron. The present conclusion of the trans-form of HDC=CH was also supported by the ab initio calculation in the CCSD(T)/cc-pVTZ level since the trans-form is calculated to be located by 30.04 cm−1 lower than the cis-form due to the difference in the zero point energy. As a result, the tunneling components in the ground state of HDC=CH behave as two different isomers localized at the trans- and cis-wells of the asymmetric double minimum potential. Observed hyperfine constants for HDC=CH were compared with those for H2C=CH to be consistent with each other.

The ortho to para conversion of water ion, H₂O⁺, due to the interaction between the magnetic moments of the unpaired electron and protons has been theoretically studied to calculate the spontaneous emission lifetime between the ortho- and para-levels. The electron spin–nuclear spin interaction term, T_ab(S_aΔI_b + S_bΔI_a) mixes ortho (I = 1) and para (I = 0) levels to cause the “forbidden” ortho to para |ΔI| = 1 transition. The mixing term with T_ab = 72.0 MHz is 4 orders of magnitude higher for H₂O⁺ than for its neutral counterpart H₂O where the magnetic field interacting with proton spins is by molecular rotation rather than the free electron. The resultant 10⁸ increase of ortho to para conversion rate possibly makes the effect of conversion in H₂O⁺ measurable in laboratories and possibly explains the anomalous ortho to para ratio recently reported by Herschel heterodyne instrument for the far-infrared (HIFI) observation. Results of our calculations show that the ortho ↔ para mixings involving near-degenerate ortho and para levels are high (∼10^–3), but they tend to occur at high energy levels, ∼300 K. Because of the rapid spontaneous emission, such high levels are not populated in diffuse clouds unless the radiative temperature of the environment is very high. The low-lying 1₀₁ (para) and 1₁₁ (ortho) levels of H₂O⁺ are mixed by ∼10^–4 making the spontaneous emission lifetime for the para 1₀₁ → ortho 0₀₀ transition 520 years and 5200 years depending on the F value of the hyperfine structure. Thus the ortho ↔ para conversion due to the unpaired electron is not likely to seriously affect thermalization of interstellar H₂O⁺ unless either the radiative temperature is very high or number density of the cloud is very low.