Using a Combination of Experimental and Computational Methods To

LABORATORY EXPERIMENT pubs.acs.org/jchemeduc

Using a Combination of Experimental and Computational Methods To Explore the Impact of Metal Identity and Ligand Field Strength on the Electronic Structure of Metal Ions Naomi C. Pernicone, Jacob B. Geri, and John T. York* Department of Chemistry, Stetson University, DeLand, Florida 32723, United States

bS Supporting Information ABSTRACT:

In this exercise, students apply a combination of techniques to investigate the impact of metal identity and ligand field strength on the spin states of three d5 transition-metal complexes: Fe(acac)3, K3[Fe(CN)6], and Ru(acac)3, where acac is acetylacetonate. Students first use crystal field theory to predict the most likely spin state based on the metal identity (3d versus 4d metal) and the ligand field strength of the acac and CN ligands (weak-field versus strong-field ligands). Next, students use density functional theory (DFT) to determine the geometries and the energies of the high- and low-spin electronic configurations of each complex, allowing them to predict the most energetically favorable configuration and to compare their computed geometries with X-ray structural data. Finally, students experimentally determine the magnetic susceptibility and spin state of each complex and compare these results with their predictions. This combined application of basic chemical principles, computational chemistry, and experimental measurement provides students with practical insight into the application of complementary methods to better understand chemical properties. KEYWORDS: Second-Year Undergraduate, Upper-Division Undergraduate, Inorganic Chemistry, Laboratory Instruction, HandsOn Learning/Manipulatives, Computational Chemistry, Coordination Compounds, Crystal Field/Ligand Field Theory, Magnetic Properties, Synthesis

A

n important goal in modern chemical education is to provide students with experiences that reinforce fundamental concepts learned in the classroom while simultaneously providing training in the use of tools and methodologies that are encountered in “real-world” research. Experimental tools such as NMR spectroscopy have therefore been widely incorporated throughout all levels of the undergraduate chemistry curriculum, providing students with invaluable practice in using modern research tools to solve chemical problems.1 Another tool that is playing an increasingly important role in chemical research is computational chemistry. Indeed, in most fields of chemistry, electronic structure programs are routinely used in combination with traditional experimental techniques to gain insight into chemical systems.2 4 Given the usefulness of such programs for understanding important problems, exposing students to the complementary application of experimental and computational methods is a worthy objective. Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.

One successful approach for introducing students to electronic structure calculations is to apply these tools in existing laboratory experiments.4 7 Such “wet dry labs” that integrate traditional laboratory activities and computational methods have been developed for many “core” chemical courses such as physical8 and organic chemistry.9 These exercises allow students to apply computational techniques in a manner that replicates real investigations, with electronic structure calculations and experimental measurements used synergistically to study a given chemical problem. This strategy also provides students with the unique opportunity to directly compare computational and experimental data. By observing the accuracy possible with computational methods, students gain an enhanced appreciation for the use of these tools as a legitimate part of modern chemical research.4 9 Published: June 17, 2011 1323

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Figure 1. M(acac)3 and [Fe(CN)6]3- complexes explored in this investigation.

In inorganic chemistry, an important property that is well suited for study using this type of integrated experimental computational approach is the d-electron configuration of a metal center. Students typically learn to determine the electronic structure of metal complexes by applying crystal field theory in the classroom and by measuring properties such as magnetic susceptibility in the laboratory.10,11 Research investigations of transitionmetal complexes also routinely include electronic structure calculations as a complement to experimental data, making the inclusion of computational methods a logical extension of traditional undergraduate inorganic laboratory experiments. Moreover, the relative ease of performing calculations can allow students to explore the electronic structures of metal complexes more thoroughly. Thus, instead of simply determining the electronic structure of one or more metal complexes, students can explore the impact of changing important experimental variables such as ligand field strength and metal identity. Presented herein is an integrated laboratory exercise in which students employ complementary experimental and computational techniques to determine the d-electron configuration of the d5 metal complexes Fe(acac)3, Ru(acac)3, and K3[Fe(CN)6] (where acac is acetylacetonate) (Figure 1), thereby examining the effect of metal identity and ligand field strength on the electronic configuration. Students first use crystal field theory and the spectrochemical series of ligands to predict the preferred spin state for each of these complexes. Next, students use density functional theory to determine the geometries and the energies of the high- and low-spin electronic configurations of each complex, allowing them to compare computed structures with experimental X-ray data and to predict the most energetically favorable configuration. Finally, students experimentally measure the magnetic susceptibility of each complex and compare these results with their predictions. This exercise provides students with practical computational and experimental skills, as well as improved insight into applying a variety of complementary methods for understanding important properties.

