P. R. Bunker

A THEORETICAL CALCULATION OF THE ABSORPTION SPECTRUM OF CH2

Abstract The ground X 2 A 1 electronic state of CH 2 + is quasilinear with a small barrier to linearity, and at linearity the state becomes degenerate with the A 2 B 1 electronic state forming a 2 Π u state. Because of the nonzero electronic angular momentum the rovibrational basis states belonging to the two electronic states strongly interact due to both the Renner effect and spin-orbit coupling. In a previous paper (P. Jensen, M. Brumm, W. P. Kraemer, and P. R. Bunker, J. Mol. Spectrosc. 172 (1995) 194) we calculated the rovibronic energies of the states using ab initio potential energy surfaces that we generated. In the present paper we use the electronic wavefunctions of the previous ab initio calculation to determine the dipole moment and transition moment surfaces, and we develop the theory that allows us to use these to calculate intensities. As a result we now calculate both the positions and intensities of the lines in the absorption spectrum of CH 2 + , and its deuterated isotopomers, making full allowance for the effects of the Renner interaction and of spin-orbit coupling. We predict the appearance of the absorption spectrum over the whole wavenumber range from 0 cm −1 to beyond 15xa0000 cm −1 ; this involves only the X and A electronic states. We hope that these results allow experimentalists to search successfully for the features that we predict, and thereby to achieve a better spectroscopic characterization of this important molecular ion.

The Renner effect in triatomic molecules with application to CH2+, MgNC and NH2

We have developed a computational procedure, based on the variational method, for the calculation of the rovibronic energies of a triatomic molecule in an electronic state that become degenerate at the linear nuclear configuration. In such an electronic state the coupling caused by the electronic orbital angular momentum is very significant and it is called the Renner effect. We include it, and the effect of spin-orbit coupling, in our program. We have developed the procedure to the point where spectral line intensities can be calculated so that absorption and emission spectra can be simulated. In order to gain insight into the nature of the eigenfunctions, we have introduced and calculated the overall bending probability density function f(p) of the states. By projecting the eigenfunctions onto the Born-Oppenheimer basis, we have determined the probability density functions f+(rho) and f-(rho) associated with the individual Born-Oppenheimer states phi(-)elec and phi(+)elec. At a given temperature the Boltzmann averaged value of the f(p) over all the eigenstates gives the bending probability distribution function F(rho), and this can be related to the result of a Coulomb Explosion Imaging (CEI) experiment. We review our work and apply it to the molecules CH2+, MgNC and NH2, all of which are of astrophysical interest.

A theoretical study of the absorption spectrum of singlet CH2

Abstract This paper is a continuation of our earlier work aimed at characterizing the electronic states of the methylene free radical CH2. In the present paper we focus attention on the lowest pair of singlet states, a 1 A 1 and b 1 B 1 . These states are degenerate when they are linear and therefore participate in a Renner interaction. Our previous refinement of the a state potential energy surface ignored the Renner effect. Now we include this effect and refine both the potential energy surfaces by a fitting of the data. Using these two new potential energy surfaces, allowing for the Renner effect, and making an ab initio calculation of the dipole moment surfaces and transition moment surface, we make a simulation of the absorption spectrum associated with this pair of interacting electronic states. These predictions have been of use for the assignment of the spectrum. Further experimental work aimed at identifying rotational levels belonging to the vibrational ground state of the b state is necessary before we can consider better refinements of the potential surfaces. Also spectra that fill other gaps in the data available for the two states would be highly desirable. One important new feature to emerge is that the adiabatic Renner effect correction A〈Lz2〉 to the a-state potential energy surface causes a significant increase in the energy of the a state; this means that the experimentally derived vibrationless singlet-triplet splitting in methylene, T e ( a ), is reduced by 64xa0cm−1 to 3159xa0cm−1. This is essentially in perfect agreement with the best theoretical value for this quantity.

Structure of the Benzene Dimer—Governed by Dynamics†

Author Institution: Center for Free-Electron Laser Science, 22761 Hamburg, Germany; Max-Planck-Institut fur Kernphysik, 69117 Heidelberg, Germany; Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany; National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada; Institut fur Physikalische Chemie und Elektrochemie, Gottfried-Wilhelm-Leibniz-Universtat, 30167 Hannover, Germany; Institute for Molecules and Materials, Radboud University, 6525 AJ Nijmegen, The Netherlands

Unraveling the internal dynamics of the benzene dimer: a combined theoretical and microwave spectroscopy study

