**6. References**

[1] Buchachenko A.L, Wasserman A.M (1973) Stable Radicals, Moscow: Khimiya. 410 p. (in Russian).

[2] Robinson B.H, Tomann H, Beth A.H, Fajer P, Dalton L.R (1985) In EPR and Advanced EPR Studies of Biological Systems. Dalton L.R, editor. Boca Raton: C.R.C.Press, pp. 68- 72.

106 Nitroxides – Theory, Experiment and Applications

1. Tilt of hfi-tensors relative to g-axes.

individual spectral line (Voigt profile).

high frequency (quasi-librations).

10. Up to 5 different paramagnetic centers.

7. Tilt of the libration axes relative to the g-axes.

2. Forbidden transitions.

Lorentzian line widths.

9. Up to 5 magnetic nuclei.

transitions.

*Program esrD* 

**6. References** 

Russian).

The program allows taking into account the following:

5. Tilt of the Gaussian and Lorentzian tensors relative to the g-axes.

8. The orientation distribution functions of the paramagnetic probe.

loaded from the same site with the examples of the program applications.

useful as well for visual comparison of experimental and calculated spectra.

http://www.chem.msu.ru/rus/lab/chemkin/esrD/.

3. Convolution of the Gaussian and Lorentzian functions for description of the shape of

4. Anisotropy of the line widths described by the second-rank tensors of the Gaussian and

6. Stochastic rotational oscillations of paramagnetic molecules with limited amplitude and

The EPR spectra are computed in accordance with explicit formulas presented in [81]. Two types of spectrum calculation can be performed. Both types of calculation use the Hamiltonian within the perturbation theory of the second order. The first type of calculation assumes the coincidence of g-tensor frame with hfi-tensor frame. The second type of calculation takes into account any tilt of hfi-tensors relative to g-axes and forbidden

The formats for the input-output files are described in the document ODF3.pdf that can be

The purpose of the program esrD is the treatment of experimental EPR spectra and preparation of spectra to the fitting procedure. This preparation ordinarily involves removal of the unnecessary tails, subtraction of the base line or base spectrum, double integration, normalizing of area under the spectrum, etc. All these procedures can be carried out using the standard software. On the other hand, when the spectra were recorded in different and possibly irregular points of the magnetic field, the mentioned operations were rather time-consuming. The program esrD allows carrying out necessary operations with the set of such spectra at once. It is

The program is presented free for any use with only the conditions that the authors are not responsible for any consequences and insist on the citation of the source if the results obtained using the program are published. The program can be loaded from the site

[1] Buchachenko A.L, Wasserman A.M (1973) Stable Radicals, Moscow: Khimiya. 410 p. (in



[37] Meirovitch E, Freed J.H (1984) Analysis of slow-motional electron spin resonance spectra in smectic phases in terms of molecular configuration, intermolecular interactions, and dynamics. J Phys Chem. 88: 4995–5004.

108 Nitroxides – Theory, Experiment and Applications

Moscow, 1986) pp. 61-78

130: 104502.

[18] Molin Yu.N, Salikov K.M, Zamaraev K.I (1980) Spin Exchange. Principles and Applications in Chemistry and Biology. Berlin; New York: Springer-Verlag, 1980. 242 p. [19] Kokorin A.I in Method of Spin Labels and Probes: Problems and Perspectives (Nauka,

[20] Kurban M.R, Peric M, Bales B.L (2008) Nitroxide spin exchange due to re-encounter

[21] Kurban M.R (2009) Experimental correlation of nitroxide recollision spin exchange with free volume and compressibility in alkane and aromatic compounds. J. Chem. Phys.

[22] Kurban M.R (2011) A study of the relation between translational and rotational diffusion through measurement of molecular recollision. J. Chem. Phys. 134: 034503.

[25] Dennis J.E, Gay D.M, Welseh R.E (1981) An Adaptive Nonlinear Least-Squares

[26] Abragam A, Bleaney B. (1970) Electron paramagnetic resonance of transition ions.

[27] Abramowitz M, Stegun I.A Eds. (1964) Handbook of Mathematical Functions. National

[28] Lebedev Ya.S, Grinberg O.Ya, Dubinsky A.A, Poluektov O.G (1992) Investigation of Spin Labels and Probes by Millimeter Band EPR. In: Zhdanov R.I, editor. Bioactive Spin Labels. Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, Barcelona,

[30] Freed J.H (1976) Theory of slow tumbling ESR spectra for nitroxides. In: Berliner L.J, editor. Spin Labeling: Theory and applications. New York: Academic Press. pp. 53-132. [31] Chernova D.A, Vorobiev A.Kh (2009) Temperature Dependence of ESR Spectra of Nitroxide Spin Probe in Glassy Polymers. Journal of Polymer Science: Part B: Polymer

[33] Kuznetsov A.N, Wasserman A.M, Volkov A.U, Korst N.N (1971) Determination of rotational correlation time of nitric oxide radicals in a viscous medium. Chem.Phys.Lett.

