We have been developing EPR-lineshape and time-resolved Echo Envelope Modulation theory, using accurate modeling of spin- and motional dynamics, for several years (1987-1999).
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We have started for several years ago with studying theoretically and
experimentally, chemical reorganizations that can be considered
as site-exchange processes and we treated complicated systems, including
full anisotropy of the magnetic interactions with respect to motional effects
on the EPR lineshapes.
Later, the classical stepless-rotor model of motion was studied thoroughly. In this model, motion is treated in greater detail than in the site model, including all possible intermediate configurations of the system. Currently, quantum effects of the motion, from free rotating to strongly hindered methyl fragments, on the EPR lineshape and ESEEM are under careful consideration.
Regarding the classical stepless-rotor model , our method treats the problem as isotropic, one-dimensional diffusion in a periodic potential with a certain barrier height, as one of the adjustable variables. By the nonperturbative Liouville formalism employed we were able to account even for both the more widely used limiting cases in this field, i.e. site-exchange and stepless diffusion. The conditions for the validity of these two limiting cases were clearly defined in the light of this general theory. In addition, there were found intermediate cases where neither site-exchange nor stepless diffusion was adequately describing the motion of the system. Furthermore, some interesting empirical macroscopic parameters, like the activation energy and the pre-exponential factor used in the Arrhenius law, were related to more fundamental, microscopic physical quantities by this investigation. We were thus able to relate the temperature dependence of the kinetic constants of methyl rotation to the potential barrier and the friction coefficient of the torsional rotation for the C3-symmetry rotor.
Further, connections of the kinetic constants to molecular microscopic quantities is worth to be investigated. Regarding these queries, we refer to an interesting dynamics behavior of the beta-proton -CH3 rotor and beta-deuteron -CD3 methyl rotors with respect to temperature. The most recent, low temperature study of irradiated methyl malonic acid , exhibits different activation energies than the potential barrier of the hindered rotation of these rotors. In addition to that, the activation energies were different for the proton and deuteron rotors, in contrast to previously studied high-temperature diffusional case .
The progress on Electron Spin Echo Envelope Modulation (ESEEM) theory can be summarized as follows: The two-pulse, primary echo was initially simulated for different systems by using a totally new nonperturbative theory. In particular, an elementary study of motional effects on the echo modulation will be mentioned here, demonstrating the applicability of this method to study a vast range of motional rates in an interval of several orders of magnitude. Recently, a novel effect of motion leading to ESEEM signal in systems containing isotropic-proton methyl rotors, based on the mixing of the nuclear spin states by torsional motion, has been predicted theoretically . Several systems, some of them previously studied by EPR lineshape simulations, are scheduled to be tested in order verify experimentally the prediction of this theory. Due to the high frequency components involved here, this method is limited by the contemporary instrumental development. However, by choosing appropriate systems one can register the tunneling frequency directly, giving this method great applicability. Normally, the tunneling frequency is obtained indirectly, involving complicated experimental setups.
The motion of the methyl rotors has been found to be important in understanding the experimental EPR lineshape, ESEEM and ENDOR properties in solid state. For low temperatures it is probably one of the dominant relaxation mechanisms still present, while other types of motion are practically stopped. This is due primarily to the possibility of quantum tunneling. At higher temperatures, equally important for the motion of the methyl rotor can also be its coupling to the phononic degrees of freedom in the solid, leading to random modulation of the rotary motion. We have incorporated this last motion, in a simplified way, on the top of a pure quantum-coherent tunneling of the rotors, with the additional novelty of treating the actual degree of freedom for intramolecular rotation explicitly in the Hamiltonian. The contemporary literature treatments are in contrast based on a kind of effective, pure-spin Hamiltonian, incorporating the effect of motion as a parameter, in a way that reminds of the Heisenberg-exchange splitting.
