Bobby Deimler
Computational Analysis Portion of the Cr(acac)3 Lab Report
Computational Analysis: So far in this laboratory, the Cr(acac)3 complex has been studied
through both experimental and instrumental techniques. These techniques give much
information about the characteristics of the compound. Unfortunately, these techniques
are unable to give an adequate picture of what is occurring structurally within the
complex itself. To obtain this information it is necessary to utilize another area of
chemistry. The type of analysis most equipped to solve this problem is computational
chemistry. As its name suggests computational is a branch of chemistry that uses
computers to assist in determining information about experimental compounds. Some
information that computational chemistry can reveal includes bond lengths, angles,
molecular structure, and molecular orbital diagrams. Over the course of this laboratory,
all of the prior listed information was determined using computational methods. It should
be noted that this computational analysis was performed on Mn(acac)3 not Cr(acac)3. The
reason for this is that the Cr compound had several problems associated with it
throughout the course of the analysis. Since these problems could not be resolved in a
reasonable amount of time relative to the semester, a new compound was selected to be
analyzed. The compound Mn(acac)3 was selected because it has a very similar structure
and shares many characteristics with Cr(acac)3.The analysis of Mn(acac)3 was performed
using the ADF (Amsterdam Density Functional) program version 2006.01. One defining
characterisitic of this type of analysis is that it uses Slater type orbitals (STO) rather than
Gaussian type orbitals (GTO) during the course of its calculations. Other important
aspects of this program include the fact that it used the General Gradient Approximation
as well as the Becke and Perdue mathematical subroutines during the course of each run.
In order for any kind of calculation to be performed at all it was necessary to build a zmatrix within another program. This program was called Molden and it was a graphical
interfaced used to create the structures that the calculations would be performed upon.
This interface built the structure based on our estimated values specified for the bond
lengths, bond angles and dihedral angles between the atoms in the system. Once the
structure was constructed in Molden it was to go through several steps to convert the zmatrix file into a form that the ADF could run successfully. The most important of these
preparatory steps was the specification of the number of electrons free in the system and
the whether it was a restricted or unrestricted calculation. All of the calculations done on
the Mn(acac)3 system were done in the unrestricted electron mode. The reason for this
being that if the calculation had been run in the restricted mode there would have been
intense amounts of electron smearing and the calculation would not be likely to converge
at all. Electron smearing is undesirable, because it is when the system takes individual
electrons and splits them in half in order to arrange them in a mathematical feasible way.
Through general scientific knowledge we know that this is not possible in a real life
system so, in order for the answer to be accurate it should not have electron smearing
involved. The ADF program then selected the basis set and the method that is was going
to use to do the calculations on the system. The basis set of the system for Mn(acac)3 was
Mn, C, O, and H. There are several methods that could have been used to help to help the
system converge properly. During the course of our calculations we chose to use the
double zeta (DZ) method. This method does the calculation with certain orbitals of the
atoms frozen so that they cannot be changed. Specifically, the 3p of the Mn, the 1s of the
O, and the 2s of the C were frozen. One of the prominent things that the ADF program
does over the course of its work is determine the geometry of the structure. ADF
calculates the overall energy of several different geometries of the compound. The
geometry with the lowest amount of energy is the most stable and is thus adopted for the
rest of the calculations. ADF found the Mn(acac)3 to be an octahedral structure with a D3
symmetry. Based on this geometry it also calculated what the bond lengths and angles for
the system should be. These calculated values were then compared against that of the
values in literature to determine their accuracy. These values are compared in Table 1 and
Table 2 below.
Type of Bond:
Mn-O
Mn-O
O-C
C-C
C-H
Calculated Value:
2.038
2.038
1.314
1.515
1.098
Literature Value: (1)
1.979
2.020
1.254
1.463
0.994
Table 1: The bond lengths in the table above are the averages of all of the bond lengths
listed of the same type. The reason that the lengths were averaged is because the
Mn(acac)3 structure that was created in this lab and the one that was constructed in the
literature were put together in different ways. This means that the connection of our Mn
and O(1) may not be the same as theirs. Their Mn-O(1) connection might actually be our
Mn-O(2) connection. Because of this fact the values of all the literature Mn-O values
were averaged and the value of all our computational Mn-O values were averaged. These
averaged values were then compared against one another in the chart above.