[34] Kovarski A.L (1997) Molecular dynamics of Additives in Polymers. Utrecht: VSP. 276 p. [35] Polanszek C.F, Freed J.H (1975) Electron spin resonance studies of anisotropic ordering, spin relaxation, and slow tumbling in liquid crystalline solvents. J Phys Chem. 79: 2283–

[36] Meirovitch E, Nayaman A, Freed J.H (1984) Analysis of protein-lipid interactions based on model simulations of electron spin resonance spectra. J Phys Chem. 88: 3454–3465.

[23] Chumakova N.A, Nikitina V.A, Pergushov V.I (2012) Russ.J.Phys.Chem. In press. [24] Khairy K, Budil D, Fajer P (2006) Nonlinear-least-squares analysis of slow motional

Algorithm. ACM Transactions on Mathematical Software 7(3): 348-383.

[29] Seber G.A.F, Wild C.J (1989) Nonlinear regression. New York: Wiley. 768 p.

[32] Redfield A.G (1966) The theory of relaxation processes. Adv. Magn. Res. 1: 1–32.

collisions in a series of n-alkanes. J. Chem. Phys. 129: 064501.

regime EPR spectra. J. Magn. Reson. 183: 152–159.

Oxford: Clarendon press. 911 p.

Bureau of Standards 1050 p.

Budapest: Springer-Verlag.

Physics. 47: 563–575.

12(1): 103-105.

2306.


	- [53] Veksli Z, Andreis M, Rakvin B (2000) ESR spectroscopy for the study of polymer heterogeneity. Prog. Polymer Sci. 25(7): 949-986.
	- [54] Dzuba S.A, Salnikov E.S., Kulik L.V (2006) CW EPR, echo-detected EPR, and fieldstep ELDOR study of molecular motions of nitroxides in o-terphenyl glass: Dynamical transition, dynamical heterogeneity and beta-relaxation. Appl. Magn. Reson. 30(3-4): 216-222.
	- [55] Cameron G.G, Miles I.S, Bullock A.T (1987) Distribution in correlation times for rotational diffusion of spin probes in polymers. Br. Polymer J. 19: 129-134.
	- [56] Faetti M, Giordano M, Leporini D, Pardi L (1999) Scaling analysis and distribution of the rotational correlation times of a tracer in rubbery and glassy poly(vinyl acetate). Macromolecules. 32(6): 1876 -1882.
	- [57] Shantarovich V.P, Kevdina I.B, Yampolskii Y.P, Alentiev A.U (2000) Positron Annihilation Lifetime Study of High and Low Free Volume Glassy Polymers: Effects of Free Volume Sizes on the Permeability and Permselectivity. Macromolecules. 33: 7453– 7466.
	- [58] Bercu V, Martinelli M, Massa C.A, Pardi L.A, Leporini D (2005) Signatures of the fast dynamics in glassy polystyrene: First evidence by high-field Electron Paramagnetic Resonance of molecular guests. J Chem Phys. 123: 174906.
	- [59] Saalmueller J.W, Long H.W, Maresch G.G, Spiess H.W (1995) Two-Dimensional Field-Step ELDOR. A Method for Characterizing the Motion of Spin Probes and Spin Labels in Glassy Solids. J Magn Reson A. 117(2): 193-208.
	- [60] Saalmueller J.W, Long H.W, Volkmer T, Wiesner U, Maresch G.G, Spiess H.W (1996) Characterization of the motion of spin probes and labels in amorphouspolymers with two-dimensional field-step ELDOR. J Polym Sci Part B Polym Phys. 34(6): 1093-1104.
	- [61] Bogdanov A.V, Vorobiev A.Kh (2011) Rotational mobility and rate of photoisomerization of spin-labeled azobenzenes in glassy polystyrene. Chemical Physics Letters 506: 46–51.
	- [62] Nakatsuji S, Fujino M, Hasegawa S, Akutsu H, Yamada J, Gurman V.S, Vorobiev A.Kh (2007) Azobenzene Derivatives Carrying A Nitroxde Radical. J.Org.Chem. 72: 2021- 2029.
	- [63] Friesner R., Nairn J.A, Sauer K (1979) Direct calculation of the orientational distribution function of partially ordered ensembles from the EPR line shape. J. Chem. Phys. 71(1): 358-365.
	- [64] Friesner R., Nairn J.A (1980) A general theory of the spectroscopic properties of partially ordered ensembles. I. One vector problems J. Chem. Phys. 72 (1): 221-230.
	- [65] Shimada S., Hori Y., Kashiwabara H (1985) Structure of Peroxy Radicals Trapped in Irradiated Isotactic Polypropylene and Molecular Disorder of the Polymer Chain, Related with Hydrogen Abstraction Reaction of the Radicals. Macromol. 18: 170-176.
	- [66] Shimada S., Hori Y., Kashiwabara H (1988) Distribution of Molecular Orientation and Stability of Peroxy Radicals in the Noncrystalline Region of Elongated Polypropylene. Macromol. 21: 979-982.

