9.1. Orbital and Density Plots

There are two types of graphics output possible in ORCA - two dimensional contour plots and three dimensional surface plots. The quantities that can be plotted are the atomic orbitals, molecular orbitals, natural orbitals, the total electron density or the total spin density. The graphics is controlled through the block %plots.

9.1.1. Contour Plots

The contour plots are controlled via the following variables

%plots
  #*** the vectors defining the cut plane
  v1 0, 0, 0  # pointer to the origin
  v2 1, 0, 0  # first direction
  v3 0, 1, 0  # second direction
  #*** alternative to defining vectors. Use atom coordinates
  at1 0 # first atom defining v1
  at2 2 # second atom defining v2
  at3 4 # third atom defining v3
  #*** resolution of the contour
  dim1  45   # resolution in v2-direction
  dim2  45   # resolution in v3-direction
  #*** minimum and maximum values along v2 and v3
  min1  -7.0 # min value along v2 in bohr
  max1   7.0 # min value along v2 in bohr
  min2  -7.0 # min value along v3 in bohr
  max2   7.0 # max value along v3 in bohr
  #***
  UseCol   true   # Use color in the plot (blue=positive,
                  # red=negative)
  Skeleton true   # Draw Skeleton of the molecule of those
                  # atoms that are in or close to the cut
                  # plane
  Atoms    true   # Draw the atoms that are in the plane as
                  # circles
  NCont    200    # Number of contour levels.
  ICont    0      # Draw NCont equally space contours
           1      # Start with 1/NCont and the double the 
                  # value for each additional contour
  #*** the format of the output file
  Format   Origin   # straight ascii files
           HPGL     # plotter language files 
  #*** the quantities to plot
  MO("MyOrbital-15xy.plt",15,0);  # orbital to plot
  v3= 0, 0, 1                     # change cut plane
  MO("MyOrbital-16xz.plt",16,0);  # orbital to plot
  ElDens("MyElDens.plt");         # Electron density
  SpinDens("MySpinDens");         # Spin density
end

The input was:
v1 = 0, 0, 0; v2 = 1, 0, 0; v3 = 0, 1, 0; min1= -8; max1= 8; min2= -8; max2= 8; dim1= 50; dim2=50; Format = HPGL; NCont = 200; Icont = 1; Skeleton= true; Atoms = true; MO("Test-DFT-H2CO+-MO7xy.plt",7,1);

NOTE:

• The command MO("MyOrbital-15xy.plt",15,0); is to be interpreted as follows: MO means that a MO is to be plotted. “MyOrbital-15xy.plt” is the file to be created. 15 is the number of the MO to be drawn (remember: counting starts at orbital 0!) and 0 is the operator the orbital belongs to. For a RHF (or RKS) calculation there is only one operator which has number 0. For a UHF (or UKS) calculation there are two operators - the spin-up orbitals belong to operator 0 and the spin-down orbitals belong to operator 1. For ROHF calculations there may be many operators but at the end all orbitals will be collected in one set of vectors. Thus the operator is always \(=\)0 in ROHF.

• The ELDENS (plot of the total electron density) and SPINDENS (plot of the total spin density) commands work analogous to the MO with the obvious difference that there is no MO or operator to be defined.

• Analogous to ELDENS and SPINDENS, post-HF densities can be selected using the keyword extended by the respective method. ELDENSMDCI / SPINDENSMDCI will plot the MDCI density, of course only if is available. ELDENSMP2RE and SPINDENSMP2RE will work with the MP2 relaxed density, while ELDENSMP2UR and SPINDENSMP2UR will yield the MP2 unrelaxed density. The OO-RI-MP2 densities can be requested by ELDENSOO or SPINDENSOO. Similarly, AutoCI relaxed densities can be plotted by using the ELDENSAUTOCIRE and SPINDENSAUTOCIRE keywords, and the unrelaxed densities by using ELDENSAUTOCIUR and SPINDENSAUTOCIUR.

• The UNO option plots natural orbitals of the UHF wavefunction (if they are available). No operator can be given for this command because there is only one set of UHF-NOs. Similarly, using UCO option can be used to plot the UHF corresponding orbitals.

