### Symmetry aspects of Dalton

Posted:

**30 Mar 2014, 07:26**It seems from recent postings that there may be some confusion about the use of symmetry in Dalton, and I thought it might be useful to post some notes here. There is more material along these lines in the Dalton manual (the current version, with the 2013.2 release, I mean).

There are three ways to handle symmetry in Dalton. The original approach is in some ways still the simplest: one specifies the point group (at most D_{2h}) to be used in the calculation explicitly, using generators (see the manual, any version). Then one knows which group will be used, how many irreducible representations are present (1, 2, 4, or 8) and therefore that if one specifies orbital occupation explicitly there has to be a certain number of quantities defined. For example, running the water molecule in C_{2v} symmetry means that for the ground state occupation (which has 3 doubly occupied a_1 MOs, one doubly occupied b_2, and one doubly occupied b_1) one needs to specify
(full details of the ordering of symmetries, etc., are in the 2013.2 version of the manual). Note that the program will figure out for itself a best guess at orbital occupancy if this is not specified, so the above lines are not necessary for a simple case like water, although they might be for more complicated cases.

Now, there are keywords for which quantities for each symmetry are \emph{required} by the code. An example would be the number of excited states to calculate in a response calculation. Here there is no alternative but to specify, e.g.,
to get an A_1 and A_2 excited state for water (and no B_1 or B_2). Once the program "knows" there are four irreducible representations in the group being considered, any input line of this sort \emph{must} comprise four numbers, or the program will fail with an input error.

The second way to handle symmetry in Dalton is to explicitly turn symmetry off, by using the "Nosymmetry" option in the .mol file. This means that the molecule will in effect be treated in C_1 symmetry, with only one irreducible representation, irrespective of whether symmetry is present or not. For some calculations turning off symmetry may seem like the simplest option, but this is usually illusory. One cannot easily identify which excited state is which, for example. A few moments thinking about the symmetry of the system, and using it, is usually worth the investment of time, especially because the computational work is reduced overall by at least the order of the group, and for some parts of the calculation by the order of the group squared!

The third way to handle symmetry in Dalton is to allow the program to determine the symmetry itself, and for many people this seems to be the most popular option. Bear in mind, however, that in such a situation the program \emph{will} find symmetry if it's present. And so if one is interested in calculating (say) excited states by response, the number of states required for each symmetry must be specified, as in the water example above. The program is incapable, for instance, of just calculating the lowest excited state because since the response calculation is completely symmetry-blocked there is no way in advance for the program to which symmetry block will correspond to the lowest excited state. Further, care may be required to understand how the labelling of irreducible representations or ordering of irreducible representations within the program corresponds to other work or published studies: as noted in the 2013.2 manual section it is conventional for a planar C_{2v} system that B_2 labels the irreducible representation that is symmetric with respect to reflection in the plane of the molecule, and that B_1 labels the one that is antisymmetric, but not everyone sticks to this convention! And in other cases the use of automatic symmetry detection may reorient the molecule and change the ordering of irreducible representations anyway.

In general, if the information is available to specify the symmetry explicitly, this is probably the "safest" option. Using "Nosymmetry" is likely to lead to inefficiencies unless the molecule really has no symmetry (in which case that would be detected by the automatic symmetry routines anyway). And allowing the program to do the job will certainly work, but one needs to know in advance how many irreducible representations the group contains, etc. I repeat, when the molecule has symmetry, the best option is to specify it explicitly. Then you, the user, are in charge.

Best regards

Pete

There are three ways to handle symmetry in Dalton. The original approach is in some ways still the simplest: one specifies the point group (at most D_{2h}) to be used in the calculation explicitly, using generators (see the manual, any version). Then one knows which group will be used, how many irreducible representations are present (1, 2, 4, or 8) and therefore that if one specifies orbital occupation explicitly there has to be a certain number of quantities defined. For example, running the water molecule in C_{2v} symmetry means that for the ground state occupation (which has 3 doubly occupied a_1 MOs, one doubly occupied b_2, and one doubly occupied b_1) one needs to specify

Code: Select all

```
.DOUBLY OCCUPIED
3 1 1 0
```

Now, there are keywords for which quantities for each symmetry are \emph{required} by the code. An example would be the number of excited states to calculate in a response calculation. Here there is no alternative but to specify, e.g.,

Code: Select all

```
1 0 0 1
```

The second way to handle symmetry in Dalton is to explicitly turn symmetry off, by using the "Nosymmetry" option in the .mol file. This means that the molecule will in effect be treated in C_1 symmetry, with only one irreducible representation, irrespective of whether symmetry is present or not. For some calculations turning off symmetry may seem like the simplest option, but this is usually illusory. One cannot easily identify which excited state is which, for example. A few moments thinking about the symmetry of the system, and using it, is usually worth the investment of time, especially because the computational work is reduced overall by at least the order of the group, and for some parts of the calculation by the order of the group squared!

The third way to handle symmetry in Dalton is to allow the program to determine the symmetry itself, and for many people this seems to be the most popular option. Bear in mind, however, that in such a situation the program \emph{will} find symmetry if it's present. And so if one is interested in calculating (say) excited states by response, the number of states required for each symmetry must be specified, as in the water example above. The program is incapable, for instance, of just calculating the lowest excited state because since the response calculation is completely symmetry-blocked there is no way in advance for the program to which symmetry block will correspond to the lowest excited state. Further, care may be required to understand how the labelling of irreducible representations or ordering of irreducible representations within the program corresponds to other work or published studies: as noted in the 2013.2 manual section it is conventional for a planar C_{2v} system that B_2 labels the irreducible representation that is symmetric with respect to reflection in the plane of the molecule, and that B_1 labels the one that is antisymmetric, but not everyone sticks to this convention! And in other cases the use of automatic symmetry detection may reorient the molecule and change the ordering of irreducible representations anyway.

In general, if the information is available to specify the symmetry explicitly, this is probably the "safest" option. Using "Nosymmetry" is likely to lead to inefficiencies unless the molecule really has no symmetry (in which case that would be detected by the automatic symmetry routines anyway). And allowing the program to do the job will certainly work, but one needs to know in advance how many irreducible representations the group contains, etc. I repeat, when the molecule has symmetry, the best option is to specify it explicitly. Then you, the user, are in charge.

Best regards

Pete