Basics

Atoms and atomic ions in their ground-states (and in an isotropic space) show a monotonically decreasing charge density ρ(r) as a function of the radial distance r from the nucleus (assumed free from electrical moments). This distribution is spherically symmetrical, since it is induced by a spherically symmetrical Coulomb potential: H. Weinstein, P. Politzer & S. Srebrenik, Theor.Chim.Acta(Berl.) 38,159-163(1973) show, that this follows from Poisson's equation, valid in Quantum Mechanics. Most chemists have images in their minds, where many-electron atoms show a shell structure with radial maxima and minima. This is correct but pertains to the radial distribution function 4πr2ρ(r). It is well known, that every closed and highspin half filled shell of atomic orbitals is spherically symmetrical (e.g. N([He]2s22p3)4S3/2 or FeIII([Ar]3d5)6S5/2. Partially filled shells seem not to obey this. E.g. the F atom has a ground-state population of 1s22s22px22py22pz1. Since the p-orbitals are equivalent, the single electron in pz is arbitrary. To keep the symmetry of the problem we have to take (at least) three Slater one-electron determinants with the single elctron once in every 2p-orbital (making a 2p-shell with 5/3 average occupation of the three components). That restores formal spherical symmetry to the isolated free atom, an approximation often used in quantum chemical computations (e.g. in Hatree-Fock-Slater codes). With this recipe every atom can be shown in its spherically symmetrical ground-state.
Conclusion: Atoms do not have "rabbit ears", unless there is some cabbage nearby!
In order to produce an excited state, e.g. by photon absorption, we need an electrical moment - the transition moment - to couple to the radiation field. This happens, when we excite H(1s, l=0) to H(2p) with angular momentum l=1. Now we have an axially deformed excited state density, which shortly relaxes
to its spherically symmetrical ground-state shape by emission of a photon which elopes with its energy hν, angular momentum 1ħ and chirality.
We can break the spherical symmetry by other external fields, like electric, or magnetic fields, and, especially important in our context, by the neighborhood of other atoms. They render the atoms nonspherical: E.g. the spherical Li(1s22s1) atom becomes polarized, i.e. its most loosely bound 2s electron cloud shifts from the Li atom center towards a nearing H(1s) atom or Li- towards H+, a process which ends by formation of a chemical bond as shown here with Li- harpooning a proton, forming LiH:

The question is whether the Li(2s) shift (and change of radius) leads to a complete polarization to Li+H-, the usual qualitative (incorrect) Kimball picture with non-overlapping unpolarized spheres (forming the salt {LiH} when condensed), or only to a partial sharing of electron density between Li and H, as the quantitative (correct) Kimball model or Quantum Chemistry has found, see Tutorial4. And, what is the chemically relevant difference between the two LiH results?