Todays computational chemisty will not far from those above two words. DFT or density functional theory and HF or Hatree Fook. The last term is sometimes called as ab initio model. What is DFT or HF? and what is the different between them? That question is rather complicated to be answer as it takes long detail explanation, complicated, and required good understanding in basic physical chemistry science. Anyway, I hope this simple explanation will tell you correctly about those two ‘magical’ words.
It is better to start from HF or Hartree Fook teory which is classified as ab initio model of quantum chemistry. And also better to review our knowledge about atom and electron. We can describe ‘part’ of the electron behaviour similar to a wave function, especially when we deal with movement, interaction, existance, and so on. Each electrons in an atom has different wave function. No electron in an atom has same wave function. As it follows wave function, we can not predict exactly the static position of electron, we just able to know the probability of its exsistance in a specific region. This theory is called uncertainty Heissenberg. Now how they formed or arranged on an atom. Electron will locate on the place where the lowest energy is available. In atom structure, the lowest energy is 1s (1 means 1st shell and s means orbit). Shell and orbit? Lets see our astronomical system of our sun and its planet. 1st shell is the shell of 1st plane, Mercurius. And orbit is the way how planet moves 360o to the sun which can be perfectly round shape, parabolic, elips, and so on. The orbital types in atom are classified as s, p, and d. I think you already get this knowledge when you were high school. Now, how about if there are electrons in 1s? the ‘new’ electron will find another empty shell or orbital. Still, the criteria to find it is: as lower as possible, in this case it could be 2s, and so on. This algorithm is called as aufbau principle. We will come back to the HF theory. Actually still many more as the basic for knowing better about HF and DFT, e.g. Pauli restriction to distinguish the double electrons in one shell and orbital by spin introduction terminology.
As each electron has different wave function, we can collect all of the wave functions into a combination set of those wave functions called atomic orbital. Again, to build a molecule from atoms, we will combine it those all atom orbital into single molecular orbital. Many ways to do it, one most famous is called as LCAO (linier combination of atomic orbital) or LCMO (linier combination of molecular orbital). If I can make in mathematical term, it looks like: Total=aA+bB+cC+… where a is coefficient for atom or molecule A (applied to b, c, and d .. for atom or molecule B, C, and D) and A is the atomic orbital or molecular orbital of A structure.
Shortly, this is the way of HF doing the calculation. That is the reason why it is called ab initio because it is created from very small (electrone wave function combination) and basic thing to build the bigger one. When you make a calculation from H2O for example, this method will calculate the electron to build H and O atom and continued to H2O molecule. How about the energy, charge, ingeraction, spin, and so on? Don’t worry. Wave fanction of electron brings already so many informations about it. Correct combination calculation will give you ‘magic’ things like atom-atom distance, surface energy, and other properties.
Now, lets move to DFT. Is it different? DFT thinks it is too complicated to calculate and consider single electrone wave functions on every calculation. Heavy and takes long time. For example benzene which has 6 C atom and 6 H atom. so many electrons there. So how? DFT will think it as combination of electron density function. Electron has a kinetic energy compared to nucleus (atom core) and to it environmental (to other nucleus atoms, electrons). Lets take an example, probably not 100% correct as it is difficult to find the perfect ecample. There are 100 people live in a village and you want to characterized those people inside. Using the ab initio method, what you do? You will investigate the exact type of people may be how old (young people will be more active than old ones), where is his/her position whether stay in the top of mountain which less people or in downtown which is many people (mountainous people are usually close mind people than they who live in downtown), their interaction (what happen if one people meet others, may be they will do gozzip or fight each other, and so on). Based on this data you will make a report on avarage characteristic of people on that village. How about DFT. As DFT more concern to the density, DFT will ask the data: how far this person from the first person, second and based on that distance one to the others, you can make a guess (with help of some reference data) to characterized the people behaviour. Based on this you can also make a report on the characteristic of the people. Now, lets see the advantage and disadvantage. Using ab intio sampling method, you will spend more time, as you have to know detail about each person (his age, his location, his relation to specific person) compared to DFT (you just need a data about distance one person to other). First method you will need 300 data (3 sampling point x 100 people) but DFT just 100 as only 1 sampling data x 100 people. Which one is better? you can easily say the first one. More complete data and exact. Now the question, how about the correctness of DFT? as I said above DFT just thinks about the distance of people to others but the reference can be very important. If that reference is perfect, DFT method can be as good as ab initio.
That is the idea comparison between HF and DFT. DFT will combine between experimental and numerical to cut the expense of expensive HF calculation method. DFT will not answer totally about what happen there in the system as part of the method come from experimental. Very brief explanation but hope you will understand.
For further reading, I suggest you to read:
1. Szabo and Ostlund, modern quantum chemistry, Dover publications (primary material)
2. Jack Simons, An experimental chemist’s guide to ab initio quantum chemistry, J. Phys. Chem., 1991, 95(3): 1017 – 1029