’ PREDICTING ELECTRONIC STRUCTURE WITH CRYSTAL FIELD THEORY Preparation for this exercise begins in the classroom with an introduction to crystal field theory and the use of the spectrochemical series of ligands to predict the electronic structures of metal ions.12,13 While several factors can affect the d-electron configuration of a metal complex, two of the most important are the identity of the metal and the nature of the supporting ligands.12,13 Students use crystal field theory to predict the most likely spin state of the complexes Ru(acac)3, Fe(acac)3, and [Fe(CN)6]3 . For an octahedral d5 metal complex, there are two possible electronic configurations: five unpaired electrons

Figure 2. General d-orbital splitting diagrams for the high-spin and lowspin electron configurations of an octahedral d5 metal complex.

(high-spin, S = 5/2) and one unpaired electron (low-spin, S = 1/2) (Figure 2). Because acac is a weak-field ligand and CN is a strong-field ligand, students should predict that Fe(acac)3 will be high-spin (S = 5/2) and that [Fe(CN)6]3 will be low-spin (S = 1/2). Moreover, because ruthenium(III) is a 4d transition metal, students should predict that Ru(acac)3 will be low-spin, despite having the weak-field acac ligand.

’ DENSITY FUNCTIONAL THEORY CALCULATIONS Students next utilize density functional theory (DFT) to calculate the energy of both the high-spin and low-spin electronic configurations for each complex and choose the spin state that yields the lowest calculated energy. Students use the Gaussian 03W14 suite of electronic structure programs for these calculations, but this exercise could be readily adapted for use with any available electronic-structure software. These calculations are performed using a combination of the popular B3LYP functional and LANL2DZ basis set for all atoms because this and similar model chemistries have been shown to yield accurate results for iron and ruthenium complexes15 20 at a reasonable computational cost (see the Supporting Information for computational details). For each metal complex investigated, students must (i) build the input molecular geometry, (ii) obtain the lowest-energy geometric configuration (i.e., perform a “geometry optimization”) for both the high- and low-spin electronic configurations, and (iii) perform a frequency calculation on the optimized geometries to obtain important thermodynamic corrections and to verify the identity of each geometry as an energetic minimum by the absence of imaginary frequencies2 4 (Figure 3). This sequence of calculations is representative of the general procedure used in routine computational investigations and provides students with a good introduction to the application of electronic structure programs. Inexperienced students can perform these calculations with relative ease using the student handout provided in the Supporting Information. However, for instructors wishing to provide students with a more detailed introduction to electronicstructure calculations, a number of excellent resources are recommended for this purpose.2 7 1324

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Figure 3. DFT-optimized structures of Fe(acac)3 (1), Ru(acac)3 (2), and [Fe(CN)6]3- (3).

Table 1. DFT-Calculated Energies and Metal Ligand Bond Lengths for Optimized Geometries Complex

Electronic Energy/(Hartrees)

Electronic + ZPE/(Hartrees)

Metal Ligand Bond Lengths/(Å)

Fe(acac)3 Fe(acac)3

S = 1/2 S = 5/2

1159.0478 1159.0599

1158.7055 1158.7209

1.92 2.02 (1.99)a

Ru(acac)3

S = 1/2

1129.4724

1129.1312

2.04 (2.00)a 2.20

Ru(acac)3

S = 5/2

1129.3931

1129.0563

[Fe(CN)6]3

S = 1/2

680.3216

680.2741

1.98 (1.90)a

3

S = 5/2

680.2712

680.2296

2.24

[Fe(CN)6] a

Spin State

Average metal ligand bond lengths from refs 21 23.

To maximize the use of computational resources and to reduce repetition for students, the complexes and spin states are divided up among the class and each student is responsible for completing the calculations for a single spin state of a particular metal complex. The results for the entire class are subsequently pooled to provide students with a complete data set for analysis. The atomic coordinates for all of the optimized geometries in this exercise are included for instructors in the Supporting Information. The gas-phase calculated electronic energies are listed in Table 1 for both the high- and low-spin configuration of each complex (in energy units of hartree), including the zero-point vibrational energy (ZPE) correction.2 4 By converting to energy units of kJ/mol (1 hartree = 2625.5 kJ/mol), the high-spin electronic configuration for Fe(acac)3 is calculated to be 40 kJ/mol lower in energy than the low-spin configuration, as predicted by crystal field theory for the first-row Fe3+ ion with the weak-field acac ligand. Substitution of the acac ligands by the strong-field CN ligands on the Fe3+ center results in a dramatic change in the relative energies of the two spin states, with the low-spin configuration now predicted to be 117 kJ/mol lower in energy than the high-spin configuration. Again, this shift is consistent with the predictions of crystal field theory for the strong-field CN ligands. Finally, substitution of the 3d Fe3+ ion with the 4d Ru3+ ion in the M(acac)3 complexes results in the low-spin configuration being favored by 197 kJ/mol. Thus, as predicted by crystal field theory, metal substitution and ligand field strength dramatically affect the relative energies of the high-spin and lowspin electronic configurations for the metal centers. Mirroring another important step used in real-world investigations, students compare their calculated metal ligand bond lengths with bond lengths provided from the experimental X-ray crystal structures of the three complexes.21 23 As seen in Table 1,

