DOT1 Complications are of electromagnetic nature. Nucelus possess mass,
charge, shape and certain energy levels. Multipole expansion lets making a priori
shape and energy corrections. Thus it is also possible to distinguish that
each nucleus is interacting with an electron cloud that surrounds it. Atoms also
don’t spawn as free systems – they have charged vicinity, so the nucleus is interacting
with other nearby nuclei. Moreover electrons themselves interact with each other, neighboring
atoms and (in solids) crystall lattice. Having not performed a multipole expansion
would lead sadly to mixing energy and shape terms erasing in effect reasonable properties
of the entire system.
DOT2 (1) As long as the system behaves linearly. Otherwise linear methods such as multipole,
Taylor, Maclaurine don’t work.
(2) The first order perturbation calculus approximation
is invalid as long as E_i^0 is not degenerate. As it becomes degenerate, the denominator
can become zero.
(3) Parameters for nuclear electric moments have to be predefined,
put in agreement with experimental values.
Higher orders of multipole expansion fields are becoming yet smaller, so do perturbations
of level higher than first. It is also challenging for numerical computations. Accuracy of
numerical calculations drains the operating resources in supercomputer facilities.