Use of Ab Initio Calculations to Help Interpret the UV-Visible Spectra of Aquavanadium Complexes: A New Look at an Old Experiment 1

Use of Ab Initio Calculations to Help Interpret the UV-Visible Spectra of Aquavanadium Complexes: A New Look at an Old Experiment 1 Wayne P. Anderson,* Department of Chemistry, Bloomsburg University of Pennsylvania and James B. Foresman, Department of Physical Science, York College of Pennsylvania Introduction Ligand field theory has been a central theme of inorganic chemistry for many years. Interpretation of d-d transitions in transition metal complexes is discussed in many advanced inorganic chemistry textbooks, with the emphasis frequently placed on extraction of values of Δ o and the Racah B parameter from experimental spectra (1, 2). With the increasing speed of personal computers, it is now possible to do ab initio calculations on relatively large systems using basis sets of moderate sizes. Visualization of the computed results using programs such as GaussView (3), Molekel (4), and gopenmol (5) allows students to interpret the results of the calculations more easily than was possible when only tables of numerical data were derived as output. Recently, we have been exploring novel ways in which electron density differences can be used to interpret results of quantum mechanical calculations. As part of that exploration, we have re-visited an experiment involving the synthesis and investigation of the uv-visible spectra of [VO(H 2 O) 5 ] 2+, [V(H 2 O) 6 ] 3+, and [V(H 2 O) 6 ] 2+ that was reported in 1984 (6). Ab initio 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. We report the results of these calculations in this paper. Description of the Exercise (more detailed instructions appear at the end of this manuscript) Experimental Spectra The vanadium complexes may be synthesized by the students or prepared by the instructor. Caution must be exercised since the synthesis requires the use of mercury(ii) chloride to prepare the zinc amalgam. The UV-Vis spectra are then recorded by the students. Values for the absorption bands in these complexes can be found in the literature (6-8). Computations All calculations employed the B3LYP density functional along with the LANL2DZ 1 2014 James Foresman. This manuscript was prepared June 2001 and posted online in May 2014. *deceased

effective core basis set using Gaussian 98W (9). Although larger basis sets are preferred for calculation of electronic transitions, the LANL2DZ basis set is a reasonable compromise between speed and accuracy for teaching purposes. In preparation for the quantum mechanical calculations, a starting geometry must be constructed for the complexes. This can be done graphically using GaussView or other commercial programs. It is important to have reasonable bond distances in the initial structure or convergence problems can occur in the SCF procedure. It is sometimes necessary to allow a very large number of iterations to achieve SCF convergence. The geometry of each complex is optimized. Then time-dependent perturbation theory is used to calculate the energies and intensities of the first 20 excited states of each complex at the optimized geometry of the ground state. Finally, cube files of the electron density are calculated for the ground state and excited states and a cube file of the electron density difference between each excited state and the ground state computed. In addition, the natural bond order (NBO) charges on each atom are computed for the ground state and each excited state. Sample input files that illustrate the Gaussian keywords for each type of calculation are included in the on-line version of this paper. Visualization of the electron density differences are carried out in GaussView or Molekel. RESULTS [V(H 2 O) 6 ] 2+ Although the hydrogen atoms lower the symmetry somewhat, the local symmetry of the VO 6 fragment is O h. Thus, the metal d orbitals are split energetically into a lower energy set of approximate t 2g symmetry and higher energy set of approximately e g symmetry. The three 3d electrons on vanadium fill the t 2g orbitals and no Jahn-Teller distortion occurs. All the calculated V-O bond lengths are 215 pm, while the NBO charges on vanadium and the oxygen atoms are +1.24 and -0.98 respectively. Although the formal oxidation state of the vanadium is +II, the natural bond order (NBO) charge on the vanadium is smaller as a result of electron donation from the ligands to the metal. This is common for transition metal complexes. Pertinent bands of the calculated electronic spectrum of [V(H 2 O) 6 ] 2+ are compared to the experimental spectrum in table 1. Based on a Tanabe-Sugano diagram (10), a d 3 octahedral system should exhibit three d-d excitations: 4 A 1g 4 T 2g (F) ; 4 A 1g 4 T 1g and 4 A 1g 4 T 2g (P). Since the last transition involves a double excitation, it will not be observed in the singles only calculated spectrum. The first two bands involve triply degenerate excited states, so calculated transitions 1-3 are degenerate, and transitions 4-6 are degenerate. Although the calculated energies for the bands are 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.

