Z. Phys. D 36, 301-309 (1996) ZEITSCHRIFT FORPHYSIK D © Springer-Verlag 1996 Ab initio calculations of electron-spin magnetic moments for Li, Be and B hydrides in XeX, + states G.H. Lushington, P.J. Bruna, F. Grein* Department of Chemistry, University of New Brunswick, Bag Service Number 45222, Fredericton NB, Canada E3B 6E2 Received: 28 September 1995/Final version: 6 November 1995 Abstract. Electron-spin magnetic moments, in the form of g-shifts, have been computed at the ROHF level for the X2Z + states of LiH +, Bell 2+, LiH-, Bell and BH +. A perturbative approach, complete to second-order in appropriate Breit-Pauli operators, has been used. Reten- tion of two-centre integrals has proven vital. First-order terms are important, especially in describing the negative gII shifts observed experimentally in 2S+ molecules. The relativistic mass correction dominates in first-order, ex- cept for LiH- where the two-electron spin-Zeeman gauge correction supersedes. Second-order terms contribute negatively, and only to the Agi component. Along the isoelectronic series LiH- ~ Bell --* BH +, the magnitude of Agz increases due to the dependence of spin-orbit coupling on nuclear charge. The relation of g-shifts to electronic structure and bonding is explored. PACS: 33.45.B; 31.10; 31.20.E 1 Introduction The magnetic moment of a paramagnetic radical is intri- cately related to the localization of spin-density and the motion of electrons [1, 2]. Compared with their electrical analogues, molecular magnetic moments have been the subject of rather few ab initio studies. The main reason for this deficiency has been computational complexity. While electric dipoles may be obtained as expectation values of a one-electron position operator r, magnetic dipoles are a function of both r and the momentum p of all charged particles. This includes contributions due to electronic orbital motion #c, electron spin/~s, nuclear spin ¢ts, and molecular rotation #R. Since a complete ab initio description of all molecular magnetic moments and their interactions is prohibitively complicated, we restrict ourselves in this work to a study * Corresponding author. E-mail: fritz@unb.ca of the electronic magnetic moments of 2Z ÷ hydrides XH as observed in the electronic Zeeman effect. A theoretical study of electronic g-factors, using a sec- ond-order perturbative expansion of seven Breit-Pauli operators, was performed recently by Lushington and Grein [3], who investigated NO2, H20 + and CO + at the restricted open-shell Hartree-Fock (ROHF) level. We report here similar calculations on small XH hy- drides for which correlation effects should be relatively minor. The electronic g-tensors for the X2S, + states of LiH ÷, LiH-, Bell 2+, Bell and BH + are studied over a range of R(XH) distances. Selected atomic g-values are also given. There are no theoretical g-tensor data on these hy- drides for comparison. Experimental results are available only for Bell 1-4]. 2 Theory Magnetic moments of radicals are experimentally meas- ured via electron paramagnetic resonance (EPR) spectro- scopy. In EPR, the presence of an external magnetic field B induces an energetic splitting, called the electronic Zee- man effect, in the ms levels of the radical. Resonant transitions between these levels can be quantified as hv = -/~. t3 = - (m + ~) B (1) where/~ is the radical's total electronic magnetic moment, having contributions from the electron spin t~s = --gdzBS (2) and orbital u¢ = -~B~' (3) magnetic moments. In the above, /~B is the Bohr mag- neton, 9~ = 2.002319304386 [5] is called the free-electron g-factor, and S and E are the spin and orbital angular momentum vectors, respectively. For doublet radicals with orbitally nondegenerate ground states, the only orbital angular momentum is