Thursday, April 18, 2013

What is LDA?

Dear Diary,

I learned about another way to use DFT today called the Local Density Approximation.

Normally quantum mechanics works by solving a Hamiltonian for a wave function and then determining all the properties from that wave function.  If you take the modulus of the wave function, you can find the density of the electrons in the system.

Now, Density Functional Theory relies on having the density and plugging that into something called a functional which takes a function (here, our density) to a number.  If you write down an approximation to a functional using only powers of the density (and not the derivatives), then you're using a Local Density Approximation (LDA).

Monday, April 15, 2013

Notes and Computers

Dear Diary,

The group Computer Whiz has set me up with several computers.  First, there is a computer that he works on.  I am to run all the code for that on this computer.  Second, there is a software hub on the internet named GitHub that the group uses to make available its software.  There are also several big computers to run larger codes that I can use if I make something that big.

Now, there is also a server called pbe (PBE is a functional that Professor Burke made with two of his friends...we'll have to talk about that later, diary!) that is public for everyone in the group.  So, work that I create needs to be on that server.  Professor Burke says that if I'm hit by a bus, then the next, younger, brighter, and more machine-like student should be able to pick up my current research in a snap.

I have my own personal folder under the home directory marked by my username.  I've formatted it so I can find things easily in there.  I also need to make sure that a copy of all the work is under /home/pbe/gamma where everyone else's stuff is.

Thursday, April 11, 2013

What is Hartree Fock?

Dear Diary,

Today we learned in the ABC of DFT about Hartree Fock. 

Finding the wave function for all electrons is difficult because the electrons push on each through a Coulomb force.  It would be advantageous to calculate the wave function of one electron with the others stationary and then calculate the rest of the electrons sequentially.  Once you go around the set of electrons a few times, then things will stop changing and you have a good approximation as to where the electrons should be.  One way to do this is by writing the wave function as a Slater determinant.

Density Functional Theory is all about approximations, and there are a lot of them, so I'll try to keep you in the loop, diary.

My first project

Dear Diary,

Professor Burke wants me to take a warm up project to start off with.  His prized student Lucas and post-doc Miles are comparing what Density Functional theory looks like in 1D against the highly accurate DMRG.  The end goal is to find lessons on how to apply DFT in three dimensions with these comparisons.

One project, which seems to be lurking around in pieces on the group server is an investigation with expellium (exponential interaction + jellium) where the regular Coulomb interaction has been replaced by an exponential interaction.  I am to find all the pieces of this project and formulate a paper on it before August.

As a part of a weekly, individual meeting with Professor Burke, I should type up an individual meeting note and send it to him.  I included a sample of my first note in the new person folder on pbe for new students.  It's located inside the Beginner's Guide.

Tuesday, April 9, 2013

I joined the group!

Dear Diary,

I finally got a chance to accept Professor Burke's offer.  I can't help but wonder if I've played right into his plans.  He said as soon as a desk opens up, I could move into the building with the rest of the group.

He also wants me to take the ABC of DFT introductory course.  He's written a book over the past few years with his students to introduce the topic.  The Chemistry department offers the course as a class for credit, so I'll take some units and show up for all the meetings.

Thursday, April 4, 2013

I'm in the group!


Professor Burke took a poll of everyone in the group and offered me the last spot on the group.  I guess I didn't make everyone angry!  I'm very keen to accept and will tell him that tomorrow.

Right now, the quarter is taking up a lot of my time, and I should probably concentrate on the classes since they're only a few weeks long.  I only get once chance to do well in my classes, but I'll make sure I put in a lot of effort over the summer to produce high quality research.

Maybe I can sneak in some research anyway...