Electron density difference plots for electronic transitions 1 and 4 of the calculated electronic spectrum are shown in figure 1. The darker color indicates the region from which electron density was removed, while the 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, transitions 14-16, the lowest energy transitions with non-zero calculated intensity, can be characterized as vanadium to oxygen charge transfer from the electron density difference plot. Natural bond order charges confirm these assignments. The charge on vanadium is only slightly higher in excited states 1-6 than in the ground state as expected for d-d transitions. The vanadium charge in excited state 14, however, is 0.54 units more positive than in the ground state. This is consistent with a metal to ligand charge transfer. [V(H 2 O) 6 ] 3+ Because of the presence of 2 electrons in the t 2g orbitals of this pseudo-octahedral complex, the calculated VO 6 local geometry is expected to show a Jahn-Teller distortion. All the calculated V-O bond distances are 203 pm. As expected, the bond distances in the V(III) system are somewhat shorter than for the corresponding V(II) complex. The NBO charges on V and O are +1.47 and -0.93 respectively. Thus, the calculated charge on the metal is only 0.23 units more positive than for [V(H 2 O)6] 2+. Although the V-O bond distances are all equal, the Jahn-Teller effect is reflected in the calculated electronic spectrum. A d 2 octahedral cpmplex should exhibit three d-d excitations: 3 T 1g (F) 3 T 2g;, 3 T 1g (F) 4 T 1g (P) and 3 T 1g (F) 3 A 2g. However, a Jahn-Teller distortion to D 3d local symmetry leads to the diagram in figure 2. Calculated low energy electronic transitions are given in table 2. The transition to the higher energy 3 E g component derived from the 3 T 1g (P) state is not observed in the calculated spectrum because it involves a double excitation. Calculated transitions 3-5 most likely occur under the experimental band envelope at about 17,000 cm -1. An allowed O V CT transition is calculated at 35,100 cm -1 (figure 3). [VO(H 2 O) 5 ] 2+ Pertinent geometric data obtained at the B3LYP/LANL2DZ level are given in table 3. The vanadium - oxo bond is considerably shorter than the vanadium-water bonds, as expected, and the water molecules that are cis to the oxo group are bent away from the oxo group by 4-8 degrees. Since the four water molecules that are cis to the oxo group are not equivalent, the C 4v local symmetry of the V-O linkages is reduced to C 2v. This will remove slightly the degeneracy of 3

the d xz and d yz orbitals on vanadium. Because of π-donation from the oxo group to the metal, the charge on the oxo group is considerably less negative than that on the oxygen atoms of water. For a d 1 complex, the electronic states have the same symmetry as the metal d orbitals that contain the unpaired electron. The ligand field diagram for a C 4v complex is given in figure 1 of reference 6. Therefore, one expects 3 d-d transitions for [VO(H 2 O) 5 ] 2+ ; 2 B 2 (xy) 2 E (xz,yz), 2 B 2 (xy) 2 B 1 (x 2 -y 2 ), and 2 B 2 (xy) 2 A 1 (z 2 ). Reduction in symmetry to C 2v removes the degeneracy of the first transition. Calculated electronic transitions are listed in table 4. Electron density difference plots for calculated transitions 1-4 and 9 in the electronic spectrum are shown in figure 4. As expected, the first two bands involve an electron transfer from the vanadium d xy orbital to the vanadium d xz and d yz 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 d xz and d yz orbitals. The third band is a d xy to d x2-y2 transition. Band 4, however, which was assigned as the third d-d transition in reference 6, is clearly an oxygen to vanadium charge transfer band in the calculated spectrum. The remaining d-d transition (xy z 2 ) is transition 9 in the calculated spectrum and 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 28,600 cm -1 in the experimental spectrum is probably a charge transfer band and not a d-d transition. The excited state NBO charges on the V=O fragment are shown in table 5. These charges are consistent with the assignment of the 4 th transition as oxygen to vanadium charge transfer band. 4

Literature Cited 1. Miessler, Gary L.; Tarr, Donald A. Inorganic Chemistry, 2 nd Ed.,Upper Saddle River, NJ: Prentice Hall, 1998, pp. 366-378. 2. Wulfsberg, Gary. Inorganic Chemistry, Sausalito: University Science Books, 2000,pp. 889-898. 3 GaussView 2.1, Gaussian, Inc. 4. Stefan Portmann & Hans Peter Lüthi. Chimia, 2000, 54,766. 5. gopenmol, http://www.csc.fi/english/pages/g0penmol, last accessed 28 May 2014. 6. Ophardt, C. E.; Stupgia, S. J. Chem. Ed., 1984, 61, 1102. 7. Figgis, B. N.; Hitchman, M. A. Ligand Field Theory and Its Applications: New York, Wiley-VCH, 2000, pp. 204-207. 8. Lever, A. B. P. Inorganic Electronic Spectroscopy: New York, Elsevier,1968, pp. 256-274. 9. Gaussian 98W, Revision A.9, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1998. 10. 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. 5

