Investigations of NMR Chemical Shifts Using DFT-B3LYP-GIAO

Chapter 5

Investigations of NMR Chemical Shifts Using DFT-B3LYP-GIAO Calculations Downloaded by CORNELL UNIV on October 30, 2016 | http://pubs.acs.org Publication Date (Web): September 15, 2016 | doi: 10.1021/bk-2016-1225.ch005

Arlie C. Bagley, Ibrahim AbuNada, Jun Yin, and Thomas C. DeVore* Department of Chemistry and Biochemistry, James Madison University, Harrisonburg, Virginia 22807, United States *E-mail: [email protected]

The dramatic increase in the computing power of computers coupled with rapid advances in relatively low cost software has made it possible to include sophisticated calculations in the undergraduate curriculum. Coupling these calculations with experimental measurements provides insights about a system that cannot be obtained from experimental measurements alone. Since there are no limitations caused the potential hazards or the expense of the chemicals and no instruments needed to make the measurements, calculations can be performed for any system. Examples where DFT-B3LYP-GIAO calculations were used to enhance student knowledge at JMU are presented. These calculations show how electron density and electronegativity of neighboring groups influence the chemical shift observed for the molecule. A project investigating the calculations is also presented.

© 2016 American Chemical Society Soulsby et al.; NMR Spectroscopy in the Undergraduate Curriculum: Upper-Level Courses and Across the Curriculum Volume 3 ... ACS Symposium Series; American Chemical Society: Washington, DC, 2016.

Downloaded by CORNELL UNIV on October 30, 2016 | http://pubs.acs.org Publication Date (Web): September 15, 2016 | doi: 10.1021/bk-2016-1225.ch005

Introduction An easy way to obtain the 1H NMR spectrum of small gaseous molecules in air, and some laboratory exercises using this technique to make measurements in the physical chemistry laboratory, were presented in the first volume of this series (1). The significant downfield chemical shift observed for the vapor molecules caused by the paramagnetic O2 in the atmosphere was used as the basis of a laboratory exercise to determine the magnetic susceptibility and magnetic moment for the O2 molecule and presented in the second volume (2). DFT-B3LYP-GIAO calculations were introduced as an integral part of this experiment. These calculations were also used in the procedures to determine the enthalpy of dimerization for methanol and to determine the methanol-solvent binding enthalpies in dilute solutions presented in this volume (2). Although all of the examples presented used methanol as the test molecule, other alcohols, hydrocarbons, or ketones have also been used in these exercises. The rapid development of computer technology has led to more powerful personal computers that do quantum mechanical calculations using sophisticated software packages like Gaussian 03 or Gaussian 09. The basic programs are easily learned and can generate research level results making them a valuable addition to the students’ toolkits. While more knowledge is always desirable, it is not necessary for either the students or the instructor to be experts in quantum calculations to extract useful information from this software. Since it is assumed that most instructors who adopt these exercises will have little desire to tweak the software, only exercises that use the standard software are presented. All exercises presented used the popular DFT-B3LYP-GIAO method. A textbook discussion of the advantages and limitations of this method can be found in Levin (3). Several basis sets are available in Gaussian 03. It is generally established that the 6-31G** is the minimal basis set needed to obtain reasonable results. The DFT-B3LYP-GIAO is the 6-311+G(2d.p) is a convenient basis set since calculations for TMS are included in the software. This makes it easy to determine the chemical shifts relative to TMS. The easiest way to add theoretical calculations into the laboratory exercise is to add them to an existing exercise. While the calculations are not needed to complete the exercise, students can be introduced to the calculations and calculate something related to the original exercise. The results of the calculations offer insights that allow the students to “discover” additional information that is not obvious from the experimental measurements. It is also a good way to explore the strengths and weaknesses of the calculations since the results can be compared to the experimental measurements. For example, by comparing the results of calculations using different basis sets, the students quickly realize that not all methods are created equal. The method chosen is always a trade-off between the accuracy obtained verses the time needed to complete the calculation. The calculations can also be integrated into the procedure to provide additional information needed to complete the exercise. The exercises presented in Reference (2) are examples that use this approach. The third possibility is to have the calculation be the exercise. There are several experiments that cannot be done in the lab due to lack of instrumentation, safety issues, or other difficulties. These 68 Soulsby et al.; NMR Spectroscopy in the Undergraduate Curriculum: Upper-Level Courses and Across the Curriculum Volume 3 ... ACS Symposium Series; American Chemical Society: Washington, DC, 2016.

experiments can be done in-silico and the results used to generate more complete data sets. These computer based exercises can also be used as problem sets for the lecture portion of the course.


