Prof. Per Jensen, Ph.D.

Molecular symmetry  

BUNKER AND JENSEN   Research on molecular symmetry focusses on the application of the molecular symmetry group whose elements consist of nuclear permutations with and without the inversion. A recent application has been to spherical top molecules such as CH4, SF6 and C60. The second edition of the book `Molecular Symmetry and Spectroscopy' has been written in collaboration with P. R. Bunker, and this was published by NRC RESEARCH PRESS in mid August 1998. The first edition, written by P. R. Bunker, was published by Academic Press in 1979. The preface and table of contents are available from the NRC Research Press Web Site.


Recent publications on molecular symmetry  

(111) Per Jensen and P. R. Bunker: The Symmetry of Molecules, prepared by invitation for "Encyclopedia of Chemical Physics and Physical Chemistry", (J. H. Moore and N. D. Spencer, Eds.), IOP Publishing, Bristol.

(107) Per Jensen and P. R. Bunker: Nuclear Spin Statistical Weights Revisited, Mol. Phys., 97, 821-824 (1999).

(105) P. R. Bunker and Per Jensen: Spherical top molecules and the molecular symmetry group, Mol. Phys., 97, 255-264 (1999).

(71) Per Jensen and P.R. Bunker: The Molecular Symmetry Group for Molecules in High Angular Momentum States, J. Mol. Spectrosc. 164, 315 (1994).


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The Formation of Fourfold Rovibrational Energy Level Clusters in Triatomic Molecules

It is now an established, experimentally verified fact that in the vibrational states of the H2Se molecule, at high J and Ka values the rotational energies form four-member groups of nearly degenerate levels, so-called energy clusters. Realistic quantum mechanical calculations have shown that the H2S and H2Te molecules exhibit similar effects. In recent years we have been concerned with the theoretical description of the energy clusters, mostly by variational calculations, i.e., calculations of the rotation-vibration energies by diagonalization of a matrix representation of the rotation-vibration Hamiltonian. The four-fold clusters were initially predicted by classical and semi-classical theory, and we have shown how these predictions are borne out by experiment and by quantum mechanical calculations. Analysis of rotation-vibration wavefunctions obtained from variational calculations provides a simple picture of the rotational motion in the cluster states: The molecule rotates around one of its two bonds in a clockwise or an anticlockwise manner. The two choices for the bond, and the two choices for the sense of the rotation provide a total of four equivalent situations corresponding to a four-fold energy cluster.

The energy level structure of a rigidly rotating H2130Te molecule. The term values are plotted relative to the highest term value for each J multiplet.


The rotational energy level structure in the vibrational ground state of the H2130Te molecule, calculated directly from the potential energy function of the molecule. The term values are plotted relative to the highest term value for each J multiplet. The calculated spacings are in good agreement with values derived from experiment.

Comparison of the two figures shows that when we allow the molecule to vibrate, its rotational energy structure changes drastically at high J: four-fold energy clusters are formed.

Recent Publications on Four-fold Energy Clusters

Per Jensen, G. Osmann, and I. N. Kozin: The Formation of Four-fold Rovibrational Energy Clusters in H2S, H2Se, and H2Te, in: "Advanced Series in Physical Chemistry", vol. 9, "Vibration-Rotational Spectroscopy and Molecular Dynamics" (D. Papousek, Ed., ISBN 981-02-1635-1), pp. 298-351, World Scientific Publishing Company, Singapore, 1997.

(99) P. C. Gomez, L. F. Pacios, and Per Jensen: Fourfold Clusters of Rovibrational Energies in H2Po Studied with an ab initio Potential Energy Function, J. Mol. Spectrosc. 186, 99 (1997).

(98) P. C. Gomez and Per Jensen: A Potential Energy Surface for the Electronic Ground State of H2Te Derived from Experiment, J. Mol. Spectrosc. 185, 282 (1997).

