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Simulation of EPR-spectra of randomly oriented samples
C-674 Computer Physics Communications 21 (1981) 385-395 © North-Holland Publishing Company
S I M U L A T I O N O F EPR-SPECTRA O F R A N D O M L Y O R I E N T E D SAMPLES C. D A U L , C.W. S C H L ~ P F E R Institute of lnorganic Chemistry, University of Fribourg, 1700 Fribourg, Switzerland B. M O H O S Brown Boveri Company, Baden, Switzerland J. A M M E T E R and E. GAMP Institute of lnorganic Chemistry, University of Ziirich, 8052 Ziirich, Switzerland Received 27 November 1979; in revised form 29 September 1980
PROGRAM SUMMARY
Title o/program: POWDER Catalogue number: ABVG Computer: CDC 6000; Installation: Rechenzentrum der ETHZ, 8052 Ziixieh, Switzerland Operating system: SCOPE 3.4 Programming language used: FORTRAN IV G High speed storage required: 130 000a words No. of bits in a word: 60 Overlay structure: none No. of magnetic tapes required: none Other peripherals used: card reader, line printer, plotter, disk space No. of cards in combined program and test deck: 826 Keywords: EPR, anisotropic g-tensor, anisotropic hypert'metensor, anisotropic perturbation calculation, numerical integration and differentiation, noise triter. Nature of the physical problem The EPR spectra of polycrystalline paramagnetic samples exhibits often complex features due to hypert'me and/or
dipole-dipole and/or quadrupole interaction of the electronic and nuclear spins. This progzam calculates the first derivative of the EPR absorption spectrum of randomly oriented samples using the following approximations: i) the eigenvalues of the spin Hamiltonian are given by second order perturbation theory; ii) the intensities of the EPR transitions are determined by Zeeman interaction only; iii) the paramagnetic species are uniformly or randomly distributed in space. iv) "allowed" transitions (AMI = 0) are calculated only.
Method of calculation The single crystal spectra for particular orientations are calculated. They are summed over all spacial orientations (Simpson rule) and convoluted with a line shape function giving the absorption line. A subsequent numerical derivation yields the 1st derivative spectrum and reduces the random deviations due to the limited number of orientations [ 1 ]. Restriction on the complexity of the problem In the present version, the stick spectrum is convoluted with a lineshape function after the summation over all orientations has been carried out. This implies that only line widths independent upon orientation and mI can be treated. Furthermore, since a perturbation calculation is used, it is required that ~C(Zeeman)> ~C(hypert'me), ~(Zeeman) > ~C(dipoledipole) and that Jf(hyperf'me) > ~f(quadrupole). Typical running time Ranges between 10 s and 10 rain on the CDC 6000. References [1] B. Mohos et al., Anal. Chem. 48 (1976) 231; J. Chem. Phys. 60 (1974) 4633.
S I M U L A T I O N O F EPR-SPECTRA O F R A N D O M L Y O R I E N T E D SAMPLES C. D A U L , C.W. S C H L ~ P F E R Institute of lnorganic Chemistry, University of Fribourg, 1700 Fribourg, Switzerland B. M O H O S Brown Boveri Company, Baden, Switzerland J. A M M E T E R and E. GAMP Institute of lnorganic Chemistry, University of Ziirich, 8052 Ziirich, Switzerland Received 27 November 1979; in revised form 29 September 1980
PROGRAM SUMMARY
Title o/program: POWDER Catalogue number: ABVG Computer: CDC 6000; Installation: Rechenzentrum der ETHZ, 8052 Ziixieh, Switzerland Operating system: SCOPE 3.4 Programming language used: FORTRAN IV G High speed storage required: 130 000a words No. of bits in a word: 60 Overlay structure: none No. of magnetic tapes required: none Other peripherals used: card reader, line printer, plotter, disk space No. of cards in combined program and test deck: 826 Keywords: EPR, anisotropic g-tensor, anisotropic hypert'metensor, anisotropic perturbation calculation, numerical integration and differentiation, noise triter. Nature of the physical problem The EPR spectra of polycrystalline paramagnetic samples exhibits often complex features due to hypert'me and/or
dipole-dipole and/or quadrupole interaction of the electronic and nuclear spins. This progzam calculates the first derivative of the EPR absorption spectrum of randomly oriented samples using the following approximations: i) the eigenvalues of the spin Hamiltonian are given by second order perturbation theory; ii) the intensities of the EPR transitions are determined by Zeeman interaction only; iii) the paramagnetic species are uniformly or randomly distributed in space. iv) "allowed" transitions (AMI = 0) are calculated only.
Method of calculation The single crystal spectra for particular orientations are calculated. They are summed over all spacial orientations (Simpson rule) and convoluted with a line shape function giving the absorption line. A subsequent numerical derivation yields the 1st derivative spectrum and reduces the random deviations due to the limited number of orientations [ 1 ]. Restriction on the complexity of the problem In the present version, the stick spectrum is convoluted with a lineshape function after the summation over all orientations has been carried out. This implies that only line widths independent upon orientation and mI can be treated. Furthermore, since a perturbation calculation is used, it is required that ~C(Zeeman)> ~C(hypert'me), ~(Zeeman) > ~C(dipoledipole) and that Jf(hyperf'me) > ~f(quadrupole). Typical running time Ranges between 10 s and 10 rain on the CDC 6000. References [1] B. Mohos et al., Anal. Chem. 48 (1976) 231; J. Chem. Phys. 60 (1974) 4633.