Experimental Section The procedure used to obtain NMR spectra of neat liquids, vapor species, or dilute solutions has been described in detail previously (1, 2). Briefly, a double tube is used for liquid or vapor phase samples. D2O is placed in the inner tube and used as the lock solvent. The HDO that is always present in the D2O is used as a secondary standard to determine the chemical shift. The liquid sample is placed in the outer tube. Emptying the outer tube leaves enough liquid in it to obtain the vapor spectrum. Solutions are made by using a microliter syringe to add 1 μl increments of the sample to 1 ml of the deuterated solvent. Since the signal strength of the most dilute samples is comparable to the intensity observed for the impurities in the solvent, it is advisable to obtain the spectrum of the solvent before adding the sample. The deuterated solvent serves as the lock solvent in these experiments. A Bruker Spectrospin Advance DRX-400 NMR equipped with a variable temperature 5 mm broadband auto tune probe with a Z gradient or a 300 MHz Bruker DPX equipped with a 5 mm variable temperature probe are used for these exercises. Most spectra are obtained using 8 scans, with a receiver gain of 1300 and a spectral width set between 15 ppm - 30 ppm. Probe temperatures between 295 and 330 K are used for the vapor samples since heating the sample causes the intensity of the vapor peak to increase relative to the intensity of the liquid peak. NMR spectra of dilute solutions are usually obtained with the temperature set at 295 K. Theoretical calculations are done using the DFT-B3LYP-GIAO method with the Gaussian 03 PC software package. There are newer approaches, such as DFT-O3LYP available in Gaussian 09, that are reported to give more accurate results (4), but we have not used them with students. While calculations performed using the 6-31+G(d,p) basis set are adequate for student use, larger basis sets such as the 6-311+G(2d,p) or even the very large 6-311++G(3df,3pd) basis sets that are used for research (4–10) have also been done for small molecules. Even with the larger basis sets, many of the exercises presented require much less than three hours allotted to a standard laboratory session. In all cases, the structure is initially optimized and the vibrational frequencies are determined to establish that the optimized structure is at least a local minimum. After the structures are optimized, the shielding constants are determined using the GIAO method and the chemical shifts are determined by subtracting the value of the screening constant (σ) calculated from the value of the screening constant calculated for TMS using the same level of theory. This calculation is done by the software for the 6-311+G(2d,p) basis set.

69 Soulsby et al.; NMR Spectroscopy in the Undergraduate Curriculum: Upper-Level Courses and Across the Curriculum Volume 3 ... ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


Investigating the Calculations Many papers comparing the various methods for calculating accurate chemical shifts have been published (4–10). Many of these investigations used sophisticated methods to determine the values of the chemical shifts as accurately as possible. Jain et al have pointed out that this discourages NMR practitioners from using these techniques since these high level calculations are not practical for large molecules (5). They have shown that less accurate methods can still be used to make reasonable predictions about the NMR spectrum by scaling the results. They conclude that it would be advantageous for students to learn about these methods so that they could apply them to aid in the interpretation of NMR spectra. Since the WP04 functional they recommend requires changing the software, it is likely many instructors would be hesitant to try to use it in a teaching laboratory. Procedures such as the GIAO/B3LYP/6-311++G** method recommended by Rablen et al (6) that can be used with no modifications are more likely to be used. While this is probably still too large of a basis set for large molecules, the smaller 6-31+G(d,p) may also gave reasonable results for large molecules when scaled (7). The purpose of this chapter is to illustrate where calculations using unmodified software can be done and the type of information that can be obtained from them. While the examples are from the physical chemistry labs at JMU, it is likely that the calculations could also be used in organic chemistry where students are first learning about NMR spectroscopy. A simple example of integrating calculations with measurements is provided by the spectroscopic investigation of benzene. The main object of this experiment is to measure the infrared and Raman spectra of benzene and DFT-B3LYP calculations are used to help assign the observed bands. The calculations clearly establish that no IR mode is Raman active, no Raman active mode is IR active (the Mutual Exclusion Rule) and some modes are neither IR nor Raman active. 1H NMR spectra of benzene liquid and vapor are used to confirm that the molecule has the expected D6h symmetry. The GIAO calculations are added to introduce students to these calculations. The NMR analysis for liquid benzene gives one peak in the 13C NMR spectrum (128 ppm) and one peak in the 1H NMR spectrum (7.28 ppm). As shown in Figure 1, the proton signal shifts to ~10.2 ppm in the vapor sample. The 1H and 13C NMR chemical shifts calculated using three basis sets are presented in Table 1. There are three “discoveries” that students learn from this exercise. The first is that the calculated chemical shift is consistent with the value observed for the liquid, but not the vapor. This lack of agreement is caused by the paramagnetic oxygen mixed with the vapor as discussed previously (2). The second is that each calculation predicts two (2) peaks in both the 13C and 1H NMR spectra. This is probably an artifact of these calculations, caused by a slightly different value for the electron density for C1 and C4 carbons relative to the others in the ring. This is a demonstration that the electron density influences the chemical shift. Reminding students of resonance illustrates why only one peak would be expected even if this result were real. This is also an opening to point out that NMR is a relatively slow technique and only one signal will be observed even when multiple species are present such as with the methanol monomer-dimer 70 Soulsby et al.; NMR Spectroscopy in the Undergraduate Curriculum: Upper-Level Courses and Across the Curriculum Volume 3 ... ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


