Computation of Chemical Shifts for Paramagnetic Molecules: A

Laboratory Experiment pubs.acs.org/jchemeduc

Computation of Chemical Shifts for Paramagnetic Molecules: A Laboratory Experiment for the Undergraduate Curriculum Benjamin P. Pritchard, Scott Simpson, Eva Zurek,* and Jochen Autschbach* Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, Unites States S Supporting Information *

ABSTRACT: A computational experiment investigating the 1H and 13C nuclear magnetic resonance (NMR) chemical shifts of molecules with unpaired electrons has been developed and implemented. This experiment is appropriate for an upper-level undergraduate laboratory course in computational, physical, or inorganic chemistry. The chemical shift range for paramagnetic systems differs substantially from the well-known range of diamagnetic compounds. Students carried out density functional theory calculations of the chemical shifts of an organic radical and a related closed-shell system. This simple exercise illustrated that a single unpaired electron may result in dramatically different chemical shifts. Organometallic systems were also considered. The chemical shifts of the closed shell molecule ferrocene were compared to those of vanadocene and nickelocene, which afford three and two unpaired electrons, respectively. A natural bonding orbital (NBO) analysis was employed to study the electronic structure of NiCp2. KEYWORDS: Upper-Division Undergraduate, Inorganic Chemistry, Laboratory Instruction, Physical Chemistry, Computer-Based Learning, Computational Chemistry, Molecular Modeling, Molecular Properties/Structure, NMR Spectroscopy, Quantum Chemistry

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n a typical college undergraduate chemistry curriculum, the discussion of NMR spectroscopy, taught in second year organic chemistry, is restricted to diamagnetic compounds, that is, molecules without unpaired electrons. In organic chemistry, this restriction can be justified to some extent because organic radicals tend to be unstable. A counter-example is the relatively stable organic radical 2-methylphenyl-t-butylnitroxide (mpbn) for which experimental proton chemical shifts range from +60 to −55 ppm depending on their relative location to the NO group.1 This chemical shift range is far more extended than the proton shift range of diamagnetic organic compounds. Moreover, the signs of the shifts are not intuitive to interpret without some theoretical calculations. The NMR for molecules with unpaired electrons, which is often abbreviated as pNMR (for paramagnetic NMR) in the literature, can be very peculiar. An example from organometallic chemistry are the “sandwich” complexes MCp2, where Cp is cyclopentadienyl (C5H5−) or a derivative thereof, and M is a metal ion. The most famous of these sandwich complexes is ferrocene, FeCp2. Its discovery triggered intense research on metallocenes, leading to the Nobel Prize in Chemistry being awarded to Fischer and Wilkinson in 1973. The general structure of a metallocene complex is shown in Figure 1. For diamagnetic ferrocene, the 13 C and proton chemical shifts of the Cp ligands are 68 ppm for 13 C and 4 ppm for 1H.2−4 Even though the presence of the Fe2+ ion renders these values noticeably different from those of benzene or cyclopentadienyl (with 13C shifts around 130 and 100 ppm and proton shifts around 7 and 6 ppm,5 respectively), the ferrocene values are well within the ordinary carbon and © XXXX American Chemical Society and Division of Chemical Education, Inc.

Figure 1. Structure of a metallocene “sandwich” complex. Different relative orientations of the cyclopentadienyl (Cp) ligands lead to staggered (left) vs eclipsed (right) conformers. The labels D5h and D5d are the corresponding symmetry point groups.

proton chemical shift ranges. A cousin of ferrocene is nickelocene, where the Fe2+ center is replaced by Ni2+. This ion has two additional electrons (3d8), resulting in a paramagnetic spin-triplet (↑↑) electronic ground state configuration of the complex. The pNMR shifts for nickelocene are dramatically different from ferrocene: 1514 ppm for 13C6,7 and −253 ppm for the Cp protons.8 The sign change of the chemical shift from carbon to hydrogen has been explained by the mechanism of “spin polarization”.9 The details of the sign change will not be discussed further. It is noted, however, that in organic systems such as Cp or phenyl, paramagnetic effects for carbons and protons are coupled to each other and tend to exhibit opposite signs.10 Another member of the 3d metallocene series is vanadocene, VCp2. This complex has experimental 13C and proton chemical