the experimental metal ligand bond lengths of Fe(acac)3 (Fe Oaverage = 1.99 Å) are most consistent with the calculated high-spin structure (Fe Oaverage = 2.02 Å),22 those of Ru(acac)3 (Ru Oaverage = 2.00 Å) are most consistent with the calculated low-spin structure (Ru Oaverage = 2.04 Å),23 and those in K3[Fe(CN)6] (Fe Caverage = 1.90 Å) are most consistent with the calculated low-spin structure (Fe Caverage = 1.98 Å).21 These findings corroborate the predictions of the lowest energy configurations determined by the DFT-calculations and help to confirm the reliability of the chosen computational methodology.

’ EXPERIMENTAL MAGNETIC SUSCEPTIBILITY MEASUREMENTS As the final step, students experimentally determine the magnetic susceptibility (χ) and the related effective magnetic moment (μeff) for each complex. For transition metals, μeff is related to the number of unpaired electrons in a complex and can therefore be used to help determine the spin state.10 13 Although other factors including the orbital angular momentum of electrons and spin orbit coupling can also contribute to the magnetic properties of metal complexes,10 13 the measurement of μeff nonetheless provides a useful approximation of the number of unpaired electrons and works particularly well for the three complexes in this investigation. Students first synthesize Fe(acac)3 using established methods as a “wet” component to this lab, thereby providing important laboratory experience11 (details are available in the Supporting Information. Both K3[Fe(CN)6] and Ru(acac)3 are purchased from commercial chemical suppliers, and because these compounds are not consumed during the course of this experiment, they can be recovered and reused for multiple experimental measurements. Students then use a magnetic susceptibility 1325

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Table 2. Student Experimental Magnetic Susceptibility and Spin State Data Complex Fe(acac)3 Ru(acac)3 K3[Fe(CN)6] a

Calculated μeff/(μB)

Unpaired Electrons

Spin State

a

5

high-spin

a

1 1

low-spin low-spin

5.91 (5.92)

1.88 (1.73) 2.32 (1.73)a

complexes, and additional notes for the instructor. This material is available via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

Spin-only predicted values.

balance to determine the magnetic susceptibility and, subsequently, the μeff and spin state of each complex. Other methods of measuring magnetic susceptibility such as the Evans NMR method could potentially be adapted for use in this exercise as well.10,11 A representative example of student magnetic susceptibility data is given in Table 2. The experimental data show that Fe(acac)3 has five unpaired electrons, confirming the high-spin (S = 5/2) electronic configuration predicted by crystal field theory and DFT. Conversely, the magnetic susceptibility data for K3[Fe(CN)6]) and Ru(acac)3 are most consistent with each having only one unpaired electron, indicative of the low-spin (S = 1/2) configuration. Again, these experimental findings are consistent with the predictions from crystal field theory and DFT.

’ HAZARDS All compounds were purchased from Sigma-Aldrich Chemicals and used as received. Tris(acetylacetonato)iron(III) (Fe(acac)3) was synthesized according to published procedures.11 FeCl3 3 6H2O is corrosive and a strong skin, eye, and gastrointestinal irritant.24 Sodium acetate is a potential skin, eye, and gastrointestinal irritant.25 Acetylacetone (2,4-pendanedione) is a potential skin and eye irritant and toxic if swallowed or absorbed through the skin.26 Methanol is a flammable and toxic liquid if swallowed or absorbed through the skin.27 Fe(acac)3 is a potential eye, skin, respiratory, and gastrointestinal irritant.28 Ru(acac)3 is a potential eye, skin, respiratory, and gastrointestinal irritant.29 K3[Fe(CN)6] is a potential eye, skin, respiratory, and gastrointestinal irritant, and can form toxic fumes when brought in contact with acids.30 For all compounds, the use of gloves, goggles, fume hoods, and safe laboratory practices are important to avoid contact and breathing of dust. ’ CONCLUSION This exercise allows students to apply a combination of crystal field theory, density functional theory, and experimental measurement to elucidate the impact of ligand field strength and metal identity on the spin state of d5 metal complexes. Students gain insight into the properties of metal complexes, valuable computational and experimental skills, and experience in using several complementary methods to solve chemical problems. In addition, by observing the excellent agreement between experimental and computational data, students gain an appreciation for the accuracy and usefulness of DFT methods in modern chemical research. ’ ASSOCIATED CONTENT

bS

Supporting Information Background information, experimental and post-lab instructions for the students, atomic coordinates for all metal

