Anisofit 2.0: A Program for Fitting Magnetization Data

The computer program Anisofit 2.0 was developed for use in estimating the zero-field splitting parameters of high-spin clusters by fitting magnetization data. It is implemented on the Matlab¹ platform and assumes that only the spin ground state of the molecule is significantly populated, the Landé g value is isotropic (g = g_iso), and the principal axes of D and g coincide. Accordingly, it utilizes a spin Hamiltonian² of the following form:

Ĥ = DŜ_z² + E(Ŝ_x² + Ŝ_y²)+ g_isoµ_BS · B

The symbol µ_B represents the Bohr magneton, D, E, S, and B stand for the axial and rhombic zero-field splitting (ZFS) parameters, and the spin and magnetic field vectors, respectively. Anisofit 2.0 uses angle sets derived through the Zaremba, Conroy, and Wolfsberg (ZCW)³ method for powder integration. The calculated values of D, E, and g_iso are optimized relative to the data through a least-squares minimization routine. Parameter refinement utilizes experimental data from all applied magnetic fields and temperatures simultaneously. Ideas presented by Day and others were closely followed throughout the development of this program.^4,5

This program requires that the user have Matlab 5.3.1 or a newer version. To use the fitting functionality of Anisofit 2.0, the user must also possess the Optimization Toolbox add-on; simulations can be performed without the Toolbox. To start the program, place all downloaded *.m files in one directory which is already in the Matlab path and type "anisofit2" at the prompt followed by pushing the Enter key.

Anisofit 2.0 (in zip format) can be downloaded below. A *.pdf file is contained in the download and contains further details about the program including example input and output files which must be written by the user. The file is a condensed version of Chapter Four in ref. 6. The figure below shows a successful fit of magnitization data for a Mo-Ni cyano cluster from ref. 7, which should be cited when using Anisofit 2.0.

Download Anisofit2.0

References and Notes

(1) Matlab, 5.3.1; MathWorks, Inc.: Natick, MA; 2000.

(2) For a justification of this formalism, see Bencini, A.; Gatteschi, D. Electron Paramagnetic Resonance of Exchange-Coupled Systems, Springer-Verlag: New York, 1990; Section 2.5 and Appendix A, and references therein.

(3) (a) Conroy, H. J. Chem. Phys. 1967, 47, 5307. (b) Zaremba, S. K. Ann. Mat. Pur. Appl. 1966, 73, 293. (c) Cheng, V. B.; Suzukawa, H. H.; Wolfsberg, M. J. Chem. Phys. 1973, 59, 3992. (d) Edén, M.; Levitt, M. H. J. Mag. Res. 1998, 132, 220. (e) Hodgkinson, P.; Emsley, L. Prog. Nucl. Mag. Res. Sp. 2000, 36, 201.

(4) (a) Vermaas, A.; Groeneveld, W. L. Chem. Phys. Lett. 1974, 27, 583. (b) Marathe, V. R.; Mitra, S. Chem. Phys. Lett. 1974, 27, 103.

(5) Day, E. P. Methods Enzymol. 1993, 227, 437.

(6) Sokol, J. J., Ph.D. Thesis, University of California, Berkeley, 2003.

(7) Shores, M. P.; Sokol, J. J.; Long, J. R. J. Am. Chem. Soc. 2002, 124, 2279-2292. pdf