E. H. T. Olthof

STRUCTURE, INTERNAL MOBILITY, AND SPECTRUM OF THE AMMONIA DIMER : CALCULATION OF THE VIBRATION-ROTATION-TUNNELING STATES

We have obtained a potential for (NH3)2 by calculating the six‐dimensional vibra‐ tion–rotation‐tunneling (VRT) states from a model potential with some variable parameters, and adjusting some calculated transition frequencies to the observed far‐infrared spectrum. The equilibrium geometry is strongly bent away from a linear hydrogen bonded structure. Equivalent minima with the proton donor and acceptor interchanged are separated by a barrier of only 7 cm−1. The barriers to rotation of the monomers about their C3 axes are much higher. The VRT levels from this potential agree to about 0.25 cm−1 with all far‐infrared frequencies of (NH3)2 observed for K=0, ‖K‖=1, and ‖K‖=2 and for all the symmetry species: Ai=ortho–ortho, Ei=para–para, and G=ortho–para. Moreover, the dipole moments and the nuclear quadrupole splittings agree well with the values that are observed for the G states. The potential has been explicitly transformed to the center‐of‐mass coordinates of (ND3)2 and used to study the effects of the de...

Tunneling dynamics, symmetry, and far-infrared spectrum of the rotating water trimer. II. Calculations and experiments

With the Hamiltonian derived in the preceding paper and the ab initio potentials of T. Burgi, S. Graf, S. Leutwyler, and W. Klopper [J. Chem. Phys. 103, 1077 (1995)] and of J. G. C. M. van Duijneveldt‐van de Rijdt and F. B. van Duijneveldt [Chem. Phys. Lett. 237, 560 (1995)], we calculate the pseudo‐rotation tunneling levels in a rotating water trimer. The internal motions are treated by a three‐dimensional discrete variable representation and the Coriolis coupling with the overall rotation is included. Also the effects of donor tunneling are included, by introducing semi‐empirical coupling matrix elements. New experimental data are presented for the c‐type band at 87.1 cm−1 in (H2O)3, which show that specific levels in the donor tunneling quartets of this band are further split into doublets. With the results of our quantitative calculations and the model of the preceding paper we can understand the mechanisms of all the splittings observed in the earlier high‐resolution spectra of (H2O)3 and (D2O)3, as ...

Tunneling dynamics, symmetry, and far‐infrared spectrum of the rotating water trimer. I. Hamiltonian and qualitative model

A Hamiltonian is derived for the rotating water trimer with three internal motions—the rotations of the monomers about their hydrogen bonds. We obtain an expression of the kinetic energy operator, which is a non‐trivial extension of earlier heuristic forms used for the non‐rotating trimer. The Coriolis coupling operator between the single‐axis monomer angular momenta and the overall trimer rotation is given for the first time. To analyze the effects of the tunneling and Coriolis splittings on the energy levels of the trimer, we introduced a qualitative model for the pseudo‐rotation and donor tunneling. By perturbation theory and application of the permutation‐inversion groups G6 and G48 we obtain algebraic expressions for the splittings due to pseudo‐rotation and donor tunneling, respectively. The pseudo‐rotation does not produce any internal angular momentum and does not yield first order Coriolis splitting, but in second order the Coriolis coupling lifts various degeneracies and gives rise to observable...

VIBRATION AND ROTATION OF CO IN C60 AND PREDICTED INFRARED SPECTRUM

We present the Hamiltonian for the vibrations and rotations of CO inside a freely rotating or fixed C60 molecule and we calculate its eigenstates from an atom–atom model potential. The ensuing level structure can be understood in terms of three basic characteristics. (i) Simultaneous rotations of CO and its position vector R, which give rise to a rotational structure similar to that of free CO. The effective rotational constants differ considerably, however. (ii) Splittings of the levels by the icosahedral field of C60 which perturb the regular rotational structure, because they are of the same order of magnitude as the rotational spacings. (iii) Large frequencies associated with the (nearly harmonic) vibrations of CO against the hard walls of the C60 cage: 209 cm−1 for the radial excitation and 162 cm−1 for the twofold degenerate libration. These vibrations give a rovibrational level structure similar to that of a linear triatomic molecule, the radial excitation resembles a bond stretch (Σ) state, the li...