’ ACKNOWLEDGMENT We would like to thank Stetson University for financial support in the development and implementation of this exercise. ’ REFERENCES (1) Modern NMR Spectroscopy in Education; Rovnya, D., Stockland, R., Jr., Eds.; ACS Symposium Series 969; American Chemical Society: Washington, DC, 2007. (2) Bell, S.; Dines, T. J.; Chowdhry, B. Z.; Withnall, R. J. Chem. Educ. 2007, 84, 1364. (3) Cramer, C. J. Essentials of Computational Chemistry: Theories and Models, 2nd ed.; John Wiley and Sons: Chichester, England, 2004. (4) Foresman, J. B.; Frisch, A. Exploring Chemistry with Electronic Structure Methods, 2nd ed.; Gaussian, Inc., 1996. (5) Pearson, J. K. J. Chem. Educ. 2007, 84, 1323. (6) Martin, N. H. J. Chem. Educ. 1998, 75, 241. (7) Clauss, A. D.; Nelsen, S. F. J. Chem. Educ. 2009, 86, 955. (8) Karpen, M. E.; Henderleiter, J.; Schaertel, S. A. J. Chem. Educ. 2004, 81, 475. (9) Rowley, C. N.; Woo, T. K.; Mosey, N. J. J. Chem. Educ. 2009, 86, 199. (10) Girolami, G. S.; Rauchfuss, T. B.; Angelici, R. J. Synthesis and Technique in Inorganic Chemistry, 3rd ed; University Science Books: Sausalito, CA, 1999; pp 117 132. (11) Glidewell, C. In Inorganic Experiments, 3rd ed.; Woollins, J. D., Ed.; Wiley-VCH: Weinheim, 2010; p 116 126. (12) Housecroft, C. E.; Sharpe, A. G. Inorganic Chemistry, 3rd ed.; Pearson Education Limited: Harlow, England, 2008; pp 637 682. (13) Shriver, D.; Atkins, P. Inorganic Chemistry, 4th ed.; W. H. Freeman and Company: New York, 2006; pp 459 490. (14) Frisch, M. J. ; et al. Gaussian 03W; Revision E.01. Gaussian, Inc.: Wallingford, CT, 2004. (15) Hirao, H; Kumar, D.; Que, L., Jr.; Shaik, S. J. Am. Chem. Soc. 2006, 128, 8950. (16) Said, B. R.; Hussein, K.; Tangour, B.; Sabo-Etienne, S.; Barthelat, J.-C. J. Organomet. Chem. 2003, 673, 56. (17) Quinonero, D.; Morokuma, K.; Musaev, D. G. J. Am. Chem. Soc. 2005, 127, 6548. (18) Quinonero, D.; Musaev, D. G.; Morokuma, K. Inorg. Chem. 2003, 42, 8449. (19) Macgregor, S. A.; Eisenstein, O.; Whittlesey, M. K.; Perutz, R. N. J. Chem. Soc., Dalton Trans. 1998, 291. (20) Paulat, F.; Kuschel, T.; Nather, C.; Praneeth, V. K. K.; Sander, O.; Lehnert, N. Inorg. Chem. 2004, 43, 6979. (21) Figgis, B. N.; Gerloch, M.; Mason, R. Proc. R. Soc. London, Sec. A 1969, 309, 91. (22) Stabnikov, P. A.; Pervukhina, N. V.; Baidina, I. A.; Sheludyakova, L. A.; Borisov, S. V. J. Struct. Chem. 2007, 48, 186. (23) Chao, G. K.-J.; Sime, R. L.; Sime, R. J. Acta. Crystallogr., Sect. B 1973, 29, 2845. (24) Iron(III) Chloride Hexahydrate; MSDS No. 236489; SigmaAldrich: St. Louis, MO, March 12, 2010. (25) Sodium Acetate; MSDS No. S2889; Sigma-Aldrich: St. Louis, MO, August 2, 2010. (26) Acetylacetone; MSDS No. P7754; Sigma-Aldrich: St. Louis, MO, March 14, 2010. 1326

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(27) Methanol; MSDS No. 322415; Sigma-Aldrich: St. Louis, MO, March 12, 2010. (28) Iron(III) Acetylacetonate; MSDS No. 517003; Sigma-Aldrich: St. Louis, MO, March 4, 2011. (29) Ruthenium(III) Acetylacetonate; MSDS No. 2282766; SigmaAldrich: St. Louis, MO, February 27, 2010. (30) Potassium Hexacyanoferrate(III); MSDS No. 244023; SigmaAldrich: St. Louis, MO, February 26, 2010.

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