Few questions about Gaussian terminology

[mycotheology]

I'm learning about how Gaussian works and I'm reading about potential energy surfaces which Gaussian uses to calculate very properties of a molecule. Right now I'm reading about optimisations, I understand the concept that to optimise the structure of a molecule, it needs to find the global minimum (I'm still not sure what local minima represent) but there is a lot of terminology I don't understand. Firstly what do they mean when they say "convergance criteria"? They say that when convergance is reached, the structure is optimised but what does this mean? Secondly they say that a minimum is reached when the force is 0. Is the force just the first derivative of the energy? That would make sense. They also mentioned force constants a few times, what does this mean in the context of potential energy surfaces?

 

[JohnRC]

(1) local minimum -- bottom of a "pothole" in the potential surface, where the gradient is zero, and the surface is concave upward (positive second derivative) along every normal co-ordinate, but there are regions of the potential surface as a whole at lower potential.

If you are a chemist, you may understand a specific example: the trans- conformation of 2-butene is a global minimum; the two gauche- conformations are local minima on its potential surface.

(The "global minimum" statement ignores the fact that physicists might like to bring up -- that there is no potential surface for 2-butene, and all isomers of butene, along with 2 ethylene molecules, acetylene plus ethane, and many other such structures share the same potential surface).

(2) Convergence criteria: the Gaussian program uses an iterative procedure -- it starts with an approximation, and then uses the results of that approximation to arrive at a better approximation and so on. The "convergence criteria" are little mathematical tests that it does to tell it when the approximation is good enough that it can stop.

(3) "Force" in this context indeed means the first derivative of the potential energy. In cruder MO calculations it simply means gradient of the potential surface; I am not sure whether in Gaussian it is modified to take into account some of the dynamic effects -- do not think it should be.

(4) "Force constant" is the second derivative of the potential energy function. Relates to an harmonic oscillator treatment of potential energy as an approximation for any potential well (local minimum), but the concept is extended to include the second derivative at points where there is a non-zero gradient.

 

[JohnRC]

If you are a chemist, you may understand a specific example: the trans- conformation of 2-butene is a global minimum; the two gauche- conformations are local minima on its potential surface.
.

This is complete nonsense -- I was, of course, referring to the conformations of n-butane.

The various isomers I mention in the next bit (in parentheses) are those of 2-butene; I should have been talking about isobutane, and ethane plus ethene sharing the same potential surface with n-butane.

 

[mycotheology]

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.

 

[JohnRC]

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}.

 

[Einstein Mcfly]

Good posts JohnRC.