Table 1. Calculated Low Energy Electronic Transitions in [V(H 2 O) 6 ] 2+ Wavelength, nm Energy, cm -1 Oscillator Strength Assignment Experimental, cm -1 NBO Charge on V 1-3 646 15,500.0000 4 A 1g 4 T 2g (F) 11,800(6), 12,400(8) +1.40 4-6 459 21,800.0000 4 A 1g 4 T 1g 17,700(6), 18,500(8) +1.37 4 A 1g 4 T 2g (P) 27,800(6), 27,900(8) 14-16 257 39,000.0007 V O CT +1.78 6

Table 2. Calculated Low Energy Electronic Transitions in [V(H 2 O) 6 ] 3+ Wavelength, nm Energy, cm -1 Oscillator Strength Assignment D 3d (O h ) Experimental, cm -1 NBO Charge on V 1-2 2260 4,400.0000 3 A 2g 3 E g ( 3 T 1g (F) 3 T 2g ) +1.51 3 526 19,000.0000 3 A 2g 3 A 1g ( 3 T 1g (F) 3 T 2g ) 4-5 465 21,500.0000 3 A 2g 3 E g ( 3 T 1g (F) 3 T 1g (P)) 16,100(6), 17,200(7), 17,800(8) +1.64 +1.60 6 400 25,000.0000 3 A 2g 3 A 2g ( 3 T 1g (F) 3 T 1g (P)) 23,800(6) 25,600(7), 25,700(8) +1.56 7-8 285 35,100.0170 O V CT +0.58 7

Table 3. Calculated Bond Lengths, Bond Angles and NBO Charges in [VO(H 2 O) 5 ] 2+ Bond (Angle) Bond length, pm (Bond Angle, deg) NBO Charges V=O 158 V +1.25 O -0.25 V-O t (O=V-O t ) 220 (180) O t -0.98 V-O a (O=V-O a ) 206 (98) O a -0.92 V-O b (O=V-O b ) 206 (94) O b -0.94 V-O c (O=V-O c ) 206 (98) O c -0.92 V-O d (O=V-O d ) 206 (94) O t -0.94 8

Table 4. Calculated Low Energy Electronic Transitions in [VO(H 2 O) 5 ] 2+ Wavelength, nm Energy, cm - 1 Oscillator Strength Assignment C 4v Symmetry Experimental, cm -1 1 605 16,500.0002 2 B 2 (xy) 2 E (xz,yz) 13,000(6,7), 13,100(8) 2 567 17,600.0002 2 B 2 (xy) 2 E (xz,yz) 3 541 18,500.0000 2 B 2 (xy) 2 B 1 (x 2 -y 2 ) 15,900(6), 16,000(7,8) 4 358 27,900.0019 O V CT 28,600(6) 5 322 31,000.0000 6 313 32,000.0000 7 293 34,100.0005 O V CT 8 281 35,600.0005 O V CT 9 276 36,300.0000 2 B 2 (xy) 2 A 1 (z 2 ) 9

Table 5. Calculated NBO Charges in [VO(H 2 O) 5 ] 2+ Ground State Excited State 1 Excited State 2 Excited State 3 Excited State 4 Excited State 9 V +1.25 +1.58 +1.57 +1.36 +0.61 +1.35 O -0.25-0.64-0.63-0.28 +0.44-0.36 10

Figure 1. Electron Density Difference Plots for [V(H 2 O) 6 ] 2+ Transition 1,.05 contour Transition 4,.05 contour Transition 14,.05 contour Transition 14,.005 contour 11

Figure 2. Effect of a D 3d Jahn-Teller Distortion on the Electronic States of [V(H 2 O) 6 ] 3+ 3 A 2g 3 A 2g 3 E g 3 T 1g (P) 3 A 2g 3 E g 3 T 2g 3 A 1g 3 T 1g (F) 3 E g 3 A 2g O h D 3d 12

Figure 3. Electron Density Difference Plots for [V(H 2 O) 6 ] 3+ Electronic Transition 3,.05 contour Electronic Transition 7,.05 contour 13

Figure 4. Electron Density Difference Plots for [VO(H 2 O) 5 ] 2+ Electronic transition 1,.05 contour Electronic transition 2,.05 contour Electronic transition 3,.05 contour Electronic transition 4,.05 contour Electronic transition 9,.05 contour 14

