By default, Gaussian makes no explicit effort to maintain the point-group symmetry of the system under optimization. (I do not now how exactly the above-mentioned option  Symm=Follow works, which I was not aware by now.)

However, in practice the initial point symmetry is preserved in most cases, for the following reason: The geometry changes during optimization are driven by the forces on the nuclei. These forces, in turn, have the same symmetry as the geometry. For instance, if you optimize ammonia with a planar geometry, the nuclear forces will always be within the molecular plane, and the atoms will be moved around only within this plane. Thus, you will wind up with the planar transition state of the NH3 inversion rather than the stable pyramidal geometry.

There may be exceptions to this rule: In DFT calculations, the orientation of the integration grids may break the symmetry of the initial geometry, and the optimization may arrive at a geometry with lower symmetry. However, this is nothing to rely on. Thus, as Teemu mentioned above, always do frequencies to characterize the optimized geometries you get.

On the other hand, it is not so uncommon that the optimization leads you to a higher symmetry than the initial one. This will happen, for instance, if you calculate benzene and start with a slightly puckered C6 ring. The optimization will make this ring planar. Note that Gaussian not always will tell you this: Gaussian has, by default, very tight constraints for recognizing a point symmetry. Thus, in the case of benzene, it may happen that your optimization finishes with a C6 ring that is still slightly puckered. This ring is then planar enough to meet the convergence criteria of the optimization but not planar enough to be recognized as planar (and thus D6h) by the symmetry module. Thus, if symmetries are relevant, always make sure that you use initial geometries with proper symmetries. GUI's do not always accomplish this.

Best regards,

Jürgen

In a geometry optimization the default is NOT constrained.

To constrain, see Geom=Addredundant keyword

http://www.gaussian.com/g_tech/g_ur/k_geom.htm

You can specify the coordinates you want to constrain

Thank you, Pablo!

Indeed, the symmetry of the system can change durng gaussian optimization. However, gaussian always notifies about the change of symmetry "Omega: Change in point group or standard orientation."

You actually don't need to use Geom=Addredundant for constraining the symmetry - a smart definition of z-matrix is often enough and a better way to do it. A very nice tutorial on symmetry in gaussian can be found at: http://www.cup.uni-muenchen.de/ch/compchem/geom/internal.html

You can also completely turn off any symmetry by using Symmetry=None.

Gaussian takes the advantage of using highest order symmetry from your Cartesian input.

When it recognize the symmetry, it will keep the same symmetry during the geometry optimization, or during the optimization it can turn out to order symmetry?

Dear Mr. Sethio, 

as others have already stated, gaussian checks for the symmetry of the molecule and tries to maintain that symmetry during the optimization. It is not guaranteed to stay on that symmetry. Gaussian manual has several useful keywords that allow you to control or disable the symmetry detection, and use of symmetry.

As a hint, it is quite possible that a highly symmetric structure converges quickly to some point in the potential energy surface, but it is not a minima. The symmetry constraint can prevent the molecule from reaching the lower-symmetry and lower-energy minima. This is one of the reasons why you should always perform vibrational analysis on your optimized structures. 

With all the best, Teemu

By default, Gaussian makes no explicit effort to maintain the point-group symmetry of the system under optimization. (I do not now how exactly the above-mentioned option  Symm=Follow works, which I was not aware by now.)

However, in practice the initial point symmetry is preserved in most cases, for the following reason: The geometry changes during optimization are driven by the forces on the nuclei. These forces, in turn, have the same symmetry as the geometry. For instance, if you optimize ammonia with a planar geometry, the nuclear forces will always be within the molecular plane, and the atoms will be moved around only within this plane. Thus, you will wind up with the planar transition state of the NH3 inversion rather than the stable pyramidal geometry.

There may be exceptions to this rule: In DFT calculations, the orientation of the integration grids may break the symmetry of the initial geometry, and the optimization may arrive at a geometry with lower symmetry. However, this is nothing to rely on. Thus, as Teemu mentioned above, always do frequencies to characterize the optimized geometries you get.

On the other hand, it is not so uncommon that the optimization leads you to a higher symmetry than the initial one. This will happen, for instance, if you calculate benzene and start with a slightly puckered C6 ring. The optimization will make this ring planar. Note that Gaussian not always will tell you this: Gaussian has, by default, very tight constraints for recognizing a point symmetry. Thus, in the case of benzene, it may happen that your optimization finishes with a C6 ring that is still slightly puckered. This ring is then planar enough to meet the convergence criteria of the optimization but not planar enough to be recognized as planar (and thus D6h) by the symmetry module. Thus, if symmetries are relevant, always make sure that you use initial geometries with proper symmetries. GUI's do not always accomplish this.

Best regards,

Jürgen

From my experience with Gaussian, it keeps the point group during geometry optimization when using electronic structure methods. This is possibly a result of the initial guess and subsequent optimization of orbitals, which is typically projected for the irreducible representations to save computer time, as irreps do not mix. Typically this constraint does not resolve during further optimization of geometries.

My advice is that you first check if your symmetry is below or equal to the geometry of the molecule you want to optimize. If you have a reasonable initial guess, this will almost always be the case. In the case of transition states this gets more tricky.

As mentioned above, run a vibrational frequency calculation to check if you really reached a minimum structure. If all frequencies are real (the rotations and translations may differ slightly from zero, both below and above) the Hessian is positive definite, hence you obtained a minimum. If there are negative frequencies, have a look at those vibrations and follow their normal modes to obtain better initial guess structures. Alternatively, find out in how far following the normal modes would change the point group of your system and reduce the point group in your input properly. Alternatively you can also use guess=LowSym in your input for initial optimization and see if it helps.