In the Classroom
Identifying the Isomers of Octahedral Complexes with 119Sn and 207Pb NMR Spectroscopy: A Computational Exercise Craig M. Davis Department of Chemistry, Xavier University, Cincinnati, Ohio 45207-4221, United States
[email protected] In this computational exercise, the 119Sn and 207Pb NMR spectra (data provided to the students) of the octahedral complexes [SnClnF6-n]2- and [PbClnF6-n]2-, respectively, are examined. The pairwise-additivity model is applied to the NMR spectra of the complexes [MClnF6-n]2- (n = 0, 1, 5, 6) to obtain the Cl-Cl, Cl-F, and F-F pairwise-additivity parameters for each set of complexes; these parameters then are employed to predict the appropriate chemical shift for each pair of isomers of the complexes [MClnF6-n]2- (n = 2, 3, 4). By comparing the chemical shifts predicted by the pairwise-additivity model with the experimental values, the students are able to identify the one isomer of each pair that either is the only one that exists in solution or is the more abundant isomer. Molecular modeling (semiempirical PM3) is employed to see which geometric isomer of each pair is more stable. This computational exercise is designed to be used as a supplement to our experimental exercise (1), which uses the pairwise-additivity model to study the 27Al NMR spectra of the tetrahedral tetrahaloaluminate anions. In the experimental exercise, the spectra of the homoleptic complexes [AlX4]- and the dihalide anions [AlX4Y4-n]- (X, Y = Cl, Br, or I) are acquired, then the pairwise-additivity parameters are used to predict the chemical shifts of the trihalide anions [AlClmBrnI4-m-n]-. Alternatively, the exercise presented here could be combined with a second computational exercise to fill a 3-h laboratory session or be used as a homework assignment in an inorganic lecture course when studying multinuclear NMR spectroscopy. Pairwise-Additivity Model The pairwise-additivity model (PAM) for NMR spectroscopy was developed for tetrahedral complexes by Vladimiroff and Malinowski (2) and extended to octahedral complexes by Kidd and Spinney (3). PAM recognizes that each substituent on the central atom changes the wave function of each of its neighboring substituents. Parameters are determined for each type of adjacent pair (Cl-Cl, Cl-F, etc.), and the chemical shift of the central atom can be calculated by summing the parameters for all nearest-neighbor pairs: six for a tetrahedron, 12 for an octahedron. Kidd and Spinney demonstrated that PAM allows the unambiguous identification of specific geometric isomers of the hexahaloniobate anions, [NbBrnCl6-n]- (3). Because the anions [NbBr2Cl4]-, [NbBr3Cl3]-, and [NbBr4Cl2]- each have two geometric isomers, a 93Nb NMR spectrum of the [NbBrnCl6-n]- system could display a total of up to 10 lines; 306
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Table 1. Heats of Formation of [SnClnF6-n]2- Complexes Complex
ΔfH/(kJ/mol)
Complex
ΔfH/(kJ/mol)
cis-[SnCl2F4]2-
-1463.298
trans-[SnCl2F4]2-
-1457.207
fac-[SnCl3F3]2-
-1377.988
mer-[SnCl3F3]2-
-1371.703
cis-[SnCl4F2]
2-
-1283.376
trans-[SnCl4F2]
2-
-1273.179
Table 2. Heats of Formation of [PbClnF6-n]2- Complexes Complex
ΔfH/(kJ/mol)
Complex
ΔfH/(kJ/mol)
cis-[PbCl2F4]2-
-1066.922
trans-[PbCl2F4]2-
-1056.780
fac-[PbCl3F3]2-
-1009.638
mer-[PbCl3F3]2-
cis-[PbCl4F2]
2-
Table 3.