Instructions for the Exercise: 1. Prepare samples of [VO(H 2 O) 5 ] 2+, [V(H 2 O) 6 ] 3+ and [V(H 2 O) 6 ] 2+ according to Procedures 1, 2 and 3 under Stock Solutions in "Synthesis and Spectra of Vanadium Complexes", Ophardt, C. E.; Stupgia, S. J. Chem. Ed., 1984, 61, 1102 or obtain samples of these complexes from your instructor. 2. Record the absorption spectrum in both the UV and VIS regions. Print out the spectrum for your records and note the principle absorption peaks with their strengths. 3. Sketch the complex using GaussView. Here are some hints. You may follow these or try it using your own procedure. a. Place a six-coordinated Vanadium atom at the center of the screen b. Place oxygen atoms at each of the six coordinated positions. Be sure to just place oxygen atoms there and not =O or O- atoms there. c. Now pick 5 of the oxygen atoms and using the add valence button, create two additional valences at each. Hydrogens should appear as you do this. d. Finally polish the structure by setting the V=O bond length to 1.5 A and the five V-O distances to 2.0 A. This is a reasonable starting point for the optimization. Do not clean the structure with the clean button. 4. Optimize the geometry using the B3LYP/LANL2DZ model. This model combines density functional theory (necessary for transition metals) and pseudopotentials which replace the core electrons of the V. Record the bond lengths and bond angles in your notebook. Compare your theoretical structure to any experimental data which can be found (crystal data may exist for this species or similar complexes). 5. Now using the optimized geometry found above, create a new gaussian file which solves for the excited states. Use the TD B3LYP LANL2DZ model. Specify 5 excited states to be found (instead of the default 3). Compare the theoretical spectrum to the one you obtained experimentally. Which of the 5 excited states are seen in the optical excitation spectrum? Which are not? How well do the vertical excitation energies compare? You will need to properly assign the peaks from your spectrum. Use the spectrum generator (from W.P. Anderson) to convert the gaussian output file into a theoretical spectrum to assist you in performing the comparison. 6. In preparation for the next step, create a gaussian cube file containing the ground state electron density for the complex. Give it a name such as state0.cube which is specified at the bottom of the gaussian input file separated by a blank line above and below. You may save time by reusing the checkpoint file from the previous gaussian job and specifying guess=read. At the same time request a natural population analysis of the ground state (Pop=NPA). This will give charges and orbital occupancies for the state. The command line for Gaussian should look like this: # B3LYP LANL2DZ Guess=Read Cube=Density Density=SCF Pop=NPA Record the atomic natural charges of the ground state. Keep the cube file for use later. 7. Electronic transitions occur as electrons are shifted from one place to another within a molecule. You can see this by examining electron density changes. For each of the excited states that were experimentally observable in your spectrum, run a new gaussian job. Use the same checkpoint file as the excited state calculation. You can reuse the information stored there and create a gaussian density cube for the excited state. Here is the entire input file for gaussian in the case of excited state 1: 15

%chk=filename.chk # Geom=AllCheck Cube(Density) Guess(Read,Only) Density(Checkpoint,CIS=1) Pop=NPA state1.cube END Be sure to include a blank line at the end (the END is not included). You see again we have requested the natural population analysis. Record the atomic charges for the excited state. 8. Repeat step 7 for the other two excited states that are observable from your spectrum. 9. Compare the atomic charges for the ground and excited states. What significant changes occur? What does that indicate about the direction of electron flow for those transitions? 10. Now visualize the difference densities (ground to excited state) to discover the nature of the transitions. Use Molekel to read in the Gaussian cube for the excited state then subtract the ground state density. Create an isosurface (first try 0.004 as the value, but experiment with this number). Be sure to click on the both signs box so that both positive and negative values are seen. What is the significance of the colors? 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? In the literature you find terms such as d-d, MLCT (metal-ligand charge transfer), LMCT (ligand-metal charge transfer), CT(charge transfer), etc. Here are some hints on reading the cube files with Molekel. Windows will pop up. Move them to the side so that you can always see the main window. If windows are too large (going off the screen, then change your display resolution until they fit on the screen). a. Right-Mouse click in the main window. Choose Load > gaussian cube. b. Right-Mouse click again and choose Surface. c. Click on the gaussian cube radio button. d. Load the excited state gaussian cube (wait a minute for this to finish) e. Subtract the ground state gaussian cube (wait a minute for this to finish) f. Specify the isovalue in the cutoff box. Click on both signs g. Create Surface 11. For your report, save images generated from Molekel and paste them on your webpage for this experiment. Also include table of results comparing experiment to theory for the vertical excitation energies and bond lengths and angles of the optimized ground state. Another table should contain the atomic charges for all the states. You should also have an ISIS drawing or image from Gaussview of the structure itself, labeling the atoms for the bond length and angle table. 16