equilibrium if there is a pathway to make the protons equivalent on the NMR time scale (2). The final observation is that none of these calculations gives exact agreement with the experimental measurements for either the bond lengths or the chemical shifts. While adding terms to the basis set improves the energy, it does not give significantly better results for the chemical shifts.

Figure 1. 1H NMR spectra of benzene liquid and vapor in a double tube with D2O as the lock solvent. The experimental conditions and the assignments are given.

Table 1. Comparison of Molecular Parameters Determined for Benzene Using the A = 6-31+G(d,p), B = 6-311+G(2d,p) and 6-311++G(3df,3pd) Basis Sets. The number of equivalent atoms are given by (#) in the table. Parameter

A

B

C

Lita

RC-C (pm)

139.84

139.14

139.10

139.14

RC-H (pm)

108.62

108.36

108.19

108.02

δC (ppm)

124.72(2)

132.54(2)

133.64(2)

130.9

124.62(4)

132.35(4)

133.49(4)

7.50(2)

7.588(2)

7.622(2)

7.49(4)

7.566(4)

7.618(4)

δH (ppm)

a

7.236

From Ref (8).



Investigating the Effect of Configurations An example of the effect of multiple configurations on the 1H NMR spectrum is provided by calculations for acetone done as part of the classic bromination of a ketone kinetics experiment. As shown in Figure 2, there are three reasonable symmetric structures possible for acetone; structure A - a C2V structure with one hydrogen aligned with the oxygen, structure B - a C2V structure with one hydrogen oriented 180° from the oxygen, and structure C – a hybrid structure with one methyl group in each orientation. Optimization with any of the tested basis sets produced an optimized structure for each orientation with relative energies [6311+G(2d,p)] of A = 0.00 kJ, B = 8.19 kJ/mol and C = 2.42 kJ/mol. The first discovery is that intramolecular hydrogen bonding stabilizes the configuration. The chemical shifts calculated for acetone are compared to those measured for the vapor in Table 2.

Figure 2. The configurations for acetone used in Table 1. Structures A and B are C2V structures with a CH3 H atom pointed toward and away from the O atom respectively. Structure C is a combination of the A and B. The final structure is the actual minimum structure. Hydrogen atoms oriented toward the oxygen have different chemical shifts than the ones oriented away from the oxygen confirming that neighboring atoms influence the observed values. Since hindered rotation around each C-C bond is expected, the observed signal would be a weighted average of the shifts observed for each configuration. The relative contribution of each is determined by its Boltzmann population. The second discovery is that each of these structures has a calculated imaginary frequency indicating that none is a minimum of the potential energy curve. Pretty structures are not always correct structures. The minimum 72

Soulsby et al.; NMR Spectroscopy in the Undergraduate Curriculum: Upper-Level Courses and Across the Curriculum Volume 3 ... ACS Symposium Series; American Chemical Society: Washington, DC, 2016.

structure is a slightly twisted version of structure A lying 14.8 kJ/mol lower in energy than structure A. This structure has three proton orientations producing three unique 1H NMR chemical shifts. The observed 1H NMR spectrum is the average of these.


Table 2. Comparison of Measured Chemical Shifts for Acetone to Those Calculated Using the 6-311+G(2d,p) Basis Set for Structures A, B, C and the Minimum Structure Method

1H

13CO

13CH3

Vapor

2.1a

205.6b

34.5b

A

1.82(2)

210.27

30.08

212.55

29.77

211.13

33.60

2.13(4) B

1.97(2) 2.23(4)

C

1.82(3)

26.72

2.12(1) 2.23(2) Minimum

1.81(2)

210.29

30.11

2.08(2) 2.17(2) a

Corrected measurements from JMU.

b

From Ref (8).

