According to Quantum-Mechanics, the ultimate solution to the question, of Wave-Particle Duality, no matter how deeply this solution is buried, lies in the idea, that Particles cause Waves. Hence, the particles are more-ultimately real, and waves are not. In certain cases such as phonons, this even extends beyond waves-in-a-vacuum, to sound waves, that can be modeled as quasi-particles.
One rule which this evokes is the notion, that if (A) causes (B) with certainty, then it cannot be true that (B) causes (A). And to my mind, this has presented the greatest challenge with Chemistry.
The way Chemistry is understood to work today, the electrons that were loosely stated to be orbiting the nucleus, are actually occupying Quantum-Mechanical states around the nucleus, thus merely being attached to the nucleus, and they occupy shells, which are subdivided into orbitals. Further, these orbitals have known wave-functions, that follow from QM. Hence, the s2 -orbitals are spherical, the p6 -orbitals are perpendicular, and the d10 and f14 -orbitals have the more-complex geometries, which are possible modes of resonance. If all the orbitals belonging to a shell are filled, then indeed the shell becomes spherical itself, and this is best exhibited with inert gasses, which therefore also have ideal cancellation of the nuclear charge at close distance, and which therefore also lack electronegativity. (:1)
The main point of confusion which is possible here, is in the fact that these orbitals and their wave-functions seemingly define the chemical and physical properties of the element, except for anything related to its mass. The suggestion follows, that since the electrical field of the nucleus is strong enough to manipulate the wave-functions, it can also end up displacing where the particle ultimately occurs. In so doing, this action on the orbital would seem to suggest that the wave-function can also be said to change the particle-parameters, thereby creating a contradiction with the way in which QM is currently taught.
There is a specific observation which we can make about this subject, which causes Chemistry to avoid contradicting QM by the width of a hair.
These s, p, d and f -orbital geometries are only thought to exist, if their electrons are unpaired. Each orbital is capable of holding up to 2 electrons, and an orbital which only holds 1 electron is said to be “half-filled”. It has these formally-defined properties when half-filled.
There has never been a precedence in Chemistry, in which a half-filled orbital can be shared by two atoms. But some sort of entity needs to be shared between 2 or 3 atoms, in order actually to form a bond, and in order to change position around either atom. (:2)
When orbitals are filled by 2 electrons each, these two electrons perform a dance which electrons are already famous for, in which both their spin-vector and their magnetic dipole moment pair up, to cancel out. This is also known as “spin-spin decoupling”, and causes the electron to resemble a Fermion less, resulting in some quasi-particle that resembles a fluid more – i.e. a massive Bose particle.
The same affinity causes electron-pairs to form Cooper Pairs, which ultimately result in superconductivity. But in Chemistry, it forms charge-droplets, which are able to change position on an atom or molecule, and which can be shared between 2 or 3 atoms, thus forming either the sigma-bond or the pi-bond known.
The important fact to understand, is that This quasi-particle does not represent a wave-function, and so its mutability also does not represent the mutability of a wave-function. This charge-droplet has mass.
What is typical about this subject in a negative way however, is that Chemistry teaches us that the single-atom state is also the original state of an element. This is not true in practice. When most elements are gained on an industrial scale, they are dug out of the ground already-bound to other elements, and chemical reactions are used to purify them. Even when they do form the only element in a quantity, the atoms are still usually bound to others of the same element, thus forming O2, N2, Cl2, etc.. (:3)
Only, in an abstract way, it is still the desire of the atom from its single-atom state, to complete its orbitals, thus completing an octet ideally, that forms the best first-approximation of how it will react. Many other behaviors are known, in which some of the electrons remain unpaired, thus resulting in paramagnetism, or in which the completed valence shell ends up with a higher number of completed orbitals, than 4. And these frequent exceptions make Chemistry harder to study, than ‘Chem 101′ would have taught it.
1:) Unlike reactive elements, the inert gasses commonly do occur in the single-atom state.
2:) The way I was taught the meaning of the phrase ‘Multi-Centered Bonds’, 3-center bonds are already extremely rare, and the main examples I know are certain hydrides – where the hydrogen atom can also be related to an unshielded nucleus, such as in Beryllium Hydride. In this example, each hydrogen atom shares a bond with 2 beryllium atoms, resulting in a chain.
Another example I know, involves the Pi bond from a double-bond, where double or triple bonds exist as Sigma bonds – which form an axis between two atoms – plus 1 or 2 Pi bonds, which stand out from the Sigma bond as mirror-images at 90⁰ angles in 3D. This involvement of Pi bonds is also what makes
quadruple bonds between two atoms impossible. Well, the Pi bond can become attracted to a 3rd atom, acting as a cation or an oxidizer, thus forming another kind of 3-center bond.
By default, a covalent bond is an electron-pair shared by only 2 nuclei, while electron-pairs attached to a single nucleus do not form a bond, but nevertheless exist, and contribute to satiating the electronegativity of the atom in question.
Further, those single-centered electron-pairs are often available, for ‘coordinate covalency’ to form, starting from an atom that is not coordinate yet, and that so far has a formal charge of zero. Once coordinate, its valence will have changed, and it will acquire the corresponding formal charge.
3:) It can happen that when a quantity of atoms belongs to the same element, each atom is bound to more than one other atom. Hence, covalent solids can form, out of one element, as opposed to the molecular solids. In this way, Sulfur can consist of the molecular solid S8. But when we heat it, shortly after melting, it will want to form the polymer Sn. And in other examples, the 3-dimensional structure of the solid is too complex to be stated fully in this notation, so that notations like Al(m) and B(s) are often written, to refer to the metal or the solid form, without being more specific.
This generally does happen, if in the abstract single-atom representation, an element has fewer than 4 valence electrons. Hence, this will happen to most of the elements in the periodic table – when pure – even though practical chemistry often tends to focus on the atypical, well-behaved elements, towards the upper-right corner, that are also the basis for life-forms.
The only way metallic beryllium can complete its octet – and thereby, its valence shell – is by forming a crystal with as many electron-pairs, as there are beryllium atoms, to balance the charge. But I think that in such crystals, as soon as 1 electron pair is being shared by 4 or more atoms, this may no longer be called a covalent bond.