I have been performing numerous gs/ts optimizations on an ensemble of small (n=15 +/- 5) compounds, and I was interested in trying to map out all the possible conformations of the ground state one could reasonably expect.
With the number of compounds I'm dealing with, I wanted to find see if there were any methods that can set up a large amount of guesses for ground states instead of having to try and manually guess states. I kind of am envisioning something like a breadth based search that uses a very cheap algorithm like UFF to find a large collection of guesses. Am I being overly optimistic or is there something out there that can help me.
Theoretically, knowledge of an eigenstate and the corresponding eigenvalue enables one to remove that eigenstate from the Hilbert space of the problem of interest. For this, if H is the N x N Hamiltonian matrix, λi its i-th eigenvalue and ui the corresponding eigenvector (a column N-vector), for the reduced Hilbert space the Hamiltonian reads H - λi ui ui†, where ui ui† is naturally an N x N matrix. A systematic search for the conformations amounts to a systematic reduction of the Hilbert space of the problem in the way just described.
Hi Skyler.
You're asking for a procedural method. You may also be seeking software. I'll outline both below.
*** PROCEDURE ***
You're touching on an area which has received much attention; seemingly everyone wants to find as many electronic ground state local (and hopefully global) minima.
I have used a protocol that has served me well over the years. It's a two step operation, or possibly three set with some software packages.
First, I find the initial structures using Monte Carlo. I set the Monte Carlo routine to vary both internal (bond lengths, angles, dihdedral angles ) and cartesian coordinates (stochastic method). I'll generate around 200 structures. These structures will then be optimized using molecular mechanics with a conjugate gradient minimization. This process will yield many structures, ranked by energy.
Finally, I take the top 10 and optimize them using DFT (M06-2X is my weapon of choice). I'm sure to perform a frequency calculation to verify that I'm at a minima on the potential energy surface and to add thermal corrections to the electronic energy (giving me Gibbs Free Energy).
Once I have the energies of these minima, I calculate their Boltzmann populations. A 1.3 kcal/mol difference between a local minima and a global minima represents a 10% population of the 1.3 kcal/mol local minima. And this is using a two-state approximation. It may be even less if there are minima between the global minima and the 1.3 kcal/mol local minima.
However, you may want to keep all minima. I've seen examples in the literature showing that higher energy local minima initiate chemical reactions.
*** SOFTWARE ***
I use the BOSS software package, utilizing the OPLS-AA force field, by Professor Bill Jorgensen. I also use the PCModel program by Serenasoft. It contains the MM3 force field
A free alternative is the Tinker suite by Jay Ponder. The MONTE program ought to perform most of what I've outlined above. It also possess a number of force fields, including MM3. All of these programs don't perform the DFT calculation. Free programs for that include NWChem and GAMESS.
BW
Wavefunction Spartan has an excellent algorithm for conformational search. If you have the software available, I'd be happy togive you details
You can perform on-line conformational search with evaluation of probability of existence of each conformer at www.chemosophia.com now for free. It can be done using “Extended Global Minimum Search + Construction of Multi-Conformational Molecular Model (4D-Structure)” or “Extended Global Minimum Search + Construction of Multi-Conformational Molecular Model for Chiral Molecules (4D-Structure)” software after registration.
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