• If the program cannot find the plot module (“Bad command or filename”) try to use ProgPlot="orca_plot.exe" in the %method block or point to the explicit path.

• The defining vectors v2 and v3 are required to be orthonormal. The program will use a Schmidt orthonormalization of v3 with respect to v2 to ensure orthonormality. If you do not like this make sure that the input vectors are already orthogonal.

• at1, at2 and at3 can be used instead of v1, v2 and v3. In this case say v1 is taken as the coordinates of atom at1. Mixed definitions where say v2 is explicitly given and say v3 is defined through at3 are possible. A value of -1 for at1, at2 and at3 signals that at1, at2 and at3 are not to be used. This type of definition may sometimes be more convenient.

• Variables can be assigned several times. The “actual” value a variable has is stored together with the command to generate a plot (MO, ELDENS or SPINDENS). Thus after each plot command the format or orientation of the plot can be changed for the next one.

• The Origin format produces a straightforward ASCII file with x, y and z values that can be read into your favorite contour plot program or you could write a small program that reads such files and converts them to whatever format is more appropriate for you.

• I usually use Word for Windows to open the HPGL files which appears to work fine. Double clicking on the graphics will allow modification of linewidth etc. For some reason that is not clear to me some graphics programs do not like the HPGL code that is produced by ORCA. If you are an HPGL expert and you have a suggestion - let me know.

9.1.2. Surface Plots

9.1.2.1. General Points

Surface plots can, for example, be created through an interface to Leif Laaksonen’s gOpenMol program. This program can be obtained free of charge over the internet. It runs on a wide variety of platforms, is easy to use, produces high quality graphics and is easy to interface[1] - thank you Leif for making this program available!

The relevant [PLOTS] section looks like this:

%output
  XYZFile  true
end

%plots
  dim1  45   # resolution in x-direction
  dim2  45   # resolution in y-direction
  dim3  45   # resolution in z-direction
  min1  -7.0 # x-min value in bohr
  max1   7.0 # x-min value in bohr
  min2  -7.0 # y-min value in bohr
  max2   7.0 # y-max value in bohr
  min3  -7.0 # z-min value in bohr
  max3   7.0 # z-max value in bohr
  Format  gOpenMol_bin        # binary *.plt file
          gOpenMol_ascii      # ascii *.plt file
          Gaussian_Cube       # Gaussian-cube format 
                              # (an ASCII file)
  MO("MyOrbital-15.plt",15,0);  # orbital to plot
  MO("MyOrbital-16.plt",16,0);  # orbital to plot
  UNO("MyUNO-48.plt",48);       # UHF-NO to plot
  ElDens("MyElDens.plt");       # Electron density
  SpinDens("MySpinDens.plt");   # Spin density
end

Note

• it is admittedly inconvenient to manually input the dimension of the cube that is used for plotting. If you do nothing such that min1 = max1 = min2 = max2 = min3 = max3=0 then the program will try to be smart and figure out a good cube size by itself. It will look at the minimum and maximum values of the coordinates and then add 7 bohrs to each dimension in the hope to properly catch all wavefunction tails.

Sometimes you will want to produce orbital plots after you looked at the output file and decided which orbitals you are interested in. In this case you can also run the orca_plot program in a crude interactive form by invoking it as:

orca_plot  MyGBWFile.gbw  -i

This will provide you with a subset of the capabilities of this program but may already be enough to produce the plots you want to look at. Note that for the name of the GBW-file you may as well input files that result from natural orbitals (normally *.uno), corresponding orbitals (normally *.uco) or localized orbitals (normally *.loc). Once in the interactive program, by entering ‘1’ for ‘Enter type of plot,’ you will access a list of available plot capabilities relevant to your current calculation file (MyGBWFile.gbw):