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dx.doi.org/10.1021/ed400902c | J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

Figure 2. Valence electron configurations for vanadocene (3d3), ferrocene (3d6), and nickelocene (3d8) are shown, along with isosurfaces for the relevant nickel 3d ↑ orbitals (see ref 22 regarding details of what these surfaces represent).

shifts of −510 and +420 ppm, respectively.11 Why do the carbon and proton chemical shifts in vanadocene and nickelocene have different signs? V2+ has a 3d3 configuration, and experiments and calculations agree that the V-containing complex has 3 unpaired electrons with a spin-quartet ground state (↑↑↑). Despite the fact that the Ni complex has one less unpaired electron, it exhibits much larger paramagnetic effects in its ligand NMR spectrumanother puzzle. In a 1957 paper,12 McConnell and Holm offered an explanation for the signs of the ligand shifts for nickelocene. However, only a year later the same authors put forward a mechanism that essentially amounts to an “inverse” of the original explanation.13 Which explanation is correct? A new computational chemistry laboratory course for third and fourth year chemistry (BA and BSc), biochemistry, as well as pharmaceutical science undergraduate students, has been introduced at our university. The course is designed to introduce these students to the broad reach of quantum chemistry. The content not only addresses the usual questions of molecular structure and energy, but a variety of spectrscopic parameters are also calculated. Most of the experiments, such as the present one, are closely related to contemporary research topics that are transferred into the undergraduate classroom. Our aim is to create an extensive library of independent computational teaching modules with applications to a variety of different topics spanning across disciplines and accessible to students with diverse backgrounds. Three of the laboratory experiments, one on carbon nanotubes,14 another dealing with the optical activity of amino acids,15 and a third regarding the molecular switch behavior of a [2]catenane,16 have recently been published. To our knowledge, a computational chemistry experiment on paramagnetic NMR has not yet been presented in this Journal. There are a number of discussions on NMR parameters, such as refs 17−20. The puzzles discussed above were sufficiently intriguing to motivate the development of a new experiment on pNMR for our third and fourth year undergraduate computational chemistry laboratory and to present it in this Journal. Because paramagnetic molecules are important in bio- and materials chemistry with applications as, for example, magnetic resonance imaging (MRI) contrast agents or molecular magnets, the experiment is appealing to students with diverse interests.

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1. pNMR spectra can be very unusual compared to the typical chemical shift ranges of diamagnetic compounds. 2. It is possible to compute pNMR shifts from first principles and gain an understanding of the relationship between the electronic structure and the shifts. 3. An analysis of the orbitals of nickelocene can give an answer to the question: “Which of McConnell’s explanations for the electronic structure of nickelocene is correct?” 4. The sign and magnitude changes of the pNMR spectrum between nickelocene and vanadocene has a rational, albeit somewhat subtle, explanation. (optional) 5. NMR chemical shifts obtained from quantum chemical calculations can be sensitive to the approximations used to render the calculations feasible, in particular for paramagnetic species. (optional)

