Download UV-Visible Spectra of Aquavanadium Complexes

The Intersection
of
Computational Chemistry
and
Experiment
UV-Visible Spectra of Aquavanadium Complexes
Angelo R. Rossi
Department of Chemistry
The University of Connecticut
[email protected]
Spring 2017
Last Updated: February 19, 2017 at 7:58am
Introduction
Vanadium abundance in earth’s crust is 120 parts per million by weight. The groundstate electron configuration of vanadium is [Ar]3d3 4s2 , and exhibits four common oxidation
states +5, +4, +3, and +2 each of which can be distinguished by its color. Vanadium(V)
compounds are yellow, whereas +4 compounds are blue, +3 compounds are green, and
+2 compounds are violet. Vanadium is used in making specialty steels like rust resistant
and high speed tools. The element occurs naturally in about 65 different minerals and in
fossil fuel deposits. Vanadium exists in biological systems as an active center of enzymes.
Vanadium oxides exhibit intriguing electrochemical, photochemical, catalytic, spectroscopic,
and optical properties. Vanadium has 18 isotopes with mass numbers varying from 43 to 60.
Of these, 51 V, natural isotope is stable.
Vanadium in Biological Systems
Vanadium plays a number of roles in the biological systems including its presence in two enzymes, vanadium dependent haloperoxidases and nitrogenase. In the human organism, it elicits a number of physiological responses, including the inhibition of phosphate-metabolizing
enzymes, such as phosphatases, ribonuclease, and ATPases, and its compounds show insulinenhancing activity. Vanadium compounds also exhibit a wide variety of pharmacological
properties Many vanadium complexes have been tested as antiparasitic, spermicidal, antiviral, anti-HIV, antituberculosis, and antitumor agents. The most stable oxidation states of
vanadium are III, IV, and V.
However, it has been demonstrated that, in blood serum, it is present in the oxidation state
IV, almost independently from its initial state. One of the most important and interesting
use of V(IV)2+ ion is as physicochemical marker of metal binding sites in proteins. Electron paramagnetic resonance (EPR) patterns of the vanadyl ions have been used to extract
specific information on the metal-binding sites of peptides and proteins such as insulin and
carboxypeptidase-A.
In the biological systems mentioned, the behavior and function of the vanadium sites depend
on the electronic structure, coordination geometry, and chemical environment. Therefore,
it is very important for a chemist and a biochemist to have the necessary knowledge to
characterize the structure of a specific vanadium complexes, to establish the geometry around
the metal ion, and to understand the spectal properties of vanadium complexes.
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Ligand Field Theory
Ligand Field Theory (Reference 5) has been a central theme of inorganic chemistry for many
years. Interpretation of d → d transitions in transition metal complexes is discussed in advanced inorganic chemistry textbooks, with the emphasis frequently placed on extraction of
values for the ligand field splitting, ∆0 for octahedral complexes, and the Racah B parameter, a measure of the electron repulsion energy between electronic states, from experimental
spectra (References 1 and 2). The colors of transition metal complexes result from absorption
of a small portion of the visible spectrum with transmission of the unabsorbed frequencies.
For example, the [Ti(H2 O)6 ]3+ complex has a d1 electron configuration,
Figure 1: Splitting of d Orbitals for d1 in Oh Symmetry.
and appears purple (i.e. red + blue), because it absorbs green light at ∼500 nm = ∼20,000
cm−1 . In the Ligand Field Theory (LFT) model, absorption causes electrons from lower
lying d orbitals to be promoted to higher levels.
For the [Ti(H2 O)6 ]3+ complex (d1 ), the absorption causes the configuration to change from
the 2 T2g electronic state (t12g e0g ) to the 2 Eg electronic state (t02g e1g ):
Figure 2: Term Splitting of d Orbitals for d1 in Oh Symmetry.
