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UV-Visible Spectra of Aquavanadium Complexes

Angelo R. RossiDepartment of Chemistry

The University of [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 ground-state electron configuration of vanadium is [Ar]3d34s2, and exhibits four common oxidationstates +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 resistantand high speed tools. The element occurs naturally in about 65 different minerals and infossil 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, 51V, natural isotope is stable.

Vanadium in Biological Systems

Vanadium plays a number of roles in the biological systems including its presence in two en-zymes, vanadium dependent haloperoxidases and nitrogenase. In the human organism, it elic-its a number of physiological responses, including the inhibition of phosphate-metabolizingenzymes, such as phosphatases, ribonuclease, and ATPases, and its compounds show insulin-enhancing activity. Vanadium compounds also exhibit a wide variety of pharmacologicalproperties Many vanadium complexes have been tested as antiparasitic, spermicidal, antivi-ral, anti-HIV, antituberculosis, and antitumor agents. The most stable oxidation states ofvanadium are III, IV, and V.

However, it has been demonstrated that, in blood serum, it is present in the oxidation stateIV, almost independently from its initial state. One of the most important and interestinguse of V(IV)2+ ion is as physicochemical marker of metal binding sites in proteins. Elec-tron paramagnetic resonance (EPR) patterns of the vanadyl ions have been used to extractspecific information on the metal-binding sites of peptides and proteins such as insulin andcarboxypeptidase-A.

In the biological systems mentioned, the behavior and function of the vanadium sites dependon the electronic structure, coordination geometry, and chemical environment. Therefore,it is very important for a chemist and a biochemist to have the necessary knowledge tocharacterize the structure of a specific vanadium complexes, to establish the geometry aroundthe metal ion, and to understand the spectal properties of vanadium complexes.

Last Updated: February 19, 2017 at 7:58am 2

Ligand Field Theory

Ligand Field Theory (Reference 5) has been a central theme of inorganic chemistry for manyyears. Interpretation of d → d transitions in transition metal complexes is discussed in ad-vanced inorganic chemistry textbooks, with the emphasis frequently placed on extraction ofvalues for the ligand field splitting, ∆0 for octahedral complexes, and the Racah B parame-ter, a measure of the electron repulsion energy between electronic states, from experimentalspectra (References 1 and 2). The colors of transition metal complexes result from absorptionof a small portion of the visible spectrum with transmission of the unabsorbed frequencies.

For example, the [Ti(H2O)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 = ∼20,000cm−1. In the Ligand Field Theory (LFT) model, absorption causes electrons from lowerlying d orbitals to be promoted to higher levels.

For the [Ti(H2O)6]3+ complex (d1), the absorption causes the configuration to change from

the 2T2g electronic state (t12ge0g) to the 2Eg electronic state (t02ge

1g):

Figure 2: Term Splitting of d Orbitals for d1 in Oh Symmetry.


Selection Rules for Electronic Spectra ofTransition Metal Complexes

The selection rules governing transitions between electronic energy levels of transition metalcomplexes are:

• ∆S = 0, spin selection rule

Allowed transitions must involve the promotion of electrons without a change in theirspin.

• ∆l = ±1, orbital angular momentum rule

The LaPorte rule states that, in molecules with a center of symmetry (centrosymmetricmolecules), transitions within a subshell are forbidden, when ∆l = 0. In centrosymmet-ric 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 thismixing is symmetry forbidden. Octahedral complexes can be centrosymmetric, and insuch 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) orantisymmetric (u), with respect to an inversion center, forbidden. Allowed transitionsin 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 isallowed, and so 3p → 3p and 3d → 3d transitions may appear stronger, because asmall amount of another orbital may be mixed into the p or d orbital, since LaPorte’srule is not violated.

• Symmetry - transitions which are either allowed or forbidden based on symmetry con-siderations.

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 themolecule 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 longerpurely d− d, allowing a transition to take place.

