Electronic Properties of the low-lying spin states of dimethylnitrosamine coordinated to
Fe(III) heme models: an ab-initio study
Ezequiel F. V. Leitão, Elizete Ventura, Otávio L. de Santana, Silmar A. do Monte*
Supplementary material
Lowest energy wavefunctions (obtained at both UHF and ROHF levels), UHF
wavefunctions with lowest spin contaminations and shapes of the 3d orbitals (obtained
at the ROHF level).
1) Results obtained for both cations using the cc-pVDZ basis set.
1.1) Sextet at the UHF level.
From the point of view of the schemes shown in Figures 1(a) and 1(b) the lowest
energy UHF solution (for both systems) for the sextet state has been obtained from the
default Harris guess36 and from the sextet ROHF wavefunction 1.3 shown in Figure
1(a). In other words, the sextet UHF wavefunctions 1 and 1.3.3 (see Figure 1(a)) are
identical. In the case of the sextet state the lowest energy UHF wavefunction it is also
the wavefunction with the smallest spin contamination.
For both systems the sextet ROHF wavefunction generated from the Harris
guess did not converge (wavefunction 4 in Figure 1(b)). Consequently, the UHF
wavefunctions 4.1 (sextet), 4.2 (quartet) and 4.3 (doublet, see Figure 1(b)) could not be
obtained. Similarly, for both systems the sextet UHF wavefunction obtained from the
closed shell singlet RHF solution did not converge. On the other hand, the sextet UHF
wavefunctions obtained from the closed shell (singlet) B3LYP wavefunctions
converged to much higher energy solutions (5.2 eV higher than the lowest energy
solution). If the open shell sextet B3LYP wavefunction is used as the guess for the
sextet UHF wavefunction the same lowest energy solution 1 (or 1.3.3) is obtained for
both systems.
1.2) Sextet at the ROHF level.
At the ROHF level the wavefunction 1.3 (sextet, see Figure 1(a)) corresponds to
the lowest energy wavefunction for both systems. As aforementioned the ROHF
wavefunction 4 (sextet) did not converge. For the larger system the sextet ROHF
wavefunction obtained from the sextet B3LYP did not converge, while for the smaller
system it converged to the wavefunction 1.3 (see Figure 1(a)). Another difference
between the two systems is observed when the sextet ROHF wavefunction is generated
from the closed shell singlet B3LYP wavefunction. For the smaller system the
calculation did not converge, while for the larger system it converged to a higher energy
solution. For both systems the sextet ROHF wavefunctions obtained from the closed
shell RHF wavefunctions converged to much higher energy solutions.
1.3) Quartet at the UHF level.
The lowest energy UHF wavefunction for both cations has been obtained by
using the sextet UHF wavefunction as the starting guess, that is, it is the wavefunction
1.1 of Figure 1(a). The quartet UHF wavefunctions which carry less spin
contaminations (for both cations) have been obtained from the default Harris guess
(wavefunction 2 in Figure 1(a)) and are  1.94 and 2.07 eV higher than the
corresponding lowest energy UHF wavefunctions (wavefunction 1.1 in Figure 1(a)) for
the larger and the smaller cations, respectively. Wavefunction 2 of Figure 1(a) is equal
to the wavefunctions 1.3.4 and 1.3.1.1. They are also equal to the wavefunction
generated from the open-shell quartet B3LYP wavefunction as the starting guess.
While in the case of the sextet state the UHF wavefunctions obtained from the
closed shell singlet RHF solution did not converge in the case of the quartet state they
converged to much higher energy solutions ( 4.8 eV higher than the lower energy
solution). Similarly to what has been found for the sextet state, the quartet UHF
wavefunctions obtained from the closed shell (singlet) B3LYP wavefunctions
converged to higher energy solutions. Differently to what has been found for the sextet
state, if the open shell quartet B3LYP wavefunction is used (for both systems) as the
guess for the quartet UHF wavefunction higher energy solutions are obtained.
1.4) Quartet at the ROHF level.
At the ROHF level the lowest energy wavefunction for the quartet state of both
cations corresponds to the wavefunction 1.3.1 in Figure 1(a). An important difference
between the lowest energy ROHF wavefunctions of the quartet and sextet states is that,
while the latter has been generated from the sextet UHF wavefunction, the former has
been obtained from the sextet ROHF wavefunction (see Figure 1(a)).
1.5) Doublet at the UHF level.
