Introduction
In this document you will find basic examples on how to prepare UNEX inputs for some typical jobs, run them and analyse respective outputs. In the various examples below I have tried to utilize real experimental data as much as possible, so you can see realistic use cases. Some theoretical values, mostly from quantum chemical calculations, occasionally can appear. They also correspond to modern state of the art in this field.
Rotational spectroscopy
In context of rotational spectroscopy UNEX can be used for refinement of molecular structure from rotational constants.
A simple example of structure refinement
As a simple example we take sulfur dichloride SCl2, for which rotational constants have been experimentally determined in the work of Bizzocchi et al. [1]. Below you will find a step-by-step tutorial on how to refine the structure of this molecule using UNEX.
First steps
In the C2v symmetry SCl2 molecule has only two independent geometrical parameters and we can refine them from three experimental rotational constants of only single parent isotopologue. Lets create UNEX input file and as the very first lines we add the following minimal set of commands:
BASE: READ <BASE>,</BASE>
ZMATRIX: READ mol <ZMAT>,</ZMAT>
LSQFUNC: MINIMIZE ROTCON
STOP:
UNEX will interpret these commands line by line:
-
BASE:READ
— reading of basic information, including definition of the molecule, which is located between tags<BASE>
and</BASE>
. -
ZMATRIX:READ
— for the moleculemol
reading of Z-matrix located between tags<ZMAT>
and</ZMAT>
. -
LSQFUNC:MINIMIZE
— minimization of least squares functional consisting of rotational constants, i.e. refinement of the molecular structure. -
STOP
— termination of UNEX execution.
Now we need to provide the field of data expected by the BASE:READ
command.
Add to the input file the block:
<BASE>
Molecules=mol
</BASE>
which contains the only single keyword Molecules
. We use it to define the
identifier mol
for our molecule. When interpreting this keyword UNEX
expects a molecule-specific field between tags constructed on the basis of
the molecule identifier as <mol>
and </mol>
.
Lets create and fill in this field with required for our purposes data:
<mol>
Formula=SCl2
RotConModel=rrpatm
# Experimental constants from Bizzocchi et. al, J. Mol. Spectr., 204 (2000) 275.
RotAExpVal=14613.57789
RotAExpStdev=0.00057
RotBExpVal=2920.86641
RotBExpStdev=0.00013
RotCExpVal=2430.69088
RotCExpStdev=0.00012
</mol>
Here we define:
-
the formula of the molecule as
Formula=SCl2
; -
for demonstration purposes, the model for rotational constants as
rrpatm
, although this is not strictly necessary in our case; -
experimental values for rotational constants using the
RotAExpVal
,RotBExpVal
andRotCExpVal
keywords. Note, the input units are MHz, which is the default option in UNEX; -
respective standard deviations with the keywords
RotAExpStdev
,RotBExpStdev
andRotCExpStdev
.
Now for the ZMATRIX:READ
command we need to provide the actual Z-matrix of our molecule.
Add to the file the following block:
<ZMAT>
Cl
S 1 Rscl
Cl 2 Rscl 1 Aclcl
Rscl 2.0 1
Aclcl 103.0 2
</ZMAT>
This Z-matrix defines two internal geometrical parameters, the bond length Rscl
(one parameter for both bonds) and the angle Aclcl
, with respective initial values.
We want the refine both parameters, so next to their values we also define refinement
group numbers as 1
and 2
. Note, here we use two different groups, thus the
parameters will be refined independently from each other.
Now your input file is ready, its content must be similar to that of the file SCl2_1.inp
coming with this tutorial. We can run UNEX with this file and inspect the
produced output file.
The part of the output from the refinement goes after the line LSQ functional processing …
.
You can see some information on experimental data, parameters to be refined,
the convergence of the iterative procedure and different statistics.
