It's not what we have in mind today either, since virtually nothing in your summary describes the modern understanding of atoms.
Besides a nucleus of clusters [yes] of neutrons and protons comprised of quantum-behaving subatomic particles [yes] which in turn are made of vibrating (waveform) energy [yes], surrounded by electrons statistically distributed into a variety [yes] of energy shell patterns [yes], these non-material [yes] atoms also manifest by vibrating in their associated fields. [yes]
Apparently you never really got that whole vibration thing, let alone fields.
They have state vectors in Hilbert Space which describe their properties, some -- but NOT ALL -- components of which are colloquially called "wave functions." Their wavefunctions are not "energy," and they are not "vibrating."
Electrons are not "statistically distributed." They exist in linear superpositions of their energy eigenstates, which, upon measurement collapse with statistical probability into measurable observables. That does not mean they exist with "statistical distribution," only that their measurement results have statistical outcomes.
Matter, by definition is not "non-material."
Atoms do not "vibrate in their fields."
Please actually read a book about quantum mechanics sometime, and stop channeling Deepak Chopra and quoting lunacy from The Tao of Physics.
Yet more absolute nonsense.