PRACTICAL CONSIDERATIONS The theoretical background and references are provided in the accompanying document Notes for Instructors, which is part of a multi-file Supporting Information package. The computational details (software, technical settings), additional references, additional calculated data, insights on the student’s computational background, common problems encountered by the students, and solutions to these problems are also given in this document. A step-by-step guide with detailed instructions on performing the calculations can be found in the Student Handouts included in the Supporting Information. The handout doubles as a lab manual, and it also provides suitably simplified explanations of the pNMR chemical shift phenomenon that are complementary to those in the Instructor notes, as well as a set of specific Questions and Tasks to be performed. The grading rubric included in the Supporting Information refers to these questions and has been used in this form in our first installment of the experiment (year 2013). Furthermore, the Supporting Information includes examples of input and output files from the quantum chemistry program used for the experiment, and a file containing the molecular coordinates employed for the calculations. A preparatory lecture based upon the Notes for Instructors was given to the students in the class. This pre-lab lecture served to address practical matters regarding the computations, familiarize the students with the theoretical background described in their handouts, and to pique their interest in the topic of pNMR by pointing out some of the aforementioned peculiarities. During this lecture it is important to explain to the students that a spin-unrestricted molecular orbital

LEARNING GOALS

In this computational experiment, the students learn that B




(a) Geometry optimizations for an organic radical (spinunrestricted) and a related diamagnetic molecule. Exploration of the differences in their geometries. (b) Calculation of “regular” NMR shielding constants for the organic species. (c) Calculation of the hyperfine constants and g-factors for the radical. (d) Assembly of the NMR chemical shifts and comparison with experiment.

calculation for a system with unpaired electrons gives separate (and somewhat differing) α (↑) and β (↓) spin-orbitals and corresponding orbital energies. The occupation of a spin orbital can be zero or one. The orbital diagrams in Figure 2, therefore, need to be read in a way such that each horizontal black bar represents a pair of spin-orbitals. An arrow then counts the occupation of either α or β. The schematic molecular orbital energy level diagrams shown in Figure 2 correspond to those typically presented in textbooks and are based upon the results of crystal field theory, ignoring any differences in α and β orbital energies and a dependence of the orbital energies on the occupations. See ref 21 for the molecular orbital energy level diagrams obtained from hybrid density functional theory calculations. A pre-lab quiz (see the SI) followed the lecture, and preceded the hands-on portion of the experiment. In the experiment itself, molecules were initially built and visualized using the open-source molecular editor Avogadro.23 Computations were carried out using the web browser-based WebMO24 interface to the quantum chemistry package Gaussian ’09.25 The Avogadro-generated structures were imported into WebMO, optimized using a first-principles approach, and subsequently, the NMR shielding tensors, hyperfine couplings, and g-factors were computed.

Organometallic Systems

The students then study the relative stability of metallocene conformers, and their pNMR shifts. The experiment involved the following specific tasks: (a) Optimization of staggered versus eclipsed conformers of the metallocenes with V, Fe, and Ni. Determining which conformer is the most stable. (b) Calculation of “regular” NMR shielding constants (ferrocene). (c) Calculation of the hyperfine constants and g-factors for the V and Ni systems. (d) Use of the relevant equations to generate chemical shifts and pNMR shifts, and comparison with experiment. (e) Further analysis of the electronic structure of nickelocene with NBO methods. A list of optional exercises and suitable variations of some of the tasks can be found in the Supporting Information (Notes for Instructors).

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TASKS PERFORMED BY THE STUDENTS The preparatory lecture, computational steps taken, and the preparation of the laboratory report were designed to lead each student toward the learning goals outlined above. To introduce the students gradually to the problem of calculating the metallocene pNMR shifts, and to render the experiment more broadly appealing, the task list includes a set of relatively quick calculations for a small organic radical and its diamagnetic counterpart. Organic Molecules

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Including di-tert-butyl-hydroxylamine (DTBNOH) and di-tertbutyl nitroxide (DTBNO) in the experiment (Figure 3) has

Selected calculated bond lengths of the organic molecules shown in Figure 3 are collected in Table 1. The hydrogen

HAZARDS There are no physical hazards involved with this experiment. COMPUTATIONAL RESULTS AND DISCUSSION

Organic Molecules

Table 1. Typical Student Data Calculated for the DTBNOH and DTBNO Bond Lengthsa Length/Å

a

Figure 3. Optimized geometry and Lewis structure of (A) di-tert-butylhydroxylamine (DTB-NOH) and (B) di-tert-butyl nitroxide (DTBNO).

