Computational Modeling of the Optical Rotation of Amino Acids: An 'in

Mar 4, 2013 - A computational experiment that investigates the optical activity of the amino acid valine has been developed for an upper-level undergr...
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Laboratory Experiment pubs.acs.org/jchemeduc

Computational Modeling of the Optical Rotation of Amino Acids: An ‘in Silico’ Experiment for Physical Chemistry Scott Simpson, Jochen Autschbach,* and Eva Zurek* Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States S Supporting Information *

ABSTRACT: A computational experiment that investigates the optical activity of the amino acid valine has been developed for an upper-level undergraduate physical chemistry laboratory course. Hybrid density functional theory calculations were carried out for valine to confirm the rule that adding a strong acid to a solution of an amino acid in the L configuration renders the optical rotation more positive. Correspondingly, if the optical rotation becomes more negative, the amino acid is of the D configuration. The students employed the open-source molecular editor Avogadro to build the molecules, conduct conformer searches, and calculate the energies of the conformers with a molecular mechanics force field. Subsequent geometry optimizations and optical rotation calculations were performed with a quantum chemistry program, using the WebMO graphical interface. The role of the solvent in stabilizing the zwitterionic form of an amino acid was investigated. KEYWORDS: Upper-Division Undergraduate, Biochemistry, Laboratory Instruction, Physical Chemistry, Computer-Based Learning, Computational Chemistry, Quantum Chemistry, Molecular Modeling, Molecular Properties/Structure, Chirality/Optical Activity

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To engage the significant number of students whose primary interest lay in organic chemistry or biochemistry, an experiment was developed in which the students calculated the optical activity of amino acids from first principles. These chiral molecules are the building blocks of proteins, are employed in chiral catalysis, and are widely used in the pharmaceutical industry. The lab also touches on a number of important aspects in computational modeling, such as the calculation of molecular properties related to the response to external fields, determination of energies via molecular mechanics force fields and (hybrid) density functional theory (DFT), as well as gasphase calculations versus calculations with continuum solvation models. These topics were discussed briefly in a prelab lecture, and more information ideal for inquisitive students can be found in Cramer’s textbook.7 The physical background related to linear and circular light polarization, refractive indices, and absorption is perhaps most easily demonstrated with the help of animated computer graphics.8−10 A survey given out at the end of the laboratory course showed that the experiment described herein challenged the students knowledge about optical activity and contributed significantly to their experience on how quantum chemistry programs are utilized in research.

nantiomers of chiral molecules can be distinguished by the sign of their optical activity. Optical rotation (OR) is one of the manifestations of natural optical activity.1,2 OR has been first observed in 1811 by Arago and has found widespread application in the characterization of natural products and other chiral substances. A number of experimental laboratories focusing on OR have been published in this Journal.3−6 Our aim is the use of first-principles theory and quantum chemistry calculations to further an understanding of optical rotation at the undergraduate level. We have recently developed and implemented a practical computational chemistry laboratory course for third- and fourth-year undergraduate students. The enrollment in the class was diverse, spanning from chemistry majors who had already successfully completed or were currently enrolled in a quantum chemistry and spectroscopy course, to medicinal chemistry and pharmaceutical science majors who had completed a physical chemistry class for life-sciences but had very little theory background. As part of this course, the students carried out four computational experiments, as well as an independent project that they designed themselves (in consultation with the laboratory instructor and professor; about half of the initial ideas submitted were not feasible and the students were advised on how to modify their original proposals accordingly). Both a laboratory writeup and a 15 min in-class oral presentation were required for the final project, whereas only a writeup was required for the regular laboratory experiments. © XXXX American Chemical Society and Division of Chemical Education, Inc.

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BACKGROUND The sign and magnitude of the OR cannot be determined from the molecular structure alone. For example, even though Dalanine is dextrorotatory, D-fructose is levorotatory. Clough,

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deviation between gas-phase calculations and solution-phase measurements on the order of 25 to 30% for DFT17,19 and similarly at the coupled cluster level.18 The computational protocol used for this laboratory experiment is suitable for qualitative purposes. In order to reach semiquantitative, not to mention quantitative, agreement with experiment, all the aforementioned factors would have to be considered in a balanced way. A priori it is difficult to tell how much exactly these different factors contribute to the optical rotation of a particular molecule. An instructor with the intent to have the students investigate the influence of diffuse functions in the basis set might want to adopt the aug-cc-pVDZ basis set, or alternatively the less well balanced 6-31+G(d) basis, in addition to 6-31G(d).