We report a combined theoretical and microwave spectroscopy study of the internal dynamics of the benzene dimer, a benchmark system for dispersion forces. Although the extensive ab initio calculations and experimental work on the equilibrium geometry of this dimer have converged to a tilted T-shaped structure, the rich internal dynamics due to low barriers for internal rotation have remained largely unexplored. We present new microwave spectroscopy data for both the normal (C6H6)2 and partially deuterated (C6D6)(C6H6) dimers. The splitting patterns obtained for both species are unraveled and understood using a reduced-dimensionality theoretical approach. The hindered sixfold rotation of the stem can explain the observed characteristic 1u2009:u20092u2009:u20091 tunneling splitting pattern, but only the concerted stem rotation and tilt tunneling motion, accompanied by overall rotation of the dimer, yield the correct magnitude of the splittings and their strong dependence on the dimer angular momentum J that is essential to explain the experimental data. Also the surprising observation that the splittings are reduced by 30% for the mixed (C6D6)(C)(C6H6)(S) dimer in which only the cap (C) in the T-shaped structure is deuterated, while the rotating stem (S) monomer is the same as in the homodimer, is understood using this approach. Stark shift measurements allowed us to determine the dipole moment of the benzene dimer, μ = 0.58 ± 0.051 D. The assumption that this dipole moment is the vector sum of the dipole moments induced in the monomers by the electric field of the quadrupole on the other monomer yields a calculated value of μ = 0.63 D. Furthermore, the observed Stark behavior is typical for a symmetric top, another confirmation of our analysis.

Forbidden electric dipole rotation and rotation–vibration transitions in H2+

Previous studies of the interaction between the rotation-vibration levels of the 1s sigma(g) and 2p sigma(u) electronic states of H-2(+) have focussed on explaining the large hyperfine structure observed in some rovibronic transitions between these electronic stales. The interaction is an ortho-para interaction between levels of the two electronic states and it gives electric dipole intensity to forbidden rotation and rotation-vibration transitions within each electronic state. We determine the transition moments and Einstein A factors for the most significant of these transitions and point out their relevance to the problem of observing interstellar H-2(+).

Coulomb explosion imaging: the CH2+, H2O+ and NH2+ ions as benchmarks

Abstract In a previous paper we calculated the average distribution of bending angles for CH 2 + ions at 300 K using ab initio surfaces for the pair of Renner interacting ground state potentials in order to test the results of Coulomb explosion imaging (CEI) experiments. Here we calculate state selected bending angle distributions, and Boltzmann-averaged bond length distributions for CH 2 + in order to inspire more CEI experiments. Using published potential energy curves for H 2 O + and NH 2 + , we predict their bending angle distributions (and that of ND 2 + ) to provide further benchmarks to test the CEI method.

A dispersed fluorescence and ab initio investigation of the (X)over-tilde²B₁ and òA₁ electronic states of the PH2 molecule

In this work, the X2B1 and A2A1 electronic states of the phosphino (PH2) free radical have been studied by dispersed fluorescence and ab initio methods. PH2 molecules were produced in a molecular free-jet apparatus by laser vaporizing a silicon rod in the presence of phosphine (PH3) gas diluted in helium. The laser-induced fluorescence, from the excited A2A1 electronic state down to the ground electronic state, was dispersed and analyzed. Ten (upsilon1upsilon2upsilon3) vibrationally excited levels of the ground electronic state, with upsilon1 < or = 2, upsilon2 < or = 6, and upsilon3 = 0, have been observed. Ab initio potential-energy surfaces for the X2B1 and A2A1 electronic states have been calculated at 210 points. These two states correlate with a 2Pi(u) state at linearity and they interact by the Renner-Teller coupling and spin-orbit coupling. Using the ab initio potential-energy surfaces with our RENNER computer program system, the vibronic structure and relative intensities of the A2A1 --> X2B1 emission band system have been calculated in order to corroborate the experimental assignments.

Predicted rovibronic spectra of CH2+ and CD2+

We present simulations of the A2B1←X2A1 electronic band systems of CH2+ and CD2+ in absorption at 200 K. For each isotopomer we calculate the spectrum over the range from 5000 to 18000cm−1 for the purpose of assisting the experimental search of the spectrum in a cooled hollow-cathode discharge. We make use of our previously determined ab initio potential energy surfaces, dipole moment and transition moment surfaces in a calculation that includes the Renner–Teller effect and spin–orbit coupling. To complete the picture we also present simulations of the rotation and rotation–vibration spectra of CD2+.

Stark effect in the benzene dimer.

Ab initio calculations of the six-dimensional intermolecular potential have shown the benzene dimer to be an asymmetric top molecule at equilibrium with one benzene moiety forming the stem and the other a tilted cap in a T-shaped structure. Internal rotation of the cap about its C6 axis is essentially free; the barriers for cap tilting and for internal rotation of the stem about its C6 axis are hindered by successively higher barriers. In previous work we have validated these theoretical results using Fourier transform microwave spectroscopy in conjunction with dynamics calculations. We have also measured the Stark effect, and despite the fact that the equilibrium structure is that of an asymmetric top, the assigned transitions involving K = 0 exhibit a second-order Stark effect whereas those involving K = 1 exhibit a first-order Stark effect. This is typical for a symmetric-top molecule, but anomalous for an asymmetric-top molecule. We use symmetry arguments to explain how this asymmetric-top molecule can have a first-order Stark effect in certain states that have excitation of cap internal rotation. Cap internal rotation is essentially the twisting of the monomers relative to each other about the intermolecular axis, and such torsional motion occurs in other asymmetric top dimers such as benzene-CO and benzene-H2O. These latter dimers will also have levels that exhibit a first-order Stark effect, which we can explain using our symmetry arguments.