https://orcid.org/0000-0001-8803-3568
Abstract
Lutoslaw Wolniewicz has spent two or three months each summer from 1976 to 1994 as guest of Kurt Dressler in Zurich to use the Computer Centre of the ETH for ab-initio calculations of rovibronic energies and transition moments in the hydrogen molecule.
GRAPHICAL ABSTRACT
How did this unlikely (but very fortunate) collaboration between a theoretician in Torun, Poland, and an experimentalist in Zurich, Switzerland, come about?
Lutoslaw Wolniewicz and I first met personally in September 1974 at a Symposium on Perspectives in Spectroscopy, organised by the NRC, the National Research Council of Canada, in the Mont Tremblant Lodge (north of Montreal), in Honour of the 70th Birthday of Dr. Gerhard Herzberg, Director of NRC’s Spectroscopy Laboratory in Ottawa, world famous among molecular spectroscopists for his textbooks on atomic and molecular spectroscopy and for his research, honoured in 1971 with the Nobel Prize in Chemistry.
During the opening ceremonies of the Conference, the President of NRC announced
Council’s intent to set up an Institute of Astrophysics within the National Research Council. In recognition of Dr. Herzberg’s outstanding scientific contributions, his interest in and contributions to astrophysics, and his distinguished role as a scientist and scientific leader at NRC, the new Institute is to be named The Herzberg Astrophysics Institute.
I knew Dr. Herzberg because he was a friend of my doctoral advisor, Prof. Ernst Miescher at the University of Basel where I did my thesis research in vacuum UV molecular spectroscopy. Herzberg used to visit Miescher, and after obtaining my degree in 1955 I was awarded a Postdoctoral Fellowship in Herzberg’s Laboratory in Ottawa.
At NRC I collaborated closely with Dr. Donald Ramsay who then helped me find my next temporary position, 1957–1959, at NBS, the U.S. National Bureau of Standards, Washington D.C. This was the Free Radicals Research Program set up to study low-temperature matrix-isolated hydrogen atoms, to see whether this might lead to a more powerful rocket fuel than the ones used rather unsuccessfully during those early years of the U.S. space effort. My contribution involved vacuum UV spectroscopy.
In Washington I received a call from Princeton University to help with the design of a high-resolution vacuum UV spectrometer for inclusion in an Orbiting Astronomical Observatory. The Director of this project and of Princeton’s Astronomy Department, Prof. Lyman Spitzer, had asked Dr. Herzberg to recommend to him an experimental spectroscopist with the required vacuum UV experience. The aim of the instrument was to measure the absorption lines of interstellar hydrogen molecules in the far-UV continuum light of distant very hot stars.
While at Princeton, 1959–1968, I maintained contact with Prof. Miescher in Basel. I had been his last doctoral student who did not work on the spectrum of the NO molecule. Now I started to collaborate with Miescher on NO. I visited him twice for extended periods in order to analyse some of the vacuum UV absorption spectra of the NO molecule which he had photographed in very high resolution with Herzberg’s 10-meter vacuum spectrograph in Ottawa.
In 1956 Gerhard Herzberg, Albin Lagerquist (Stockholm) and Ernst Miescher had published an analysis of the rovibronic structure of two electronic excited states of NO, perturbed by an avoided crossing of their potential energy curves. This was the first comprehensive description and analysis of a so-called homogeneous perturbation, attributed to diabatic electronic states characterised by potential curves which cross each other.
In 1968 I followed a call into a professorship at the ETH Zurich (instigated by Miescher). I continued to analyze perturbed excited states of NO and of N2. I became interested in investigating the perturbed excited states of H2.
I knew the 1969 paper by Kolos and Wolniewicz [Citation1] on the EF double-minimum potential curve in molecular hydrogen. I wanted to see whether the pattern of vibrational energy levels above the potential barrier between the two minima could be represented in an electronic diabatic basis of an E and an F state with potential curves which cross each other, instead of using an adiabatic electronic basis with a double-minimum potential curve. That required an extension of the computations by Kolos and Wolniewicz to include higher electronic states and to include non-adiabatic effects.
Therefore I was delighted to learn that Lutoslaw was looking for opportunities to work with more powerful computers than available to him at Torun. Luckily my professorship at ETH Zurich was vested with a sufficiently comfortable yearly budget that I could afford to invite Lutoslaw to spend two or three months each summer in Zurich, where he could use the powerful computer centre of ETH.
He used those opportunities with amazing efficiency. He considered extended lunches a waste of time. During his first stay in Zurich, in June 1976, the nobelist Prof. Robert S. Mulliken, whom Lutoslaw knew from his time at the University of Chicago, made a stop-over in Zurich on his way from Chicago to Lindau, on the German shore of Lake Konstanz, to attend a meeting of Nobel Laureates in chemistry. My wife had him for dinner in our home together with Lutoslaw before I drove Mulliken to Lindau next day. I had met him years before while visiting Dr. P. G. Wilkinson’s vacuum UV spectroscopy laboratory in Chicago. My friend Donald Ramsay in Ottawa was a great fan of Mulliken and in 1975 he had republished a collection of his important papers in a book entitled Selected Papers of Robert S. Mulliken.
The work on the excited states of the hydrogen molecule involved the numerical solution of the coupled equations of non-adiabatic theory. Lutoslaw transformed the ab initio clamped-nuclei (Born–Oppenheimer) potential curves of the adiabatic electronic states of H2 into a basis of electronically coupled diabatic potentials. But these latter ones did not look like pretty potential curves which nicely crossed each other.