Bond

DTBNOH

DTBNO

N−O C−N C−CH3 C−H

1.431 1.495 1.537 1.099

1.272 1.508 1.525 1.099

Data calculated with PBE0/cc-pVDZ.

abstraction mainly affects the N−O distance. The calculated NMR data are collected in Table 2. The shielding constants and chemical shifts are given in dimensionless units of ppm (10−6). The agreement with experiment is not quantitative, but certainly sufficient for an assignment of the spectrum. For the radical, the different signs for the methyl and the t-butyl carbon shifts, and the negative proton shifts, are correctly reproduced by the calculations, and so are the orders of magnitude of the pNMR shifts. Due to the extremely large paramagnetic chemical shift range, the calculated data are sensitive to approximations in the computational model, such as the choice of the density functional, absence of solvent effects, basis set truncation, and other factors. The students should be reminded that similar considerations apply to the metallocenes.

been motivated by the very large changes in the chemical shifts that arise simply by removing a hydrogen atom from a diamagnetic compound to generate a paramagnetic radical. Most students recall from their organic chemistry courses that typical 1H and 13C NMR chemical shifts fall within 0−10 ppm for proton, and 0 to ∼200 ppm for carbons. Many of the students, however, have limited experience with metal complexes. NMR shifts for paramagnetic systems are therefore first introduced via a more familiar organic molecule. The students perform the following calculations: C




Table 2. Experimental and Typical Calculated Student Data for the (p)NMR Parameters and Shifts of DTBNOH and DTBNO DTBNOHa C(CH3)3 S (S + 1) Calculatedb giso σorb (ppm) Aiso (MHz) δFC (ppm) σtotal (ppm) δtotal Experiment Aiso (MHz) δtotal

DTBNOa CH3

CH3

C(CH3)3

0

CH3

CH3 0.75 2.0061

134.7

161.0

30.2

134.7 61.9

161.0 35.7

30.2 1.1

1.22

e

127.3 −8.8 −928.5 1055.8 −859.2

165.0 6.9 732.7 −567.7 764.3

30.0 −0.8 −21.1 51.1 −19.8

−8.65f −1235d

8.26f 1277d

−8c

a

The nucleus for which the parameters are provided is indicated by underlining in the table. Data calculated with PBE0/cc-pVDZ. TMS Shieldings: C, 196.6 ppm; 1H, 31.3 ppm bDescriptions of S (spin quantum number), giso (isotropic g-factor), σorb(isotropic orbital shielding), Aiso (isotropic electron−nucleus hyperfine coupling constant), δFC (Fermi-contact shift), σtotal, and δtotal are given in the Notes for Instructors in the Supporting Information. cRef 26. dRefs 27 and 28. eRef 29. fAssuming g = ge. Ref 27. 13

Table 3. Typical Calculated Student Data for the Energies (E), Zero Point Energies (ZPE), Total Energies (Etotal) of the Eclipsed and Staggered Metallocene Conformers, and the Relative Energy (Erel, Including Zero-Point Corrections) of the Staggered Conformer with Respect to the Eclipsed Onea,b Staggered

Fe Ni V

Eclipsed

E/a.u.

ZPE/a.u.

Etotal/a.u.

E/a.u.

ZPE/a.u.

Etotal/a.u.

Erel/ kJ/mol

−509.932 735 −555.786 558 −457.891 237

0.170 468 0.168 433 0.169 436

−509.762 267 −555.618 125 −457.721 801

−509.931 512 −555.786 434 −457.890 868

0.170 376 0.168 456 0.169 323

−509.761 136 −555.617 978 −457.721 545

3.0 0.4 0.7

a

The energy E is defined as the energy gained by the formation of the molecule in a given geometry from electrons and atomic nuclei separated at infinite distances, not including zero-point energies (ZPEs) for the nuclei. The total energy is the sum of the ZPE and E; 0.00010 Hartree (a.u.) corresponds to 0.26 kJ/mol. bData calculated with PBE0/LANL2DZ.

