Surprises in Quantum Mechanics (SiQuM) 2. Quantum Water

Let's enter the QM world in terms of a well-known candidate with a tiny size of about 3 angstroms: Water [1], chemistry calls it H₂0 is the most common molecule on earths' surface and by far the most important one for live. Interesting to note, that still buries some mysteries - or let's say - strange behaviours. Some of them I would like to uncover here.

The constituents of water and its physical phases

We know water to exist in the following physical phases:

1. Ice: Below a certain temperature, water employs a cristaline structure which pontially makes us smile in form of snowflakes and make our drinks cold: Ice cubes (I remember sitting down in "Thomas' Travern" in Batavia serving the 'biggest cocktails (bowls) in the US': 10 ice cubes and 10 shots ...).
2. Water of course, which has the astonishing quality to arrive its densest point at 4 degrees Celsius (40 degrees Fahrenheit) allowing the fishes to survive in a frozen pond while the surface is covered by ice (well, we know a large and fragile system as north pole).
3. Steam, where the number of atoms/molecules (of an ideal gas) in a certain volume does not depend on the 'molecules' but rather only on the (internal) temperature and the (external) pressure: The Avogadro constant [2] telling how many atoms/molecules are in a mol (about 6 * 10²³ constituents per mol corresponding to about 22.4 liter or 6 gallons at sea level and 20 degrees celsius) .

Now let's look at the structure of the water molecule consisting of

1. one oxygen atom (O with 8 electrons and 8 protons together with the same amount of neutrons in the nucleus) and
2. two hydrogen atoms (carrying one electron and one proton only).

We realize the following (well-known) setting:

Given the oxygen atom the inner orbital is complete saturated by the two electrons, while the following orbital lacks two electrons to be complete (six auf of eight) and thus tries to compensate for that while capturing those electrons from their fellow atoms. This makes oxygen very aggressive (and make iron rusty) since the amount of energy to be saved in the particular saturated sate is one of the highest for all atoms.

On the other hand, the hydrogen has one spare electron. Since it is very low weighted it can be easyly caught be the oxygen atom which perfers to pick up a couple. We call this oxidation: 0 + 2 H -> H₂0 and it releases about 572 kJ/mol.

It is interesting to know, that the tough binding results in some remarkeable physical attributes:

1. The combustion 2 O₂ + 2 H₂ -> 2 H₂O is the one of strongest exotherme reactions, given the released energy.
2. The resulting expansion speed can be up to 4600 m/s depending on the mixture of hydrogen and oxygen.

Water's isotops

Apart from the standard hydrogen - including one proton and one electron - we recognize:

• Heavy Water based upon an oxygen atom and two deuterium atoms , where the hydrogen is replaced by its deuterium derivant consisting of a couple of protons and neutrons in the nucleus: (2 * ²₁H) + O.
• Half heavy Water including one oxygen atom, one hydrogen and one deuterium atom. This is more frequent than heavy water.
• Super heavy Water featuring a couple of tritium (³₁H) atoms substituting the single proton in the hydrogen by a (unstable) 'menage a trois' consisting of a neutron-proton-neutron nucleus.

Water's Spin and the Nuclei

Even if considering just standard water H₂O, things are not so simple, since nature is rich even in the simplest case. While the 'V' shaped water is due to the electro-magnetic forces of the atomic shell, where the electrons try to find a place with least potential (= e.m. energy) preserving a 'net charge', the involved nuclei come into the game:

• The 'spin' of the oxygen nucleus is 'O' and plays no role here.
• The 'spin' of each hydrogen nuclei is '1/2' and forces the entire spins (typically called the 'z' direction) to be either parallel or anti-parallel aligned.

While this does not impact its chemical behavior it does however have physical consequences, since it implies different states.

Water's Quantum States

Water exists therefor in two different states (we may call that its 'hyperfine' constitution since it is due to the nucleus spin):

1. Ortho-water has a sum spin state of the nuclei of '1' since the spin of the hydrogen atoms are parallel (1/2 + 1/2 = 1).
2. Para-water posseses an anti-parallel alignment of the hydrogen spins: 1/2 - 1/2 = 0 .

In fact, from a physical point of view these are differnt beasts! The question is: Does it make a difference? The answer is: Yes and No; depending on the observers's view. Lets try to understand this.

Superposition

The first question to ask is: Is it possible for ortho-water to become para-water and vice versa?

The answer is: Yes. But the only mechanism is via (elastic) scattering and not via photon exchange. Photon exchange is a matter of the atomic shell and of course can not change the nucleus spin states.

As a consequence, we need energy to allow ortho- and para-water to exchange their states: This is simply temperature: In case the water molecules have high enough temperature (= energy) we we see an equilibrium of both states. This happens at about 50 Kelvin.

The second question is: What is happening below that limit?

The answer is: We see two distinct 'species' of water, but only if the (thermal) energy is small enough. Now both 'species' decouple and the relative frequency of both 'species' depends on their (internal) energy difference.

What does this mean? The (energy) ground state(s) of the para-water is smaller than that of ortho-water, since the ortho-water has a residual magnetic moment (spin = 1), while para-water (spin = 0) is not impacted by magnetic fiels. The (very tiny) energy difference is in the range between 2.15 and 6.3 meV (1 meV = 10^-3eV); depending on the residual orbital state of the hydrogen. Howerver, given the magnet moment of the ortho-water, we can separate both 'species'.

If we 'remove' all energy of the water finally all water molecules will be para-water. Increasing the temperature (thus heating it up and including a small amount of energy) - before any possible state is washed-out - we observe the following:

1. The possible states of para-water are simply |↓↑> and |↑↓> which are identical and subject of exchange by any hydrogen atom (and thus are in-distinguishable).
2. For ortho-water we have: |↓↓> and |↑↑> (they are in-distinguishable) and in addition a mixture of 1/2(|↑↓> + |↓↑>).

We call the last result superposition and it is an unique quantum world behavior. Given a spin 0 we have 1 (one) state (singlett), and with a spin 1 state we end up with three (3) states (triplett). Thus we conclude: S = 2*L + 1, where L is the angular momentum (including the spin) and S is the amount of possible states.

In the quantum world we do have state mixing as intrinsic property, called superposition!

Water Isomers

Given low temperatures and low densities, water just behaves as two different species. In order to meet an equilibrium, kinetic energy exchange is needed ... and this takes time until the molecules actually meet. Until then, we call those (different) species Isomers.

Water isomers are in turn as natural as hydrogen isomers [8], if degeneration [9] is still not present:

• Water in the high atmosphere of earth
• Water in outer space

While we observe a comparable pattern for hydrogen itself [8], the behavior of water is more important for us, as inhabitants of earth. Futhermore, the physical organisation of molecules is results in structures like the RNA/DNA yielding in a complexity requiring sophisticated computational methods [5].

Additional reading [4, 10].