Research Accomplishments of Kevin Lehmann

1. Provided the first correct description of the nature of the reaction between H2 and H2+, which is of fundamental importance in chemical dynamics and Astrochemistry. (1)

2. Performed one of the first Resonance Enhanced, Multiphoton Ionization Studies of a diatomic molecule, leading the discovery of several new electronic states of I2. (2)

3. Ph.D. thesis work was the first systematic attempt to use high resolution overtone spectroscopy to study the nature of intramolecular vibrational energy redistribution (IVR). This work demonstrated that rapid IVR is not universal in small polyatomic molecules, even at an excitation of ~50% of a C-H bond dissociation energy. This work also set a standard for the careful comparison of polyatomic vibrational spectra at high energy with theoretical predictions based upon variational calculations of the ro-vibrational dynamics. (4-8,10,14) These studies where later extended by Lehmann to high energy using novel spectroscopic methods of increasing sensitivity, and has most recently allowed the study of vibrational states of HCN with ~75% of the dissociation energy (137). Even at this energy, which is twice the barrier for the HCN <-> HNC chemical isomerization, the molecule does not isomerizes, despite the fact that statistical reaction rate theory predicts sub-ps isomerization.

4. Demonstrated the formal equivalence of Harmonically Coupled, Anharmonic Oscillator Model of Mark Child and others with the older Darling-Dennison resonance model. This work demonstrated how local mode vibrational dynamics arises from a normal mode treatment of the anharmonic oscillator problem. (9). The work was then extended to show how a Darling-Dennison type resonance model can be constructed for any molecule (18, 33). Later work demonstrated how the local ro-vibrational limit naturally arises when the local mode tunneling rate becomes longer than the rotational precession rate and how this leads to a further reduction in tunneling rates and the transformation of the spectrum into four fold degenerate clusters of levels (43, 54). These spectral structures were later discovered in overtone spectra of H2S and other molecules and physically interpreted in terms of the model that Lehmann developed. The Child local mode model was extended to treat the interaction of two degenerate bending modes (55), such as found in C2H2, anticipating the evolution of this system of local mode dynamics as well. This work has been recently been greatly extended by Robert Field and co-workers.

5. Developed the highly sensitive and state specific method of Microwave detected, Microwave-Optical double resonance (MD-MODR) (13). This method was used for an extensive study of the entire overtone spectrum of NH3 (13, 17, 27, 29). This spectrum had been studied by several generations of spectroscopists but there were essentially no firm assignments before Lehmann's work. Double resonance was used to make firm assignments and then complete band assignments were made by spectral predictions, combination-differences, and the temperature dependence of absorption spectra. The very complex and highly perturbed vibrational structure was fit to an effective Hamiltonian that included four different anharmonic resonances involving all of the normal modes of this molecule. From this effective Hamiltonian, with spectroscopic parameters determined from the spectrum, the detailed IVR for the first ~ 1 ps following overtone excitation could be predicted. This was the first molecule with a complex set of interacting resonances that had its intramolecular dynamics determined from molecular spectroscopy. This work influenced later work on the multiple resonances of acetylene, and the development of similar IR-IR double resonance methods by Tom Rizzo and others. This method was also applied to the UV spectrum of ammonia, providing an improved excited state structure and dissociation lifetime as a function of vibrational and rotational quantum numbers (81, 82).

6. The MD-MODR method was used for the first systematic study of the statistical character of the spectrum of NO2 (16, 20, 26). This spectrum was long known for its hopeless complexity, but the modern theories of `Quantum Chaos' provided a novel approach to asking if the complexity was intrinsic or only a result of our not knowing the nature of the best quantum numbers to use in analysis of the spectrum. This work demonstrated that the then existing theories, based upon Random Matrix Models, were too simplistic and that the NO2 ro-vibronic spectrum had some but not all of the expected characteristics of a `chaotic' spectrum. Modeling of the spectrum required development of a novel statistical ensemble (22, 35) that incorporated more of the physics of the problem. Also, realistic treatment of the effect of finite signal to noise and precision had to be incorporated into the statistical tests used on spectra (23). This work on the ro-vibronic chaos in NO2 has been greatly extended by a long series of papers by Remi Jost and coworkers.