-----------------------------------------------------------------------
Plot-Type is presently: 1
-----------------------------------------------------------------------
Searching for Ground State Electron or Spin Densities:              ...
-----------------------------------------------------------------------
     1 -   molecular orbitals                          
     2 -   (scf) electron density                              ......  (scfp                     )  => AVAILABLE
     3 -   (scf) spin density                                  ......  (scfr                     )  => AVAILABLE
     4 -   natural orbitals                               
     5 -   corresponding orbitals                         
     6 -   atomic orbitals                                
     7 -   mdci electron density                               ......  (mdcip                    )  - NOT AVAILABLE
     8 -   mdci spin density                                   ......  (mdcir                    )  - NOT AVAILABLE
     9 -   OO-RI-MP2 density                                   ......  (pmp2re                   )  - NOT AVAILABLE
    10 -   OO-RI-MP2 spin density                              ......  (pmp2ur                   )  - NOT AVAILABLE
    11 -   MP2 relaxed density                                 ......  (pmp2re                   )  - NOT AVAILABLE
    12 -   MP2 unrelaxed density                               ......  (pmp2ur                   )  - NOT AVAILABLE
    13 -   MP2 relaxed spin density                            ......  (rmp2re                   )  - NOT AVAILABLE
    14 -   MP2 unrelaxed spin density                          ......  (rmp2ur                   )  - NOT AVAILABLE
    15 -   LED dispersion interaction density                  ......  (ded21                    )  - NOT AVAILABLE
    16 -   Atom pair density                           
    17 -   Shielding Tensors                           
    18 -   Polarisability Tensor                       
    19 -   AutoCI relaxed density                              ......  (autocipre                )  - NOT AVAILABLE
    20 -   AutoCI unrelaxed density                            ......  (autocipur                )  - NOT AVAILABLE
    21 -   AutoCI relaxed spin density                         ......  (autocirre                )  - NOT AVAILABLE
    22 -   AutoCI unrelaxed spin density                       ......  (autocirur                )  - NOT AVAILABLE
-----------------------------------------------------------------------
Searching for State or Transition State AO Electron Densities:      ...
-----------------------------------------------------------------------
    23 -   CIS unrelaxed transition AO density                 ......  (Tdens-CIS                )  - NOT AVAILABLE
    24 -   ROCIS unrelaxed transition AO density               ......  (Tdens-ROCIS              )  - NOT AVAILABLE
    25 -   CAS unrelaxed transition AO density                 ......  (Tdens-CAS                )  - NOT AVAILABLE
    26 -   ICE unrelaxed transition AO density                 ......  (Tdens-ICE                )  - NOT AVAILABLE
    27 -   MRCI unrelaxed transition AO density                ......  (Tdens-MRCI               )  - NOT AVAILABLE
    28 -   LFT unrelaxed transition AO density                 ......  (Tdens-LFT                )  - NOT AVAILABLE
-----------------------------------------------------------------------
Searching for State or Transition State MO Electron Densities:      ...
-----------------------------------------------------------------------
    29 -   CIS unrelaxed transition MO density                 ......  (Tdens-CISMO              )  - NOT AVAILABLE
    30 -   ROCIS unrelaxed transition MO density               ......  (Tdens-ROCISMO            )  - NOT AVAILABLE
    31 -   CAS unrelaxed transition MO density                 ......  (Tdens-CASMO              )  - NOT AVAILABLE
    32 -   ICE unrelaxed transition MO density                 ......  (Tdens-ICEMO              )  - NOT AVAILABLE
    33 -   MRCI unrelaxed transition MO density                ......  (Tdens-MRCIMO             )  - NOT AVAILABLE
    34 -   LFT unrelaxed transition MO density                 ......  (Tdens-LFTMO              )  - NOT AVAILABLE
-----------------------------------------------------------------------
Searching for State or Transition State QDPT AO Electron Densities: ...
-----------------------------------------------------------------------
    35 -   CAS QDPT unrelaxed transition AO density            ......  (Tdens-CASQDSOC           )  - NOT AVAILABLE
    36 -   DCDCAS QDPT unrelaxed transition AO density         ......  (Tdens-CASDCDQDSOC        )  - NOT AVAILABLE
    37 -   CAS CUSTOM E QDPT unrelaxed transition AO density   ......  (Tdens-CASCUSTOMEQDSOC    )  - NOT AVAILABLE
    38 -   NEVPT2 QDPT unrelaxed transition AO density         ......  (Tdens-CASPTQDSOC         )  - NOT AVAILABLE
    39 -   QDNEVPT2 QDPT unrelaxed transition AO density       ......  (Tdens-CASQDPTQDSOC       )  - NOT AVAILABLE
    40 -   MRCI QDPT unrelaxed transition AO density           ......  (Tdens-MRCIQDSOC          )  - NOT AVAILABLE
    41 -   ROCIS QDPT unrelaxed transition AO density          ......  (Tdens-ROCISQDSOC         )  - NOT AVAILABLE
    42 -   LFT QDPT unrelaxed transition AO density            ......  (Tdens-LFTQDSOC           )  - NOT AVAILABLE

Fig. 9.1 The \(\pi^{\ast}\) orbital of H\(_{2}\)CO as calculated by the RI-BP/VDZP method.