The nature of monomer inversion in the ammonia dimer

A model is presented for calculating the splittings due to umbrella inversion of the monomers in (NH3)2. Input to the model are the six‐dimensional dimer bound state wave functions for rigid monomers, calculated previously [E. H. T. Olthof, A. van der Avoird, and P. E. S. Wormer, J. Chem. Phys. 101, 8430 (1994)]. This model is based on first‐order (quasi) degenerate perturbation theory and adaptation of the wave functions to the group chain G36⊆G72⊆G144. The umbrella inversion splittings depend sensitively on the intermolecular potential from which the bound state wave functions are obtained. A complete interpretation of the observed splitting pattern [J. G. Loeser, C. A. Schmuttenmaer, R. C. Cohen, M. J. Elrod, D. W. Steyert, R. J. Saykally, R. E. Bumgarner, and G. A. Blake, J. Chem. Phys. 97, 4727 (1992)] and quantitative agreement with the measured splittings, which range over three orders of magnitude, are obtained from the potential that reproduces the far‐infrared spectrum of (NH3)2 and the dipole m...

Is (NH3)2 hydrogen bonded

Abstract Vibration-rotation-tunneling (VRT) splittings have been computed for the dimer (NH 3 ) 2 by the use of four different model potentials. The six-dimensional nuclear motion problem is solved variationally in a symmetry adapted basis consisting of analytic radial functions and rigid rotor functions depending on the five internal angles, as well as on the three overall rotation angles. Two of the potentials are designed such that they have no barrier for interchange tunneling and the other two potentials have barriers of 31.1 and 24.4 cm −1 , respectively. The top of the barrier corresponds to a cyclic structure and the two equivalent minima on either side of the barrier to nearly linear hydrogen bonds. Energy splittings, dipole moments, nuclear quadrupole splittings, and the amount of quenching of the monomer umbrella inversions are computed and compared with the available experimental numbers. The potential that gives best agreement with the observed quantities has an equilibrium hydrogen bonded structure close to linear, but a VRT-averaged ground state structure that is nearly cyclic.

Stark effect and dipole moments of the ammonia dimer in different vibration–rotation–tunneling states

In this paper we present Stark measurements on the G:K=−1 vibration–rotation–tunneling (VRT) transition, band origin 747.2 GHz, of the ammonia dimer. The observed splitting pattern and selection rules can be explained by considering the G36 and G144 symmetries of the inversion states involved, and almost complete mixing of these states by the applied electric field. The absolute values of the electric dipole moments of the ground and excited state are determined to be 0.763(15) and 0.365(10) D, respectively. From the theoretical analysis and the observed selection rules it is possible to establish that the dipole moments of the two interchange states must have opposite sign. The theoretical calculations are in good agreement with the experimental results: The calculated dipole moments are −0.74 D for the lower and +0.35 D for the higher state. Our results, in combination with the earlier dipole measurements on the G:K=0 ground state and the G:K=1 transition with band origin 486.8 GHz, confirm that the amm...

The Nuclear-Quadrupole Coupling-Constants and the Structure of the Para-Para Ammonia Dimer

Expressions are derived for the nuclear quadrupole splittings in the E3 and E4 (para–para) states of (NH3)2 and it is shown that these can be matched with the standard expressions for rigid rotors with two identical quadrupolar nuclei. The matching is exact only when the off‐diagonal Coriolis coupling is neglected. However, the selection rules for rotational transitions are just opposite to those for the rigid rotor. Hyperfine splittings are measured for the J=2←1 transitions in the E3 and E4 states with ‖K‖=1; the quadrupole coupling constants χaa=0.1509(83) MHz and χbb−χcc=2.8365(83) MHz are extracted from these measurements by the use of the above mentioned correspondence with the rigid rotor expressions. The corresponding results are also calculated, with and without the Coriolis coupling, from the six‐dimensional vibration–rotation–tunneling (VRT) wave functions of (NH3)2, which were previously obtained by Olthof et al. [E.H.T. Olthof, A. van der Avoird, and P.E.S. Wormer, J. Chem. Phys. 101, 8430 (1...