Table 4. Experimental and Typical Calculated Student Data for the EPR and NMR Parameters of the Eclipsed Conformers of Ferrocene, Nickelocene, and Vanadocenea FeCp2 C S (S + 1) Calculated giso σorb (ppm) Aiso (MHz) δFC (ppm) σtotal (ppm) δtotal Experiment giso Aiso (MHz) δtotal

VCp2 H

C

0

NiCp2 H

C

H

3.75

129.4

27.8

129.4 67

27.8 3

1.9451 101.4 −1.3 −683.2 784.6 −588.0

2.00

27.4 2.4 312.1 −284.7 316.0

2.1990 106.2 8.0 2483.0 −2376.8 2573.4

1.994 b

68

−510

b

4

d

27.4 −4.1 −317.9 345.3 −314.0

2.04 2.33c 320d

c

1514

−3.53c −253e

a

Data calculated with PBE0/LANL2DZ. TMS Shieldings: 13C, 196.1 ppm; 1H, 32.6 ppm. The spin multiplicities are 0 (singlet) for Fe, 4 (quartet) for V, and 3 (triplet) for Ni. bReferences 2−4. cReferences 6 and 7. dReference 11. eReference 8.

Organometallic Systems

optimized structures are minima. Because the rotations of the Cp rings correspond to low-frequency vibrations, it is necessary to use very fine integration grids and tight optimization criteria to calculate these modes accurately. For example, even though the D5h eclipsed conformations are minima for all of these metallocenes (in the gas phase),30 spurious imaginary frequencies may be obtained if the default criteria for the optimizations are used. For FeCp2 and VCp2, the staggered D5d conformation is a transition state, whereas for NiCp2, it

The students were asked to determine the energy difference between the eclipsed and staggered conformations of the metallocenes. Representative data in Table 3 show that even though the eclipsed conformer is more stable, the differences are small. At room temperature the Cp rings will rotate freely. An optional exercise would be to have the students perform calculations of the vibrational frequencies to calculate the zero point vibrational and free energies, and to confirm whether the D




whereas the initial explanation is seen to be of secondary importance. The β-spin 3dπ NBOs, expected to be vacant, show a population of 0.38e indicating strong ligand to metal donation. This confirms mechanism (ii). All other Ni 3d spin-orbitals have occupations very close to 1, which is expected.