• Spin-Orbit Coupling can give rise to weak spin-forbidden bands, but the effect is usuallysmall for first row transition metal atoms.


Types of Transitions

• Charge transfer transitions, either ligand to metal or metal to ligand, are often ex-tremely intense and are generally found in the UV, but they may have a tail into thevisible.

• 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 canmix as a result of small vibrations.

Transition type Example Typical valuesof ε (m2mol−1)

Spin forbidden, Laporte forbidden [Mn(H2O)6]2+ 0.1

Spin allowed (octahedral complex), Laporte forbidden [Ti(H2O)6]3+ 1 - 10

Spin allowed (tetrahedral complex),Laporte partially allowed by d-p mixing [CoCl4]

2− 50 - 150Spin allowed, Laporte allowed: charge transfer bands [TiCl6]

2−, MnO−4 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 octahedralcomplex, the absorption intensity, ε < 10 m2mol−1.

• Extinction coefficients for tetrahedral complexes are expected to be around 50-100times larger than for octrahedral complexes.

• The value of the electron repulsion parameter, B′, for first-row transition metal freeions is around 1000 cm−1. Depending on the position of the ligand in the nephelaux-etic series, the electron repulsion parameter, B in transition metal complexes, can bereduced by about 60%.


In the chemical literature, terms such as MCT (d→ d, metalcharge transfer), MLCT (metal-ligand charge transfer), LMCT (ligand-metal charge transfer), and LL (ligand-ligand chargetransfer) are used. A schematic diagram showing the various types of transitions is givenin Figure 3.

Figure 3: Schematic Diagram Showing Possible Types of Electronic Transitions in TransitionMetal Complexes

Density Functional Calculations of Excited States in TransitionMetal Complexes

It is not always the case that TD-DFT calculations agree with experiment, and there is everyreason to be critical about the calculational results. Very carefully compare the TD-DFTcalculations with experiment. In many cases, artifacts will arise: charge transfer states tendto appear much too low in the spectrum; double excitations are entirely missing; neutral-to-ionic transitions are poorly predicted; and spin-flip transitions cannot be predicted.

The calculations requested here represent one of the cases where TD-DFT with normalGGA functionals like BP86 fails badly, and predict LMCT states where there should bed-d excitations (in the region below ∼15000 cm−1). The calculation should, instead, beperformed 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 thedesired four ligand field states in order to capture the states of interest, since they may notcome in order of increasing orbital energy difference. To be on the safe side, a calculationrequesting more exited states should be performed


Vanadium Oxidation States

Vanadium displays variable oxidation states of varying colors including the blue oxovana-dium(IV) ion, usually written more simply as VO2+ but will have water molecules attachedto it as well - [VO(H2O)5]

2+, the green hexaaquavanadium(III) ion - [V(H2O)6]3+, and the

purple-violet hexaaquavanadium(II) ion - [V(H2O)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(H2O)5]2+ (d3), [V(H2O)6]

3+

(d2), and [V(H2O)6]2+ (d1) complexes shown in Figure 4 and are also compared to experi-

mental results (Reference 4).

Figure 4: The [V(H2O)6]2+/3+ and [VO(H2O)5]

2+ Complexes

Along with these calculations, ways in which electron density differences can be used tointerpret the results of calculations will also be explored.

Geometry Optimization

Calculations are carried out to optimize the geometries of these complexes and to calculatethe energies and intensities of the low-lying electronic transitions. Electron density differenceplots are used to assign the nature of the transitions. Features such as Jahn-Teller distortionsand 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 ofthe complexes. It is important to have reasonable bond distances in the initial structure orconvergence problems can occur in the SCF procedure. The geometry of each complex isthen optimized.


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 atthe 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 stateis then computed. Visualization of the electron density differences is then carried out withappropriate visualization software.