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Selection Rules for Electronic Spectra of
Transition Metal Complexes
The selection rules governing transitions between electronic energy levels of transition metal
complexes are:
• ∆S = 0, spin selection rule
Allowed transitions must involve the promotion of electrons without a change in their
spin.
• ∆l = ±1, orbital angular momentum rule
The LaPorte rule states that, in molecules with a center of symmetry (centrosymmetric
molecules), transitions within a subshell are forbidden, when ∆l = 0. In centrosymmetric molecules, the various s, p, d, f orbitals cannot mix within a subshell. For example,
the 3d orbital cannot mix with the 3p orbital in a centrosymmetric molecule, since this
mixing is symmetry forbidden. Octahedral complexes can be centrosymmetric, and in
such a case, 3p → 3p or 3d → 3d transitions would be forbidden by LaPorte’s rule.
It also states that electronic transitions that conserve parity, either symmetric (g) or
antisymmetric (u), with respect to an inversion center, forbidden. Allowed transitions
in such molecules must involve a change in parity, either g → u or u → g.
Tetrahedral molecules do not have a center of symmetry and p − d orbital mixing is
allowed, and so 3p → 3p and 3d → 3d transitions may appear stronger, because a
small amount of another orbital may be mixed into the p or d orbital, since LaPorte’s
rule is not violated.
• Symmetry - transitions which are either allowed or forbidden based on symmetry considerations.
Relaxation of the Selection Rules
Relaxation of the Rules can occur through the following:
• Vibronic coupling in an octahedral complex may have allowed vibrations where the
molecule becomes asymmetric, and absorption of light at that moment is then possible.
• π-acceptor and π-donor ligands can mix with the d-orbitals, so transitions are no longer
purely d − d, allowing a transition to take place.
• Spin-Orbit Coupling can give rise to weak spin-forbidden bands, but the effect is usually
small for first row transition metal atoms.
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Types of Transitions
• Charge transfer transitions, either ligand to metal or metal to ligand, are often extremely intense and are generally found in the UV, but they may have a tail into the
visible.
• d → d transitions can occur in both the UV and visible regions, are formally forbidden,
but these transitions can have small intensities because different electronic states can
mix as a result of small vibrations.
Transition type
Example
Spin forbidden, Laporte forbidden
[Mn(H2 O)6 ]2+
Spin allowed (octahedral complex), Laporte forbidden [Ti(H2 O)6 ]3+
Spin allowed (tetrahedral complex),
Laporte partially allowed by d-p mixing
[CoCl4 ]2−
Spin allowed, Laporte allowed: charge transfer bands [TiCl6 ]2− , MnO−
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Typical values
of ε (m2 mol−1 )
0.1
1 - 10
50 - 150
1000 - 106
Table 1: Expected Intensities of Electronic Transitions
Expected Values Ligand Field Splitting
The following values for the Ligand Field Splitting, ∆, provides a rough guide:
• For M2+ complexes, ∆ = 7500 cm−1 − 12500 cm−1 , or λ = 800 nm − 1350 nm.
• For M3+ complexes, ∆ = 14000 cm−1 − 25000 cm−1 , or λ = 400 nm − 720 nm .
• For a typical spin-allowed, but Laporte (orbitally) forbidden transition in an octahedral
complex, the absorption intensity, ε < 10 m2 mol−1 .
• Extinction coefficients for tetrahedral complexes are expected to be around 50-100
times larger than for octrahedral complexes.
• The value of the electron repulsion parameter, B0 , for first-row transition metal free
ions is around 1000 cm−1 . Depending on the position of the ligand in the nephelauxetic series, the electron repulsion parameter, B in transition metal complexes, can be
reduced by about 60%.
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In the chemical literature, terms such as MCT (d → d, metalcharge transfer), MLCT (metalligand charge transfer), LMCT (ligand-metal charge transfer), and LL (ligand-ligand charge
transfer) are used. A schematic diagram showing the various types of transitions is given
in Figure 3.