corresponds to a second shallow minimum. The pNMR calculations were carried out using the eclipsed conformers. Computational data for the pNMR shifts of the metallocenes are collected in Table 4. To speed up the calculations, the students used the small LANL2DZ basis. Improved results for nickelocene can be obtained with more flexible basis sets, see ref 31 and the Notes for Instructors in the Supporting Information (TZVP basis). As the results demonstrate, the computations produce the expected very unusually large chemical shifts for the ligand atoms in the V and Ni complexes, and the same signs that were observed experimentally. The main trends are correctly predicted: (i) The 13C shift for nickelocene is positive and that for the V system is negative. (ii) The magnitude of the 13C shift for the Ni system is much larger than for the V system. (iii) In both of the paramagnetic metallocenes, the proton shifts are opposite in sign to the carbon shifts. Excellent agreement with experiment was obtained for ferrocene. Given the small basis set used, there is likely a significant degree of error cancellation between the shielding constants of ferrocene and those in the reference TMS. The carbon pNMR chemical shifts for nickelocene and vanadocene are caused by different mechanisms.31 The two alternative mechanisms suggested by McConnell and Holm for nickelocene are as follows: (i) unpaired α-spin metal orbitals “push” α spin density to the ligand or (ii) the ligand donates βspin density into empty metal β-spin orbitals. Both mechanisms are able to create an excess of α-spin density at the ligand carbon atoms. The associated hyperfine coupling constants and the pNMR shifts are then expected to be positive. In the case of nickelocene, the main mechanism is no. (ii).32 All of the α-spin Ni 3d orbitals are filled, but the two β -spin dπ are empty acceptor orbitals. For vanadocene, it has been shown that a variant of mechanism (i) dominates.31 However, as the α-spin 3dσ orbital pushes α-spin density into the Cp ligands, α-spin density in the occupied carbon-centered orbitals needs to “make room” because of the Pauli principle. Somewhat unintuitively, this mechanism leaves an excess of β-spin density in the carbon 1s shells. The corresponding 13C hyperfine coupling constants and the pNMR shifts are negative. For nickelocene, the students were asked to perform a calculation with the “natural bond orbital” (NBO) methodology32 available in Gaussian ’09. The relevant Ni 3d orbitals are classified as Ni “lone pairs” (LP labels) in the output. The WebMO graphical interface used by us easily allows the user to visualize the NBOs, which helps assigning the σ, π, and δ symmetries of Figure 2. The β donation mechanism is verified as follows: The two singly occupied 3d α-spin orbitals have π symmetry with respect to rotation around the linear symmetry axis of the complex. These correspond to the unoccupied ferrocene 3d orbitals in Figure 2. In the output section that characterizes the corresponding NBOs, metal to ligand (ML) α density donation would show up as occupations of less than one. Ligand to metal (LM) β donation would show up instead as non-zero occupations of the corresponding β-spin NBOs. The occupations for the β-spin orbitals of nickelocene, as obtained from the NBO analysis, were 0.995 (dσ), 0.982 and 0.982 (dδ), 0.384 and 0.384 (dπ). Direct excerpts from WebMO are given in the Notes for Instructors in the Supporting Information. The data indicate that both mechanisms are present, but the second mechanism is stronger: The McConnell explanation from 1958 describes the dominant LM mechanism

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SUMMARY An upper-level undergraduate computational chemistry experiment where the NMR chemical shifts of paramagnetic molecules are determined from first-principles has been developed. Calculations on a small diamagnetic molecule and the corresponding dehydrogenated radical illustrate that the presence of a single unpaired electron can have a dramatic impact on the chemical shifts, and highlight that the chemical shift range for the 13C and 1H nuclei is much larger than what students are familiar with for closed-shell molecules. Next, ferrocene and its paramagnetic analogs, nickelocene and vanadocene, were considered. An NBO analysis was performed to find the α and β spin-density at the metal center in NiCp2, and to provide an explanation for the positive sign of the carbon shifts in this complex. Learning goals were met as evident by student responses on a pre-exercise quiz based on information presented in the introduction of the laboratory manual and upon the student written laboratory reports. In 2013, nine students were enrolled in the class, and the median score on the pre-exercise quiz was 12 out of 15 points. The median score on the laboratory report was 83 out of 100 points, with a majority of the deducted points in completed reports resulting from algebraic errors. This summative assessment provides evidence qualitatively understood the underlying chemical and physical concepts and would likely improve their scores with further practice with calculations.

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ASSOCIATED CONTENT

S Supporting Information *

Further theoretical and practical information (Notes for Instructors); student handouts including the experiment manual, pre-lab quiz and an answer key, a grading rubric; Cartesian coordinates and electronic energies of optimized structures. Sample inputs and outputs. This material is available via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: ezurek@buffalo.edu. *E-mail: jochena@buffalo.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the National Science Foundation (Grant DMR-1005413 to E.Z.) and the U.S. Department of Energy, Basic Energy Sciences, Heavy Element Chemistry (Grant DE-FG02-09ER16066 to J.A.) for financial support. E.Z. thanks the Alfred P. Sloan Foundation for a Research Fellowship (2013−2015). We acknowledge the Center for Computational Research (CCR) at SUNY Buffalo for computational support, in particular Cynthia Cornelius. E



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Computation of Chemical Shifts for Paramagnetic Molecules: A

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