In the statistics we may be particularly interested in line
Rotational constants: ESD=3.279e+00 MaxD=2.29e+00 RMSD=1.89e+00 WRMSD=2.09e+00 MHz
,
which gives us maximal, root-mean-square and weighted root-mean-square deviations
of rotational constants in MHz. In particular the weighted root-mean-square deviation is equal to 2.09 MHz.
Also after the convergence a table with parameters is printed, for example:
Refined parameters: Errors are 1.00 times LSQ standard deviations. ----------------------------------------------------------------------------------------- Group Type Old value Refined value Error RelErr d(X^2)/dP ----------------------------------------------------------------------------------------- 1 ZmR 2.0000000000e+00 2.0129185079e+00 6.2e-04 3.1e-04 1.2e+04 2 ZmAng 1.0300000000e+02 1.0282286064e+02 3.7e-02 3.6e-04 1.1e+04 -----------------------------------------------------------------------------------------
The meaning of the table content is essentially self-explaining. The refined values of the parameters are now r(S—Cl) = 2.0129(6) Å and α(Cl—S—Cl) = 102.82(4) degrees, with least-squares standard deviations in parentheses. Note, we used rotational constants A0, B0 and C0 without any vibrational corrections. Thus, the refined structure is in fact of the r0 type.
After the table with parameters you can find the matrix of correlations printed as
Matrix of correlations: ----------------------------------------------------------------------------- 1.0000 0.1553 1.0000 -----------------------------------------------------------------------------
Fortunately, in our example this matrix is very compact. It shows that the refined parameters have correlation coefficient equal to 15.5 %.
Adding isotopologues
Bizzocchi et al. [1] determined rotational constants not only
for the parent molecule of sulfur dichloride but also for its three isotopologues.
We can utilize these data in our structural refinement.
First of all, in the input UNEX file we need to define additional molecules
corresponding to the three additional isotopologues.
For this, we use the keyword IsotopMols
in the field of the parent molecule:
# Parent isotopologue <mol> Formula=SCl2 IsotopMols=iso1;iso2;iso3 # Bizzocchi et al., J. Mol. Spectr., 204 (2000) 275. # The values for the parent molecule: RotAExpVal=14613.57789 RotAExpStdev=0.00057 RotBExpVal=2920.86641 RotBExpStdev=0.00013 RotCExpVal=2430.69088 RotCExpStdev=0.00012 </mol>
Accordingly, we add three molecule-specific fields with data for iso1
, iso2
and iso3
:
# [32]S[35]Cl[37]Cl <iso1> Formula=SCl2 # Bizzocchi et al., J. Mol. Spectr., 204 (2000) 275. RotAExpVal=14490.19459 RotAExpStdev=0.00058 RotBExpVal=2841.19803 RotBExpStdev=0.00013 RotCExpVal=2371.96585 RotCExpStdev=0.00013 </iso1> # [32]S[37]Cl2 <iso2> Formula=SCl2 # Bizzocchi et al., J. Mol. Spectr., 204 (2000) 275. RotAExpVal=14365.1421 RotAExpStdev=0.0026 RotBExpVal=2763.20280 RotBExpStdev=0.00024 RotCExpVal=2314.12120 RotCExpStdev=0.00019 </iso2> # [34]S[35]Cl2 <iso3> Formula=SCl2 # Bizzocchi et al., J. Mol. Spectr., 204 (2000) 275. RotAExpVal=14024.5853 RotAExpStdev=0.0068 RotBExpVal=2921.00225 RotBExpStdev=0.00056 RotCExpVal=2413.85131 RotCExpStdev=0.00034 </iso3>
Just like for the parent molecule, we must define Z-matrices also for the
additional isotopologues using the ZMATRIX:READ
command:
ZMATRIX: READ iso1 <ZMAT1>,</ZMAT1> ZMATRIX: READ iso2 <ZMAT2>,</ZMAT2> ZMATRIX: READ iso3 <ZMAT3>,</ZMAT3>
and by providing the respective data fields:
<ZMAT1> Cl 36.96590260 S 1 Rscl Cl 2 Rscl 1 Aclcl Rscl 2.0 1 Aclcl 103.0 2 </ZMAT1> <ZMAT2> Cl 36.96590260 S 1 Rscl Cl 36.96590260 2 Rscl 1 Aclcl Rscl 2.0 1 Aclcl 103.0 2 </ZMAT2> <ZMAT3> Cl S 33.96786700 1 Rscl Cl 2 Rscl 1 Aclcl Rscl 2.0 1 Aclcl 103.0 2 </ZMAT3>
Notice how the atomic masses for the non-standard isotopes are declared right in Z-matrix bodies,
next to atomic symbols. In this way we indicate only non-standard isotopes.