119
-936.597
trans-[PbCl4F2]
2-
[SnCl6]2-733.0
[SnCl5F]2-698.4
[SnClF5]2-750.4
Complex
[SnCl4F2]2-
[SnCl3F3]2-
[SnCl2F4]2-
b
δ (ppm)
-919.372
Sn NMR Data for Octahedral Tin Complexes
Complex δ (ppm)a a
-996.671
-685.5
b
-697.0
[SnF6]2-810.8
-716.8b
a
Shifts are relative to Sn(CH3)4 in CDCl3. Data from ref 4. b Only isomer observed.
however, only seven lines are observed. They used PAM to predict the chemical shifts for the two isomers of each of the above three anions and observed that only one resonance of each pair was present. These isomers proved to be those with the same halide in adjacent positions (3).1 Predicting Chemical Shifts The extraction and application of the pairwise-additivity parameters is demonstrated using the [NbBrnCl6-n]- anions (3). The [NbBr6]- anion has 12 Br-Br interactions; its 93 Nb NMR chemical shift is -731 ppm, so each Br-Br pairwise parameter is -60.9 ppm. Chemical shifts in 93Nb NMR spectrometry are relative to the [NbCl6]- anion, so its 93 Nb NMR chemical shift (and each Cl-Cl pairwise parameter) is 0 ppm. The Br-Cl pairwise parameter is calculated from both [NbBr5Cl]- and [NbBrCl5]-, and the two values are averaged. The [NbBr5Cl]- anion (with eight Br-Br and four Br-Cl pairwise interactions) has a chemical shift of -621 ppm; because each Br-Br pairwise parameter is -60.9 ppm, each Br-Cl pairwise parameter must be -33.4 ppm. The [NbBrCl5]- anion (eight Cl-Cl and four Br-Cl interactions) has a chemical shift of -132 ppm; because each
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In the Classroom
Cl-Cl pairwise parameter is 0 ppm, each Br-Cl pairwise parameter must be -33.0 ppm, giving an average value of -33.2 ppm. The [NbBr4Cl2]- anion can exist as either cis or trans isomers. The cis isomer has one Cl-Cl, five Br-Br, and six Br-Cl interactions; thus, its calculated chemical shift is (0 ppm) þ 5(-60.9 ppm) þ 6(-33.2 ppm) = -504 ppm. The trans isomer has four Br-Br and eight Br-Cl interactions; hence, 4(-60.9 ppm) þ 8(-33.2 ppm) = -509 ppm. The observed 93Nb NMR spectrum shows only one resonance at -501 ppm, so, it is concluded that only the cis isomer is present. Table 4.
207
Pb NMR Data for Octahedral Lead Complexes
Complex δ (ppm)a
[PbCl6]2-2305.8
[PbCl5F]2-2118.1
[PbClF5]2-1902.3
Complex
[PbCl4F2]2-
[PbCl3F3]2-
[PbCl2F4]2-
-1945.6, -1973.7b
-1881.2, -1920.3b
-1843.6, -1887.6b
a
δ (ppm)
[PbF6]2-1982.1
a Shifts are relative to Pb(CH3)4 in CDCl3. Data from ref 5. abundant isomer.
b
More
Table 5. Pairwise-Additivity Parameters Extracted from [SnClnF6-n]2Anions Bond
Parameter (ppm)
Cl-Cl
-61.08
Cl-F
-52.44a, -52.46b
F-F
-67.57
a
Data from [SnCl5F]2-. b Data from [SnClF5]2-.
Table 6. Pairwise-Additivity Parameters Extracted from [PbClnF6-n]2Anions Bond
Parameter (ppm)
Cl-Cl
-193.8
Cl-F
-145.1a, -145.2b -164.9
F-F a
Data from [PbCl5F]
2- b
. Data from [PbClF5]
2-
.