A totally new project, in cooperation with Prof. Einar Sagsuen in Oslo
University has started during 1998. It concerns biological application
of recent and new theory of tunneling methyl-proton rotors in structural
and dynamics investigation of irradiated genetic material, part of the
DNA helix . It seems for the moment that a previously unknown in literature
analytic expression for the tunneling frequency of beta-proton methyl rotors
could be derived and is presently controlled by comparison to literature.
Except from the theoretical significance of this invention, it is possible
that simplification of the calculation of the tunneling frequency, which
was earlier obtained by numerical computations, can have some impact in
As a first application of this theory the effects of exchange on EPR lineshapes for anisotropic spin systems have been studied in detail and compared with appropriate experiments.
We have recently started to study the effects of dynamics on ESEEM signals.
A new research project for including the effects of hindered rotation to ESEEM is under development.
Basic theoretical treatment of pulsed ENDOR has also been initiated.
The resolution and the sensitivity of detection improves
by pulsed methods
comparison to conventional CW techniques. Furthermore, the accessible range
of observable dynamics rates improves dramatically.
Recent experimental indications of correlation between chemical kinetics and motional dynamics are currently under investigation. Conventional relaxation and exchange approximations in theory support also this thesis but only an exact theory can confirm it.
The Jahn-Teller effect on the temperature dependent EPR lineshapes of benzene cation, stabilized in a cold halocarbon matrix was recently explained and compared to contradicting results in other experimental and theoretical works.
The development of methods for simulating motional and
spin dynamics is led by Nikolas Benetis and is divided in three parts,
Free Quantum Rotation in Inert Gas Matrices
A systematic study of small symmetric rotor radicals in inert gas matrix (Ne, Ar, Kr, Xe) are currently under investigation. The experimentally studied systems are variations of the methyl radical CH3 structure obtained by isotopic substitution of both C and H atoms. Even mixed H-D were and will be studied. Several new quantum effects have been already discovered. They are a result of spin-rotation coupling through the anisotropic hyperfine interaction and can be possible in extra-light and highly symmetric systems. At least exchange symmetry between two boson or fermion nuclei was required. The motional part of the model simulations is a basic 3-Dimensional rotor being part of a full spin-rotation hamiltonian.
Considering the interaction of the alfa-methyl proton rotors with the
Ar matrix, it was shown that, at least for small temperatures, a free rotating
planar-rotor model was adequate to account for the experimental findings
. In other words, no hindering potential was found to be present here.
Still, several significant new quantum effects other than tunneling, were
discovered by studying free-methyl radicals in Ar matrix. It was possible,
for example, to observe and identify both the stopped proton- and deuteron-methyl
EPR signal at the lowest experimental temperatures close to 5 K. Severe
distortion of the EPR lineshapes, due to exclusion of several EPR transitions
attributed to the Pauli principle, was observed in particular in deuteron
rotors. Surprisingly enough, even mixed CH2D
and CHD2 rotors, that have solely fundamental
symmetry, were characteristically affected by exchange symmetry of identical
fermions or bosons, respectively. The above effects and the unexpected
for anisotropic systems extreme sharpness of the EPR spectra at low temperatures
were explained theoretically and resulted to a submitted work during 1998.
Further theoretical investigation, including detailed simulation of the
experimental spectra and obtaining important dynamics and magnetic parameters
of free methyl radicals, is currently in process.
The Methyl Rotor Spin Dynamics in the Smoluchowski Drift Diffusional Model Framework.
A.R. Sørnes and N.P. Benetis J. Magn. Res. 125 (1997) 52
Radical Cations of Naphthalene on Solid Oxide Surfaces and in CFCl3 Matrix, Studied by EPR, ENDOR and ESEEM.
R. Erickson, and N.P. Benetis, A. Lund and M. Lindgren J. Phys. Chem. 101 (1997) 2390
Effect of Isotopic Substitution on the Electron Spin Dynamics of the Radical in X-Irradiated Methyl Malonic Acid Powder. Intrinsic Potentials and Activation Energies.
