Electronic Zeeman interaction energy matrices

These represent the nuclear spin Zeeman interaction, the rotational Zeeman interaction, the nuclear spin-rotation interaction, the nuclear spin-nuclear spin dipolar interaction, and the diamagnetic interactions. Using irreducible tensor methods we examine the matrix elements of each of these five terms in turn, working first in the decoupled basis set rj J, Mj /, Mi), where rj specifies all other electronic and vibrational quantum numbers this is the basis which is most appropriate for high magnetic field studies. In due course we will also calculate the matrix elements and energy levels in a ry, J, I, F, Mf) coupled basis which is appropriate for low field investigations. Most of the experimental studies involved ortho-H2 in its lowest rotational level, J = 1. If the proton nuclear spins are denoted I and /2, each with value 1 /2, ortho-H2 has total nuclear spin / equal to 1. Para-H2 has a total nuclear spin / equal to 0. 

An important addition to the literature of EPR spectrum simulation was presented as an Appendix in this work. A spin system consisting of one 5 = 3 and four / = I results in an energy matrix of order 2592. Even with the approximation of collinear matrices for electronic Zeeman and hyperfine interactions, matrix diagonalisation techniques are effectively unrealistic. The authors argue that starting from an uncoupled spin-Hamiltonian representation ... 

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