For design purposes one needs to relate the structure of proposed materials to their NLO
(nonlinear optical) and other properties which is a situation where theoretical approaches can
be very helpful in providing suggestions for candidate systems that subsequently can be
synthesized and studied experimentally. This brief describes the quantum-mechanical treatment
of the response to one or more external oscillating electric fields for molecular and
macroscopic crystalline systems. To calculate NLO properties of large systems a linear
scaling generalized elongation method for the efficient and accurate calculation is introduced.
The reader should be aware that this treatment is particularly feasible for complicated
three-dimensional and or delocalized systems that are intractable when applied to conventional
or other linear scaling methods.
