How long does it take to numericaly solve the time-independant schrodinger equation for molecules of different complexity?

Like water, CH4, benzene, cholesterol, DNA, etc...

Up to which molecule is it reasonable to attempt it on my 3.06ghz computer? Lets say that reasonnable is a simulation time less than 1 hour. furthermore, are there ny downloadable software on the internet that could do it?

if i remember p chem correctly (thats a big if!!!) The Hydrogen atom is the only one that can be solved exactly and the others are approximations. That being said your question would depend on how precise you choose to be with your calculations.

Let me do some refreshing and try to get back to you

or anybody else tell me how far off I probably am right now

Let me at least ellaborate and say that when you solve a wave eqn for something with more than 1 electron you basically get an N*N matrix and you need to solve for each electrons energy with regards to the nucleus and also the energy (electron-electron repulsion) between the N electrons themselves. This is the term that can only be solved via computational methods and can never be exact. You must then also add in an energy term dealing with the ability of the electrons to exchange spin states.

Basically, it depends on the resolution required. In 2D is possible to solve time dependent SE in realtime on the resolution 300x300 easily - so I suppose, using a PixelShader technique (which is 20-40-times more effective in speed, than pure C/C++) it would be possible to obtain to about 1 iteration/second at the same resolution in 3D, but the convergence speed will be 10 - 30x lower, than in 2D. It corresponds to about 1 - 5 timestep per minute at the 300x300x300 resolution. It's the lowest speed limit on todays HW, of course.

Both huskerdrew and zephir are correct.

Approximation methods are used for anything beyond, I believe, He. But approximation methods are fine, like zephir said, are dependent upon the level of resolution. Also, these are time-INdependent SE's, as TD SE's aren't usually necessary, given the end goals, like the examples I gave below.

You max out your resolution, due to the inherent issues w/ your approximation basis sets you choose in the first place, however.

It largely doesn't matter, though. The reason why it doesn't matter, is that, take ozone or benzene for example. You would use approximation methods to find out where the electron nodes are for the energies you're interested in. Once you get that, then you use specific types of software, like Gaussian v0.3, to get the total number of possible orbitals for that energy range (usually 10-16 or so). You then look at the shapes of these excited states to solve the problem that interests you.

Examples like this are often used to find hyperfine electron shifts and triplet v. singlet electron states in molecules or the more likely hybrid molecular orbitals that a particular molecule is employing at a given energy level, to explain whatever phenomenon is observed empirically. Once you get the computational data, it's then easier to design an experiment to prove or disprove the hypothesis.

-ss