Figure 3: Schematic Diagram Showing Possible Types of Electronic Transitions in Transition
Metal Complexes
Density Functional Calculations of Excited States in Transition
Metal Complexes
It is not always the case that TD-DFT calculations agree with experiment, and there is every
reason to be critical about the calculational results. Very carefully compare the TD-DFT
calculations with experiment. In many cases, artifacts will arise: charge transfer states tend
to appear much too low in the spectrum; double excitations are entirely missing; neutral-toionic transitions are poorly predicted; and spin-flip transitions cannot be predicted.
The calculations requested here represent one of the cases where TD-DFT with normal
GGA functionals like BP86 fails badly, and predict LMCT states where there should be
d-d excitations (in the region below ∼15000 cm−1 ). The calculation should, instead, be
performed with a functional that includes more HF exchange. B3LYP is recommended,
which introduces some HF exchange. It may also be necessary to calculate more than the
desired four ligand field states in order to capture the states of interest, since they may not
come in order of increasing orbital energy difference. To be on the safe side, a calculation
requesting more exited states should be performed
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Vanadium Oxidation States
Vanadium displays variable oxidation states of varying colors including the blue oxovanadium(IV) ion, usually written more simply as VO2+ but will have water molecules attached
to it as well - [VO(H2 O)5 ]2+ , the green hexaaquavanadium(III) ion - [V(H2 O)6 ]3+ , and the
purple-violet hexaaquavanadium(II) ion - [V(H2 O)6 ]2+ .
In the following sections, oxidation states of aquavanadium complexes will be discussed.
Excited-State Calculations and Electron Density Shifts
This exercise explores calculations of the UV-Visible spectra of [VO(H2 O)5 ]2+ (d3 ), [V(H2 O)6 ]3+
(d2 ), and [V(H2 O)6 ]2+ (d1 ) complexes shown in Figure 4 and are also compared to experimental results (Reference 4).
Figure 4: The [V(H2 O)6 ]2+/3+ and [VO(H2 O)5 ]2+ Complexes
Along with these calculations, ways in which electron density differences can be used to
interpret the results of calculations will also be explored.
Geometry Optimization
Calculations are carried out to optimize the geometries of these complexes and to calculate
the energies and intensities of the low-lying electronic transitions. Electron density difference
plots are used to assign the nature of the transitions. Features such as Jahn-Teller distortions
and charge-transfer bands, as well as d → d transitions are apparent from the calculations.
In preparation for the calculations, a starting geometry must be constructed for each of
the complexes. It is important to have reasonable bond distances in the initial structure or
convergence problems can occur in the SCF procedure. The geometry of each complex is
then optimized.
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Calculations of Excited States
Following the calculation of optimized structures, time-dependent perturbation theory (TDDFT)
is used to calculate the energies and intensities of several excited states for each complex at
the optimized geometry of the ground state.
In addition, charges on each atom are computed for the ground state and each excited state.
Calculations of Electron Density
Cube files for electron density can be calculated for both the ground state and excited states.
A cube file of the electron density difference between each excited state and the ground state
is then computed. Visualization of the electron density differences is then carried out with
appropriate visualization software.
Discussion
[V(H2 O)6 ]3+ - d2 Configuration
Jahn-Teller Distortions
Because of the presence of two electrons in the t2g orbitals of this pseudo-octahedral complex,
the calculated VO6 local skeletal geometry is expected to show a Jahn-Teller distortion. All
the calculated V-O bond distances may not be equal. As expected, the bond distances in
the V(III) system are somewhat shorter than for the corresponding V(II) complex. Thus,
the calculated charge on the metal is slightly more positive than for [V(H2 O)6 ]2+
Although constraints can be applied, such that the V-O bond distances are all equal, the
Jahn-Teller effect is still reflected in the calculated electronic spectrum.
Excited States
The Tanabe-Sugano splitting diagram for the d2 configuration, shown in Figure 5, indicates
that a d2 octahedral complex should exhibit three d → d excitations: 3 T1g (F) → 3 T2g ,
3
T1g (F) → 3 T1g (P), and 3 T1g (F) → 3 A2g .
