Contents

        1. Orient: Using the Display : Orient versions to 4.8
        2. Generating the display data using CamCASP
        3. Orient input file for display
      2. Display pre-computed reference energies
      3. Display using van der Waals surfaces
        1. Difference maps using Orient
      4. Differences against references calculated with Orient
    2. Define the reference
    3. Making the difference map
  2. Rank 4
  3. Rank 3
  4. Rank 0

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Orient: Using the Display : Orient versions to 4.8

The Orient program can be used to create 3D maps of energies or other quantities mapped onto a surface. These can be scalar or vector maps. Here we will look into using scalar maps.

The idea is to create something that looks like this: formamide_b_df_z0.1_aqzset2_l0l0.png In this map, I have visualised the difference in the electrostatic potential arising from a rank 0 (charge only) multipole model (from the ISA) against a reference potential from SAPT(DFT). Actually, rather than calculate a potential, I have calculated the electrostatic energy between either the charge model or actual density of formamide and a unit point charge. This point charge has been placed at various points on a 0.001 a.u. isodensity surface. Orient allows us to visualise the errors made by the point charge model. This is only one view of an image that can be rotated/moved around using a mouse.

Consider what we need to make such an image:

We will usually have the first two so let's consider the others here.

Generating the display data using CamCASP

The CamCASP program can be used to generate an isodensity surface using the Display module. And then the ENERGY-SCAN module can be used to calculate the reference energies for this surface. ajm:camcasp:energy-scan-display

Orient input file for display

Let's start with the Orient file for display as its requirements will become clearer once you see it. The input files used below have been created from an Orient display file generated using the Cluster program.

Display pre-computed reference energies

Here's the input file for displaying a reference energy already calculated, in this case, using the DISPLAY and ENERGY-SCAN modules in CamCASP: <code | formamide-display-reference.ornt> ! ORIENT display commands

UNITS BOHR

Parameters

End

Types

End

Molecule formamide at 0.0 0.0 0.0

End Edit formamide

End

Units Bohr kJ/mol

! This is a probe of the induction energy Atom X at 0.0 0.0 0.0 rank 0

End

Display energy

End

Finish </code> Points to note:

Run this using Orient compiled with OPEN_GL and you will see something like this: Formamide : E1elst (SAPT(DFT)) for molecule and 1e charge probe mapped on a 0.001 a.u. iso-density surface

The Orient output should look like this: <code> $ orient < HCONH2_display.ornt

...

Molecule 1 (Site 1): formamide Origin position (cartesian) 0.00000 0.00000 0.00000

Site 2: C Type C Position (cartesian) 0.73690 -0.29016 0.00000

...

Preparing display: formamide...Q 1.0 elst Importing grid and values from file formamide_1.00E-03_iso_aQZ_Q.elst 4704 points and 9404 triangles read from file formamide_1.00E-03_iso_aQZ_Q.elst Displaying values read from file formamide_1.00E-03_iso_aQZ_Q.elst Minimum energy = -174.19700 kJ/mol Maximum energy = 204.53000 kJ/mol Colour scale:

4704 points, 9404 triangles

</code> The code prints out the Minimum and Maximum energies encountered. Use these values to set the range of the energy scale using the Colour-scale command.

Display using van der Waals surfaces

It is also possible to generate a display within Orient, using the van der Waals surfaces for each atom to create a molecular surface. Orient has default radii for each atom, but they can be set manually (see the Orient manual). Here we use the standard radii. Here's the input file: <code | formamide-display-vdWsurface.ornt> ! ORIENT display commands

UNITS BOHR

Parameters

End

Types

End

Molecule formamide at 0.0 0.0 0.0

End Edit formamide

End

Units Bohr kJ/mol

! This is a probe of the induction energy Atom X at 0.0 0.0 0.0 rank 0

End

Display energy

End

Finish </code> Formamide : Elst from ISA multipoles on 1.5 x vdW surface Points to note:

Difference maps using Orient

Now we know how to display energies, but what about differences in energies? We often want to compare two models: say, the rank 0 multipole model may need to be compared with SAPT(DFT) or, perhaps more appropriately, with a rank 4 model. How to we do this?