Lutz, and Jirgensons (CLJ) noted in the early twentieth century that the OR of solutions of L-amino acids becomes more positive if a strong acid is added11−14 (the CLJ rule). Conversely, if the specific rotation becomes more negative, then the amino acid is of the D configuration. With the help of computational chemistry, the reasons for this behavior were discovered.15 The laboratory experiment reported herein has been based largely on the computational model put forward by Kundrat and Autschbach.15 Almost all of the naturally occurring amino acids, which are of L-type, have the (S)-configuration according to the Cahn−Ingold−Prelog rules of priority. Unfortunately, in this nomenclature, L-cysteine and L-cystine have an (R)-configuration. Because of this, we have opted to use the L/D, as opposed to the R/S, notation in this laboratory experiment. The notation employed extensively in the laboratory manual (see the Supporting Information). For a general introduction to theoretical methods used for the computation of OR and other types of optical activity, including a computational tutorial, please see a review by Autschbach.16 One important application of first-principles calculations of OR is the determination of the absolute configuration (AC) of a chiral molecule. A computation for one of the enantiomers is compared with experiment. If the signs match, the AC is the same as that used in the computation; if not, the AC is the opposite one. When a large number of computational results for ORs, in the range of up to a few hundred degrees, are compared with solution-phase experimental data for molecules with known ACs, it emerges that for a variety of reasons16 there is on average roughly a 30 deg/[dm (g/cm3)] difference between the calculated and experimental specific rotations.17−20 Among the factors contributing to the deviations are solvent effects, concentration effects, and vibrational effects, which are typically not modeled, approximations in the computations (basis set, electron correlation treatment), but also occasionally an inaccurate measurement.21 These average deviations create an “indeterminate zone”17 of small ORs for which computation-based AC assignments are unreliable. Nonrigid molecules with two or more thermally populated conformers (which may have very different ORs) are even more challenging. The OR of most amino acids falls into this zone. However, the CLJ effect is reliably reproduced by DFT calculations at a level suitable for a computational laboratory experiment. The performance of different basis sets for optical rotation calculations has been determined for amino acids,22,23 as well as other optically active molecules.19,24 The optical rotation of conformer 1 of valine (see below) with increasing the basis set size in terms of diffuse functions [cc-pVDZ (no diffuse functions), aug-cc-pVDZ (one diffuse set), d-aug-cc-pVDZ (double augmentation with diffuse functions)] is seen to converge slowly, yielding specific rotations of −18.26, −62.70, and −58.05 deg/[dm (g/cm3)], respectively. Basis set saturation creates another problem, namely linear dependencies due to finite precision of the floating point numbers in digital computers, which must be removed by the program. Fitting procedures can be used to extrapolate to the basis set limit.24 However, fully converged gas-phase values are not particularly relevant if one wishes to reproduce solution-phase optical rotation data. Effects from solvent and dynamic effects can also be influencing factors.25−27 Zero-point energy vibrational corrections on optical rotation may reach 20% or more of the uncorrected value.28 All of these effects are system dependent and create a seemingly random median relative

