On Friday 05 October 2007 12:13:32 pm, Richard Loosemore wrote: > Try walking into any physics department in the world and saying "Is it > okay if most theories are so complicated that they dwarf the size and > complexity of the system that they purport to explain?"
You're conflating a theory and the mathematical mechanism necessary to apply it to actual situations. The theory in Newtonian physics can be specified as the equations F=ma and F=Gm1m2/r^2 (in vector form); but applying them requires a substantial amount of calculation. You can't simply ignore the unusual case of chaotic motion, because the mathematical *reason* the system doesn't have a closed analytic solution is that chaos is possible. > In fact, your example is beautiful, in a way. So it turns out to be > necessary to resort to approximate methods, to simulations, in order to > deal with the MINUSCULE amout of nonlinearity/tangledness that exist in > the interactions of the atoms in a small molecule? Well, whoop-dee-do!! Think again, Hammurabi. DFT is a quantum method that searches a space of linear combinations of basis functions to find a description of the electron density field in a molecular system. In other words, the charge of each electron is smeared over space in a pattern that has to satisfy Shrödinger's equation and also be at equilibrium with the force exerted on it by the charge distributions of each other electron. It's approximately like solving the Navier-Stokes equation for each of N different fluid flow problems simultaneously, under the constraint that each volume experienced a pressure field that was a function of the solution of every other one. Given the solution to that system, you're in a position to evaluate the force on each nucleus, whereupon you can either take it one iteration of a molecular dynamics simulation, or one step of a conjugate gradients energy minimization -- and start out all over again with the electrons, which will have shifted, sometimes radically, due to the different forces from the nuclei. Allow me to quote: "What you said above was pure, unalloyed bullshit: an exquisite cocktail of complete technical ignorance, patronizing insults and breathtaking arrogance. You did not understand word one..." Josh ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=50491496-da7692