The visible/ultraviolet spectrum for [V(H2 O)6 ]3+ is shown in Figure 6
The transitions, ν1 (3 T1g (F) → 3 T2g ) at 17,200 cm1 and ν2 (3 T1g (F) → 3 T1g (P)) at 25,000
cm1 are shown, but the ν3 (3 T1g (F) → 3 A2g ) at 38,000 cm1 falls in the UV, and is not shown,
because this state involves a two-electron transition, and will not appear in the present
calculations which involve only single-electron excitations. In addition, the 3 T1g (F) → 3 A2g
transition is unlikely, and its band is often weak or unobserved.
Calculated lower-energy transitions most likely occur under the experimental band envelope
at about 17,000 cm−1 , while an allowed ligand metal charge transfer (LMCT) transition, from
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Figure 5: Tanabe-Sugano Diagram for Spin-Allowed and Forbidden Electronic Transitions of
an Octahedral d2 Complex such as[V(H2 O)6 ]3+ .
Figure 6: The Visible/Ultraviolet Spectrum of [V(H2 O)6 ]3+ .
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ligand molecular orbital localized on O atoms of H2 O → to the vanadium ion is calculated
at approximately 35,000 cm−1 .
In addition to the three possible spin-allowed transitions, there are seven singlet states that
suggest there could be as many as seven multiplicity (spin) forbidden transitions. Transitions
from the 3 T1g ground state to any of the singlet states would have extremely low ε values
and are seldom observed in routine work. Some singlet states (e.g., 1 A1g , 1 Eg ) are so high in
energy that transitions to them would fall in the UV, where they would likely be obscured
by the intense LMCT band.
[V(H2 O)6 ]2+ - d3 Configuration
Although the hydrogen atoms lower the symmetry somewhat, the local symmetry of the VO6
skeletal framework is approximately octahedral symmetry (Oh ). Thus, the metal d orbitals
are split energetically into a lower energy set of approximate t2g symmetry and higher energy
set of approximately eg symmetry. The three d electrons on vanadium fill the t2g orbitals,
and no Jahn-Teller distortion occurs. Although the formal oxidation state of the vanadium
is V(II), the charge on the vanadium is smaller as a result of electron donation from the
ligands to the metal, and is common for transition metal complexes.
Excited States
Important bands of the calculated electronic spectrum of [V(H2 O)6 ]2+ should be compared
to the experimentally observed spectrum. Based on a Tanabe-Sugano Diagram (Reference
7) shown in Figure 7, a d3 octahedral system should exhibit three d → d excitations: 4 A2g
→ 4 T2g (F); 4 A2g → 4 T1g , and 4 A2g → 4 T1g (P).
Since the last transition involves a double excitation, it will not be observed in the singles
only calculated spectrum. The first two low-energy bands with non-zero intensity involve
triply degenerate excited states, and so both sets of calculated transitions are degenerate.
Although the calculated energies for the bands are probably higher than the experimental
values, the trend is sufficient to assign the bands in the experimental spectrum. One would
not expect quantitative agreement even at a higher level of theory because of the lack of
inclusion of the solvent in the calculated spectrum.
Charges and Electron Density
Electron density difference plots should be obtained for the lowest electronic transitions
of the calculated electronic spectrum. A darker color will indicate the region from which
electron density was removed, while a lighter color indicates the region in which the electron
density is enhanced. Since both the dark and the light electron density difference isosurfaces
are located close to the metal, the d → d character of these excitations can be readily
ascertained. In contrast, the lowest energy transitions with non-zero calculated intensity, can
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Figure 7: Tanabe-Sugano Diagram for Spin-Allowed and Forbidden Electronic Transitions of
an Octahedral d3 Complex such as[V(H2 O)6 ]2+ .
be characterized as vanadium to oxygen charge transfer from the electron density difference
plot.
