A.R. Hoy

A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule

Abstract In this paper we report the results of improving the non-rigid bender formulation of the rotation-vibration Hamiltonian of a triatomic molecule [see A. R. Hoy and P. R. Bunker, J. Mol. Spectrosc., 52, 439 (1974)]. This improved Hamiltonian can be diagonalized as before by a combination of numerical integration and matrix diagonalization and it yields rotation-bending energies to high values of the rotational quantum numbers. We have calculated all the rotational energy levels up to J = 10 for the (v1, v2, v3) states (0, 0, 0) and (0, 1, 0) for both H2O and D2O. By least squares fitting to the observations varying seven parameters we have refined the equilibrium structure and force field of the water molecule and have obtained a fit to the 375 experimental energies used with a root mean square deviation of 0.05 cm−1. The equilibrium bond angle and bond length are determined to be 104.48° and 0.9578 A respectively. We have also calculated these energy levels using the ab initio equilibrium geometry and force constants of Rosenberg, Ermler and Shavitt [J. Chem. Phys., 65, 4072 (1976)] and this is then the first complete ab initio calculation of rotation-vibration energy levels of high J in a polyatomic molecule to this precision. the rms fit of these ab initio energies to the experimental energies for the H2O molecule is 2.65 cm−1.

Sulfur dioxide: Rotational constants and asymmetric structure of the C̃1B2 state

Abstract Eight bands of the 2350 A system of sulfur dioxide have been rotationally analyzed as A-type transitions of a prolate asymmetric rotor, confirming that the electronic transition is 1 B 2 ← 1 A 1 [2b 1 (π ∗ ) ← 1a 2 (π)] . The electronic energy and rotational constants of the 0-0 band are, in cm−1: T 0 42573.450±0.005 δ J (0.041±0.05)10 −5 , A 000 1.15053±0.00014 δ JK (1.34±0.04)10 −5 , B 000 0.34744±0.00002 δ K (0.73±0.09)10 −5 , C 000 0.26543±0.00002 δ J (0.009±0.003)10 −5 , δ(u A 2 0.339±0.005 δ K (0.42±0.21)10 −5 These constants correspond to the average structure r 0 = 1.560 A and θ0 = 104.3°. However, the vibrational structure can only be satisfactorily accounted for on the hypothesis of a double-minimum potential in the antisymmetrical stretching coordinate Q3, the energies of the fundamental levels in the three modes of the B2 state being: (100), 960 cm−1; (010), 377 cm−1; and (001), ∼220 cm−1 The (001) level is not observed in the spectrum but can be calculated from the distortion constants and inertial defect of the rotational analysis: the level (002) = 561 cm−1, obtained directly from the vibrational structure, establishes that there is strong, positive anharmonicity in the first three levels of this vibration, as required by the assumption of a double-minimum potential function. Preliminary values are reported for the barrier to the symmetrical configuration, V hc ∼ 100 cm −1 , and for the difference in bond distances in the equilibrium configuration, Δ r⋍0.12 A . Coon and his co-workers have previously considered the possible asymmetry of this state but the Q3 inversion barrier obtained by them, 656 cm−1, is much higher than in the present work, and reasons for this are discussed.

The E-B band system of diatomic iodine

Abstract Sequential pump and probe pulses are used to excite state-selected E ← B ← X transitions in I 2 vapor, and the E ← B bands recorded by polarization-labeling spectroscopy at relatively high dispersion. Molecular constants and Dunham expansion coefficients Y n ,0 ( n = 0–7), Y n ,1 ( n = 0–3), and Y n ,2 ( n = 0, 1) for the E state are obtained in the range 0 ≤ v E ≤ 96, based on a global least-squares fit of 1050 assigned rotational transitions. Definite evidence is cited to show that the EO g + ion-pair state correlates diabatically with the ground state I − ( 1 S 0 ) + I + ( 3 P 2 ) of the separated ions.

High order Coriolis interactions in NO2

Abstract A small widespread Coriolis perturbation in the infrared bands of NO 2 has been quantitatively analyzed. The resonance which affects all levels which differ by two quanta in the bending vibration and one in the antisymmetric stretch has been included explicitly in the reanalysis of five infrared bands. This reanalysis has led to improved constants for the bands analyzed and five consistent values for the interaction parameter. Two theoretical estimates of this interaction parameter are also presented.