The lowest energy UHF wavefunction for the doublet state of both systems has
been obtained from the closed shell singlet B3LYP wavefunction, differently of what
has been obtained for the other spin states. The same behavior here obtained for the
doublet state has been observed by Wondimagegn and Rauk30 for the low-lying spin
states of the Fe(II) and Fe(III) porphines. It is important to mention that, for both quartet
and doublet states of both systems studied in this manuscript, UHF solutions of slightly
higher energies ( 0.2 eV higher) are obtained if the closed shell singlet RHF
wavefunction is used as the guess. Differently from the previous spin states the doublet
UHF wavefunction which carries less spin contamination for one cation differs from the
corresponding UHF wavefunction of the other. In the case of the smaller cation it is the
wavefunction 1.3.2.1 of figure 1(a), while for the larger cation it is the wavefunction
1.3.5. They are  0.75 and  1.17 eV higher in energy than the corresponding lowest
energy UHF wavefunctions, respectively.
1.6) Doublet at the ROHF level.
At the ROHF level the lowest energy solution for the doublet state of both
cations (wavefunction 1.3.2 in Figure 1(a)) has been obtained from the lowest energy
sextet ROHF wavefunction (wavefunction 1.3 of Figure 1(a)). Slightly higher energy
solutions (differing at most  0.41 eV from the lowest energy solution) have been
obtained from the converged calculations generated from the remaining types of guess.
While for the smaller cation all calculations converged in the case of the larger cation
ROHF calculations 1.3.1.2, 6 (see Figure 1(a) and 1(b)) and the ROHF calculation
which uses the singlet B3LYP wavefunction as the starting guess did not converge.
Besides, the open-shell doublet B3LYP calculation did not converge as well. Thus, the
ROHF wavefunction generated from this wavefunction could not be obtained.
2) Results obtained for the smaller cation using the mixed cc-pVDZ/aug-cc-pVDZ(Fe)
basis set.
2.1) Sextet at the UHF level
The lowest energy and less spin contaminated wavefunctions are again the same
wavefunctions and correspond to the same wavefunctions obtained for the cc-pVDZ
basis set, that is, wavefunction 1 of Figure 1(a). As before, they are also equal to the
wavefunction 1.3.3 of Figure 1(a) and to the wavefunction obtained from the open shell
(sextet) B3LYP as the starting guess. The other features discussed previously for the
smaller cation (in 1.1)) also apply for the mixed cc-pVDZ/aug-cc-pVDZ(Fe) basis set.
The only difference is that for the cc-pVDZ/aug-cc-pVDZ(Fe) basis set the closed-shell
singlet B3LYP calculation did not converge.
2.2) Sextet at the ROHF level.
As in the case of the previous basis set at the ROHF level the wavefunction 1.3
(sextet, see Figure 1(a)) corresponds to the lowest energy wavefunction. Again the
ROHF wavefunction 4 (sextet) could not be obtained, since the calculation did not
converge. Conversely to what has been obtained for the previous basis set the sextet
ROHF calculation obtained from the sextet B3LYP did not converge
An important difference between the results obtained from the two basis sets is
observed when the sextet ROHF wavefunction is generated from the closed shell singlet
B3LYP wavefunction. For the cc-pVDZ basis set the calculation did not converge,
while for the mixed cc-pVDZ/aug-cc-pVDZ(Fe) basis set it converged to a much higher
energy solution.
For both basis sets the sextet ROHF wavefunctions obtained from the closed
shell RHF wavefunctions converged to much higher energy solutions.
2.3) Quartet at the UHF level.
The same characteristics of the results obtained in 1.3) have also been obtained
here.
2.4) Quartet at the ROHF level.
As in the case of the previous basis set the lowest energy ROHF wavefunction
for this spin state corresponds to the wavefunction 1.3.1 of Figure 1(a). Some
similarities between the other ROHF calculations performed with both basis set can be
pointed out: (i) ROHF calculations starting from both the default Harris guess and from
the RHF wavefunction converged to higher energy solutions; (ii) ROHF calculations
starting from the open shell quartet B3LYP wavefunctions did not converge. However,
while for the previous basis set the ROHF calculation starting from the closed shell
(singlet) B3LYP wavefunction converged to a higher energy solution in the case of the
cc-pVDZ/aug-cc-pVDZ(Fe) basis set it did not converge.
2.5) Doublet at the UHF level.
Differently of what has been obtained for the previous basis set the lowest
energy UHF solution has been obtained from the RHF wavefunction as the starting
guess. However, as it has been obtained for the previous basis set, it is equal to the
wavefunction 6.1 of Figure 1(a). Again, the UHF wavefunction with lowest spin
contamination is the wavefunction 1.3.2.1 of figure 1(a). It is  0.69 eV higher in energy
than the corresponding lowest energy UHF wavefunction.
2.6) Doublet at the ROHF level.