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EXPERIMENT

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HAZARDS

The experiment consists of three sections. In the first section, students draw Newman projections for each rotamer of L-valine (both the zwitterionic and cationic forms), use the rotamer search in the molecular editor Avogadro to determine the relative energies of the conformers (via a molecular mechanics force field), and compare these to the relative energies obtained from DFT calculations carried out with the solvent water, using a continuum solvation model. In the second section, students calculate the optical and molar rotation of the zwitterionic and protonated species to determine which rotamers obey the CLJ rule and calculate the Boltzmann-averaged optical rotation, which is compared to experiment. In the final section, the students compare the geometric parameters, total energies, and specific and molar rotations of the D and L enantiomer of one of the conformers of valine. The experiment was performed in two 4-h sessions, which were held in a technology classroom where each student had access to their own workstation. Students could also access the computational software online. A number of students carried out part of the laboratory experiment from home. A lab manual, a tutorial on how to perform the conformer search, Cartesian coordinates, electronic energies of optimized structures, and prelab quizzes are provided in the Supporting Information. The OR computations were carried out with the B3LYP functional and a 6-31G(d) basis set. (Improved results would be obtained with a basis set that includes diffuse functions,15 such as aug-cc-pVDZ which is often applied in computational studies of OR.) Molecules were built and visualized using the open-source molecular editor Avogadro,29 and computations were carried out using the Web browser-based WebMO30 interface to Gaussian ‘03.31 Avogadro is available for Windows, Mac and Linux distributions and can be downloaded from the openmolecules Web site.32 Whereas the 1.0 branch of Avogadro is sufficient for this experiment, version 1.1 is recommended. For the conformer generation and geometry optimization, any one of the force fields implemented in the OpenBabel33 software package may be used. For the systems studied here, the default MMFF9434 was employed. Unless stated otherwise, a continuum solvation model with water as the solvent was used during the geometry optimizations.

There are no hazards involved with this experiment. B

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THE CONFORMERS OF VALINE AND PROTONATED VALINE For the laboratory experiment, the amino acid valine was selected because it is amenable to quick computations, has three conformers among which the OR changes sign, and the CLJ rule applies to each of the conformers. In the paper by Kundrat and Autschbach,15 12 amino acids were investigated, including several aromatic ones. The instructor might want to select a different amino acid to increase or reduce the complexity of the computational problem. The students were asked to draw the structure of one of the conformers of L-valine in Avogadro, which was subsequently employed to generate and optimize the geometries of various rotamers using a molecular mechanics (MM) force field. The rotamers that were obtained, as well as their relative energies as determined using MMFF94 are provided in Figure 1. These

results provided in Figure 2 illustrate that the order of stability remains the same as for the zwitterionic form, but the relative

Figure 2. Optimized geometries and Newman projections of the conformers of protonated valine. The relative energies as obtained using the MMFF94 force field (MM) and B3LYP/6-31G(d) quantum mechanical calculations (QM) are also provided.

energy differences as calculated using first principles are somewhat smaller.

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THE CLOUGH, LUTZ, JIRGENSONS RULE To determine if valine obeys the CLJ rule, the specific rotation, [α]λ, of the zwitterionic rotamers and their corresponding protonated forms, illustrated in Figures 1 and 2, was calculated at the wavelength of the Na D-line (λ = 589.3 nm) commonly used in polarimetry. The specific rotation given in the program output was converted to the molar rotation, [φ]λ via:

Figure 1. Optimized geometries and Newman projections of the conformers of zwitterionic valine. The relative energies as obtained using the MMFF94 force field (MM) and B3LYP/6-31G(d) quantum mechanical calculations (QM) are also provided.

[φ]λ = [α]λ ·(M /100)

(1)

where M, the molar mass of the molecule in g/mol, was also taken from the program output. The difference between the molar rotation of the cation and the zwitterion,

were employed as starting structures for geometry optimizations carried out using hybrid DFT. Because the zwitterionic form of valine is not stable in the gas phase, it was of great import to perform the calculations using water as a solvent. For one of the rotamers the students were asked to carry out a geometry optimization in the gas phase, which results in the transfer of an −NH3+ proton to COO− to give −NH2 and COOH. The observation that in the gas phase the optimized DFT structure does not correspond to the one obtained via MM may pique the curiosity of some of the students. To help answer this question, the instructor may wish to elaborate further on the theoretical background of the computational methods employed. A comparison was made between the Newman projections of the rotamers of valine, as well as those found using the conformer search in Avogadro, see Figure 1. Even though the relative energies as determined using the MM were about twice as large in magnitude as those calculated via DFT, the energy ordering was the same. The relative energies are in qualitative agreement with those computed by Kundrat and Autschbach.15 The same steps were carried out for protonated valine. The

