mycotheology said:
Thanks for the reply! Its starting to make sense to me now. So to help me understand what local minima represent, you mention the conformations of n-butane. I know that the staggered conformation will be the global minimum since its the most stable possible conformation. Will the other conformation (the staggered conformation being the only other conformation for n-butane) be represented as a local minimum? That makes sense to me.
As for structural isomers, I'm a bit confused there. Are you saying structural isomers are all part of the same potential energy surface? For example, n-propanol and isopropanol, they are 2 different compounds so I would have assumed they would each have their own PES. Saying ethane and ethene have the same PES really confuses me. Ethane has 2 extra hydrogens so its not even an isomer of ethylene.
To make sure we have our terminology straight, suppose that we are looking along the 2-3 bond of n-butane and rotating in a series of 60° steps.
We start with the global minimum -- staggered, but a trans- conformation. Then we come to a saddle point (eclipsed, but with each methyl group aligned with a H atom in a chiral conformation), a local minimum (staggered gauche-, also chiral), another, higher saddle point (methyl aligned with methyl in D
3h symmetry), local minimum (staggered gauche, the other enantiomer), and saddle point (eclipsed chiral, the other enantiomer).
Regarding
structural isomers I was not meaning to say that ethane and ethene have the same PES, but that ethane shares the same PES with (ethene plus dihydrogen).
And yes, I am saying that structural isomers share the same potential surface, and n-propanol and isopropanol is a good example.
A potential surface must be seen as a (3N-6) dimensional contour map, which shows the potential energy as a function of the relative positions of the N atoms in the system. N atoms would give 3N components; the '-6' represents translations and rotations of the whole system. In practice, you use one of the N atoms to fix the origin, set the x and y co-ordinates of another to zero to fix the direction of the z-axis, and set the x co-ordinate of a third atom to zero to fix the direction of the y (or xz) plane.
If you work in a local region close to the potential minimum for a particular isomer, then Gaussian will give you a fix on that minimum. But if you are working with a shallow local minimum when there is a much lower global minimum, Gaussian is quite capable of moving to the wrong minimum, and you may need to be quite close with your initial guess at geometry to get the program to home in on the right minimum. For example, if you are trying to find an optimum geometry for ethenol, you are quite likely to find that Gaussian will converge on acetaldehyde.
The other important point that arises in using Gaussian is that because they share the same potential surface, you can actually use Gaussian to track the potential surface for an elimination reaction like ethane → ethene + dihydrogen, or for an isomerization reaction like methyl isocyanide → methyl cyanide (acetonitrile) {assuming that the latter is an intramolecular reaction}.