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The Renner Effect

The effect on the spectrum of electronic orbital and spin angular momentum in triatomic molecules is being investigated in collaboration with P. R. Bunker, W. P. Kraemer (Max Planck Institute of Astrophysics, Garching, Germany), R. J. Buenker (University of Wuppertal) and others. This is generally termed the Renner effect. We have developed a computer program with which we can calculate both the positions and intensities of the lines in a spectrum that arise from transitions between the two halves of a Renner state. Applications to free radicals and molecular ions are being undertaken using potential energy surfaces calculated by ab initio methods. We have predicted the electronic spectra of the NH2+ and CH2+ ions, and these predictions will be of assistance in their search.

For CH2+ it has been conjectured, on the basis of the interpretation of data obtained using the Coulomb explosion imaging (CEI) method, that there is a large nonadiabatic contribution to the low-lying wavefunctions beyond that coming from the Renner effect. Very recently, we have calculated the energies of the lowest excited electronic states and find, in agreement with results already in the literature, that the excited electronic states of CH2+ are at much too high an energy (greater than 6 eV) for such nonadiabatic interaction to be significant. To compare with the CEI results we calculate the Boltzmann averaged bending angle distribution using our previously calculated ab initio potential energy curves of the X,A pair of Renner interacting potentials, and make full allowance for the Renner effect in the calculation of the wavefunctions. This ab initio calculation leads to a distribution that is significant over a narrower range of bending angles than that obtained experimentally by the CEI method. Depending on the accuracy of the CEI distribution this could indicate an error in the ab initio potential energy surfaces. We have modified the shape of the X-state surface in order to approximately reproduce the CEI result, and the change we have to make is rather large. An experimental determination of some of the bending energy level separations for CH2+ would be a more definitive way of testing the shape of the potential surface.

The CH2 and HO2 molecules are subjects of further calculations.

Recent Publications on the Renner Effect

(108) G. Osmann, P. R. Bunker, W. P. Kraemer, and Per Jensen: Coulomb Explosion Imaging and the CH2+ Molecule, Chem. Phys. Lett., 309, 299-306 (1999).

(105) G. Osmann, P. R. Bunker, Per Jensen, R. J. Buenker, J.-P. Gu, and G. Hirsch: A Theoretical Investigation of the Renner Interactions and Magnetic Dipole Transitions in the A - X Electronic Band System of HO2, J. Mol. Spectrosc., 197, 262-274 (1999).

(103) J.-P. Gu, G. Hirsch, R. J. Buenker, M. Brumm, G. Osmann, P. R. Bunker and P. Jensen: A theoretical study of the absorption spectrum of singlet CH2, J. Mol. Struct., in press.

(101) G. Osmann, P. R. Bunker, P. Jensen and W. P. Kraemer: An Ab Initio Study of the NH2+ Absorption Spectrum. J. Mol. Spectrosc. 186, 319 (1997)

(100) G. Osmann, P. R. Bunker, P. Jensen and W. P. Kraemer: A Theoretical Calculation of the Absorption Spectrum of CH2+. Chem. Phys. 225, 33 (1997).

(85) J.-P. Gu, R. J. Buenker, G. Hirsch, P. Jensen and P. R. Bunker: An ab initio calculation of the BH2- rovibronic energies: a very small singlet-triplet splitting. J. Mol. Spectrosc. 178, 172 (1996).

(79) M. Kolbuszewski, P. R. Bunker, W. P. Kraemer, G. Osmann and P. Jensen: An ab initio calculation of the rovibronic energies of the BH2 molecule. Mol. Phys. 88, 105 (1996).

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Quasibound States

We have implemented the stabilization method of Mandelshtam, Taylor and co-workers to calculate the quasibound states of a triatomic molecule. So far, the resulting computer program has been applied to 1B2 ozone and to H2O++ in its electronic ground state.

Recent Publications on Quasibound States

(106) P. R. Bunker, O. Bludský, Per Jensen, S. S. Wesolowski, T. J. Van Huis, Y. Yamaguchi, and H. F. Schaefer III: The H2O++ Ground State Potential Energy Surface, J. Mol. Spectrosc., in press.

(95) O. Bludský and Per Jensen: The Calculation of the Bound and Quasibound Vibrational States of Ozone in its 1B2 Electronic State, Mol. Phys. 91, 653 (1997).

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