Δ[φ]λ = [φ]λ (protonated) − [φ]λ (zwitterion)

(2)

was calculated. As illustrated in Table 1, each one of the conformers was found to obey the CLJ rule. The experimentally determined molar rotations for the zwitterion and cation of valine are 6.6 and 33.1 (deg cm2)/ dmol, respectively.14 The signs of the optical rotation of the conformers are in agreement with those from Kundrat and Autscbach15 (the magnitudes differ because of differences in the basis sets and the density functionals that were used). The deviation between the computation and the experiment is not untypical, as mentioned in the Background section. The fact that there is (partial) cancellation among the ORs in the Boltzmann average renders the case more challenging for accurate computational predictions. For molecules where a CLJ-type effect applies,35 an AC assignment can be made much more reliable if the change of the OR upon protonation is considered in addition to the OR values themselves. C

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Table 1. The Calculated Specific Rotation, [α] (deg/[dm (g/cm3)], and Molar Rotation, [φ] (deg cm2/dmol), of the Conformers of Valine (λ = 589.3 nm) Conformera

[α](Z)b

[φ](Z)b

[α](P)c

[φ](P)c

Δ[φ]d

Obey CLJ

1 2 3 Boltzmann Av.e

−25.71 76.43 −58.25 −2.2

−30.12 89.54 −68.24 −2.5

97.65 128.29 44.22 100.7

115.38 151.58 52.25 119.0

145.50 62.05 120.49 121.5

Yes Yes Yes Yes

a

The conformers of valine are illustrated in Figures 1 and 2. Experimental molar rotations 6.6 (Z), 33.1 (P). bThe zwitterion is represented by Z. The protonated form is represented by P. dThe difference between the molar rotation of the protonated form and the zwitterion. eBolzmann averages at room temperature were obtained with the relative energies calculated at the QM level. c

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THE D-ENANTIOMER OF VALINE To further investigate the concept of optical isomerism, the students were asked to determine the most stable conformer of the zwitterion of L-valine and construct the corresponding D enantiomer. The DFT optimized geometries and energies of these two molecules were compared and shown to be the same (to within the settings used for convergence), whereas the specific rotations were found to be of the same magnitude, but opposite sign.

Engineering Node Services (SENS) at SUNY Buffalo for administering the technology classroom used for the laboratory course.

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(1) Barron, L. D. Molecular Light Scattering and Optical Activity, 2nd ed.; Cambridge University Press: Cambridge, 2004. (2) Berova, N., Polavarapu, P., Nakanishi, K., Woody, R., Eds.; Advances in Chiroptical Methods; Wiley Blackwell: New York, 2011. (3) Mahurin, S. M.; Compton, R. N.; Zare, R. N. J. Chem. Educ. 1999, 76, 1234−1236. (4) Lisboa, P.; Sotomayor, J.; Ribeiro, P. J. Chem. Educ. 2010, 87, 1408−1410. (5) Sheardy, R.; Liotta, L.; Steinhart, E.; Champion, R.; Rinker, J.; Planutis, M.; Salinkas, J.; Boyer, T.; Carcanague, D. J. Chem. Educ. 1986, 63, 646−647. (6) Baar, M. R.; Cerrone-Szakal, A. L. J. Chem. Educ. 2005, 82, 1040− 1042. (7) Cramer, C. J. Essentials of Computational Chemistry; John Wiley & Sons: New York, 2002. (8) Autschbach, J. “Optical Rotation and Ellipticity” from The Wolfram Demonstrations Project. http://demonstrations.wolfram. com/OpticalRotationAndEllipticity/ (accessed Feb 2013). (9) Autschbach, J. “Circular and Elliptic Polarization of Light Waves” from The Wolfram Demonstrations Project. http://demonstrations. wolfram.com/CircularAndEllipticPolarizationOfLightWaves/ (accessed Feb 2013). (10) Novak, I. J. Chem. Educ. 1995, 72, 1084−1085. (11) Clough, G. W. J. Chem. Soc., Trans. 1918, 113, 526−554. (12) Lutz, I. O.; Jirgensons, B. Ber. Dtsch. Chem. Ges. B 1930, 63B, 448−460. (13) Lutz, O.; Jirgensons, B. Ber. Dtsch. Chem. Ges. B 1931, 64B, 1221−1232. (14) Greenstein, J. P.; Winitz, M. Chemistry of the Amino Acids; John Wiley & Sons: New York, 1961; pp 84−87, 91. (15) Kundrat, M. D.; Autschbach, J. J. Am. Chem. Soc. 2008, 130, 4404−4414. (16) Autschbach, J. Chirality 2009, 21, E116−E152. (17) Stephens, P. J.; McCann, D. M.; Cheeseman, J. R.; Frisch, M. J. Chirality 2005, 17, S52−S64. (18) Crawford, T. D.; Stephens, P. J. J. Phys. Chem. A 2008, 112, 1339−1345. (19) Srebro, M.; Govind, N.; de Jong, W.; Autschbach, J. J. Phys. Chem. A 2011, 115, 10930−10949. (20) Polavarapu, P. L. Chem. Rec. 2007, 7, 125−136. (21) Dewey, M. A.; Gladysz, J. A. Organometallics 1993, 12, 2390− 2392. (22) Kundrat, M.; Autschbach, J. J. Phys. Chem. A 2006, 110, 12908− 12917. (23) Kundrat, M.; Autschbach, J. J. Phys. Chem. A 2006, 110, 4115− 4123. (24) Hedegård, E. D.; Jensen, F.; Kongsted, J. J. Chem. Theory Comput. 2012, 8, 4425−4433. (25) Kundrat, M.; Autschbach, J. J. Chem. Theory Comput. 2008, 4, 1902−1914.