For the other atoms UNEX automatically assigns built-in atomic masses of the most abundant isotopes,
in this case 32S and 35Cl.
Also note that the initial values of bond lengths and angles in all isotopologues are the same and
constitute two refinement groups, 1
and 2
. Thus, we are going to refine two parameters under assumption
that all isotopologues have the same r0 structure.
Now your input file must be similar to the file SCl2_2.inp
of this tutorial
and it is ready to be processed by UNEX.
The least squares refinement converges very quickly and takes less than a second
on modern hardware. Note that we have now in total 12 experimental constants:
Statistics: Number of refined parameters: 2 Number of data: 12 Degrees of freedom: v=10
Interestingly, the overall agreement of model with data is now even slightly better,
WRMSD=2.03e+00 MHz
, than in the previous case of only one isotopologue with three
experimental constants in total. Due to the increased number of statistically
independent experimental data the refined parameters are now more precise,
r(S—Cl) = 2.0129(2) Å and α(Cl—S—Cl) = 102.82(1) degrees,
and the correlation coefficient has lowered to 10 %.
We can also print Cartesian coordinates of atoms in all or selected isotopologues.
After the LSQFUC
command add the line
PRINT: MOLXYZ mol
This will give you the coordinates of atoms in mol
.
In the default format you can also see the atomic masses actually used by UNEX.
In context of rotational spectroscopy it makes sense to print Cartesian coordinates
in the system of principal axes of inertia tensor.
For this, add the keyword PrintXYZPAS=true
to the field of basic information.
On the output you should get
Cartesian coordinates (Angstroms) of atoms in mol Format: UNEX Orientation: PAS -------------------------------------------------------------------------------------------------- N | At | An | Mass | X | Y | Z -------------------------------------------------------------------------------------------------- 1 Cl 17 34.968852690000 -1.57337179879261e+00 3.93893392440875e-01 0.00000000000000e+00 2 S 16 31.972071173500 0.00000000000000e+00 -8.61627008214962e-01 0.00000000000000e+00 3 Cl 17 34.968852690000 1.57337179879261e+00 3.93893392440875e-01 0.00000000000000e+00 -------------------------------------------------------------------------------------------------- Rot. const. (RRPATM, MHz): 1.46117876060391e+04 2.91906050564133e+03 2.43300790959393e+03
The coordinates can be visualized producing a structure like in the figure below.

Using vibrational corrections
Until now we refined r0 structure directly from experimental rotational constants A0, B0 and C0.
Omitting a discussion of disadvantages related to this type of structure,
we can proceed directly to the example on how to refine structures corrected for vibrational effects.
For this, next to experimental rotational constants we need to define respective vibrational corrections.
Nowadays in many cases they can be routinely calculated theoretically with reasonable confidence.
Even better is when you have them refined from experimental ro-vibrational spectra.
In any case they must be introduced in UNEX using the keywords RotAVibCorVal
, RotBVibCorVal
and RotCVibCorVal
.
Taking your previous input file you can add the following data to the field of the parent molecule:
RotAVibCorVal=-19.2076 RotBVibCorVal=9.4715 RotCVibCorVal=9.5976
to the first isotopologue iso1
:
RotAVibCorVal=-18.6655 RotBVibCorVal=9.1457 RotCVibCorVal=9.2892
to iso2
:
RotAVibCorVal=-18.1413 RotBVibCorVal=8.8313 RotCVibCorVal=8.9889
and to iso3
:
RotAVibCorVal=-18.6646 RotBVibCorVal=9.3391 RotCVibCorVal=9.4141
All these values are quantum-chemically calculated corrections to equilibrium structure.
As a reference this tutorial provides a file SCl2_3.inp
, which should also contain all the required information.
Running UNEX with the prepared input leads to a much better fit with WRMSD equal to 3.50e-02 MHz.
This may be compared with the previous value (2.03e+00 MHz) from the example above
without any vibrational corrections. Thus we are getting here more consistent model.
The refined parameters, rese(S—Cl) = 2.011023(3) Å and αese(Cl—S—Cl) = 102.6808(2) degrees,
are now much more precise, at least nominally. Also, in comparison to the previous values,
r0(S—Cl) = 2.0129(2) Å and α0(Cl—S—Cl) = 102.82(1), we see significant
deviations due to the different types of structures. Note, we use the rese designation
to underline that the structure is in fact semi-experimental (also known as semi-empirical)
due to using theoretical vibrational corrections.
Please keep in mind that obtained in this example very small
standard deviations manifest only random noise in experimental data.
Of course, the total errors must be larger at least due to uncertainties in vibrational corrections.
This is, however, a different topic.
What we can also do in this example is to print details about rotational constants.
For this, you can add the following line after the LSQFUNC
command:
PRINT: ROTCON mol
On the output you get the following data for the parent molecule mol
:
Model rotational constants for mol Units: MHz Model: rrpatm-vibc-elc1 ------------------------------------------------------------------------------------- RRPATM | El. Cor. | Vib. Cor. | Total Model ------------------------------------------------------------------------------------- A 1.459434063286e+04 0.000000000000e+00 -1.920760000000e+01 1.461354823286e+04 B 2.930307872201e+03 0.000000000000e+00 9.471500000000e+00 2.920836372201e+03 C 2.440329187413e+03 0.000000000000e+00 9.597600000000e+00 2.430731587413e+03 ------------------------------------------------------------------------------------- Experimental and model rotational constants for mol Units: MHz Model: rrpatm-vibc-elc1 Errors are 1.00 times standard deviations. ------------------------------------------------------------------------------ Experimental | Error | Model | Error | Delta ------------------------------------------------------------------------------ A 1.461357789000e+04 5.70e-04 1.461354823286e+04 7.80e-02 2.97e-02 B 2.920866410000e+03 1.30e-04 2.920836372201e+03 1.35e-02 3.00e-02 C 2.430690880000e+03 1.20e-04 2.430731587413e+03 9.41e-03 -4.07e-02 ------------------------------------------------------------------------------ For the defined values: RMSD=3.39e-02 WRMSD=3.61e-02 MHz
Here in the first table you can see the particular components of the model values, including
the vibrational corrections.
Note, in sulfur dichloride these corrections constitute about
0.1 — 0.5 % of the total rotational constants.
The default model rrpatm-vibc-elc1
has also electronic correction,
which will be discussed in the next example.
In the second table are provided experimental and model values and respective deviations
for the rotational constants separately.
Applying electronic corrections
In addition to vibrational correction our model for rotational constants
contains also an electronic correction (consult UNEX manual for details).
Usually they are negligibly small but in investigations of some molecules can play significant role.
In UNEX the corrections are internally calculated from diagonal aa
, bb
and cc
components of rotational g-tensors.
The latter can be determined experimentally or, most usually, calculated theoretically.
In the input file we define them with the keywords RotGTaaVal
, RotGTbbVal
and RotGTccVal
for each molecule.
In this example we add the following values for the parent isotopologue mol
:
RotGTaaVal=-0.0361 RotGTbbVal=-0.0147 RotGTccVal=-0.0232
for iso1
:
RotGTaaVal=-0.0358 RotGTbbVal=-0.0143 RotGTccVal=-0.0226
for iso2
:
RotGTaaVal=-0.0355 RotGTbbVal=-0.0139 RotGTccVal=-0.0221
and for iso3
:
RotGTaaVal=-0.0348 RotGTbbVal=-0.0147 RotGTccVal=-0.0231
Now the file is ready for running and must be similar to SCl2_4.inp
from this tutorial.
After the least-squares refinement with LSQFUNC:MINIMIZE
you can see that the
overall agreement is now even better, WRMSD=3.13e-02 MHz
, although to a very small extent.
Thus, the vibrational corrections do the major job and the electronic corrections
lead to only slight improvement. The latter can sometimes even slightly worsen the agreement
due to inaccuracy and inconsistency with other data.
Looking at the refined parameters,
rese(S—Cl) = 2.011010(3) Å and αese(Cl—S—Cl) = 102.6811(2) degrees,
we can see some notable shift in the bond length compared to the previous refinement
without electronic corrections,
i.e. rese(S—Cl) = 2.011023(3) Å and αese(Cl—S—Cl) = 102.6808(2) degrees.
Formally, if we consider only the provided in parentheses standard deviations,
this effect could be accepted as significant.
However, we keep in mind that the other sources of uncertainties are not taken into account
and thus the seeming effect is rather unreliable in this particular case.
After the refinement we can get lots of interesting information by executing PRINT: ROTCON all
.
This variant of the command prints rotational constants for all defined molecules,
so that you do not need to call PRINT
for each molecule individually.
In particular, for mol
we get
Model rotational constants for mol Units: MHz Model: rrpatm-vibc-elc1 ------------------------------------------------------------------------------------- RRPATM | El. Cor. | Vib. Cor. | Total Model ------------------------------------------------------------------------------------- A 1.459462922084e+04 -2.870183433458e-01 -1.920760000000e+01 1.461354980250e+04 B 2.930334240812e+03 -2.346613381449e-02 9.471500000000e+00 2.920839274678e+03 C 2.440355543757e+03 -3.084242581278e-02 9.597600000000e+00 2.430727101331e+03 ------------------------------------------------------------------------------------- Experimental and model rotational constants for mol Units: MHz Model: rrpatm-vibc-elc1 Errors are 1.00 times standard deviations. ------------------------------------------------------------------------------ Experimental | Error | Model | Error | Delta ------------------------------------------------------------------------------ A 1.461357789000e+04 5.70e-04 1.461354980250e+04 6.98e-02 2.81e-02 B 2.920866410000e+03 1.30e-04 2.920839274678e+03 1.21e-02 2.71e-02 C 2.430690880000e+03 1.20e-04 2.430727101331e+03 8.43e-03 -3.62e-02 ------------------------------------------------------------------------------ For the defined values: RMSD=3.08e-02 WRMSD=3.23e-02 MHz
Now you can see how large are the absolute values of electronic corrections in sulfur dichloride. For the parent molecule, as well as for other isotopologues, they are of the order 3×10-1 MHz for A and 3×10-2 HMz for B and C, which is 0.5 — 1.5 % of the corresponding vibrational correction or 0.001 — 0.002 % of the total rotational constant.
At this point we can consider our refinement as complete.
Gas electron diffraction
Historically UNEX has been designed as a full-featured software for comprehensive support of experimental gas-phase electron diffraction (GED) studies. Below are presented some use cases with usually appearing scenarios.
Structure refinement
One of the most important stages in a typical GED investigation is the structure refinement. In this chapter you can learn how to solve this problem using UNEX.