Type of Angle:
O-Mn-O
O-Mn-O
Mn-O-C
O-C-C
O-C-C
C-C-C
H-C-H
Calculated Value:
91.56
91.56
124.31
124.58
124.58
119.8
110.92
Literature Value: (1)
89.9
178.5
127.2
125.4
114.5
121.6
111.4
Table 2: The angles listed above were handled in the same way as the bond lengths. The
bond angles of all similar connections were averaged and these averages were compared
in the table above. For example, the literature O(1) – Mn – O (2) angle might not be
speaking of the same angle as the one the computational method is referencing. Thus, it
would be hard to compare them in an angle to angle fashion. A better method would be to
compare the average of the computational O-Mn-O angles against the average of the
literature O-Mn-O angles. This laboratory made use of this type of method to determine
its conclusions about the structure.
Once a geometry, bond angles and bond lengths were determined it was then possible to
place the structure into another facet of the ADF program called ADF viewer. This
program is significant because it allowed the calculation of the MO diagram for the
Mn(acac)3 as well as visual representations of the HOMO and LUMO as well. These
diagrams are shown in the Figures below:
Figure 1: LUMO of
Mn(acac)3 as shown
by ADF view.
Figure 2: HOMO of
Mn(acac)3 as shown by ADF
view.
shown by A
Figure 3: This is the MO diagram of Mn(acac)3 as
shown by ADF view.
If one were to look at the values for the bond angles and bond lengths they would see that
the values calculated computational are very similar to those in the literature. The values
tend to be within 1 angstrom of each other for the bond lengths and 10 degrees of one
another for the angles. This shows a successfully computation was performed as the
values that were returned by the program were reasonably close to those determined
experimentally in the literature. Despite most of the values being similar to one another
there is an angle that was calculated that differed from the literature by as much as 86.94
degrees. This difference occurred in the O-Mn-O bond angle. This difference in value
was confounding at first as something with a regular octahedral shape should not have
differencing bond angles around the center. A literature search was done on the subject
and it was determined that Mn(acac)3 should actually take the distorted octahedral shape
not the regular. This distortion is due to the Jahn-Teller effect. The MO diagram (Figure
3) returned by ADF view supports the existence of this structural distortion. If one were
to look at the HOMO of this diagram they would see that there is only one electron
occupying the highest level. This is a prime example of a compound where the JahnTeller effect would occur. The complex would not want to have that extra electron sitting
in the higher by itself. Instead it would seek to pair that electron in a lower orbital so that
the structure could be more stable overall. This is exactly what the Mn(acac)3 does in the
lab. This conclusion is supported by the literature, which also decided to apply JahnTeller distortion to the structure. (1) One of the reason it was applied in the literature is
that at least one of the crystalline modifications indicates a tetragonally compressed
octahedron. (1) Also the values in the literature for the bond lengths indicate that two if
the Mn-O length are slightly longer than the other four. These two slightly longer length
are only about 0.1 larger but the two longer bonds occur trans to one another in the
structure.(1) This is significant because structures that take on distortions tend to have
two bonds that are trans to one another extended or shortened. This helps to support the
fact that a distortion occurs in the structure. Finally, the difference in values for the
angles in the table above can be attributed to the program attempting to conform the
structure to a Jahn-Teller distortion but being unable to due to geometry constrictions.
When ADF performs a calculation it has to stay within the restraints of the geometry set
on the system. In this case the program had determined that this structure had a D3
symmetry. Through the course of the calculation it could have determined that the
structure should have been distorted but it would be unable to apply this distortion to the
calculation because it would cause the structure to break the symmetry that had been set
for it. Thus, the program may have tried to compensate for this distortion by changing
values in other places on the structure while still maintaining the geometry resulting in
differences in values like the 87.03 degree angle difference. This may have happened
with the bond lengths as well. When the structure was built it was constructed as if
Mn(acac)3 were a regular octahedron. Thus, all the bond lengths around the center were
exactly the same. Again, the ADF program may have determined the lengths should have
been elongated but were unable to change it due to symmetry constrictions. This is
significant because this is probably why all the values for the internal Mn-O bond lengths
remained the same in the computation. This is shown best in the first table above. The
calculated Mn-O bonds are the exactly the same in both cases, whereas the values in the
literature differ slightly.
References:
1. Fackler, J.P.; Avdeef, A; “Crystal and molecular structure of tris(2,4pentanedionato)manganese(III), Mn(O2C5H7)3, a distorted complex as predicted
by Jahn-Teller arguments”. J. Inorg. Chem. 1974, 13, 1864-1875.
Acknowledgements:
I would like to thank Justin Huddleston for his help in working through this assignment. I
would also like to thank the Department of Chemistry and Physics for the opportunity to
use the lab and the equipment necessary for this experiment to take place.