The Exercise Part 1: Molecular Modeling (Performed by Students) The first task for the students is to calculate the heat of formation for all complexes to be studied: the cis and trans isomers of [SnClnF6-n]2- and [PbClnF6-n]2- (n = 2, 4) and the fac and mer isomers of [SnCl3F3]2- and [PbCl3F3]2-. Working with SPARTAN 0 08 at the semiempirical PM3 level, the calculations take only several seconds for each structure.2 Results are given in Tables 1 and 2. Part 2: Experimental NMR Data (Provided to Students) The students are given the NMR data in Tables 3 and 4. Applying PAM to the first row of data in Tables 3 and 4 enables the students to obtain the Cl-Cl, Cl-F, and F-F pairwise-additivity parameters for each set of complexes. Next, the parameters are used to predict the appropriate chemical shift for each pair of isomers of the complexes [SnClnF6-n]2- and [PbClnF6-n]2- (n = 2, 3, 4). Results and Discussion Pairwise-Addivity Calculations The pairwise-additivity parameters extracted for each system are given in Tables 5 and 6, and the observed and predicted and chemical shifts are given in Tables 7 and 8. Analysis The objective is for the students to identify the one isomer of each pair that either is the only one that exists in solution or is the more abundant isomer. Students compare the chemical shifts predicted by the pairwise-additivity model with the experimental values. Consider the [SnCl4F2]2- anion. The observed 119Sn NMR spectrum shows one resonance at -685.5 ppm, whereas the calculated chemical shifts for the cis and trans isomers are -687.7 ppm and -663.9 ppm, respectively. Thus, it is determined that only the cis isomer is present, because the predicted chemical shift for this isomer is closer to the observed chemical shift. Molecular modeling indeed predicts the cis isomer to be more stable than the trans isomer (-1283.376 kJ/mol versus -1273.179 kJ/mol, respectively). For both series of complexes, the more stable isomer proves to be either the only isomer observed in solution or the more abundant isomer.
Table 7. Observed and Predicted Chemical Shifts for [SnClnF6-n]2- Anions Observed δ (ppm)
Predicted δ (ppm)
Complex
Observed δ (ppm)
Predicted δ (ppm)
cis-[SnCl2F4]2-
-716.8a
-713.6
trans-[SnCl2F4]2-
(no)
-689.9
2-
a
-697.0
-700.6
mer-[SnCl3F3]2-
(no)
-676.9
-685.5a
-687.7
trans-[SnCl4F2]2-
(no)
-663.9
Complex
fac-[SnCl3F3]
cis-[SnCl4F2]2a
Only isomer observed.
Table 8. Observed and Predicted Chemical Shifts for [PbClnF6-n]2- Anions Observed δ (ppm)
Predicted δ (ppm)
Complex
Observed δ (ppm)
Predicted δ (ppm)
cis-[PbCl2F4]2-
-1887.6a
-1889.4
trans-[PbCl2F4]2-
-1843.6
-1822.4
2-
a
-1920.3
-1943.4
mer-[PbCl3F3]2-
-1881.2
-1876.4
-1973.7a
-1997.4
trans-[PbCl4F2]2-
-1945.6
-1930.4
Complex
fac-[PbCl3F3]
cis-[PbCl4F2]2a
More abundant observed.
r 2010 American Chemical Society and Division of Chemical Education, Inc.
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In the Classroom
Notes 1. The niobium complexes are not investigated in this exercise because SPARTAN 0 08 did not have parameters for a niobium atom. 2. SPARTAN 0 08 is a licensed product of Wave function, Inc. (Irvine, CA).
2. Vladimiroff, T.; Malinowski, E. R. J. Chem. Phys. 1967, 46, 1830– 1841. 3. Kidd, R. G.; Spinney, H. G. Inorg. Chem. 1973, 12, 1967–1971. 4. Dillon, K. B.; Marshall, A. J. Chem. Soc., Dalton Trans. 1984, 1245– 1247. 5. Hutchinson, D.; Sanders, J. C. P.; Schrobilgen, G. J. Eur. J. Solid State Inorg. Chem. 1996, 33, 795–807.
Literature Cited
Supporting Information Available
1. Davis, C. M.; Dixon, B. M. J. Chem. Educ. 2011, 88, DOI: 10.1021/ ed100655x.
Student handout. This material is available via the Internet at http://pubs.acs.org.
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