You did a good job with the models (sphere + Solidify modifier), environment, and the shader.
As already mentioned in the comments you just need to tweak a few things.
The bad white points are from a point light / Only camera Depth of Field with 2000 samples (adaptive)
the IOR for glass is
1.450. This creates the distortion if you look through the glass sphere and affects the reflection on it
to get a tint for the glass add some Volume Absorption. With the Solidify modifier this creates a darker tint. It's the same effect that you see at the side of the plate of a glass table for example.
use an HDRI with a bumped boosted strength and a big environment box. The HDRI you have already. The beveled plane that you use for the background and the HDR image will be reflected in the spheres. If you want to have a "clean look" as in the reference you need to reduce the reflects a bit with a big "shield". This will also create shadows and of course, requires more light => HDRI strength
4 or 5. Note that when the environment box is too close it will tint the sphere. Scale it up a lot if you don't want this.
optional, if you want to enhance the silhouette/the rim of the glass you can add a Layered Weight node with a Color Ramp to darken the rim a bit.
Last but not least, you can increase the contrast in the Render Properties > Color Management settings to
Medium High Contrast or
Please note that the rendered result heavily depends on the used HDRI!
For the composition of the scene I recommend using Linked objects, and Collection Instances for the molecules.
The box is 250 m large. Don't forget the adjust the camera's clipping (Lens > Clip End).
Examples (128 samples, adaptive)
Beveled plane as background/environment = more reflections, noisy camera DOF
For comparison: the glass spheres have no layered color but the connections have. Used the Defocus node for depth of field effect
Different HDRIs result in different colors: