Investigating CAChe for use in freshman chemistry courses: Comparison of various
computational methods in the determination of partial charge, dipole moments, and bond
order
J. Noroski, University of Pittsburgh, Pittsburgh, PA
Abstract
A variety of computational methods in CAChe were used to determine three properties of
various small molecules: the partial charge of each atom in the molecule, the dipole moment of
the molecule, and the bond orders. For the hydrogen halides “optimized geometry/PM5
geometry” was the most successful. For various CHnXn compounds “electrostatic potential on
electron density/MM geometry with INDO/1 wavefunction” was the best. For acetic acid, NH3,
H2O, H2S, and NaF “UV-visible/ZINDO CI at PM5 geometry” performed best.
Introduction
CAChe is capable of utilizing many different theoretical approaches to determine various
molecular properties. The differences between the methods, however, are of little concern to a
freshman chemistry student. Thus, we can conduct a survey of methods in CAChe to determine
which methods provide the “best” results. Or, at least the results that agree with the framework
of chemistry as presented at the freshman level. With this approach the reader can see from the
work that follows that teachers must choose carefully from among the many available methods
when trying to use CAChe to help students learn chemistry. We begin with a few definitions of
the three properties that we wish to determine: atomic partial charge, dipole moment, and bond
order.
The help section of CAChe contains this definition of “atomic partial charge”:
Atomic partial charge provides a crude approximation for the distribution of charge in a
molecule.
The definition goes on to describe the use of these charges in determining the electrostatic
potential. Page 15-14 of the User’s Guide gives only the color scheme for partial charge: Yellow
is negative, and red is positive. In email correspondence with Dr. Bell-Loncella, she pointed out
the following quotation from a book on computational chemistry:
“On the other hand the book by Cramer that I suggested in my earlier post says the following:
The concept of a partial charge is, however, ill defined. One often sees it written that the
atomic partial charge is not a quantum mechanical observable. ... One can define
unambiguous procedures make use of well-defined quantum mechanical operators. ...
there is no universally agreed upon 'best' procedure for computing partial atomic charge.
This failure to agree is in some sense, inevitable, because partial atomic charges are used
in different ways within the context of different quantitative and qualitative models in
chemistry, so there is no reason to expect a single procedure for determining such charges
to be optimal for all purposes.”
Thus, the result is very dependent of the method chosen.
For confirmation that the “partial charge” results DO have SOME connection to reality, the
partial charges were calculated for CsF and CaF2. These gave (–1.10, 1.10) and (1.993, –0.996).
These results at least agree nicely with the expected octet rule charges. Also, for any number of
atoms in the molecule, the partial charge results always add up to zero.
As for the meaning of the “bond order” result for a given calculation, we note page 15-15 of the
User’s Guide which gives the following information:
Color of bond Range of bond order Bond type
Green
0 – 0.60
Weak
Red
0.61 – 1.60
Single
Yellow
1.61 – 2.60
Double
Cyan
> 2.60
Triple
White
Ionic
Purple
Coordination
Building the molecules N2, O2, and Cl2 and using “optimized geometry/PM5 geometry” gave the
expected results of exactly 3.00, 2.00, and 1.00.
Note that Ch. 20 of the User’s Guide contains much information on the computation types.
MOPAC is semi-empirical, quantum mechanical method and uses AM1, PM3, and PM5.
MOPAC calculates heats of formation, rather than the energy required to separate the molecule
into isolated nuclei and electrons as in quantum mechanical methods such as EHT and ZINDO.
Molecular Mechanics uses Newton’s Laws, is classical, and computes steric energy. MOPAC is
parameterized for a subset of the elements and cannot be used with all molecules, while EHT has
parameters for all elements. MOPAC parameters are obtained by fitting experimental heats of
formation, geometries, and ionization potentials, while ZINDO uses the theoretically-based
INDO parameterization. The top of page 20-16 of the User’s Guide has descriptions of the
meaning of the “energy” output.
A brief Results section follows each group of molecules that was studied.
Data/Calculations
The following table contains the results of CAChe calculations for the hydrogen halides. The
table lists the partial charge, δ, for the halogen. The partial charge on the hydrogen atom is just
the opposite. The dipole moments are (Siska) 1.82, 1.08, 0.82, 0.44. In the table Δ is the
difference between the calculated value and the experimental value.
Molecule
HF
HCl
HBr
HI
Molecule
HF
HCl
HBr
HI
Molecule
HF
HCl
HBr
HI
Molecule
HF
HCl
HBr
HI
Optimized geometry/PM5 geometry (few seconds)
δ for halogen
Dipole moment /Δ
Bond order
–0.335
2.084 / 0.26
0.888
–0.205
1.478 / 0.40
0.958
–0.152
1.324 / 0.50
0.977
–0.126
0.434 / –0.01
0.984
Optimized geometry/B88-LYP DFT geometry (1 min)
δ for halogen
Dipole moment /Δ
Bond order
–0.470
2.027 / 0.21
0.462
–0.236
1.479 / 0.40
0.506
–0.234
1.062 / 0.24
0.532
–0.169
0.700 / 0.26
0.569
Optimized geometry/B88-PW91 DFT geometry (1 min)
δ for halogen
Dipole moment /Δ
Bond order
–0.475
2.033 / 0.21
0.468
–0.249
1.518 / 0.44
0.505
–0.245
1.087 / 0.27
0.532
–0.180
0.727 / 0.29
0.571
Optimized geometry/D-VWN geometry (1 min)
δ for halogen
Dipole moment /Δ
Bond order
–0.491
2.109 / 0.29
0.470
–0.264
1.599 / 0.52
0.507
–0.267
1.189 / 0.37
0.531
–0.207
0.850 / 0.41
0.569
As a measure of the accuracy of each method, we can calculate the average of the absolute error
(Δ) in the dipole moment for each method. This gives:
Method
Average of Δ
0.29
PM5
0.28
B88-LYP DFT geometry
0.30
B88-PW91 DFT geometry
0.40
D-VWN geometry
Note that the PM5 method gives reasonable bond orders. All three quantum methods give the
nearly identical bond orders, all of which are too small. HF has the lowest bond order.
According to the scale shown above, the quantum results show that the HF bond is weak. That is
ludicrous. For this reason, for at least the HX’s series we can’t compare bond orders as a
measure of bond strength. Also, the LYP results are close to the PW-91 results.
To explore other methods in hopes of achieving better results, different “property” categories
were chosen to calculate the dipole moments, partial charges, and bond orders.
Molecule
HF
HCl
HBr
HI
Molecule
HF
HCl
HBr
HI
Molecule
HF
HCl
HBr
HI
Molecule
HF
HCl
HBr
HI
Molecule
HF
HCl
HBr
HI
Molecule
HF
HCl
HBr
HI
UV-visible/ZINDO CI at PM5 geometry (few seconds)
δ for halogen
Dipole moment /Δ
Bond order
–0.405
2.270 / 0.45
0.889
–0.305
2.397 / 1.32
0.954
–0.231
2.091 / 1.27
0.972
–0.237
2.406 / 1.97
0.985
IR transitions/MOPAC PM5 FORCE (few seconds)
Results the same as Optimized geometry/PM5
IR transitions/B88-LYP DFT geometry IR spectrum(45 sec)
δ for halogen
Dipole moment /Δ
Bond order
–0.467
2.142 / 0.32
0.424
–0.236
1.482 / 0.40
0.505
–0.234
1.063 / 0.24
0.531
–0.171
0.702 / 0.26
0.571
Electrostatic potential on electron density/MM geometry with EHT
wavefunction(5 sec)
δ for halogen
Dipole moment /Δ
Bond order
–0.673
3.787 / 1.967
0.665
–0.253
2.467 / 1.39
0.963
–0.123
2.023 / 1.20
0.990
–0.027
1.989 / 1.56
1.000
Electrostatic potential on electron density/MM geometry with PM5
wavefunction(5 sec)
δ for halogen
Dipole moment /Δ
Bond order
–0.347
2.217 / 0.40
0.880
–0.233
1.725 / 0.65
0.946
–0.184
1.601 / 0.78
0.966
–0.057
0.689 / 0.25
0.997
Electrostatic potential on electron density/AM1 geometry with AM1
wavefunction(5 sec)
δ for halogen
Dipole moment /Δ
Bond order
–0.289
1.736 / –0.08
0.916
–0.168
1.384 / 0.30
0.972
–0.087
1.385 / 0.55
0.992
1.274 / 0.83
1.000
0.010
Under the “Property:” box we also considered “all molecular orbitals” and “electrostatic
potential on electron density”. When either of these Properties was chosen, “PM5 geometry with
PM5 wavefunction” was chosen from the “Using:” box. Each way gives the same results as we
got above for “optimized geometry/PM5”. Also, the same values are obtained for “all molecular
orbitals/DFT geometry with B88-LYP DFT wavefunction” or “electrostatic potential on electron
density/DFT geometry with B88-LYP DFT wavefunction” as were obtained above for
“Optimized geometry/B88-LYP DFT geometry. So, unlike “UV-visible”, “IR
transitions/MOPAC”, “all molecular orbitals”, and “electrostatic potential on electron density”
calculations use the geometry as obtained from the Property of “optimized geometry”. Thus, the
same values are obtained for the partial charges and the dipole moments.
Results
No method gives perfect results. If we view this in terms of an assignment where the student is
told to determine the partial charge, dipole moment, and bond order for the HX’s, the “best”
method is optimized geometry/PM5 geometry. The quantum methods give bond orders of
around 0.5. This result clashes with the Lewis concept of a single bond, which beginning
students hold dear. Also, you can note above that some of the methods give dipole moments that
are off by almost 2 D.
The following table contains the results of CAChe calculations for CH3F and CH3Cl. The table
lists the partial charge for each atom in the compound. The dipole moments are (Siska) 1.81
(CH3F) and 1.87 (CH3Cl).
Molecule
CH3F
CH3Cl
Molecule
CH3F
CH3Cl
CH3Br
Molecule
CH3F
CH3Cl
Molecule
CH3F
CH3Cl
Molecule
CH3F
CH3Cl
Molecule
CH3F
CH3Cl
Molecule
CH3F
CH3Cl
Molecule
CH3F
CH3Cl
Molecule
CH3F
CH3Cl
Optimized geometry/PM5 geometry (few seconds)
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.254 / –0.065 / 0.106
2.192 / 0.38
0.939 / 0.960
–0.171 / –0.227 / 0.133
1.901 / 0.03
0.966 / 0.963
Optimized geometry/B88-LYP DFT geometry (2m15s)
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.256 / –0.335 / 0.197
1.993 / 0.18
0.547 / 0.753
–0.102 / –0.622 / 0.241
2.134 / 0.26
0.471 / 0.743
–0.140 / –0.572 / 0.237
2.049
0.461 / 0.750
Optimized geometry/B88-PW91 DFT geometry (2m25s)
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.250 / –0.350 / 0.200
1.933 / 0.12
0.523 / 0.755
–0.098 / –0.648 / 0.249
2.111 / 0.24
0.448 / 0.741
Optimized geometry/D-VWN geometry
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.218 / –0.441 / 0.220
1.875 / 0.07
0.553 / 0.754
–0.072 / –0.741 / 0.271
2.060 / 0.19
0.460 / 0.741
UV-visible/ZINDO Cl at PM5 geometry
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.343 / 0.125 / 0.073
2.221 / 0.41
0.927 / 0.933
–0.265 / 0.016 / 0.083
2.871 / 1.00
0.944 / 0.994
Electrostatic potential on electron density/MM geometry with EHT
wavefunction(5 sec)
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.649 / 0.620 / 0.010
3.347 / 1.54
0.699 / 0.987
–0.196 / 0.170 / 0.009
2.371 / 0.50
0.990 / 0.989
Electrostatic potential on electron density/MM geometry with PM5
wavefunction(5 sec)
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.264 / –0.072 / 0.112
2.304 / 0.49
0.931 / 0.960
1.926 / 0.06
0.967 / 0.962
–0.166 / –0.231 / 0.132
Electrostatic potential on electron density/MM geometry with INDO/1
wavefunction(5 sec)
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.342 / 0.116 / 0.075
2.295 / 0.49
0.923 / 0.993
–0.259 / 0.019 / 0.080
2.859 / 0.99
0.945 / 0.993
Electrostatic potential on electron density/AM1 geometry with AM1
wavefunction(5 sec)
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
–0.178 / –0.041 / 0.073
1.616 / 0.19
0.984 / 0.963
–0.116 / –0.178 / 0.098
1.511 / –0.36
0.987 / 0.973
Molecule
CH3F/CH3Cl
IR transitions/MOPAC PM5 FORCE (few seconds)
all molecular orbitals/PM5 geometry with PM5 wavefunction
electrostatic potential on electron density/ PM5 geometry with PM5
wavefunction
δ for halogen / C / H
Dipole moment /Δ
Bond order CX / CH
All results same as for Optimized geometry/PM5
Results
These results show that some of the methods are simply incapable of good results. The C can’t
be as negative as the F. All of the “optimized geometry” methods have the carbon as more
negative than the halogen. The D-VWN method gives good results for the magnitude of the
dipole moments, but the magnitudes of the partial charges can’t be right. So, the DIRECTION
of the vector is ENTIRELY wrong. Note that the “optimized geometry/PM5” method does not
even get the relative magnitude of the dipole moment right. CH3Cl has the larger dipole.
The E on D/EHT or INDO/1 methods, however, place the charge where it belongs.
Of all the attempted methods, E on D/MM geometry with INDO/1 wavefunction obtains the best
results. It places the charges well and gives good bond orders. The dipole moments, however,
are not that good. Particularly for CH3Cl.
Next, we examined the “family” of compounds as we move from CCl4 (0) to CHCl3 (1.01) to
CH2Cl2 (1.58). Dipoles in parentheses. We find:
Optimized geometry/PM5 geometry (few seconds)
δ for C / Cl / H
Dipole moment /Δ
Bond order C–Cl
0.085 / –0.021
0.002 / 0
0.969
–0.014 / –0.065 / 0.208
1.401 / 0.40
0.975
–0.114 / –0.113 / 0.170
1.846 / 0.27
0.992
UV-visible transitions/ZINDO CI at PM5 geometry
Molecule
δ for C / Cl / H
Dipole moment /Δ
Bond order C–Cl
CCl4
0.561 / –0.14
0.001 / 0
0.952
CHCl3
0.383 / –0.179 / 0.155
2.416 / 1.41
0.959
CH2Cl2
0.200 / –0.220 / 0.120
3.043 / 1.46
0.525
IR transitions/MOPAC PM5 FORCE
Molecule
δ for C / Cl / H
Dipole moment /Δ
Bond order C–Cl / H
CCl4*
0.085 / ≈ –0.20
0.001 / 0
0.970
CHCl3
–0.014 / ≈ –0.065 / 0.208
1.401 / 0.40
0.975 / 0.917
1.402 also given
CH2Cl2
–0.113 / –0.112 / 0.169
1.846 / 0.27
0.976 / 0.942
1.844 also given
Electrostatic potential on electron density/MM geometry with EHT
wavefunction(5 sec)
Molecule
δ for C / Cl / H
Dipole moment /Δ
Bond order C–Cl / H
CCl4
0.991 / –0.248
0/0
0.950
CHCl3
0.726 / –0.231 / –0.033
2.179 / 1.17
0.962 / 0.973
CH2Cl2
0.453 / –0.214 / –0.012
2.701 / 1.12
0.975 / 0.980
Electrostatic potential on electron density/MM geometry with INDO/1
wavefunction(5 sec)
Molecule
δ for C / Cl / H
Dipole moment /Δ
Bond order C–Cl / H
CCl4
0.531 / –0.133
0/0
0.943
CHCl3
0.365 / –0.172 / 0.150
2.163 / 1.15
0.954 / 0.968
CH2Cl2
0.193 / –0.214 / 0.117
2.951 / 1.37
0.954 / 0.983
Electrostatic potential on electron density/AM1 geometry with AM1
wavefunction(5 sec)
Molecule
δ for C / Cl / H
Dipole moment /Δ
Bond order C–Cl / H
CCl4
0.031 / –0.008
0.000 / 0
0.971
CHCl3
–0.036 / –0.041 / 0.158
1.156 / 0.15
0.981 / 0.940
CH2Cl2
–0.103 / –0.077 / 0.129
1.503 / 0.08
0.986 / 0.957
* = slightly different values given for each Cl and the dipole moment(0.001 and 0.042)
Molecule
CCl4
CHCl3
CH2Cl2
Results
The optimized geometry, IR transitions, and E on D/AM1 methods are not good in regards to
partial charge. Overall, E on D/INDO1 keeps the Cl’s (–) and the C and H’s (+) and is probably
the best method to choose. The dipoles are not good, however.
Next, ethanoic (acetic) acid was examined. The experimental dipole is 1.74. First, Optimized
geometry/PM5 was used. The calculation is fast. The calculation gives 2.259 for the dipole
moment and the following partial charges:
-0.422
0.158
O
0.307
H
H
-0.334
0.154 H
0.379 O
-0.396
H
0.154
Next, optimized geometry/B88-LYP DFT geometry was used. This calculation takes 12
minutes. The calculation gives 1.629 for the dipole moment and the following partial charges:
-0.308
0.233
O
0.410
H
H
-0.617
0.225 H
0.262 O
-0.430
H
0.225
Next, UV-visible/ZINDO CI at PM5 geometry was performed. The results are a dipole of
2.704 and the following partial charges:
-0.618
O
0.066
H 0.316
H
-0.070
H
0.068
0.632 O
-0.460
H
0.068
The next attempt was made with electrostatic potential on electron density/MM geometry
with EHT wavefunction. This gave a dipole moment of 3.893 and partial charges of
-1.113
O
0.025
H 0.449
H
-0.084
H
0.045
1.407 O
-0.753
H
0.045
Results
Of these four trials the UV-visible/ZINDO CI at PM5 method seems to give the most
reasonable, consistent results. The optimized geometry/PM5 and optimized geometry/B88-LYP
DFT geometry methods says that the methyl C is as or more negative than the O atoms. This is
not true. Note also that the E on D method tells us that the O atom has a partial charge of
–1.113. This number is larger than the typical values that we have gotten for polar covalent
bonds; it indicates an ionic bond, which is surely not the case. The UV-visible method gives a
polar covalent C=O bond and a big difference between the acidic proton and the methyl protons.
This makes it good for freshman use! The dipole moment, however, is significantly larger than
the experimental value. Also, an Optimized geometry/PM5 geometry in water calculation was
done. The results were very similar to the Optimized geometry/PM5 geometry calculation.
The results of a few other molecules are shown below. The dipole moments for NH3, H2O, H2S,
and NaF are 1.49, 1.85, 0.97, 8.16.
Optimized geometry/PM5 geometry(few seconds) &
IR transitions/MOPAC PM5 FORCE
Molecule
δ for A / H
Dipole moment /Δ
Bond order
NH3
–0.439 / 0.146
2.091 / 0.60
0.975
H2O
–0.484 / 0.242
1.930 / 0.08
0.941
H2S
–0.170 / 0.085
1.815 / 0.85
0.992
NaF
–0.668(F) / 0.668
6.854 / –1.31
0.609
Optimized geometry/B88-LYP DFT geometry (1 min)
Molecule
δ for A / H
Dipole moment /Δ
Bond order
NH3
–0.885 / 0.295
1.929 / 0.44
0.678
H2O
–0.767 / 0.384
2.179 / 0.33
0.559
H2S
–0.272 / 0.136
1.432 / 0.46
0.569
NaF
–0.651 / 0.651
7.49 / 0.67
0.399
Optimized geometry/B88-PW91 DFT geometry (1 min)
Molecule
δ for A / H
Dipole moment /Δ
Bond order
NH3
–0.931 / 0.310
1.955 / 0.47
0.678
H2O
–0.789 / 0.394
2.202 / 0.35
0.564
Optimized geometry/D-VWN geometry (1 min)
Molecule
δ for A / H
Dipole moment /Δ
Bond order
NH3
–0.986 / 0.329
1.979 / 0.49
0.682
H2O
–0.822 / 0.411
2.268 / 0.42
0.568
UV-visible transistions/ZINDO CI at PM5 geometry
Molecule
δ for A / H
Dipole moment /Δ
Bond order
NH3
–0.506 / 0.169
2.282 / 0.79
0.987
H2O
–0.576 / 0.288
2.418 / 0.57
0.954
H2S
–0.168 / 0.084
1.331 / 0.36
0.992
NaF
–0.796 / 0.796
8.091 / –0.07
0.525
Electrostatic potential on electron density/MM geometry with EHT
wavefunction
Molecule
δ for A / H
Dipole moment /Δ
Bond order
NH3
–0.738 / 0.246
2.145 / 0.66
0.968
H2O
–0.879 / 0.439
3.160 / 1.31
0.881
H2S
0.544 / –0.43
0.999
0.111 / –0.055
NaF
1.102(Na) / –1.102
10.847 / 2.67
0.126
Electrostatic potential on electron density/AM1 geometry with AM1
wavefunction
Molecule
δ for A / H
Dipole moment /Δ
Bond order
NH3
–0.396 / 0.132
1.847 / 0.36
0.975
H2O
–0.383 / 0.192
1.860 / 0.01
0.963
H2S
–0.097 / 0.048
1.860 / 0.89
0.997
NaF
“abnormal exit”*
* some parameters missing
Results
The optimized geometry/quantum methods again give bond orders of around 0.5 and, at times,
large partial charges. The best method appears to be “UV-visible/ZINDO CI at PM5 geometry”.
Note, however, that the “optimized geometry/PM5 geometry” and “E on D/AM1” methods give
fairly good results, too. An important lesson is learned for the NaF calculation in AM1. The
need for parameters to be available for the element in question for the method you choose.
There are no parameters for Na in AM1, and the calculation can’t be done. The User’s Guide
contains lists of what parameters are available for which elements for each method.
Additionally, note that when drawing the NaF “molecule”, one can use a single bond or use the
ionic bond. At least for “UV-visible/ZINDO CI at PM5 geometry”, both drawing methods give
the same results.
Discussion
Some methods do better at some things than other methods. What we need to find is the method
that gives consistent results. There are cases where the dipole moments are nearly correct in
magnitude but with the wrong direction. This seems to rule out use of this method. Perhaps, the
best we can do at this basic level of calculation with CAChe is to find the method that provides
the best set of partial charges and bond orders along with dipole moments that are correct in
relative magnitude. “Relative” in terms of comparing various molecules of similar structure but
that contain different atoms with varying electronegativities. This comparison method of
teaching is important for freshman. Consideration should also be given to the meaning of the
“bond order”. For a freshman class it seems most appropriate to use methods that give values of
1 for a single bond. This allows them to match that value with their Lewis idea of a single bond.
This is certainly a valuable theoretical idea, as any mechanism writer in organic chemistry will
tell you. As mentioned above, the quantum methods usually gave around 0.5.
No consideration was given as to why one method is better than another. The approach here was
to see which method gives the most reasonable, accurate answers.
The above work reveals wide differences in the calculations used by each method and the
subsequent different results. If CAChe is to be integrated into the courses we teach, it must be
decided how much of a “black box” it will be. For the freshman it seems that simply stating,
‘Different methods give different answers due to different math methods’, might be sufficient.
In this case telling them which method to use, with no explanation, can still lead to the student
obtaining very helpful results. This same approach might be sufficient for sophomores as well.
Junior level P-Chem, however, can delve into the differences, if needed.
This brings us to a second point. Of all of the people involved in this project, few are experts in
computational chemistry. It is, then, appropriate to decide these questions:
1.
How much does the instructor have to know about each method? Does it matter at all?
2.
Do graduate students need to understand each method fully to help in the design of
assignments?
These are important to decide because a thorough understanding of each method would take a
great deal of time to acquire. So, while we will surely ask freshman to use the CAChe “black
box”, will we also treat it as such? This is, perhaps, a fundamental question.