The idea here is to import a grid with values (as we did with the SAPT(DFT) reference above) and use it as a REFERENCE. We then compare the energies calculated with a model against these values. Orient will plot the difference. Here's an input file for a comparison against pre-computed SAPT(DFT) electrostatic energies: <code | formamide-compare-against-sapt.ornt> ! ORIENT display commands

UNITS BOHR

Parameters

End

Types

End

Molecule HCONH2 at 0.0 0.0 0.0

End Edit HCONH2

End

Units Bohr kJ/mol

! This is a probe of the induction energy Atom X at 0.0 0.0 0.0 rank 0

End

Display energy

! Radii scale 2.0 ! Step 0.75 B ! Grid exp

End

Finish </code> Formamide: performance of ISA L0 model Points to note:

As usual, Orient will print out a summary when you run it. Here's the tail end of the output containing the relevant details: <code> Preparing display: HCONH2...Q 1.0 Elst Importing grid and values from file formamide_1.00E-03_iso_aQZ_Q.elst 4704 points and 9404 triangles read from file formamide_1.00E-03_iso_aQZ_Q.elst Displaying calculated values Maximum difference = 14.13234 kJ/mol Minimum difference = -39.17835 kJ/mol r.m.s. difference = 14.57066 kJ/mol average difference = -7.47084 kJ/mol Standard deviation = 12.51095 kJ/mol Colour scale:

4704 points, 9404 triangles </code> The max and min differences are reported and may be used to determine the energy diference scale needed. Additionally Orient prints out the r.m.s. and average differences.

Differences against references calculated with Orient

What if we want to compare a rank 0 multipole model against a rank 4 model? Or the DMA multipoles against the ISA multipoles? In these cases, we might want to define a reference using the ISA rank 4 multipoles. Once we have this reference, we could use the above method to compare any other multipole model against the reference.

Define the reference

We first need to define a grid. It could be an isodensity grid, or we may use the Orient program to create a van der Waals grid. For the former use <code> Display energy

End </code> Notice the Import ... no values command. We want the grid only, not the energy values in the grid file.

For the internally generated, van der Waals grid, use <code> Display energy

End </code> This is exactly what we used before.

But what about the reference ISA rank 4 energies? To get these, we need to define the model, set the rank (if necessary), and then Orient will use it to calculate the energies at all grid points: <code> Molecule HCONH2 at 0.0 0.0 0.0

End Edit HCONH2

End </code>

The last step is to write out the grid and these reference energies to file. This is done using the Write command in the Display energy module, like so (for the 1.5 vdW surface generated with Orient): <code> Display energy

End </code> Of course, this could have been done with the 0.001 isosurface too. These commands would look like: <code | formamide-generate-reference-isosurface.ornt> Display energy

End </code> Now the grid and values will be in file HCONH2_0.001iso_ISA_L4L4.grid

Here's the full Orient command file for the latter case.

Now we've got the reference surface and energies in the file HCONH2_1.5vdW_ISA_L4L4_ref.grid or HCONH2_0.001iso_ISA_L4L4_ref.grid.

Making the difference map

As before, we use the calculated reference files to make difference maps. For example, the full Orient input file for the HCONH2_0.001iso_ISA_L4L4_ref.grid reference is: <code> ! ORIENT display commands

UNITS BOHR

Parameters

End

Types

End

Molecule HCONH2 at 0.0 0.0 0.0

End Edit HCONH2

End

Units Bohr kJ/mol

Atom X at 0.0 0.0 0.0 rank 0

End

Display energy

End

Finish </code> In this example we compare the ISA rank 0 model against the reference ISA rank 4 model on the 0.001 a.u. isosurface. No more figures, but here are summaries of the outputs for various ranks:

Rank 4

This one is our test: it should have no errors as this model was used to create the reference: <code> Preparing display: formamide...Q 1.0 elst Importing grid and values from file HCONH2_0.001iso_ISA_L4L4_ref.grid 4704 points and 9404 triangles read from file HCONH2_0.001iso_ISA_L4L4_ref.grid Displaying calculated values Maximum difference = 0.00001 kJ/mol Minimum difference = -0.00001 kJ/mol r.m.s. difference = 0.00000 kJ/mol average difference = -0.00000 kJ/mol Standard deviation = 0.00000 kJ/mol Colour scale:

4704 points, 9404 triangles </code>

Rank 3

<code> 4704 points and 9404 triangles read from file HCONH2_0.001iso_ISA_L4L4_ref.grid Displaying calculated values Maximum difference = 7.25748 kJ/mol Minimum difference = -4.39074 kJ/mol r.m.s. difference = 1.55204 kJ/mol average difference = 0.03929 kJ/mol Standard deviation = 1.55171 kJ/mol </code> Errors are larger.

Rank 0

<code> Maximum difference = 26.63755 kJ/mol Minimum difference = -25.66614 kJ/mol r.m.s. difference = 12.73403 kJ/mol average difference = 0.68858 kJ/mol Standard deviation = 12.71675 kJ/mol </code> Errors are much larger.