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CONCLUSIONS We have developed a computational laboratory experiment for an upper-level undergraduate physical chemistry laboratory course in which the students employ first-principles calculations to determine the optical rotation of the zwitterionic form of the amino acid valine. The determination of the absolute configuration of a molecule cannot be made based upon a single measurement of the optical activity. However, comparison of the specific rotation of an aqueous solution of an amino acid and the protonated form can be employed toward this end (the CLJ rule), as illustrated here. This laboratory also explores various topics in computational chemistry including geometry optimizations performed using molecular mechanics versus density functional theory, gas phase and solution phase calculations using a continuum solvent model, as well as the calculation of optical rotation directly from first principles. Students found the subject matter to be appealing as chirality is one of the most fundamental concepts in organic chemistry, and amino acids are of tremendous importance in biochemistry.

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ASSOCIATED CONTENT

S Supporting Information *

Student handouts including the experiment manual, pre-lab quizzes, and a grading rubric; Cartesian coordinates and electronic energies of optimized structures. This material is available via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: (J.A.) jochena@buffalo.edu, (E.Z.) ezurek@buffalo. edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the National Science Foundation [DMR-1005413 (EZ) and CHE0952253 (JA)] for financial support, the Center of Computational Research (CCR) at SUNY Buffalo for computational support, and the Science and D

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(26) Kundrat, M.; Autschbach, J. J. Chem. Theory Comput. 2009, 5, 1051−1060. (27) Mukhopadhyay, P.; Wipf, P.; Beratan, D. N. Acc. Chem. Res. 2009, 42, 809−819. (28) Mort, B. C.; Autschbach, J. J. Phys. Chem. A 2005, 109, 8617− 8623. (29) Hanwell, M. D.; Curtis, D. E.; Lonie, D.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. J. Cheminf. 2012, 4, 17. (30) Schmidt, J. R.; Polik, W. F. WebMO, Version 12.0; WebMO: Holland, MI, 2012. http://www.webmo.net/ (accessed Sept 2012). (31) Gaussian 03, Revision E.01; Frisch, M. J.; et al. Gaussian, Inc.: Wallingford, CT, 2004. (32) Avogadro Home Page. http://avogadro.openmolecules.net/ (accessed Feb 2013). (33) Open Babel Home Page. http://openbabel.org/ (accessed Feb 2013). (34) Halgren, T. A. J. Comput. Chem. 1996, 17, 490−519. (35) Nitsch-Velasquez, L.; Autschbach, J. Chirality 2010, 22, E81− E95.

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