Discussion

[V(H2O)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. Allthe calculated V-O bond distances may not be equal. As expected, the bond distances inthe 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(H2O)6]

2+

Although constraints can be applied, such that the V-O bond distances are all equal, theJahn-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, indicatesthat a d2 octahedral complex should exhibit three d → d excitations: 3T1g(F) → 3T2g,3T1g(F)→ 3T1g(P), and 3T1g(F) → 3A2g.

The visible/ultraviolet spectrum for [V(H2O)6]3+ is shown in Figure 6

The transitions, ν1 (3T1g(F) → 3T2g) at 17,200 cm1 and ν2 (3T1g(F) → 3T1g(P)) at 25,000cm1 are shown, but the ν3 (3T1g(F)→ 3A2g) 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 presentcalculations which involve only single-electron excitations. In addition, the 3T1g(F) → 3A2g

transition is unlikely, and its band is often weak or unobserved.

Calculated lower-energy transitions most likely occur under the experimental band envelopeat about 17,000 cm−1, while an allowed ligand metal charge transfer (LMCT) transition, from


Figure 5: Tanabe-Sugano Diagram for Spin-Allowed and Forbidden Electronic Transitions ofan Octahedral d2 Complex such as[V(H2O)6]

3+.

Figure 6: The Visible/Ultraviolet Spectrum of [V(H2O)6]3+.


ligand molecular orbital localized on O atoms of H2O → to the vanadium ion is calculatedat approximately 35,000 cm−1.

In addition to the three possible spin-allowed transitions, there are seven singlet states thatsuggest there could be as many as seven multiplicity (spin) forbidden transitions. Transitionsfrom the 3T1g ground state to any of the singlet states would have extremely low ε valuesand are seldom observed in routine work. Some singlet states (e.g., 1A1g,

1Eg) are so high inenergy that transitions to them would fall in the UV, where they would likely be obscuredby the intense LMCT band.

[V(H2O)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 orbitalsare split energetically into a lower energy set of approximate t2g symmetry and higher energyset 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 vanadiumis V(II), the charge on the vanadium is smaller as a result of electron donation from theligands to the metal, and is common for transition metal complexes.

Excited States

Important bands of the calculated electronic spectrum of [V(H2O)6]2+ should be compared

to the experimentally observed spectrum. Based on a Tanabe-Sugano Diagram (Reference7) shown in Figure 7, a d3 octahedral system should exhibit three d → d excitations: 4A2g

→ 4T2g(F); 4A2g → 4T1g, and 4A2g → 4T1g(P).

Since the last transition involves a double excitation, it will not be observed in the singlesonly calculated spectrum. The first two low-energy bands with non-zero intensity involvetriply degenerate excited states, and so both sets of calculated transitions are degenerate.Although the calculated energies for the bands are probably higher than the experimentalvalues, the trend is sufficient to assign the bands in the experimental spectrum. One wouldnot expect quantitative agreement even at a higher level of theory because of the lack ofinclusion of the solvent in the calculated spectrum.

Charges and Electron Density

Electron density difference plots should be obtained for the lowest electronic transitionsof the calculated electronic spectrum. A darker color will indicate the region from whichelectron density was removed, while a lighter color indicates the region in which the electrondensity is enhanced. Since both the dark and the light electron density difference isosurfacesare located close to the metal, the d → d character of these excitations can be readilyascertained. In contrast, the lowest energy transitions with non-zero calculated intensity, can


Figure 7: Tanabe-Sugano Diagram for Spin-Allowed and Forbidden Electronic Transitions ofan Octahedral d3 Complex such as[V(H2O)6]

2+.

be characterized as vanadium to oxygen charge transfer from the electron density differenceplot.

The trend in charges should confirm these assignments. The charge on vanadium shouldbe only slightly higher in the lower excited states than in the ground state as expected ford→ d transitions. The vanadium charge in the higher excited state, however, is much morepositive than in the ground state, and is consistent with a metal to ligand charge transfer.