See also

The visualization of fractional occupation weighted densities (FOD) is described in Section 5.3.2.

9.1.2.2. Interface to gOpenMol

Here is a short summary of how to produce these plots with gOpenMol:

• First of all the molecular geometry must be save by choosing XYZFile=true in the [OUTPUT] block. This will produce a straightforward ascii file containing the molecular geometry (or simply ! XYZFile).

• After having produced the plot files start gOpenMol and choose File-Import-Coords . In the dialog choose the XYZ format and select the file. Then press apply and dismiss . The molecule should now be displayed in the graphics window.

• You can change the appearance by choosing View-Atom type .

• The color of the background can be changed with Colour-Background .

• After having done all this choose Plot-Contour and select the Browse button to select the appropriate file. Then press Import File to read it in. NOTE: you can only directly read files that were produced in gOpenMol_bin format. If you have chosen gOpenMol_ascii you must first use the gOpenMol file conversion utility under Run-Pltfile (conversion) to produce the binary plt file.

• After having read the plt file choose the appropriate isocontour value (one for the positive and one for the negative lobes of an orbital) and select suitable colors via Colour(n) to the right of the isocontour value. The Details button allows you to choose between solid and mesh representation and other things.

• Once the plot looks the way you like, use File-Hardcopy to produce a publication quality postscript or bitmap picture that can be imported into any word processing or graphics software.

9.1.2.3. Interface to Molekel

The Molekel program (http://ugovaretto.github.io/molekel/) is another beautiful and easy-to-use graphics tool that is recommended in combination with ORCA. You may even find it a little easier to use than gOpenMol but this may be a matter of personal taste. In order to produce plots with Molekel follow the following procedure:

• Produce Gaussian-Cube files (and optionally also an XYZ file) with ORCA as described above.

• Start Molekel and use the right mouse button to obtain the Load menu.

• Choose the format xyz to load your coordinates

• Use the right mouse button again to select the Surface menu

• Choose the format “Gaussian Cube” and click Load Surface

• Click on Both Signs if you visualize an orbital or spin density

• Select a suitable contour value in the Cutoff box.

• Click on Create Surface. That’s it!

• In the Color menu (also available via the right mouse button) you can adjust the colors and in the main menu the display options for your molecule. Default settings are in a startup file that you can modify to suit your taste. More details are in the Molekel manual – check it out; it can do many other useful things for you too!

Visualization of three-dimensional representation of MOs, natural orbitals, electron densities, and spin densities is usually more intuitive than examining MO coefficients and it is is described in detail in section Orbital and Density Plots. The files necessary for such visualizations can be readily generated with ORCA in various ways and then opened in visualization software such as gOpenMol and Molekel.[2] In the following example, we briefly describe visualization of MOs.

To visualize MOs withgOpenMol, the plt file of MOs can be generated in the gOpenMol_bin format from the gbw file using orca_plot utility program or directly from the ORCA run through the %plots block of the input file:

! HF def2-SVP XYZFile

%plots Format gOpenMol_bin
       MO("CO-4.plt",4,0);
       MO("CO-8.plt",8,0);
       end
	   
*xyz 0 1
 C  0  0  0
 O  0  0  1.13
*

In this input file, the MO("CO-4.plt",4,0); command is used to evaluare MO labeled as 4 for operator 0 and then to strore it in the “CO-4.plt” file. For RHF and ROHF, one should always use operator 0. For UHF, operators 0 and 1 correspond to spin-up and spin-down orbitals, respectively.

When the produced plt files are opened with gOpenMol (see section Surface Plots for details), the textbook-like \(\pi\) and \(\pi^{\ast}\) MOs of the CO molecule are visualized as in Figure Fig. 9.2.

