The PDF file Solve_HAtom_AtomicUnit.pdf illustrates how to solve a Schrodinger equation using powerful analytical capabilities of Mathematica. Implement this yourself in Mathematica, and examine the wavefunction and radial probability distribution function of hydrogen. This example illustrates the essence of calculation of atomic orbitals and the role of Skater functions
The PDF file VarPrinc_HAtom_Accurate.pdf file illustrates how to calculate the energy of hydrogen atom when the accurate wave function is known. Implement this yourself in Mathematica, and think how could this program be modified such that it could optimize approximate wave functions.
Ab Initio calculations can be very demanding of computer resources and calculations of larger molecules, or calculations with larger basis sets are often practical only in dedicated workstations, computer clusters, or supercomputers. Such computers have typically large (more than 1 TB) hard disks disks and large (more than 4 GB) memories allowing to storage integrals that arise during the computation. Such computers often have a number of processors allowing either parallel execution of one job on several processors, or simultaneous execution of multiple jobs. In this tutorial you will learn to interact with one remote computer housed in the Department of Chemistry and Biochemistry; you will learn how to access and use a supercomputer in TeraGrid later in the course.
You connect to remote computers using the program ssh. You need to give a name of the computer that you are connecting to; for example ssh -X nickname.department.university.edu would connect you to the computer "nickname.department.university.edu" assuming that you have an account on this computer. The -X flag allows to run graphical programs on the remote computer using your local display as an output device. Thus, you can create the input file on the remote workstation using a molecular editor such as MOLDEN and a text editor such as nedit. Sometime, you may need to transfer files back and forth between the remote and the local computer. You can transfer files between computers using Secure Copy protocol, or scp. For example, if you have created an input file named molecule.dat on your computer, you can transfer this file to the workstation into your directory by typing scp molecule.dat nickname.department.university.edu:/home/chem226/PERMNUMBER. Similarly, if the calculation has produced the output file molecule.out, the command scp nickname.department.university.edu:/home/chem226/PERMNUMBER/molecule.out . transfers the output file to your local machine into your current directory ( . ).
You will be using a computational chemistry program Gaussian03 to perform some calculations. Gaussian is one of the most commonly used computational chemistry programs and it is important that you learn well how to use it. One valuable resource is their on-line technical documentation. Later in the course you can decide when to use Gaussian (e.g. geometry optimization with analytical derivatives) and when to use PC GAMESS (e.g. single point calculations).
You can use MOLDEN to build and save Gaussian Z-matrices. Building formaldehyde and save it as Gaussian Z-matrix and insert the following block of lines just before the structure definition.
%Mem=48MW # HF/6-31+G(d,p) Opt=CalcAll MaxDisk=1GW Formaldehyde geometry optimization by calculating Hessian at every step 0 1
Inspect your file. A typical Gaussian input file will have a section that allocates computational resources (Link 0 commands that start with %) followed by the route section (lines that start with #), the title section (free format text), and molecule specification. There are three blank lines: one separating the route section from the title section, the other separating the title section from the molecule specifications, and the last one at the end of the molecule specification. The section that you added tells the Gaussian program to allocate 16 megawords (128 MB) of memory and perform optimization while evaluating the Hessian at each point. It also specifies the charge (0) and spin multiplicity (1) for the molecule. Both the charge and the spin multiplicity are integers. Charge is the total charge of the system (e.g. zero for a zwitterionic amino acid) and the multiplicity is 1 for closed-shell molecules in the ground electronic state. Multiplicity is 2 for single radicals and 3 for diradicals, such as molecular oxygen.
Execute the calculation. You can call the program directly as in g03 < input.dat > output.out & .