Fusion methodologies Forgive my naivety but it seems to me all the attempts to create useful fusion concentrate on high temps or high pressures or both and samples of fusible material consisting of multiple nuclei.
Is there any research going on in producing fusion on a single pair of nuclei, sequentially?
The LHC accelerates protons nearly to the speed of light and can direct them to hit each other. Deuterons are electrically charged so can be similarly accelerated. LIGO has been built to such exacting standards it can detect movement of thousanths of a protons diameter. Is it therefore not possible to build an apparatus to accelerate deuterons to a precise velocity and in a precise direction so as to precisely hit another deuteron coming in the opposite direction? A sequential stream of deuterons need not fuse 100% of the time as long as enough do to be energy positive.
What am I missing here?
 A: I think you are missing that fusion research is not on whether fusion happens, that has been proven over and over. It is whether the input energy  needed to get fusion can be smaller than the energy delivered by fusion in a controlled way. The break even and over point, so that it can be  used commercially.
Have a look at Inertial confinement fusion research, the other way from magnetic confinement fusion..
Accelerators cannot compete with these bulk process designs in the balance of energy input to energy output, they are expensive instruments ,expensive in energy needed to run  etc. 
A: By tuning the beams correctly, you can make the fusion rate relatively high (generally not even close to $100\%$ though), but even if you could reach $100\%$ it wouldn't be nearly enough for this model to work as a fusion reactor.
The LHC uses more than $1~\rm GWh$ each time it accelerates one load of around $6\times 10^{14}$ protons to near the speed of light. This comes out to around $10^{11}~\rm MeV$ per proton. (Comparatively, a single fusion releases around $10~\rm MeV$). Note that each proton is accelerated to only $6.5~\times10^{6}~\rm MeV$, so even if you could recover all of the kinetic energy as well as the energy released by fusion, you're still putting in massively more energy than you get out.
You can make this better by accelerating the ions to lower energy, but the general problem remains: you put in much, much more energy than you can possibly get out. Current accelerator technologies are very inefficient in terms of how much electrical energy they require for a given amount of kinetic energy delivered to the accelerated particles.
A: The idea of using accelerators for fusion was one of the first ideas considered in fusion research, but it does not work, as collisions of accelerated ions of deuterium/tritium much more frequently end in Coulomb scattering than in fusion. One cannot make all such collisions to be "head collisions". Maybe some radically new idea will make this approach viable in the future, but as of now this is a dead end.
Cold fusion may be possible in a different approach - muon-catalyzed fusion, but so far this approach does not look very attractive for some pretty subtle reasons. 
A: 
Is there any research going on in producing fusion on a single pair of
  nuclei, sequentially?

Yes, there have been numerous attempts to use individual accelerator-driven ions to create fusion.
The first was by Rutherford's team, Oliphant in particular. In 1934 they demonstrated fusion by accelerating protons and firing them into thin metal foils that had various elements diffused into them. There's a very readable paper their experiments here.
Through these experiments they were able to calculate the cross-section of the D-Li/D-D reaction, and it demonstrated that the scattering potential was many orders of magnitude higher. In other words, when fired at each other like this, in the vast majority of cases the D's will simply reflect off each other before they fuse. It is relatively trivial to show that the amount of energy lost through these "missed connections" is many many times higher than the amount of energy released by the rare fusion reactions.
That does not mean this technique is not useful! It has been used repeatedly since the 1930s to measure the cross sections of many other reactions. But it does mean it is not useful as a power-generating system.
And this is why most research focuses on "hot fusion". Very simply, by heating up the fuel the ions are constantly bumping into each other at high energy (that's what a gas is). So instead of having one chance per ion to collide and react, it has many chances (we hope!). Unless you get thousands of such attempts, you're on the wrong side of the energy curve.
However, that has not stopped some from coming up with clever arrangements that try to do this in other ways.
One of the first was the fusor, or more generally IEC. These systems use arrangements of wires to produce was is essentially a spherical accelerator so that an extended ball of fuel is being accelerated towards the center of the chamber. This alone increases the chance of collision by increasing the density as it approaches. However, if an ion does miss a collision, when it exits the other side of the center it is accelerated back in, repeatedly travelling into the reaction area.
Unfortunately, in practice the fuel hitting the wires of the reactor removes energy very quickly. In spite of considerable work, it appears this is fundamental to the design - the wires needed to carry the required voltages have to be large enough that collisions become a problem. Making them smaller reduces collisions, but also possible acceleration.
A modified version of the fusor is the polywell. This uses an arrangement of magnets to pull the electrons into a layer that simulates the electrodes without any physical barrier to hit like the wires. There was great hope for this approach, but there are more modern reasons to believe these cannot work even in theory (see end).
Another, perhaps more direct, attempt is the migma machine. This used a very clever system to store the particles in circular orbits around a common center, sort of like a collection of comets spread out around the sun. When the are at the outside of their orbit they are spread apart, but for a short period on each orbit as they pass through the center (the "sun") they pass by many other particles. Due to the arrangement of the orbits, the ions are going in opposite directions, and have several chances to collide. This system worked, but it was pointed out that purely theoretical reasons suggested it's possible ion density was very low and that it could not be a practical machine. Research on this approach ended in the early 1980s IIRC.
More recently, Tri-Alpha Energy has developed a new design that has some parallels to the migma concept. Instead of an external storage system, it instead fires the ions into a plasma arrangement known as an FRC. I believe the idea is that the FRC's internal magnetic fields basically replicate the storage system of the migma, but I'm not sure I completely understand the design, and I cannot find any recent and clear description of the system.
All of this was upset beginning in the late 1990s, when a series of new studies on the theoretical performance of such systems appears to put the kibosh on any of these approaches. In any system where the fuel is not maxwellian, the scattering events see by the ions and their electrons rapidly cools the particles. This suggests they will all lose energy faster than they can produce it. TAE has claimed their system is maxwellian and does not suffer from this problem, but when I read it I am not so sure, but I simply don't know enough about their layout to make a good judgement.