(a)

(b)

Fig. 9.2 (a) \(\pi\) and (b) \(\pi^\ast\) MOs of the CO molecule obtained from the interface of ORCA to gOpenMol.

If the gOpenMol_ascii file format was requested, gOpenMol conversion utility or some other tools might then be needed to convert this human-readable file to the machine-readable gOpenMol_bin format.

In order to use the interface to Molekel, an ASCII file in the Cube or Gaussian_Cube format needs to be generated. Such ASCII files can be actually transferred between platforms. The Cube format can be requested in the %plots block as:

! HF def2-SVP XYZFile
 
%plots Format Cube
       MO("CO-4.cube",4,0);
       MO("CO-8.cube",8,0);
       end

*xyz 0 1
 C  0  0  0
 O  0  0  1.13
*

To visualize MOs strored in the *.cube file, start Molekel and, via a right mouse click, load the *.xyz file and/or the *.cube file. lternatively, navigate to the surface menu, select the “gaussian-cube” format, and load the surface. For orbitals, click the “both signs” button and select a countour value in the “cutoff” field. Then, click “create surface”. The colour schemes and other fine details of the plots can be easily adjusted as desired. Finally, create files via the “snapshot” feature of Molekel. Figure Fig. 9.3 demonstrates a Molekel variant of Figure Fig. 9.2.

(a)

(b)

Fig. 9.3 (a) \(\pi\) and (b) \(\pi^\ast\) MOs of the CO molecule obtained from the interface of ORCA to Molekel.

It is worth noting that there are several other freeware programs, such as UCSF CHIMERA, that can read Gaussian_Cube files and provide high-quality plots.

In some situations, visualization of the electronic structure in terms of localized molecular orbitals might be quite helpful. As unitary transformations among occupied orbitals do not change the total wavefunction, such transformations can be applied to the canonical SCF orbitals with no change of the physical content of the SCF wavefunction. The localized orbitals correspond more closely to the pictures of orbitals that chemists often enjoy to think about. Localized orbitals according to the Pipek-Mezey population-localization scheme are quite easy to compute. For example, the following run reproduces the calculations reported by Pipek and Mezey in their original paper for the N\(_{2}\)O\(_{4}\) molecule.

! HF STO-3G Bohrs

%loc 
     LocMet  PipekMezey # localization method. Choices:
                            # PipekMezey (=PM)
                            # FosterBoys (=FB)
     T_Core  -1000      # cutoff for core orbitals
     Tol     1e-8       # conv. Tolerance (default=1e-6)
     MaxIter 20         # max. no of iterations (def. 128)
     end

*xyz 0 1
 N    0.000000   -1.653532   0.000000
 N    0.000000    1.653532   0.000000
 O   -2.050381   -2.530377   0.000000
 O    2.050381   -2.530377   0.000000
 O   -2.050381    2.530377   0.000000
 O    2.050381    2.530377   0.000000
*

Based on the output file of this job, localized MOs consist of six core like orbitals (one for each N and one for each O), two distinct lone pairs on each oxygen, a \(\sigma\)- and a \(\pi\)-bonding orbital for each N-O bond and one N-N \(\sigma\)-bonding orbital which corresponds to the dominant resonance structure of this molecule. You will also find a file with the extension .loc in the directory where you run the calculation. Like the standard gbw file, it can used to extract files for plotting or as input for another calculation (warning! The localized orbitals have no well defined orbital energy. If you do use them as input for another calculation use GuessMode=CMatrix in the %scf block).

---

[1]

There were some reports of problems with the program on Windows platforms. Apparently it is better to choose the display settings as “true color 32 bit” rather than “high 16 bit”. Thanks to Thomas Brunold!

[2]

The Molekel developers ask for the following citation – please do as they ask:

MOLEKEL 4.2, P. Flukiger, H.P. Lüthi, S. Portmann, J. Weber, Swiss Center for Scientific Computing, Manno (Switzerland), 2000-2006.

S. Portmann, H.P.Łüthi. MOLEKEL: An Interactive Molecular Graphics Tool. CHIMIA (2000), 54, 766-770. The program appears to be maintained by Ugo Varetto at this time.