[67] Swartz J.C, Hoffman B.M, Krizek R.J, Atmatzidis D.K (1979) A General Procedure for Simulating EPR Spectra of Partially Oriented Paramagnetic Centers. J. Magn. Res. 36: 259-268.

110 Nitroxides – Theory, Experiment and Applications

Macromolecules. 32(6): 1876 -1882.

Physics Letters 506: 46–51.

Macromol. 21: 979-982.

216-222.

7466.

2029.

358-365.

heterogeneity. Prog. Polymer Sci. 25(7): 949-986.

[53] Veksli Z, Andreis M, Rakvin B (2000) ESR spectroscopy for the study of polymer

[54] Dzuba S.A, Salnikov E.S., Kulik L.V (2006) CW EPR, echo-detected EPR, and fieldstep ELDOR study of molecular motions of nitroxides in o-terphenyl glass: Dynamical transition, dynamical heterogeneity and beta-relaxation. Appl. Magn. Reson. 30(3-4):

[55] Cameron G.G, Miles I.S, Bullock A.T (1987) Distribution in correlation times for

[56] Faetti M, Giordano M, Leporini D, Pardi L (1999) Scaling analysis and distribution of the rotational correlation times of a tracer in rubbery and glassy poly(vinyl acetate).

[57] Shantarovich V.P, Kevdina I.B, Yampolskii Y.P, Alentiev A.U (2000) Positron Annihilation Lifetime Study of High and Low Free Volume Glassy Polymers: Effects of Free Volume Sizes on the Permeability and Permselectivity. Macromolecules. 33: 7453–

[58] Bercu V, Martinelli M, Massa C.A, Pardi L.A, Leporini D (2005) Signatures of the fast dynamics in glassy polystyrene: First evidence by high-field Electron Paramagnetic

[59] Saalmueller J.W, Long H.W, Maresch G.G, Spiess H.W (1995) Two-Dimensional Field-Step ELDOR. A Method for Characterizing the Motion of Spin Probes and Spin Labels

[60] Saalmueller J.W, Long H.W, Volkmer T, Wiesner U, Maresch G.G, Spiess H.W (1996) Characterization of the motion of spin probes and labels in amorphouspolymers with two-dimensional field-step ELDOR. J Polym Sci Part B Polym Phys. 34(6): 1093-1104. [61] Bogdanov A.V, Vorobiev A.Kh (2011) Rotational mobility and rate of photoisomerization of spin-labeled azobenzenes in glassy polystyrene. Chemical

[62] Nakatsuji S, Fujino M, Hasegawa S, Akutsu H, Yamada J, Gurman V.S, Vorobiev A.Kh (2007) Azobenzene Derivatives Carrying A Nitroxde Radical. J.Org.Chem. 72: 2021-

[63] Friesner R., Nairn J.A, Sauer K (1979) Direct calculation of the orientational distribution function of partially ordered ensembles from the EPR line shape. J. Chem. Phys. 71(1):

[64] Friesner R., Nairn J.A (1980) A general theory of the spectroscopic properties of partially ordered ensembles. I. One vector problems J. Chem. Phys. 72 (1): 221-230. [65] Shimada S., Hori Y., Kashiwabara H (1985) Structure of Peroxy Radicals Trapped in Irradiated Isotactic Polypropylene and Molecular Disorder of the Polymer Chain, Related with Hydrogen Abstraction Reaction of the Radicals. Macromol. 18: 170-176. [66] Shimada S., Hori Y., Kashiwabara H (1988) Distribution of Molecular Orientation and Stability of Peroxy Radicals in the Noncrystalline Region of Elongated Polypropylene.

Resonance of molecular guests. J Chem Phys. 123: 174906.

in Glassy Solids. J Magn Reson A. 117(2): 193-208.

rotational diffusion of spin probes in polymers. Br. Polymer J. 19: 129-134.


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