CamCASP/Notes/2

CamCASP => Notes => Energy Scan

Energy scan

This is a very high-level module that uses a lot of the lower-level modules. As a consequence, it is easy to break and has a few features. Some of these are described below.

Density-fitting repeated for each dimer

If you have set REDO-DF-ON-ROTATION to TRUE in module DF, then all is well and you don't need to worry about anything. You can call the ENERGY-SCAN module and should get correct results.

However, if you have set REDO-DF-ON-ROTATION to FALSE, things can go wrong. Consider the following example:

MOLECULE water1 at 0.0 0.0 0.0
 ...
END
MOLECULE water2 at 0.0 0.0 0.0
 ...
END

SET DF
  Eta = 0.0
  Lambda = 0.0
  REDO-DF-ON-ROTATION       False
End

Begin Energy-scan
  Probe water1 with water2
  Energy Overlap
  Units Bohr Degree
  Points
    5.0 0.0 0.0   90.0  0.0 0.0 1.0
    0.0 0.0 2.0   45.0  0.0 1.0 1.0
  ---
  Overlap-file overlap_NOredo
End

Here's what happens:

1. The molecules are defined and their MOs are consistent with the defined geometry. So far, so good.
2. In ENERGY-SCAN, water2 is translated (nothing to worry about that) and rotated, but because REDO-DF-ON-ROTATION is FALSE, the molecular orbitals of water2 are NOT updated. So they are now inconsistent with the molecular geometry.
3. At some stage, the DF module is called. This module will make the MOs of both molecules consistent with their geometry before performing the DF. That's good. But notice that the DF has been done for the rotated water2.
4. The overlap integrals in the auxiliary basis set (OVRL XAXB) are calculated and, because REDO-DF-ON-ROTATION is FALSE, the DF-INT module (called implicitly) rotates the integrals to be consistent with what it thinks is the DF solution in the original geometry of water2. Only this is false. As the DF for water2 was done not in the original geometry, but the rotated geometry.
5. And then the required overlap integrals are calculated by multiplying the DF solution (in rotated geometry) with the OVRL XAXB integrals that have been also rotated. This results in the wrong integrals.

Density-fitting done only once

So what is the correct way to do the energy scan if REDO-DF-ON-ROTATION is FALSE?

We must make sure the density-fitting is done in the original, un-rotated (translations don't matter) molecular geometries. To do this, we will make explicit calls to DF while the molecules are in thier original geometries. (The original geometries could be obtained using the EDIT module and the RESTORE command. But if you do that, make sure you reset all translational and rotational information too.) Only then will we make the call to ENERGY-SCAN.

This is no longer needed in the current version of CamCASP. The code now restores the reference geometries to all molecules and performs the density-fitting. --alston 15:48, 21 May 2012 (BST)

Here's the input file:

MOLECULEs defined as before...
          ...BUT...the Auxiliary basis MUST use Spherical GTOs.

SET DF
  Eta = 0.0
  Lambda = 0.0
  REDO-DF-ON-ROTATION       False
  ! Type OO is sufficient for first order energies and overlaps
  Type OO  
End

! You can now skip these lines with the current CamCASP
Skip
Begin DF
  Molecule water1
  Type NN
End
Begin DF
  Molecule water2
  Type NN
End
End-Skip

Begin Energy-scan
  Probe water1 with water2
  Energy Overlap
  Units Bohr Degree
  Points
    5.0 0.0 0.0   90.0  0.0 0.0 1.0
    0.0 0.0 2.0   45.0  0.0 1.0 1.0
  ---
End

NOTES:

1. Since CamCASP can perform integral rotations only with Spherical GTOs, the auxiliary basis must use Spherical GTOs for this to work. This does mean a small loss in accuracy, as, from our experience, the extra flexibility of the equivalent Cartesian GTOs results in a more accurate density-fitting, and consequently more accurate integrals.
2. This procedure is considerably faster than the above, when the density-fitting is repeated for each dimer geometry. But bear in mind that if we calculate the exchange energies in the Energy-Scan, the speed difference is reduced because the dimer density-fitting is needed for the exchange energies, and this will need to be re-done for each and every dimer configuration.
3. If you are going to calculate exchange energies, and you want a higher accuracy, you might want to consider setting REDO-DF-ON-ROTATION to TRUE and using Cartesian GTOs in the auxiliary basis. But bear in mind that both these will add to the computational cost of the calculation. In this case you will also want to use a DC auxiliary basis.

--alston 15:48, 21 May 2012 (BST)

Constrained density-fitting

Yet another problem occurs when constrained DF is used in the energy scan. The way things are done now, the density-overlap integrals can be obtained using constrained DF (see code below), but only if scanned in isolation. That is, you cannot scan both the OVERLAP (with constrained DF) and E1ELST (say). Since E1ELST does not need DF with constraints, the constraint parameters are reset and you get unexpected results.

This can be fixed, but till I do so, do not attempt this.

To scan just the OVERLAP with constraints use:

SET DF
  Eta = 0.0
  Lambda = 1000.0  (for example)
  REDO-DF-ON-ROTATION       False
End

Begin DF
  Molecule water1
  Type NN
End
Begin DF
  Molecule water2
  Type NN
End

Set E1exch
  Overlap integrals with constraints
End

Begin Energy-scan
  Probe water1 with water2
  Energy Overlap
  ...
End

--alston 19:11, 30 October 2008 (GMT)