A simple example
As an example we take a portion of experimental diffraction data measured for carbon tetrachloride CCl4 in the work of Vishnevskiy et al. [2]. The molecules of CCl4 are small and highly symmetric (Td point group) and thus are very convenient for a GED structural analysis. It is also handy from the experimental point of view, since diffraction patterns can be easily measured for this compound.
In this simple example we assume that the data reduction and electron wavelength calibration have already been done and we take for the analysis only one experimental total intensity curve. Our next steps are briefly as follows:
-
We define the complete initial model of our molecule with all parameters required for the calculation of the model molecular intensity,
-
introduce the experimental total diffraction intensity,
-
extract molecular part from the total intensity,
-
refine the molecular parameters using the least-squares method,
-
print and analyze the results.
So lets start from the very beginning. Below are described commands, which should be added line-by-line to a newly created UNEX input file.
First, we must introduce some basic information
BASE: READ <BASE>,</BASE> STOP: <BASE> Molecules=mol </BASE> <mol> Formula=CCl4 </mol>
Next we define a geometrical model for the molecule.
In this example we use geometrically-consistent GED model,
so the structure must be defined as a Z-matrix with the command (right after BASE:
)
ZMATRIX: READ mol <ZMAT>,</ZMAT>
and providing the required field
<ZMAT> Cl C 1 R1 Cl 2 R1 1 A1 Cl 2 R1 1 A1 3 A1 -1 Cl 2 R1 1 A1 3 A1 1 R1 1.763 2 A1 109.4712206344907 </ZMAT>
Note, to the R1
parameter we already assigned the group number 2
.
This is not required now, but will be used below in the actual refinement procedure.
When introducing Z-matrices it is advised to check their correctness
by printing calculated Cartesian coordinates.
This can be done with the command
PRINT: MOLXYZ mol
and visualizing the printed coordinates by any suitable software. Note, you can print data in different formats, see manual for details. You may also want to check the symmetry of your input structure by using
PRINT: MOLSYM mol
For our example this command must produce some information on symmetry elements and also the line
Point group: Td [4C3,3C2,3S4,6P,E]
which is what we expect for CCl4.
Next we introduce information on GED terms (interatomic pairs) for the molecule with the EDTERMS
command:
EDTERMS: READ mol <TERMS>,</TERMS> Format=unex
Add the corresponding data field to the input file with precalculated values:
<TERMS> #At1 At2 r_a l cor G C2 Cl1 1.7609 0.0521 -0.0066 3 C2 Cl3 1.7609 0.0521 -0.0066 3 C2 Cl4 1.7609 0.0521 -0.0066 3 C2 Cl5 1.7609 0.0521 -0.0066 3 Cl1 Cl3 2.8755 0.0676 -0.0090 4 Cl1 Cl4 2.8755 0.0676 -0.0090 4 Cl1 Cl5 2.8755 0.0676 -0.0090 4 Cl3 Cl4 2.8755 0.0676 -0.0090 4 Cl3 Cl5 2.8755 0.0676 -0.0090 4 Cl4 Cl5 2.8755 0.0676 -0.0090 4 </TERMS>
Here we are tying together amplitudes for the bonded distances C—Cl in the refinement group number 3
,
and the amplitudes for the non-bonded distances Cl…Cl in the group 4
.
At this point the molecular model is defined completely and we can introduce the diffraction data.
With the command EDDATA
UNEX will read-in the experimental total diffraction intensity:
EDDATA: READ <EDINT>,</EDINT>
The initial part of the respective data field looks like:
<EDINT> Set=ed1 Data=s;iTotExp ImolSf=1.0 ImolSfRefGrp=1 6.20 11.7659129739 6.40 11.9934137749 6.60 12.3881941876
For the complete data see the file CCl4_1.inp
supplemented to this tutorial.
For the refinement we assign the group number 1
to the scale factor of the molecular intensity.
The initial value for this factor is also explicitly defined as ImolSf=1.0
.
Now the ED data set ed1
is defined and we can use this identifier later in other commands.
