### Article ID: 1642 - Last Modified: August 22, 2013

### Why should I care about the number of canonical orbitals in my Jaguar calculations?

Molecular orbitals are linear combinations of atomic orbitals. Canonical orbitals are orthogonal linear combinations of molecular orbitals in which near-degeneracies have been removed. The number of canonical orbitals is less than or equal to the number of molecular orbitals. Generally, the more near-degeneracies are encountered in the basis set the fewer canonical orbitals have to be taken.

Near-degeneracies must be eliminated because their presence produces numerical instabilities in the self-consistent field (SCF) equations. Jaguar's pseudospectral approach is sensitive to near-degeneracies, and therefore it is not uncommon to see in Jaguar calculations that one or more linear combinations of molecular orbitals have been discarded and that the number of canonical orbitals is thus smaller than the number of molecular orbitals.

The energies (for example, for two conformations of the same molecule) can only be meaningfully compared if they were obtained with the same basis set using the same number of canonical orbitals. Comparing energies obtained with different number of canonical orbitals is dangerous; it may result in significant errors and even lead to puzzling artifacts.

Jaguar prints the number of canonical orbitals to the output file (and in Suite 2012 [Maestro v9.3] also displays it in the Project Table in Maestro). Typically a difference in one or two canonical orbitals is admissible for crude energy comparisons but for accurate energy comparisons you must make sure that the number of canonical orbitals is the same when comparing two energies.

The number of canonical orbitals in Jaguar can be controlled by the keywords `cut20` and `ncanorb` in the input file. The first keyword, `cut20`, sets the threshold for the maximal admissible eigenvalue of the atomic orbital overlap matrix. For example, if `cut20` = 5.0E-4 (which is a typical value) and if there are seven eigenvalues of the overlap matrix that are lower than 5.0E-4, then the number of the canonical orbitals will be the number of molecular orbitals minus seven. If you wish to set the number of canonical orbitals to a certain predefined number, you should use the second keyword, `ncanorb`. For example, the calculation with `ncanorb` = 342 will use 342 canonical orbitals irrespective of the number of molecular orbitals (provided 342 is equal to or smaller than the number of molecular orbitals).

For accurate energy comparisons of isomeric structures A and B we recommend setting the number of canonical orbitals equal. In the 2013-2 release, there is an option in the SCF tab of the Jaguar panel (Use consistent orbital sets when all input structures are isomers) to enforce the same number of canonical orbitals when running calculations on a set of isomers.

For earlier releases, we recommend performing initially a "dry run" on each structure using the following extra settings in the input file:

&path pre onee &

This dry run computes the number of canonical orbitals and exits without attempting to solve the costly SCF equations. Then set `ncanorb` to the minimum number of canonical orbitals obtained in the dry runs for A and B, and re-run the calculations for A and B with the otherwise original settings. This ensures that the energies of A and B are computed with the same number of canonical orbitals and that these energies can be meaningfully compared.

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