7. The determination of the bending potential of HCP over a then unprecedented range of bending angle by use of dispersed emission spectroscopy (15). This work set the stage for later Stimulated Emission Pumping experiments performed by Robert Field and collaborators (38). This SEP work was greatly added by a comprehensive study of the electronic spectrum of HCP in a cold jet (Trot ~ 1 K) performed by Mason and Lehmann. In particular, this work resolved the assignment of the high energy region of the spectrum and the nature of the C state, which allowed access to much higher vibrational levels in the ground state in SEP experiments. This work also provided a precise value for the ground state dissociation energy of HCP (63), for which no previous experimental value was available. A novel mechanism for hyperfine induced quantum beats was discovered and used to measure triplet character for excited states (63).

8. A series of studies were made to provide, for the first time, accurate systematic overtone band intensities of a polyatomic molecule (21, 24, 30, 32, 34). Theoretical modeling showed that the data could not practically be used to determine polyatomic dipole moment functions, but did provide an exceptionally sensitive test of the quality of ab initio calculations (42). This work let to the demonstration that high overtone intensities were far more sensitive to the slope on the inner wall of the X-H bond potential than the dipole moment function (40).

9. In collaboration with G. Scoles and others, Lehmann completed a series of sub-Doppler, Molecular Beam Spectroscopy studies of IVR in medium to large molecules (37, 39,44-47, 49, 59, 60, 68-72, 75, 77, 78, 80, 83, 90, 91, 97, 98, 116. 130). This work built upon previous and concurrent studies by the groups of Perry and Nesbitt, but extended beyond it in terms of spectral resolution, sensitivity, and range of vibrational energy studied. This work developed MW-IR and IR-IR double resonance spectroscopic methods to assign spectra that were too highly fractionated for assignment, even at ~ 5 MHz linewidth found in the molecular beam spectra, and provided the first sub-Doppler spectra in the second C-H overtone region (68, 71). Resonance build-up cavities were introduced to greatly increase the one beam optical intensity and improving the lineshape. This work provided the first demonstration of rigorously homogeneous Lorenztian lineshapes due to IVR, as expected in the large molecule statistical limit (46). The work unequivocally demonstrated that density of vibrational states has little to no effect on the rate of IVR, except that a minimum density is needed to provide a quasi continuous `bath' for relation on the natural decay time scale of the chromophore. The work demonstrated that delocalized combination states can relax more slowly than nearly isoenergetic pure overtone states (68), which is the opposite of what had been the accepted wisdom based upon models of small molecules with only strongly interacting modes. Experiments on the first overtone band of benzene have demonstrated that IVR dynamics can be richly hierarchical, stretching over four orders of magnitude in time and still not reaching a truly statistical final point (90, 116). A unique ‘two cavity’ IR-IR double resonance instrument was built (117), providing spectra with ~15 MHz linewidth spectra of molecules with ~2 eV of vibrational energy. This instrument was used to investigate isomer tunneling in acetylene about the barrier for formation of vinylidene, establishing that the rate of this process is at least four orders of magnitude slower than the RRKM prediction of this rate (112).

10. The IVR work was supported by a series of developments of theoretical methods for the analysis of spectra. The Molecular Symmetry group for three equivalent rotors was worked out (41), and a general program for generating Molecular Symmetry groups written. A vastly superior numerical algorithm for the Lawrence-Knight (L-K) deconvolution procedure was presented, which included for the first time error estimates for the resulting molecular parameters (45). The L-K deconvolution allows one to determine the coupling matrix elements between the optically excited state and the background of other ro-vibrational states at the same energy. It was demonstrated that high order anharmonic interactions could be quantitatively predicted from chains of cubic and quartic near resonances. (52). A more computationally efficient method to calculate vibrational density of states in nonseparable systems was developed. (61).

