Can a single molecule have a state? I was studying a book about thermodynamics of nanosystems and I got stuck with this question in my mind which I couldn't find an answer for.
For instance, does a single water molecule have a state, like being liquid or something?
Or is one molecule of TiO2 solid or gas?
I would appreciate if anyone could clarify this.
I should state that I am not considering a macromolecule in my case.
 A: You can't build a liquid from a single molecule. Neither you build ice with a single molecule.
A single particle (in your case, molecule) has no state. A water molecule isolated from the rest of the water, "doesn't know" anymore that it belonged to a liquid state or a solid state, or to vapors.
A: Traditionally, for proper phase transitions, and thus phases, to exist, you must in statistical mechanics take a thermodynamical limit, i.e. make the system infinitely large. In actuality this is a bit more involved (not to even start with nonextensive systems), but let's start working from this assumption.


*

*Given that you need a lot of particles (mathematically, infinite) to define a phase, it is then clear that one particle does not a phase make. This is to say that a single molecule is not solid or gas. 

*That said, a single molecule that is made up of many atoms most certainly can have phases and phase transitions of its own: The molecule is a system of its own and if it has enough atoms, we can approximate as if it had an infinite amount. As an example, polymers can undergo the helix-coil transition.

*Finally, consider the question of whether by looking at just a single molecule in a phase A, it is possible to identify the phase as A. Turns out that in practice it often is. In this sense a molecule does have a state identical to the macroscopic state. For example, the lipid bilayer has a gel-fluid phase transition. The gel is kind of a solid, where the molecules are packed in a rather ordered fashion, whereas in the fluid state the system is, in a sense, a 2D fluid. Now instead of looking at packing and symmetry at this scale, one could also measure the order parameters of the individual molecules: In the gel state the tails of the lipids are straight and in the fluid state they flap around more freely. This is to say that the molecules do have internal states that often correspond to the phase at the macroscale.
A: A single molecule doesn't have a state of matter. Single or individual molecules (when observed in Ion Traps) are considered to be "Gas". It requires a minimum of n(unknown to me) number of molecules to define the state of matter. 
A: From Wikipedia:

The atoms in a solid are tightly bound to each other, either in a
regular geometric lattice (crystalline solids, which include metals
and ordinary ice) or irregularly (an amorphous solid such as common
window glass).
A liquid is made up of tiny vibrating particles of matter, such as
atoms, held together by intermolecular bonds.
Gas particles are widely separated from one another, and consequently
have weaker intermolecular bonds than liquids or solids. These
intermolecular forces result from electrostatic interactions between
gas particles.

We see that a phase state is defined by the bonds between atoms/molecules rather than the particles themselves. (Although historically they were defined by more empirical properties, a solid retains its shape, etc.)
A: A simple example for this question would be $\mathrm{H_2O}$
In liquid and gaseous states, the molecules are in random motion, whereas in solid state (ICE) these molecules form bonds with adjacent ones. A single molecule is the same in all the three states, what changes is the interaction between them.
A: What is a state?
State or more precisely state of matter or thermodynamic state is a concept that is meaningful only when dealing with a thermodynamic system, i.e., a system consisting of many particles (where many usually means something of the order of the Avogadro number).
What is a molecule?
In many cases a molecule acts as a single particle - e.g., a molecule of $H_2$ in hydrogen gas or a molecule of $H_2O$ in water or water vapor or ice. However, a completely opposite situation is possible, where the molecule itself is a huge thermodynamic system with many constituing particles. Indeed, thermodynamic description is routinely applied to metals and semiconductor crystals, which aree ssentially single molecules. As an intermediate case one can think of macromolecules, such as polymers or organic molecules, which have as thermodynamical properties internal to them (e.g., one can use statistical physics to analyze the number of unzipped bonds in a DNA), as well as parts of a solution of many molecules (proteins in a cell), as well as the intermediate behavior, such as protein folding.
