Computational Report

See the print switches computation, eprint:numint, eprint:SCF, eprint:geo.

Numerical integration

General grid-generating parameter(s) and the number of generated (symmetry unique) integration points, with their distribution over the distinct kinds of integration regions: the atomic (core-like) spheres, the remaining interstitial regions between the atoms (atomic polyhedra), and the outer region, i.e. the part of space around the molecule.

Partitioning of the points in blocks. In general there are too many integration points to have all pertaining data (values of basis functions in the points etc.) in memory. A segmentation in blocks of points is therefore applied, processing a block of data at a time after loading it from disk or recomputing it (depending on the Direct options). This also determines vector lengths and hence vectorization performance in numerical integral evaluations.

Integration Tests. The generation of the points involves an adaptive procedure to tune the point distribution such that a pre-set precision of several test integrals is achieved with a minimal number of points. The generated scheme is a posteriori tested by evaluating a few integrals in the actual molecule. This does not result in any subsequent adaptation of the grid but only produces info for the user to verify that all goes well. If the results are suspicious a warning is issued and if the results are too bad, the program will abort.
The most important and significant test is the evaluation of the self-overlaps of all symmetry-adapted elementary basis functions. The maximum and root-mean-square (relative) errors are printed. The number of significant figures suggested by the rms error should roughly equal the accuracy parameter. This may not hold so well for extremely low values of the parameter (less than 1.5 say) where results become unpredictable. Likewise for very high values (greater than 6.0 say) where the adaptive procedure has not extensively been tested and hence the results might deviate more (not necessarily in the wrong direction!). This extensive testing is not carried out in Direct-SCF (bas) mode because in that case the necessary information is not available (basis functions are only computed when needed in the SCF).
A test that is always carried out is the numerical integration of the total frozen core density (summed over all atoms in the molecule). Also here a warning or even abort will occur when the result indicates that the integral has insufficient accuracy compared with the integration precision parameter.

SCF procedure

at each cycle: for each irreducible representation: the one-electron orbital energies and the occupation numbers for a contiguous sequence of orbitals. The indices of the lowest and highest MOs (in energy ordering) are printed directly after the irrep label. With this information you can check the electronic configuration. When convergence is problematic, more info appears at the higher iterations.
The involved orbitals are usually the highest few occupied and the lowest few unoccupied orbitals, see the eprint subkey eigval. During the SCF, as soon as the distribution of electrons over irreps is frozen, only the occupied orbital energies are computed and hence printed.
Also printed at each SCF cycle is the difference of the density matrix (P-matrix) with the previous cycle: the average and maximum difference in the diagonal elements.

At the end of the SCF: concise information about the density-fit precision: the error integral for the SCF density. The error integral is the integral of the difference between the exact density and the fit density, squared. Such values have very little to do with numerical integration, rather they show whether or not the employed set of fit functions are adequate to describe the SCF density. Error integral values that significantly exceed 1e-4 times the number of atoms are suspicious and may indicate some deficiency in the fit set for the actual calculation.
On the last geometry (in an optimization) the fit-error integrals are also printed (in the Results section, see below) for the initial (sum-of-fragments) density and the orthogonalized fragments (see Chapter 1.2)

• Gross atomic charges, computed from a Mulliken population analysis.
• Geometry Updates. The contents of this section depends on the RunType:
  Geometry Optimization, Frequencies.... It is absent in a Create run and in a SinglePoint calculation.
• Gradients on the atoms: derivatives of the energy w.r.t. changes in the nuclear coordinates.
• Summary of convergence issues. One of the items considered for convergence is the maximum Cartesian
  gradient. This value corresponds in principle to one of the Gradients on the Atoms.
  Differences may occur due to user-set and automatic constraints.
  The printed Gradients are the raw gradients, the maximum Cartesian gradient is the maximum over
  relevant gradients: this ignores gradients in frozen coordinates.
  Furthermore, gradients in coordinates that are forced to remain equal are averaged before the maximum
  is selected; finally the raw gradients are processed to eliminate spurious components such as gradients
  in rigid motions (translations and possibly rotations).
  In a Z-matrix optimization any user-set constraints apply to the Z-matrix coordinate-derivatives
  and the maximum Cartesian gradient is selected from the Cartesian gradients that are recomputed
  from the constrained z-matrix gradients.
• New coordinates: Cartesian and z-matrix if applicable. Optionally the new inter-atomic distance matrix
  is given (not by default).

The Computational info is repeated in all cycles (SCF and geometry) until the iterations have terminated.