A.R. Sørnes, N.P. Benetis, R. Erickson, A.S.
Mahgoub, L. Eberson and A. Lund J. Phys. Chem. 101(48)
The EPR Spectrum of the General >.C-CX3Quantum Rotor.
A.R. Sørnes and N.P. Benetis Chem.
Phys. 226 (1998) 151
Theory of ESEEM in Isotropic Tunneling Methyl Rotor Systems.
A.R. Sørnes, N.P. Benetis Chem. Phys. Lett, 287 (1998) 590
CH3 and CD3 Radicals Isolated in Argon: High Resolution ESR Spectra and Analysis by Three-Dimensional Quantum Rotor Model.
Masaru Shiotani, Tomoya Yamada, Kenji Komaguchi, Nikolas
P. Benetis, Anders Lund and Anders R. Sørnes
The Meeting on Tunneling Reactions and Low Temperature Chemistry, JAERI- Conf. 98-014, p. 58-63, 1998
High Resolution EPR and Quantum Effects on CH3, CH2D, CHD2 and CD3 Radicals Under Argon-matrix Isolation Conditions.
Tomoya Yamada, Kenji Komaguchi, Masaru Shiotani, Nikolas
P. Benetis and Anders R. Sørnes
J. Phys. Chem. A 103(25) (1999) 4823
An EPR, ENDOR and ESEEM Study of the Benzene Radical Cation in CFCl3 Matrix: Isotropic Substitution Effects on Structure and Dynamics.
Ramakant M. Kadam, Yoshiteru Itagaki, Nikolas P. Benetis,
Anders Lund, Roland Erickson, Martina Huber and
Wojciech Hilczer. Accepted in J. Phys. Chem. Chem. Phys. August 1999.
Maria Engström, Hidenori Yahiro, Nikolas P. Benetis,
Masaru Shiotani and A. Lund
Submitted to J. Phys. Chem. A, under revision, September 1999, Hiroshima
Automatic Spin-Hamiltonian Diagonalization for Electronic Doublet Coupled to Arbitrary Nuclear Spins and Full Anisotropy. Test in Theoretical 1-Dimensional and 2-Dimensional Electron-Spin-Echo Simulations of Model Systems
Nikolas P. Benetis, Anders R. Sørnes
Submitted to Concepts in Magnetic Resonance, October 27, 1999
General EPR Lineshape Theory for Anisotropic 3-D Quantum Rotors in Noble-Gas Matrices. Simulations of Experimental Spectra of Methyl- and Ammonia-Related Radical Species.
Nikolas P. Benetis, Anders R. Sørnes, Masaru
Shiotani, Kenji Komaguchi and Tomoya Yamada
Manuscript in final preparation October-November1999, Hiroshima
Observation of Methyl Tunneling and Theoretical Analysis
of Dynamics in Biologically
Significant Molecules by Using EPR Methods.
Einar Sagstuen, Nikolas P. Benetis and Anders R. Sørnes
Manuscript, with final preparation scheduled in December 1999, Hiroshima
Automatic Spin-Hamiltonian Diagonalization for Electronic Doublet Coupled to Arbitrary Nuclear Spins and Full Anisotropy. Comparison with Numerical Methods and Simulations of Experimental ESEEM Spectra.
Nikolas P. Benetis and Anders R. Sørnes, Anders
Lund and Daniele Biglino.
Manuscript in preparation
Connection of Chemical Kinetics and Motional Dynamics in Viscous Media.
Rakhim R. Rakhimov and Nikolas P. Benetis Manuscript
of Ring-Proton Motional Dynamics. Evidence of Ring-Opening in X-Irradiated
Glutarimide Single Crystals Studied by ENDOR-Enhancement and ENDOR-Induced EPR.
O. Eid, A. Lund and N.P. Benetis. Manuscript
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