Scaling the Calculations Jain et al have recommended using a calibration curve to scale the results of calculations with small basis sets to correct the systematic errors in the calculations (4). By scaling the vapor phase calculations to the chemical shifts measured in a particular solvent, it may also be possible to account for the effect of the solvent without increasing the complexity of the calculations (5). The experimental chemical shifts can either be measured in the lab or taken from the literature. This exercise is usually done by having each student be responsible for two molecules and pooling the data. A graphical comparison of the calculated 1H NMR chemical shifts [6-311+ G(2d,p) level] for 30 compounds are compared to the chemical shifts in CDCl3 reported by Fulmer et al (11) in Figure 3. A similar plot comparing the calculated and observed 13C NMR chemical shifts is given in Figure 4. The compounds selected include ten saturated, unsaturated and aromatic hydrocarbons, five alcohol compounds, three carbonyl compounds, three ether compounds, three chlorocarbons, two nitrogen containing compounds, and some small molecules such as CO2 and CS2. Consistent with the results reported by Jain et al. (5), a good linear correlation was obtained 73



for both types of chemical shifts. Only the 13C NMR chemical shifts calculated for CH2Cl2, CHCl3, and CCl4 deviate significantly from the least squares lines. The first discovery is that the scatter in the data around the least squares line indicates random errors in the data. Possible sources of this scatter are errors in the calculations caused by not using a complete basis set, errors caused by only calculating one configuration, and errors in the literature values. Students almost never consider this latter possibility. Since the slope is not 1 and the origin is not (0,0), there are also systematic errors in the calculations that are a function of the magnitude of the chemical shift. This can also be seen from the least squares fit to the differences between the calculated and measured frequencies as shown in Figures 3 and 4. Using the slope as a scaling factor largely eliminates most of this error. Students do not get much experience with correcting systematic errors and this is an easy case where it can be done.

Figure 3. A comparison of the observed 1H NMR chemical shifts in CDCl3 (A) and the difference (calculated – observed) (B) compared to the calculated value for 30 small organic molecules.

After scaling, there is still a small systematic error in the origin. The most likely cause is that the calculated chemical shift for TMS has a systematic error. Plotting the calculated chemical shift verses the measured gas phase values reported for alcohols by Chavel and True (12) and for the hydrocarbons by Zuschneid et al (7) and by Ebrahimi et al (8) confirms that this is likely the case, but some of this error could also result from comparing isolated molecule calculations to values measured in solution. This is also a reasonable place to introduce solvent induced chemical shifts (13, 14).



Figure 4. A comparison of the observed 13C NMR chemical shifts in CDCl3 (A), the chlorocarbons (B), and the difference (calculated – observed) (C) compared to the calculated value for 30 small organic molecules.

Further Insights The calculated chemical shifts only examine the intramolecular effects. Factors influencing the intramolecular contribution to the chemical shift are the electron density, the anisotropy of the induced magnetic field, and the electronegativity of the neighboring groups (12–14). Unfortunately, the Mulliken populations that are computed by the software do not correlate well with the chemical shifts (4, 10). Either the electrostatic potential using the grid based method (CHELPG) or the natural bond order (NBO) partial charges are reported to give better results for 13C NMR chemical shifts (4, 10). Since neither has been tried with students and modifications to the software are needed to calculate them, they will not be discussed further here. The chemical shifts calculated for ethane and ethene provide a clear example of anisotropy. The calculated 1H NMR chemical shift for ethane is 0.867 ppm while it is 5.65 ppm for ethene. Anisotropy is caused by the movement of electrons in a multiple bond when placed in a magnetic field. In an alkene, the electrons rotate parallel to the magnetic field producing an induced magnetic field that is oriented parallel to the applied field producing a significant downfield shift. There is also a shift caused by the electronegativity of the neighboring atom (14). While there are published experiments that use halide substituted molecules to show this effect (15), B3LYP-GIAO calculations can also be used to illustrate this. 1H NMR chemical shifts were obtained using the 6-311+G(2d,p) basis set for CH3Z for Z = F, OH, NH2, Cl and Br and plotted against the Pauling electronegativities for Z given in Levine (3). The results are presented in Figure 5. The 1H NMR chemical shift values are multiplied by 5 to allow the trend to be observed on the 13C NMR chemical shift scale. A linear relationship is obtained for both 1H and 13C NMR shifts. 75



Figure 5. Calculated 1H and 13C NMR chemical shifts as a function of the Pauling Electronegativity for CH3Z (Z = F, OH, NH2, Cl and Br). The 1H shift values are multiplied by 5 to show the trend.

