Biosapien,
We're not 100% sure about this stuff. Orbitals only came about in the last 100 years with the dawn of Quantum Mechanics.
Quantum Mechanics is largely based off the
Schrödinger equation. It's really stupidly hard to solve the Schrödinger equation, so we normally can't come up with exact solutions. At best, our idiot selves usually either simplify for analytical (mathematical) solutions or use computers to generate approximate numerical solutions. For analytical solutions, it's easiest to look at Hydrogen since it's got only one proton and one electron, making it a really simple atom.
When you solve the Schrödinger equation for Hydrogen, you get the
atomic orbitals that they teach you about in Chemistry class (which are actually
hydrogen-like atomic orbitals). These "orbitals" are literally just solutions to the Schrödinger equation if we assume that atoms are made up of a point-like nucleus with an electron. Other shapes aren't orbitals because they're
not mathematically valid solutions to the Schrödinger equation.
Technically orbitals aren't the solid shapes that you usually see in pictures; those are simplifications. Orbitals are actually waves since quantum mechanics is all about waves. For example, the first S-orbital might be drawn like a sphere, but it's actually like the upper-left wave in this picture:
.
How do you draw that upper-left wave? As a sphere, if in three dimensions, e.g. as the S1 (upper-left again) image in this figure:
Note that the orbitals drawn in this picture don't actually have discrete boundaries, but rather just have areas which are more probable than others. Folks who draw orbitals discretely, e.g. the left-most image in this figure
,
are just drawing the areas with higher probablity distribution as being part of the orbital while ignoring areas with lower probability distribution. For this reason electrons aren't actually 100% confined to the areas shown in the solid drawings of orbitals.
But as stupidly complex as the Schrödinger equation is, it's got one really nice, clean property to it: solutions to it are
linearly independent. This means that, if you have two waves which are a solution to the Schrödinger equation, then you can literally just add those two wave solutions together to get a third wave solution to the Schrödinger equation. See also:
Hybrid orbitals are solutions to the Schrödinger equation which can also be described as the sum of the solutions which we normally call atomic orbitals. Their shapes appear to be a mesh of the composing hybrid orbitals because it's just the two wave equations added together. Note that linear independence means that you can also subtract one solution from another to get a valid solution, which is where
antibonding comes from.
Orbitals have different energies since electronic charges like being near each other as described in
Coulomb's law. I don't know how accurate this is as I haven't done Quantum Chemistry in quite a while, but conceptually you can think of an orbital's energy as being something like
,
or, in an alternative notation,
,
i.e. as the energy of two separated electric charges (the electron and the nuclear of the atom) integrated over all space by the probability of the particle being in that spot in space (i.e. the square of the wave function).
See also:- Effective nuclear charge, which replaces when considering atoms that have multiple electrons (as opposed to hydrogen-like atoms).
- Table of values for effective nuclear charge. Note that Hydrogen has an effective nuclear charge of since it's the very definition of a Hydrogen-like atom.
Summary:
- Atomic orbitals aren't actually solid shapes. Drawings showing orbitals as solid shapes are just simplifications highlighting the most probable locations within the orbital.
- Hybrid orbitals are the sum of other orbitals. Their weird shapes are just the drawn solid approximations of the wave that results from adding the waves of the orbitals which are added together to form the hybrid orbital.
- Orbitals closer to the nucleus separate electric charges (the electron and the protons in the nucleus) less, so their energy is lower.
- We don't fully get quantum mechanics, so if this confuses you, it's okay.