This is a good question. The short answer is actually that the electrons aren't exactly "fixed" in particular "positions" "above" the oxygen. They reside in lone pair orbitals, which means they have a probability of existing in some region of space which is generally depicted as being "above" the oxygen, and an extremely low but finite (non-zero) probability of being outside of that region (e.g. closer to the bonds the oxygen forms with the hydrogen atoms.

But let's back up a little and first think about what comprises a water molecule. A water molecule is comprised of two hydrogen atoms, each of which are covalently bonded to an oxygen atom. There are a total of two covalent bonds in the molecule, one between the first hydrogen atom and the oxygen atom, and another bond between the second hydrogen and the oxygen. These single, covalent bonds are called "sigma" bonds. Each sigma bond has "room" for two electrons. Now let's think about how these sigma bonds are formed...

Each hydrogen atom has a single valence electron which it "shares" with the oxygen atom in its respective sigma bond. The oxygen atom, in turn, has six valence electrons available, two of which go toward the sigma bonds made with the hydrogen atoms (one valence electron to each sigma bond). That means there are four remaining electrons, which reside on the oxygen as lone pairs. In each lone pair, one of the electrons exists in a "spin up" configuration, while the other exists as a "spin down" electron. Why is this? It is energetically favorable for the electrons to exist in this configuration.

Furthermore, if the electrons existed in the same spin state AND belonged to the same orbital, we would be violating the Pauli Exclusion Principle, which forbids particles from having the exact same four quantum numbers, which you have probably learned about in your chemistry classes, but if you are rusty can look up in your old chemistry book or at the UC Davis Chem Wiki page on quantum numbers.

So why did we go through all of that? What we've said so far is that there are two sigma bond orbitals, each with two electrons, and two lone pairs, also comprised of two electrons each, associated with the oxygen atom in the water molecule. All these orbitals (bonds and lone pairs) have electrons distributed among them. The orbitals themselves are a way of describing the probability of where an electron may be found.

Look at the following figures for a clear picture of the process.

Fig. 1 depicts a cartoon version of an O-H sigma bond. The "probability density" of finding the electrons is highest between the O and H, and is extremely low outside of this area (thus, we have a bond, because the electrons are most likely to be found between the O and H). The electrons in turn attract the nuclei of the O and H atoms, thus "keeping them" "close" together.

Now, all of the electrons in the orbitals are negatively charged, which means they have a repulsive interaction with the other electrons in other orbitals. Thus, the sigma bonds and the lone pairs will be oriented in such a way as to minimize the overlap between different pairs of electrons. Hence we see the tetrahedral shape of the orbitals in Fig. 2. Note that we're using lines to depict the bonds between the O atom and the H atoms, but really there is a "cloud" of electron density between those atoms describing the likelihood to find electrons there.

At this point, you may ask, "if the electrons repel each other, why do two of them share an orbital?" And that would be a great question. Hund's Rule states that we should fill the orbitals so they have one electron each, and then start pairing them once we have exhausted all the empty orbitals. This comes back to the idea of quantum numbers. The principal quantum number (1,2,3,...) corresponds to how far away the electrons are from the nucleus, or how large the orbital is. The higher the quantum number, the larger the orbital and the higher (in general) the energy of the "state" of the system. It is more favorable/stable to be in a lower energy state, so we see that electrons typically fill the orbitals from low to high principal quantum number. For oxygen, there are 8 available "spots" for the electrons to be in the n=2 shell. In the water molecule, 6 of the electrons come from the oxygen atom itself, and the other two are "shared" with the hydrogen atoms. So why not start filling the n=3 orbitals with one electron each? It would result in a higher total energy of the system, which is less stable.

OK. That was a lot of information. Let's recap briefly: ultimately, the electrons in the orbitals (both bonding and lone pair) around the oxygen atom in a water molecule are oriented in a way to minimize electron density overlap.

I hope this helps!

You have an excellent question. You want to know why the electron holes are located “above” the oxygen in a water molecule rather than on the sides. You may have seen molecules described with a Lewis structure where electrons and holes and represented as dots on the molecule. You may have seen valence shells represented with the molecular geometry as well. One can find examples at this website click here please . The geometric model is great because it is easy to keep track of charges and we are going to use it for now.

Molecules, as most things, want to minimize their total energy. Oxygen has an orbital shape with sp4 bonds all located about 109 degrees from each other. This shape allows for the electrons to be as far apart from each other while still filling the oxygen’s valance shell. They oxygen and hydrogen are both lacking electrons to have a full valance shell so they share at two of the oxygen’s sp4 sites. The other 2 pairs of electrons want to be as far apart as possible, otherwise the energy of the molecule will increase. Those electrons pairs are located at the unused orbital location. The extra electrons pairs fill orbitals on the other side of the oxygen from the hydrogen. The Lewis structure can be misleading because they are not both sitting on top of the oxygen but rather the two pairs are at an angle. Please look at the images on University of Wisconsin’s website. On the reference given you can see that the hydrogen are actually 104 degrees apart from each other, currently that is a minor detail.

I am going to leave you with a more advanced way of thinking about electrons in molecules. Rather than assuming the electrons are distinct particles which are calmly staying at the lowest energy position of the molecule, let us think about them as clouds of negative charge with a probability of finding the particle at different places. If one was to probe the water molecule for the location of the electrons, one would find that the location would be different each time. The highest probability of finding the electron is the location given by the geometric model. Most of the time you will find the electron pairs ~109 degrees from each other. Sometimes it will be possible to find the electrons on the “side” of the oxygen atom or at different angles. There are other areas where the probability of finding the electron goes to zero. This cloud property is due to the electrons quantum mechanical nature.