Conclusions Several exercises using DFT-B3LYP-GIAO calculations to investigate 1H and 13C NMR chemical shifts are presented. These calculations permit the investigation of the effect of the electronic structure on the NMR spectrum that is not easily measured using resources available in a typical chemistry department. There are clearly some errors in the calculations. Having students investigate these errors provides insight into systematic errors. By scaling the calculations, students learn how to account for these errors to produce better values that could be used as part of other experiments such as the well- known keto-enol equilibrium of 2,4-pentanedione experiment.

Acknowledgments We gratefully acknowledge the Research Corporation Departmental Development Grant #7957, NSF-REU-CHE-1062629, NSF-REU-CHE-1461175 and the JMU Department of Chemistry and Biochemistry for supporting this research.

References 1.

2.

Drahus, C.; Gallaher, T. N.; DeVore, T. C. Gas Phase 1H NMR. In Modern NMR Spectroscopy in Education; Rovnyak, D.; Stockland, R.,Jr., Eds.; ACS Symposium Series 969; American Chemical Society: Washington, DC, 2007; pp 143−154. Bagley, A. C.; White, C. C.; Mihay, M.; DeVore,T. C. Physical Chemistry Laboratory Projects Using NMR and DFT-B3LYP Calculations. In NMR 76


3. 4.

5.


6.

7.

8.

9.

10.

11.

12. 13. 14. 15.

Spectroscopy in the Undergraduate Curriculum; Soulsby, D., Anna, L. J., Wallner, A. S., Eds.; ACS Symposium Series 1128; American Chemical Society: Washington, DC, 2013; pp 229−243. Levine, I. N. Physical Chemistry, 6th ed.; McGraw-Hill: Boston, 2007; pp 711−717. Liu, Y.; Junk, T.; Liu, Y.; Tzeng, N.; Perkins, R. Benchmarking quantum mechanical calculations with experimental NMR chemical shifts of 2-HADNT. J. Molec. Structure 2015, 1086, 43–48. Jain, R.; Bally, T.; Rablen, P. R. Calculating accurate proton chemical shifts of organic molecules with density functional methods and modest basis sets. J. Org. Chem. 2009, 74, 4017–4023. Rablen, P. R.; Pearlman, S. A.; Finkbiner, J. A comparison of density functional methods for the estimation of proton chemical shifts with chemical accuracy. J. Phys. Chem. A 1999, 103, 7357–7363. Zuschneid, T; Fischer, H.; Handel, T.; Albert, K.; Hafelinger, G. Experimental gas phase 1H NMR spectra and basis set dependence of ab-initio GIAO MO calculations of 1H and 13C NMR absolute shieldings and chemical shifts of small hydrocarbons. Z. Naturforsch. 2004, 59b, 1153–1176. Ebrahimi, H. P.; Shaghaghi, H.; Tafazzoli, M. Gauge invariant atomic orbital – density functional theory prediction of accurate gas phase 1H and 13C NMR chemical shifts. Concepts Magn. Reson., Part A 2011, 38A, 269–279. Aure, A. A.; Gaus, J.; Stanton, J. F. Quantitative prediction of gas-phase 13C nuclear magnetic shielding constants. J. Chem. Phys. 2003, 118, 10407–10417. Katritzky, A. R.; Akhmedov, N. G.; Doskocz, J.; Mohapatra, P. P.; Hall, C. D.; Guven, A. NMR spectra, GIAO and charge density calculations of fivemembered aromatic heterocycles. Magn. Reson. Chem. 2007, 45, 532–543. Fulmer, G. R.; Miller, A. J. M.; Sherden, N. H.; Gottlib, H. E.; Nudelman, A.; Stoltz, B. M.; Bercaw, J. E.; Goldberg, K. I. NMR chemical shifts of trace impurities: Common laboratory solvents, organics, and gases in deuterated solvents relevant to the organometallic chemist. Organometallics 2010, 29, 2176–2179. Chauvel, J. R.; J., P.; True, N. S. Gas-phase NMR studies of alcohols. Intrinsic acidities. Chem. Phys. 1985, 95, 435–441. Atkins, P.; dePaula, J. Physical Chemistry, 9th ed.; Freeman: New York, 2010; pp 526−531. Carey, F. A. Organic Chemistry, 7th ed.; McGraw-Hill: Boston, 2008; pp 518−550. Boggess, R. K. An improved experiment to illustrate the effect of electronegativity on the chemical shift. J. Chem. Educ. 1988, 65, 819–820.


Investigations of NMR Chemical Shifts Using DFT-B3LYP-GIAO

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