The trend in charges should confirm these assignments. The charge on vanadium should
be only slightly higher in the lower excited states than in the ground state as expected for
d → d transitions. The vanadium charge in the higher excited state, however, is much more
positive than in the ground state, and is consistent with a metal to ligand charge transfer.
[VO(H2 O)5 ]2+ - d1 Configuration
Square Pyramid Geometry and Jahn-Teller Distortion
The [VO(H2 O)5 ]2+ complex forms an approximate square pyramid with an oxo-group (=O)
in the apical positions, four H2 O molecules in basal positions, and an H2O ligand taking up
the the sixth position. The vanadium-oxo bond is considerably shorter than the vanadiumwater bonds, as expected, and the water molecules that are in the basal positions are bent
away from the oxo group by approximately 5◦ . If the complex were C4v symmetry, the four
basal V − O bonds should be equivalent, but local symmetry of the V − O skeletal linkages
is reduced to C2v , because of a Jahn-Teller distortion. This will remove the degeneracy of
the dxz and dyz orbitals on vanadium by a small amount.
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Charges and Electron Density
Because of π-donation from the oxo (=O) group to the V atom, the charge on the apical
oxygen atom is considerably less negative than on the water oxygen atoms.
Excited States
For a d1 complex, the electronic states have the same symmetry as the corresponding metal
d orbitals that contain the unpaired electron. The ligand field diagram for a C4v complex is
given in Figure 8 (Reference 4).
Figure 8: Ligand Field Diagram for the [VO(H2 O)5 ]2+ C4v Complex.
Therefore, one expects 3 d → d transitions for [VO(H2 O)5 ]2+ : 2 B2 (dxy ) → 2 E(dxz,yz ),
2
B2 (dxy ) → 2 B1 (dx2 −y2 ), and 2 B2 (dxy ) → 2 A1 (dz2 ). Reduction in symmetry to C2v removes
the degeneracy of the first transition.
As expected, the first two bands involve an electron transfer from the vanadium dxy orbital
to the vanadium dxz and dyz orbitals. The electron density on the π system of the oxo
group is enhanced as well because of the covalency that occurs between the oxo group and
the vanadium dxz and dyz orbitals. The third band is predicted to be a d → d transition
(dxy → dx2 −y2 ) in Reference 4, but the calculated transition seems to point clearly to an oxo
→ V charge transfer.
The remaining d → d transition (dxy → dz2 ) in the calculated spectrum occurs outside the
wavelength range of the observed spectrum. Although it is possible that use of a higher level
of theory and/or inclusion of the solvent in the calculation might reverse the assignment,
the current model suggests that the band observed at approximately 28,600 cm−1 in the
experimental spectrum is probably a charge transfer band and not a d → d transition.
The excited state charges on the V=O fragment are consistent with an assignment of a
charge transfer band involving the ligand (=O) orbital to the vanadium ion.
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References
1. Miessler, Gary L.; Tarr, Donald A. Inorganic Chemistry, 2nd Ed.,Upper Saddle River,
NJ: Prentice Hall, 1998, pp. 366-378.
2. Wulfsberg, Gary. Inorganic Chemistry, Sausalito: University Science Books, 2000,
889-898.
3. Stefan Portmann and Hans Peter Luthi. Chimia, 2000, 54,766.
4. Ophardt, C. E.; Stupgia, S. J. Chem. Ed., 1984, 61, 1102.
5. Figgis, B. N.; Hitchman, M. A. Ligand Field Theory and Its Applications: New York,
Wiley-VCH, 2000, pp. 204-207.
6. Lever, A. B. P. Inorganic Electronic Spectroscopy: New York, Elsevier, 1968, pp. 256274.
7. Tanabe, Y.; Sugano, S., Journal of the Physical Society of Japan, 1954, 9 (5): 753-766;
and 1954, 9 (5): 766-779; and 1956, 11 (8): 864-877.