[VO(H2O)5]2+ - d1 Configuration

Square Pyramid Geometry and Jahn-Teller Distortion

The [VO(H2O)5]2+ complex forms an approximate square pyramid with an oxo-group (=O)

in the apical positions, four H2O molecules in basal positions, and an H2O ligand taking upthe the sixth position. The vanadium-oxo bond is considerably shorter than the vanadium-water bonds, as expected, and the water molecules that are in the basal positions are bentaway from the oxo group by approximately 5◦. If the complex were C4v symmetry, the fourbasal V −O bonds should be equivalent, but local symmetry of the V −O skeletal linkagesis reduced to C2v, because of a Jahn-Teller distortion. This will remove the degeneracy ofthe dxz and dyz orbitals on vanadium by a small amount.


Charges and Electron Density

Because of π-donation from the oxo (=O) group to the V atom, the charge on the apicaloxygen 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 metald orbitals that contain the unpaired electron. The ligand field diagram for a C4v complex isgiven in Figure 8 (Reference 4).

Figure 8: Ligand Field Diagram for the [VO(H2O)5]2+ C4v Complex.

Therefore, one expects 3 d→ d transitions for [VO(H2O)5]2+: 2B2(dxy)→ 2E(dxz,yz),

2B2(dxy) → 2B1(dx2−y2), and 2B2(dxy) → 2A1(dz2). Reduction in symmetry to C2v removesthe degeneracy of the first transition.

As expected, the first two bands involve an electron transfer from the vanadium dxy orbitalto the vanadium dxz and dyz orbitals. The electron density on the π system of the oxogroup is enhanced as well because of the covalency that occurs between the oxo group andthe 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 thewavelength range of the observed spectrum. Although it is possible that use of a higher levelof 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 theexperimental 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 acharge transfer band involving the ligand (=O) orbital to the vanadium ion.


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. 256-274.

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.


Exercises

In the following exercises the B3LYP functional is used in conjunction with and LANL2DZbasis for V, which replaces the core electrons with a pseudopotential. The 6-31g(d) basis ischosen for the H and O atoms to form H2O ligands.

This combines Density Functional Theory, which can be very efficient for transition-metalcomplexes 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. Crys-tallographic data may exist for these or similar complexes.

2. Now use the optimized geometries obtained above to calculate excited states for eachof the aquavanadium complexes.

Compare the calculated spectra to the experimental one, and be sure to characterizethe 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 betweencalculated and experimental results and on properly assigning the peaks in the spec-trum.

3. Electronic transitions occur as electrons are shifted from one place to another withina molecule, which can be seen by examining electron density changes. The followingis to be performed for each transition metal complex:

• Create an electron density cube file containing the ground state electron densityfor the complex.

• Create an electron density cube file for each of the excited states that were ex-perimentally 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 ofthe transitions that were previously characterized, by utilizing the electron-densitydifference cube files.

Which color corresponds to areas where electrons are leaving? Which color correspondsto 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 andexcited states.

What significant changes occur?

What does this indicate about the direction of electron flow for those transitions?


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=allkeyword 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 binarycheckpoint file (.chk) to a formatted checkpoint file (.fchk).

3. Use the cubegen G09 utility to extract the two cubes of total electronic density fromthe formatted checkpoint file:

cubegen 0 density=SCF vocl3-ex4-es.chk vocl3-ex4-gs.cube 0 h (ground stateelectron density)

cubegen 0 density=CI vocl3-ex4-es.chk vocl3-ex4-es.cube 0 h (excited stateof interest)

Note: the electron density of both the ground state and 4th excited state, are bothstored 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 densityof the first excited state.

In this example, the electron density of the 4th excited state is requested, i.e. root=4.


4. The electron density difference between the excited and ground states can be obtainedwith 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-ex-gs-diff.cube.

Follow the above procedure for each of the excited-state difference densities to be viewedwith visualization software which can read cube files


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