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An analysis of orbital magnetization in band insulators is provided. It isshown that a previously proposed electronic orbital angular-momentum operatorgeneralizes the ``modern theory of orbital magnetization'' to include non-localHamiltonians. Expressions for magnetic transition dipole moments needed for thecalculation of optical rotation (OR) and other properties are developed. Avariety of issues that arise in this context are critically analyzed. Theseissues include periodicity of the operators, previously proposed banddispersion terms as well as, if and where needed, evaluation of reciprocalspace derivatives of orbital coefficients. Our treatment is used to determinethe optical rotatory power of band insulators employing a formulation thataccounts for electric dipole - electric quadrupole (DQ), as well as electricdipole-magnetic dipole, contributions. An implementation in the public\textsc{Crystal} program is validated against a model finite system and appliedto the $\alpha$-quartz mineral through linear-response time-dependent densityfunctional theory with a hybrid functional. The latter calculations confirmedthe importance of DQ terms. Agreement against experiment was only possible withi) use of a high quality basis set, ii) inclusion of a fraction of non-localFock exchange, and iii) account of orbital-relaxation terms in the calculationof response functions.

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Modern Theory with Modern Functionals