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Exercises
In the following exercises the B3LYP functional is used in conjunction with and LANL2DZ
basis for V, which replaces the core electrons with a pseudopotential. The 6-31g(d) basis is
chosen for the H and O atoms to form H2 O ligands.
This combines Density Functional Theory, which can be very efficient for transition-metal
complexes with a basis set for V that reduces the integral calculation time.
1. Obtain optimized structures for each of the complexes.
Compare the calculated structures to any experimental data which can be found. Crystallographic data may exist for these or similar complexes.
2. Now use the optimized geometries obtained above to calculate excited states for each
of the aquavanadium complexes.
Compare the calculated spectra to the experimental one, and be sure to characterize
the nature of the calculated excited states.
Which of the excited states are seen in the optical excitation spectra? Which are not?
How well do the vertical excitation energies compare?
Visualize the calculated spectra which can assist in performing a comparison between
calculated and experimental results and on properly assigning the peaks in the spectrum.
3. Electronic transitions occur as electrons are shifted from one place to another within
a molecule, which can be seen by examining electron density changes. The following
is to be performed for each transition metal complex:
• Create an electron density cube file containing the ground state electron density
for the complex.
• Create an electron density cube file for each of the excited states that were experimentally observable in the spectrum.
• Create an electron density difference cube file (excited state - ground state)
for each of the excited states that were experimentally observable in the spectrum.
4. Now, visualize the difference densities (ground to excited state) to verify the nature of
the transitions that were previously characterized, by utilizing the electron-density
difference cube files.
Which color corresponds to areas where electrons are leaving? Which color corresponds
to areas where electrons are going? To answer this, recall the dipole moment changes.
How would you describe the transitions qualitatively?
5. Compare the Mulliken atomic charges and overlap populations for the ground and
excited states.
What significant changes occur?
What does this indicate about the direction of electron flow for those transitions?
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Calculate Density Difference of Between Ground and
Excited State Directly from G09
1. Perform a TD-DFT single point calculation on an excited states using the Density=all
keyword option. An example to calculate the electron density for the ground and 4th
excited state is given below:
%chk=vocl3-c3v-ex4.chk
#P b3lyp/gen pseudo=read td(nstates=10,root=4) pop=full gfinput
gfprint 5D SCF=Tight guess=read geom=allcheck density=all
O Cl 0
6-31G(D)
****
V 0
LANL2DZ
****
V 0
LANL2DZ
2. Use the formchk G09 utility to format the checkpoint files, which converts the binary
checkpoint file (.chk) to a formatted checkpoint file (.fchk).
3. Use the cubegen G09 utility to extract the two cubes of total electronic density from
the formatted checkpoint file:
cubegen 0 density=SCF vocl3-ex4-es.chk vocl3-ex4-gs.cube 0 h (ground state
electron density)
cubegen 0 density=CI vocl3-ex4-es.chk vocl3-ex4-es.cube 0 h (excited state
of interest)
Note: the electron density of both the ground state and 4th excited state, are both
stored on the checkpoint file, because of the Density=all and (td, nstates=10,
root=4) keywords in the input file.
If the root keyword is not present, then the default is to calculate the electron density
of the first excited state.
In this example, the electron density of the 4th excited state is requested, i.e. root=4.
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4. The electron density difference between the excited and ground states can be obtained
with the cubman utility which subtracts one cube density from another:
cubman
• Enter su for subtract at the initial prompt.
This operation subtracts two cube files to produce a new cube file.
• name for the first input file (example: vocl3-ex4-es.cube)
Is the file formatted? Answer y for yes.
• name for the second input file (example: vocl3-ex4-gs.cube)
• Is the file formatted? Answer y for yes.
• name for the output file (example: vocl3-ex4-ex-gs-diff.cube)
Should it be formatted? Answer y for yes.
The above sequence of commands for cubman should produce the file vocl3-ex4-exgs-diff.cube.
Follow the above procedure for each of the excited-state difference densities to be viewed
with visualization software which can read cube files
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