For the calculation of model intensities we must introduce ED scattering factors.
In UNEX they can be calculated simply by calling the EDSCATFAC
command.
Add the following line after the EDDATA:READ
call:
EDSCATFAC: CALC mol Lambda=0.048707
With the keyword Lambda
we indicate the calibrated electron wavelength.
For the least-squares refinement we need experimental molecular intensity function.
It must be extracted from the total intensity, which is in the ED data set ed1
.
For this use the command EDIMOL
:
EDIMOL: GETEXP ed1 BgrSplNInflMax=3 ItotModel=mbgr
In this procedure the total intensity is decomposed into molecular and background components.
As the model we choose mbgr
, i.e. containing multiplicative background.
The background will be approximated with a cubic spline and as a smoothness criterion
we allow no more than 3
inflection points.
Note, the actual number of inflection points may be smaller. UNEX prints this information on output.
In this example you should get
Number of inflection points 2, requested 3
Finally we have both model and data ready for the refinement.
For the least-squares determination of parameters we must use the LSQFUNC
command.
Add the following line for minimization of the LSQ functional built on ED sM(s) function from the ed1
data set:
LSQFUNC: MINIMIZE EDSMS ed1
From this command UNEX prints lots of important information to the output file, including the initial values of parameters and LSQ functional, convergence during the iterations and at the end, statistics of the refinement, a table with refined parameters and correlation matrix. After the convergence we have the best (minimal) achieved R-factor
Total sM(s) Rf=6.157 wRd=6.157
Initial and refined parameters, as well as corresponding least-squares standard deviations, are printed in the table:
Refined parameters: Errors are 1.00 times LSQ standard deviations. ----------------------------------------------------------------------------------------- Group Type Old value Refined value Error RelErr d(X^2)/dP ----------------------------------------------------------------------------------------- 1 EDImolSf 1.0000000000e+00 8.8210443905e-01 7.6e-03 8.6e-03 -2.8e-14 2 ZmR 1.7630000000e+00 1.7604005167e+00 2.6e-04 1.5e-04 3.5e-07 3 EDTrmAmpl+ 5.2100000000e-02 4.7047497358e-02 8.9e-04 1.9e-02 -6.5e-08 4 EDTrmAmpl+ 6.7600000000e-02 6.9215439794e-02 5.4e-04 7.8e-03 -3.4e-07 -----------------------------------------------------------------------------------------
Next are printed the correlation coefficients:
Matrix of correlations: ----------------------------------------------------------------------------- 1.0000 0.0498 1.0000 0.4876 0.0026 1.0000 0.7298 0.0264 0.3702 1.0000 -----------------------------------------------------------------------------
As you can see, the refinement procedure has changed the values of parameters substantially.
We need to keep in mind that the EDIMOL:GETEXP
procedure used model-dependent background (see UNEX manual for details).
Thus, if the model has significantly changed, it makes sense to repeat again the combination of molecular intensity extraction
and parameter refinement. Add these two lines (same as before) to the input file:
EDIMOL: GETEXP ed1 BgrSplNInflMax=3 ItotModel=mbgr LSQFUNC: MINIMIZE EDSMS ed1
After the second LSQ functional minimization you should get a better (lower) R-factor
Total sM(s) Rf=5.054 wRd=5.054
and the refined parameters
Errors are 1.00 times LSQ standard deviations. ----------------------------------------------------------------------------------------- Group Type Old value Refined value Error RelErr d(X^2)/dP ----------------------------------------------------------------------------------------- 1 EDImolSf 8.8210443905e-01 8.6731619200e-01 6.1e-03 7.0e-03 -5.6e-14 2 ZmR 1.7604005167e+00 1.7601265599e+00 2.1e-04 1.2e-04 4.6e-07 3 EDTrmAmpl+ 4.7047497358e-02 4.6372855337e-02 7.3e-04 1.6e-02 1.6e-08 4 EDTrmAmpl+ 6.9215439794e-02 6.9282520045e-02 4.4e-04 6.4e-03 -3.3e-08 -----------------------------------------------------------------------------------------
The changes between the old (before this last refinement) and new (after the refinement) values are now much smaller. The correlation matrix remained nearly the same
1.0000 0.0498 1.0000 0.4906 0.0026 1.0000 0.7293 0.0265 0.3721 1.0000
and shows that the largest correlation (73 %) is between the molecular intensity scale factor EDImolSf
(group 1
) and the vibrational amplitudes l(Cl…Cl) tied together in group 4
.
