## Relaxation Engine

*A collection of Mathematica programs, tutorials and supporting information on the subject of automated symbolic processing of Bloch-Redfield-Wangsness relaxation theory equations.*

#### Introduction to pattern matching

pattern_matching_intro.pdf – a brief outline of pattern matching in Mathematica

tutorial_1.nb – a tutorial worksheet, demonstrating the power of pattern matching in Mathematica

brw_engine_lecture.pdf – a conference lecture on the subject of automation of BRW theory processing

#### Pattern matching practicals

practice_1.nb – practice worksheet 1 (dipolar, hyperfine and other traceless bilinear mechanisms)

practice_2.nb – practice worksheet 2 (CSA, g-anisotropy and other traceless linear mechanicsms; includes cross-correlations)

practice_3.nb – practice worksheet 3 (ZFS relaxation in a spin-3/2 electron shell coupled to a spin-1 nucleus)

practice_4.nb – practice worksheet 4 (radical pair, including g-anisotropy, hyperfine coupling to a nucleus and all cross-correlations thereof)

#### Examples of relaxation theory processors

CSA-CSA cross-correlation in a two-spin system (the general case of arbitrarily oriented CSAs with three different eigenvalues)

Point DD relaxation in a two-spin system (the classical case of point dipole relaxation in a two-spin system)

CSA-DD-CSA cross-correlation in a two-spin system (2xCSA + 1xDD, orientations arbitrary, eigenvalues different, incl. cross-correlations)

Relaxation due to the modulation of a scalar interaction in a two-spin system (HFC modulation by electron relaxation or conformational mobility)

#### Literature

R.K. Wangsness, F. Bloch, The Dynamical Theory of Nuclear Induction,

*Physical Review*89 (1953) 728-739.A.G. Redfield, On the Theory of Relaxation Processes,

*IBM Journal of Research and Development*1 (1957) 19-31.M. Goldman, Formal theory of spin-lattice relaxation,

*Journal of Magnetic Resonance*149 (2001) 160-187.I. Kuprov, N. Wagner-Rundell, P.J. Hore, Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software,

*Journal of Magnetic Resonance*184 (2007) 196-206.