That led to the insight that diabatic states with crossing potential curves were only then a convenient basis when the electronic energy gap at an avoided crossing did not much exceed the vibrational energy spacings. That was the case in those avoided crossings encountered in the NO and N2 molecules. But in the case of the EF and GK states of H2 that energy gap is very much larger than the vibrational spacings. Thus the adiabatic approach used by Kolos and Wolniewicz yields a much better first approximation to the observed pattern of vibrational energy levels.
Our first joint publication in 1977 [Citation2] presented the vibrational structures associated with the double-minimum potential curves of the first two excited 1∑g+ states, EF and GK, of H2, HD, and D2 in the adiabatic approximation and up to the dissociation limit. Lutoslaw computed the clamped-nuclei electronic energies with higher accuracy (70-term wavefunctions) and over larger R ranges (1 a0 < R < 15 a0) than previously available. Less accurate results over the same large R range were also presented for the 3rd, 4th and 5th excited 1∑g+ states. The diagonal corrections for nuclear motion were computed for the GK state and adopted from [Citation1] for the EF state.
Comparison of the calculated vibronic (vibrational-electronic) term values with experimental data made it immediately possible to assign a large number of irregular observed levels as vibrational states of the adiabatic EF and GK potential curves up to the dissociation limit. Previously most of these observed levels had falsely been interpreted as a long string of many separate hypothetical electronic states.
This first publication was followed over the years by 20 joint publications presenting the results of calculations of up to 9 non-adiabatically coupled electronic states of singlet gerade symmetry and of 4 electronic states of singlet ungerade symmetry. Many of the calculations were made for several of the isotopomers H2, D2, T2, and of their combinations HD, HT, DT, and they included transition probabilities, and the non-adiabatic coupling of excited states with the ground state which leads to non-radiative de-excitation (‘predissociation’).
The ab-initio calculations by Wolniewicz also stimulated more than 20 additional publications by myself and by other authors. E.g. the calculated outer wells in the double-minimum potential curves of the Rydberg states (2s) E 1∑g+, (3s) H 1∑g+, and (3dπ) I 1∏g accommodate local rovibronic structures which had not yet been identified spectroscopically, or only incompletely so. New spectroscopic studies in Herzberg’s laboratory in Ottawa and in Ubachs’ laboratory in Amsterdam led to the identification of these energy levels in the E,F [Citation3], H,Ħ [Citation4], and I,I’ states [Citation5].
The next to last of Lutoslaw’s papers stemming from our collaboration [Citation6], has presented the most accurate computation of ground state energy levels, including relativistic, radiative and non-adiabatic corrections in H2, HD, D2, HT, DT, T2, and comparison with experimental spectroscopic measurements, a momentous paper.
Our last joint paper [Citation7] has described the most complete ab-initio calculations on the first five excited 1∑g+ states over a wide range of internuclear distances, including adiabatic potential curves, non-adiabatic coupling functions, and some relativistic corrections. Some of the published experimental data on the fourth excited 1∑g+ state of H2 and all of those on the fifth one were shown to be wrong.
The data presented in this paper were subsequently used by my student S. Yu to calculate the rovibronic structures which arise from the simultaneous radial and angular couplings among the lowest nine excited 1∑g+ + 1∏g + 1Δg states in H2, D2, and T2. These were compared with spectroscopic measurements in all three isotopomers. Some spectroscopic assignments were thus shown to be spurious and some new assignments could be made [Citation8].
When I visited Lutoslaw with my wife in Poland after my retirement he spoiled us wonderfully, taking us in his car to show us Torun, Gdansk, Malbork, and other sights. Lutoslaw’s yearly presence among us at ETH Zurich, his modest character, and his momentous productivity have been inspiring, interesting, and fruitful for myself and my students. I am immensely grateful for having met him personally in 1974 and for having succeeded in attracting him to work in Zurich so extensively.
Acknowledgement
I acknowledge with thanks helpful input into these remembrances by Frédéric Merkt of ETH Zurich.
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No potential conflict of interest was reported by the author(s).
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References
- W. Kolos and L. Wolniewicz, J. Chem. Phys. 50, 3228 (1969). doi:10.1063/1.1671545.
- L. Wolniewicz and K. Dressler, J. Mol. Spectrosc. 67, 416 (1977). doi:10.1016/0022-2852(77)90050-9.
- P. Senn, P. Quadrelli, K. Dressler, and G. Herzberg, J. Chem. Phys. 83, 962 (1985). doi:10.1063/1.449423.
- E. Reinhold, W. Hogervorst, and W. Ubachs, Phys. Rev. Lett. 78, 2543 (1997). doi:10.1103/PhysRevLett.78.2543.
- E. Reinhold, A. de Lange, W. Hogervorst, and W. Ubachs, J. Chem. Phys. 109, 9772 (1998); A. de Lange, E. Reinhold, W. Hogervorst, and W. Ubachs, Can. J. Phys. 78 567 (2000).
- L. Wolniewicz, J. Chem. Phys. 99, 1851 (1993). doi:10.1063/1.465303.
- L. Wolniewicz and K. Dressler, J. Chem. Phys. 100, 444 (1994). doi:10.1063/1.466957.
- S. Yu and K. Dressler, J. Chem. Phys. 101, 7692 (1994). doi:10.1063/1.468263.