Several options here, but you were on the right track...
1. Displacer should be fine for this, but you probably want to use a circular gradient as the driving texture...
...in which you control the characteristics of the curve by affecting the knots in the gradient, and that white dot between them...
Also check the various modes of that gradient - Linear, for example might be more suitable for this than an exponential mode.
2. Bezier Primitive. Control the peak on a high res patch with a much lower res grid. You can think of this as a plane with an FFD pre-applied !
3. FFD On plane - the 'manual' version of the above.
4. Soft Selection. If you would prefer to edit a high res plane directly, then soft selection would be the goto here, allowing you to specify various profiles of diffusing components selections so that they affect adjacent (unselected) ones too. Dome Mode shown below...
5. Saving possibly the best until last, I would personally use Fields for this, implemented via a Plain effector which is a child of a plane, and has its deformation mode set to Points. This, I suspect is going to be most useful because if you use the contour controls in the remapping tab of a spherical field, it lets you control the character of the curve directly via a spline... like this.
...which would give us this sort of result...
So that's most of the non-mathematical approaches with the actual character / interpolation of the ramp defined in a number of different ways...
The maths-based stuff I will leave to someone more into that than I am !
As for the Atom Array aspect of your question - That will work as a parent of any of the setups above, but if you'd rather not wrangle the unnecessary vertex spheres in that, so will cloning cylinders to edges (scale edge 100%) or stealing the topology using Edge to spline (still available parametrically via a correction deformer) and sweeping the result.
CBR