We may want to check the electron diffraction data and plot various functions for better analysis. Add the following command after the last LSQ minimization:
PRINT: EDDATA ed1 Data=iTotExp;iBgr;iMolExp;iMolMod;iMolDif
With the keyword Data
is indicated that the following data types
from the set ed1
are printed together:
-
experimental total intensity,
-
background intensity,
-
experimental molecular intensity,
-
model molecular intensity,
-
difference between experimental and model molecular intensities.
These data can be visualized by any suitable software. We can use the UIntPlot program bundled together with UNEX. Starting it in the command line as
uintplot --data tot,bgr --curves ed1 CCl4_1.log
will produce a plot of the experimental total intensity with the respective background line.
Note, UIntPlot requires that the Gnuplot program [3] is already installed
and can be started simply as gnuplot
from you working directory.
Also make sure that last command line argument to uintplot
is the actual name of your UNEX output file.

Visual inspection of molecular intensity functions is also very important.
We plot them running uintplot
as
uintplot --data mol,mmol,dmol --curves ed1 CCl4_1.log
which produces the following image.

As we can see, the difference curve is rather small and shows mostly random deviations between experimental data and model. Thus the fit is acceptable.
Usually electron diffraction data are also represented in the form of radial distribution functions (RDF). UNEX will calculate them, if you add the following command:
EDRDF: CALC ed1
Also, for the visualization it is convenient to print the ED terms as
PRINT: EDTERMS mol Format=urdfplot
Now after processing of all commands your UNEX output file must contain all the data required by the URDFPlot program (also bundled together with UNEX), which is useful for plotting RDFs. Start it simply as (provide the actual name of your output file as the argument):
urdfplot CCl4_1.log
and you will get the following image.

As we can see, in the RDF representation the difference between the experimental data and model is also small.
On the basis of the R-factor value of 5.05 % and visual inspection of deviations
between experimental data and best refined model,
we may now summarize the main results of our investigation of CCl4 as
rese(C—Cl) = 1.7601(2) Å, l(C—Cl) = 0.0464(4) Å and l(Cl…Cl) = 0.0693(4) Å,
where values in parentheses are least-squares standard deviations.
Note, because of the used theoretical vibrational corrections
(we introduced them with EDTERMS:READ
) to the equilibrium geometry,
the determined structural parameter is semi-experimental rese.
The obtained here least-squares standard deviations of the refined parameters may in no case be considered as total uncertainties. In addition to random noise in experimental data, there are other various sources of errors. Their consideration is another, more difficult topic. |
References
[1] L. Bizzocchi, L. Cludi, C. Degli Esposti, & A. Giorgi, Millimeter-Wave Spectroscopy of Sulfur Dichloride. J. Mol. Spectr., 204 (2000) 275–280. https://doi.org/10.1006/jmsp.2000.8223.
[2] Y. V. Vishnevskiy, S. Blomeyer, & C. G. Reuter, Gas standards in gas electron diffraction: accurate molecular structures of CO2 and CCl4. Struct. Chem., 31 (2020) 667–677. https://doi.org/10.1007/s11224-019-01443-5.
[3] T. Williams, C. Kelley, & many others, Version 6.0, http://www.gnuplot.info/. (2025).
This document has been generated on 2025-04-17 12:12:32 +0200