As it has been obtained previously the lowest energy ROHF wavefunction for
the doublet state is the wavefunction 1.3.2 of Figure 1(a). Again, as before, slightly
higher energy solutions (in this case differing only at most  0.06 eV from the lowest
energy solution) have been obtained from the converged calculations generated from the
remaining types of guess. In the case of the mixed cc-pVDZ/aug-cc-pVDZ (Fe) basis set
only the open-shell doublet B3LYP calculation did not converge. Thus, the ROHF
wavefunction generated from this wavefunction could not be obtained.
3) Results obtained for the smaller cation using the mixed cc-pVDZ/cc-pVTZ(Fe) basis
set.
2.1) Sextet at the UHF level.
As for the cc-pVDZ basis set in the case of the mixed cc-pVDZ/cc-pVTZ(Fe)
basis set the lowest energy UHF wavefunction for the sextet state has been obtained
from the default Harris guess36 and from the sextet ROHF wavefunction 1.3 shown in
Figure 1(a). Again, as in the case of the previous basis set, the sextet UHF
wavefunctions 1 and 1.3.3 (see Figure 1(a)) are identical and also correspond to the
UHF wavefunction with lowest spin contamination.
Again, as in the case of the cc-pVDZ the sextet ROHF wavefunction generated
from the Harris guess did not converge (wavefunction 4 in Figure 1(b)). Consequently,
the UHF wavefunctions 4.1 (sextet), 4.2 (quartet) and 4.3 (doublet, see Figure 1(b))
could not be obtained.
While for the cc-pVDZ basis set the sextet UHF wavefunction obtained from the
closed shell singlet RHF did not converge in the case of the mixed cc-pVDZ/ccpVTZ(Fe) basis set it converged to a much higher energy solution (7.9 eV higher than
the lowest energy solution).
As in the case of the cc-pVDZ basis set the sextet UHF wavefunction obtained
from the closed shell (singlet) B3LYP wavefunction converged to a higher energy
solutions (3.1 eV higher than the lowest energy solution for the cc-pVDZ/ccpVTZ(Fe) basis set).
Again, similarly to what has been obtained with the cc-pVDZ basis set, if the
open shell sextet B3LYP wavefunction is used as the guess for the sextet UHF
wavefunction the same lowest energy solution 1 (= 1.3.3) is obtained.
2.2) Sextet at the ROHF level.
As in the case of the previous basis set the wavefunction 1.3 (see Figure 1(a))
corresponds to the lowest energy wavefunction at the ROHF level. As aforementioned
the ROHF wavefunction 4 (sextet) did not converge. Again, similarly to what has been
obtained for the previous (cc-pVDZ) basis set the sextet ROHF wavefunction obtained
from the sextet B3LYP converged to the wavefunction 1.3. When the sextet ROHF
wavefunction is generated from the closed shell singlet B3LYP wavefunction the
calculation did not converge. Again, as it has been obtained previously, the sextet
ROHF wavefunction obtained from the closed shell RHF wavefunction converged to a
much higher energy solution.
2.3) Quartet at the UHF level.
As it has been found for the sextet state and differently of what has been
obtained for the previous basis sets, the lowest energy UHF wavefunction for the
quartet state (wavefunction 2 of Figure 1(a)) has been obtained from the default Harris
guess. It also coincides with wavefunctions 1.3.4 and 1.3.1.1 of Figure 1(a). Again, as in
the case of the sextet state and differently of what has been found for the previous basis
sets, the lowest energy UHF wavefunction for the quartet state already carries the
smallest spin contamination.
While in the case of the cc-pVDZ basis set the quartet UHF wavefunction
obtained from the closed shell singlet RHF solution converged to a higher energy
solution in the case of the mixed cc-pVDZ/cc-pVTZ (Fe) basis set it did not converge.
Similarly to what has been found for the sextet state (with the same basis set) and for
the quartet UHF wavefunction (with the cc-pVDZ basis set) the actual quartet UHF
wavefunction obtained from the closed shell (singlet) B3LYP wavefunction converged
to a much higher energy solution.
Similarly to what has been found for the sextet state and differently to what has
been obtained for the cc-pVDZ basis set, if the open shell quartet B3LYP wavefunction
is used as the guess for the quartet UHF wavefunction the same lowest energy solution
(wavefunction 2 of Figure 1(a)) is obtained.
2.4) Quartet at the ROHF level.
As in the case of the previous basis set, the lowest energy ROHF wavefunction
for the quartet state corresponds to the wavefunction 1.3.1 of Figure 1(a).
2.5) Doublet at the UHF level.