11. Lehmann was the first to exploit the method of Cavity Ring Down Spectroscopy (CRDS) to make quantitative measurements of absorption spectra, including the first treatment for the effects of finite laser resolution (65, 79, 84). This work was also the first to provide a correct analysis of the fundamental noise sources in this method and how it determines ultimate sensitivity limits. The first quantitative studies of spectral lineshapes using CRDS, including line mixing effects, were also demonstrated and used to study collisional transfer of optical coherence (85, 96). The first general theory for the CRDS technique, properly including optical interference and dispersion effects was published (87, 94), demonstrating that limitations of the incoherent `photon bullet' model previously used. The first experiments extending CRDS to continuous wave excitation sources was performed in Lehmann's laboratory (122, 133) and the advantages of these methods first theoretically derived, leading to a US. Patent #5,528,040. The first sub-Doppler CRDS experimental method was developed in collaboration with NIST (110). A novel cavity based upon Brewster Angle roof prisms has been designed and demonstrated, allowing this high sensitivity method to be applied over a broad spectral range in a single cell (103). The first commercial CRDS based analytical instrument was developed based upon the Ph.D. thesis work of John Dudek (Princeton, 2000). A Fiber-optic loop version of CRDS was developed and used for chemical sensing (135), detection in strain (140), and single cells (143).

12. Lehmann joined with Scoles in the ongoing spectroscopic study of molecules solvated in nanometer scale He droplets. They have provided a spectroscopic analysis of the quartet state of Na3, which is bound by dispersion interactions in the ground state and undergoes a spin flip and formation of a chemical bond upon electronic excitation (86, 89). The formation of a Na-He exciplex upon electronic excitation of a Na atom above the droplet surface has been demonstrated and its formation time resolved (92, 113, 114). In this work, a novel low energy barrier, produced by the need to partially uncouple the spin-orbit coupling to form a favorable Na-He interaction, has been inferred and points the way to formation of a range of chemically highly metastable species. Other time resolved spectroscopic studies of atomic Mg (107), Al (108), K2 (123), Na3 and K3 (126) have revealed novel dynamical processes in this solvent. A bolometer based He droplet machine has been built and used for the first study CH overtone spectra, of a number of terminal acetylene compounds, inside liquid helium (115). This work has demonstrated that intramolecular IVR rates are at most weakly affected when molecules are dissolved in liquid He. This work also suggested that the lineshapes of ro-vibrational transitions (~ 1 GHz in width) are inhomogeneous. Studies of the microwave pure rotational spectra of HCCCN (99, 109) have demonstrated that the homogeneous width of transitions is ~ 10 MHz, but that the inhomogeneous broadening mechanism is dynamic. The breakdown of the adiabatic separation of rotation and helium motion was demonstrated experimentally for the case of the light rotors HCN and DCN (111). A study of spectrum of benzene and its dimers in helium droplets has revealed an unusually high increase in the effective moments of inertia and also that the helium prevents the formation of an excimer in the excited state of the dimer, which occurs in a few psec for the gas phase dimer (141).

13. Lehmann has had several notable theoretical accomplishments in the new field of helium nanodroplet spectroscopy. He developed a theory for the motion of solute molecules and ions in liquid He droplets (100, 101, 118) that has provided a framework for the interpretation of He droplet spectra taken at Princeton and other laboratories. He has developed a superfluid hydrodynamic model that quantitatively reproduces the observed large increases in effective moments of inertia of molecules dissolved in He (104, 129). This theory has also been applied to the effective mass of alkali cations in helium and found to be in quantitative agreement with Monte-Carlo calculations (127). A model was developed that for the first time reproduced the enormous effective centrifugal distortion constants of molecules in liquid helium (120). This work demonstrated that this arises not from classical centrifugal effects but due to a twist boundary condition that was earlier discussed, in the context of the “rotating bucket experiment” by A. Leggett. Lehmann provided theoretical estimates for the formation and decay of general, curved vortices in helium nanodroplets (134). This work demonstrated the importance of angular momentum conservation constraints, which had been neglected in previous discussions. He also provided a thorough study of the microcanonical thermodynamic properties (including angular momentum conservation) for helium droplets (132). This work let to the surprising result that in the rotational temperature of a molecule dissolved in a droplet is not the same as that of the droplet even when they are in equilibrium as a combined microcanonical-angular momentum conserving ensemble (136). The derived helium droplet thermodynamic functions allowed Lehmann to study the evaporative cooling of droplets including angular momentum constraints (139). This recent work has demonstrated that the droplets cool to essentially the same temperature as previously predicted (ignoring angular momentum constraints) and observed experimentally, but that the energy and angular momentum of the droplets is one to two orders of magnitude higher than for a canonical ensemble at the same temperature.

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