The emission spectrum of ArKr+, and a discussion of spectroscopic observations characterizing the heteronuclear rare gas dimer ions

The ArKr+ emission from a jet discharge has been recorded at high resolution from 6170 to 6460 A. The isotope structure due to the natural abundances of 84Kr and 86Kr establishes the vibrational analysis of the system and leads to extrapolated upper and lower state dissociation limits that are in fair agreement with photoionization data from other sources. The rotational analysis confirms the assignments of the bands to the charge transfer transition from the highest to the lowest Ω = 12 state of the ground state configurations Ar+ + Kr and Ar + Kr+, respectively. The rotational numbering of the lines follows from a careful search for common combination differences. However, the case “c” structure of the bands and the observation of only four out of a possible six branches prevent an unambiguous evaluation of the internuclear distances. The results are reviewed in the context of published high-resolution data for other rare gas dimer ions.

A deconvolution of the Ã-X̃ band system of nitrogen dioxide

Abstract The visible absorption of NO2 recorded in the supersonic beam experiments of Smalley, Wharton, and Levy is partially analyzed on the assumption that the first exicted 2B2 state of the diabatic representation is vibronically coupled to high vibrational levels of the ground state. It is shown that the model correctly reproduces the range of B values observed in the coupled state. The relationship of the discrete and “continuum” components of NO2 fluorescence to one another is discussed in terms of resonance and nonresonance emission from levels of the coupling.

Rotational coupling of the β 1 and E 0+ ion-pair states of lodine bromide

The E(Ω = 0+) and β(Ω = 1) ion-pair states of IBr are coupled by an electronic Coriolis interaction. A nonlinear, least-squares fit of term values for both states yields a set of potential and rotational constants purged of the effects of this interaction. The magnitude of the coupling constant, |W1,0| = 2.41 cm−1, is 98% of the value predicted for pure precession. Principal constants of the previously unreported β state of I79Br are Te = 39507.76, ωe = 122.09, ωeχe = 0.2546, Be = 0.02937, and αe = 8.2 × 10−4cm−1.

Constants of the second 0g+ ion-pair state of I2

Abstract The second 0 g + ion-pair state of I 2 is characterized using two-stage polarization-labeling spectroscopy. Molecular constants for this state in the range 0 ≤ v ≤ 25, based on a global leastsquares fit of 450 transitions, are (in cm −1 ) T e = 47 025.917, ω e = 104.1804, ω e x e = 0.21324, ω e y e = 2.46 × 10 −4 , B e = 2.08042 × 10 −2 , α e = 5.728 × 10 −5 , γ e = 5.8 × 10 −8 , and D e = 3.32 × 10 −9 . The diabatic potential curve correlates with the states I − ( 1 S) + I + ( 3 P 0 ) of the separated ions.

The A′(3Π2) state of ICl☆

Abstract Although A′( 3 Π 2 ) ← X( 1 Σ + ) is forbidden in near case c molecules the A ′ ← X transition can be efficiently accomplished by the three-step sequence A′( 3 Π 2 ) ← D′(2) ← A( 3 Π 1 ) ← X( 1 Σ + ) . Transitions to a range of levels of A ′, v A ′ = 2–38, have been recorded by this means, using J -selective polarization-labeling spectroscopy. Principal constants of the A ′ state of I 35 Cl are T e = 12682.05, ω e = 224.57, ω e χ e = 1.882, ω e y e = −0.0107, B e = 0.08653, and α e = 0.000675 cm −1 . The A ′ state is therefore similar in its physical characteristics to two other (relatively) deep states, A( 3 Π 1 ) and B( 3 Π 0 +) , of the 2431 configuration.

The E(O+) and f(O+) ion-pair states of lodine chloride

Abstract Spectroscopic constants for the E(O+) and f(O+) ion-pair states of ICI vapor have been determined using two-photon polarization-labeling spectroscopy. Constants for the E state in regions where perturbations due to the E(O+) − β(1) heterogeneous coupling are small are (in cm−1) Y0,0 = 39059.599(88), Y1,0 = 165.590(61), Y2,0 = −0.273(11), Y3,0 = −4.94(75) × 10−3, Y4,0 = 8.0(23) × 10−5, Y5,0 = 5.4(24) × 10−7, Y0,1 = 0.057921(64), and Y1,1 = −2.136(36) × 10−4. The previously unknown f(O+) state is not appreciably perturbed by coupling with the neighboring I(3P1) state. Constants for this state are Y0,0 = 44923.79(46), Y1,0 = 184.40(16), Y2,0 = −0.771(19),Y3,0 = 3.59(69) × 10−3, Y0,1 = 0.05777(15), and Y1,1 = −2.13(14) × 10−4cm−1. Of a total of six ion-pair states which correlate with I+(3P) + Cl−(1S) only one, O−(3P1), remains to be identified.