Differently of what has been obtained for the other spin states, in the case of the
doublet state at the UHF level the lowest energy and the wavefunction with lowest spin
contamination do not coincide. While the former has been obtained from the closed
shell singlet B3LYP wavefunction, the latter has been obtained from the default Harris
guess (wavefunction 3 of Figure 1(a)). The same result concerning the lowest energy
wavefunction has been obtained with the cc-pVDZ basis set. However, the
wavefunction with lowest spin contamination obtained with the mixed cc-pVDZ/ccpVTZ basis set differ from the corresponding wavefunction obtained with the cc-pVDZ
basis set, since the latter corresponds to the wavefunction 1.3.2.1 of Figure 1(a).
2.6) Doublet at the ROHF level.
As in the case of the cc-pVDZ basis set the lowest energy solution for the
doublet state corresponds to the wavefunction 1.3.2 of Figure 1(a).
3) Results obtained for the smaller cation using the mixed cc-pVDZ/cc-pVTZ-DK (Fe)
basis set (Douglas-Kroll-Hess 2nd order scalar relativistic calculation).
Except for the doublet state, in the case of the mixed cc-pVDZ/cc-pVTZ-DK
basis set the same lowest energy and less spin contaminated wavefunctions (from the
point of view of Figures 1(a) and 1(b)) as the ones obtained for the cc-pVTZ basis set
have now been obtained. The only difference corresponds to the lowest energy
wavefunction of the doublet state. While for the cc-pVDZ/cc-pVTZ basis set it has been
obtained from the closed shell B3LYP wavefunction as the guess, in the case of the ccpVDZ/cc-pVTZ-DK basis set it corresponds to the wavefunction 1.2 of Figure 1(a).
4) Shapes of the 3d orbitals for the sextet, quartet and doublet spin states, obtained at
the ROHF/cc-pVDZ level.
For the other basis sets the shapes are very similar and thus are not shown.
4.1) Sextet.
The shape of the metal 3d orbitals can be easily identified for all but the doublet
spin states. For the sextet state they are shown in Figure 1. The x axis is defined as the
axis which has the smallest angle with the nitrosamine plane. Despite the notation, the
3dxz and 3dyz orbitals are not exactly in the xz or yz planes. Actually, the 3dxz is almost
in the nitrosamine plane, while the 3dyz is, as expected, in a perpendicular plane. The
3dx2-y2 orbital (HOMO) is, as expected, mixed with nitrogen lone pair orbitals, and has
nodes in the Fe-N bonds, while the 3dz2 is mixed with nitrogen and oxygen lone pairs,
with nodes in both Fe-N and Fe-O bonds. The shapes of the 3d orbitals for the sextet,
quartet and doublet spin states are discussed below.
Figure 1. The 3d molecular orbitals obtained from the ROHF/cc-pVDZ wavefunction
of the sextet state (wavefunction 1.3 in Figure 1(a)) of the larger (a) and smaller (b)
cations studied in this manuscript. Hydrogen atoms have been omitted for clarity.
4.2) Quartet.
The shapes of the 3d orbitals for the ROHF wavefunction of the quartet state are
shown in Figure 3. The main difference between these orbitals and the 3d orbitals of the
sextet state lies in the 3dxy orbital. While for the sextet state it is essentially a pure 3dxy
metal orbital (see Figure 2), for the quartet state it has a significant contribution from
the meso carbon orbitals (see Figure 3). For the larger cation this contribution extends
over the phenil rings as well.
Figure 2. The 3d molecular orbitals obtained from the ROHF/cc-pVDZ wavefunction
of the quartet state (wavefunction 1.3.1 in Figure 1(a)) of the larger (a) and smaller (b)
cations studied in this manuscript. Hydrogen atoms have been omitted for clarity.
4.3) Doublet.
The shapes of the 3d orbitals for the ROHF wavefunction of the doublet state are
shown in Figure 3. Due to a great admixture with other metal orbitals the HOMO
(which is also the singly-occupied molecular orbital) orbital is an ill defined 3dyz orbital.
Similarly to what has been obtained for the quartet state the 3d xy orbital of the smaller
cation is highly mixed with the porphyrin ring orbitals, while for the larger cation it is
highly mixed with the phenyl ring orbitals. The main difference in the composition of
this orbital for the doublet and quartet spin states is that for the former it has a
significant contribution from the orbitals of the nitrosamine moieties (compare Figures
2 and 3). The shape of the 3dx2-y2 orbital is very similar for all three spin states. The 3dxz
orbital for the doublet state is highly mixed with orbitals which extend over the
nitrosamine moieties, while for the other spin states it is an almost pure 3d orbital
(compare Figure 3 with Figures 1 and 2).
Figure 3. The 3d molecular orbitals obtained from the ROHF/cc-pVDZ wavefunction
of the doublet state (wavefunction 1.3.2 in Figure 1(a)) of the larger (a) and smaller (b)
cations studied in this manuscript. Hydrogen atoms have been omitted for clarity.