(mentioned here and described in previous articles) are available for $25 each from the first author. Literature Cited
Energy
I
1. Warner, B.D.: Baehme,G.;Pool, K H . J. Chem. Edue. 198% 69,66. 2. Edsbom. R. D . J Chem Educ. 19TS,56.A169. 3. Caeeei,M. S. J Cham.Edur 1084,61,935. 4. Paris, M.R.;Aymes,D. J.; Poupon,R.;Gareaao, R. J. C h . E d u . 19W,67,507. 5. Seiuer8.D. J. Chom.Educ. 1981,68,281. 6. Wfz, E. J. Cham. Edue 1982.69.744 7. Wtz, E. J.Cham. Educ 1988,70,63. J. Chom. Edue. 19B. 70,2&&248. 8. W+s,E.;Reinhard,S. 9. vifz, E.;Reinhard,S. J Chom. Educ 19BS,70,758-761. lo. Wz, E.Sc&fJic ComputingondAuromntion 1993,9,29. 11. Fox, J. N.;Shaner, R.A. J. Cham. E d u . 1990,67,163. 12. W,llard, H.H.;Merritt, L. L.; D-, J. A,;Settle, F A Inatruwntd Methods of Andyais, 6th 4.;Wadawn&: BeLmont,CA,1981;pp 640-663. 13. Skoog,D.A.;Weat,D.M.Fu'undomntolsafAndytiml Chemistry;Holt,Rineha?tand Winston: NY,1976; pp 37-07, 14. Chnatian,G.D. Andytiml Chamistry, 3rd ed.: W i k y New Ymh,198(1:p323. 16. Gran, &Art= Chim. Smnd. 1850.4.659. 16. Sehwarte, L.M.J. Chem E d u . ISSS,E?819. ,
Reaction Coordinate
Deprotonation of Nitroalkanes
Figure 1. Energy profile for a transition structure
Semiempirical Determination of Solvation Effects on a Simple Reaction Cwrdinate William J. Pietro
York University North York, Ontario, Canada Computational chemistry is one of the most rapidly mowing areas of study in the undergraduate chemistry iurricuium. The recent advent of l'w-cost, high-speed workstations and *student-friendly" electronic structure programs have now brought quantum chemical calculations into the classroom for good! Practicing chemists no longer need a detailed knowledge of the underlying mathematical principles of quantum mechanics to explain and predict interesting and potentially useful chemical phenomena by computational methods. Moreover, researchers now may perform their calculations on "realn molecules, rather than the heavily abridged model systems necessary for the slower, smaller, and more expensive computers of just a few years ago. ,Accordingly,computational chemistry soon must become an integral part of the chemistry core curriculum (1). Amone the most i m ~ o r t a n at ~ ~ l i c a t i o n ofs computational methods is the d&rmination of optimum moleklar geometries. Most students involved in computational chemistry have likely calculated optimized equilibrium geometries of some molecules using molecular mechanics, semiempirical, or ab initio methods. An equilibrium geometry corresponds to a local minimum on the energy surface and represents one (but not necessarily the only) thermodynamically stable structure for the molecular system. The overall thermocbemistrv for a reaction. for exam~le. . can be derived using the energies of the reactants and products at their equilibrium geometries. Of course, this kind of analysis tells us nothing about a reaction's mechanism or rate. The use of com~utationalchemistrv to arrive a t mechanistic or kinetic ikormation requires a fundamentallv different kind of -eeometrv . optimization-the determination of a transition structure. A transition structure does not corres~ondto either an absolute minimum or maximum on the eAergy surface, but rather to a saddle point. A saddle point is a geometry for which the energy is minimized with respect to all normal coordinates except one, to which it is maximized. This special coordinate is called the reaction coordinate, and wrresponds to the translation from reactants to products. The lowest energy path connecting reactants with products is shown in Figure 1. The curve is a two-dimensional "slice"
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through a multidimensional surface. The peak in the curve is the saddle point. All chemists are familiar with the concept of a reaction coordinate: however, few have actually visualized motion along one. The real-time computer an~mationof a complex reaction coordinate is the subiect of a future paper in this Journal. In the present paper we use semiemp&cal electronic structure theory to generate the energy versus reaction coordinate profile for a simple chemical event, the depmtonation of nitromethane in aqueous solution. Nitmmethane and its DeprotonatedAnion
It is well known to organic chemists that hydrogens a to a nitro group are acidie and dissociate in basic aqueous solution. For nitroalkanes the proton transfer is slow as mmpared to most acid-base reactions, indicating a considerable activation barrier to depmtonation. The depGtonation kinetics of nitroakanes pronde a pedagogically beautiful demonstration of the au&tum meihani-d modeline of transition states and the Lffects of solvation on their el&ronic structures. The calculations described herein require an electmnic structure program capable of semiempirical calculations at the AM1 level (2).constrained seometrv o~timizations.and the ability to display graphicali; molec;lb electrostat;~pocenhals. Combinations of several commerciallv ava~lableorograms enable this; however, one program,- SPAR TAP^, is available that integrates molecular mechanics, semiempirical, and ab initio methods, a Cartesian optimizer capable of fullor constrained equilibrium or transition structure opti-
Figure 2. AM1 calculated geometries for nitromethane and its conjugate base.
Table 1. Semiempirical AM1 Gas-Phase and Aaueous Heat of e or mat ion and Aqueous Solvation h e r g y of Nitromethane as a Function of Position along the Deprotonation Coordinate
-100 1 0
I 1 2 3 C-H Distance ( A )
4
Figure 3. AM1 calculated gas-phase deprotonation profile for nitromethane. mizations, and a highly sophisticated graphical interface for both input and output of data.' SPARTAN is inexpensive. intuitive.. easv . to use. and runs on a varietv of modem workstations. All calculations presented in this paper have been oerformed usine SPARTAN version 2.0.' on a Silicon ~ r a ~ k i4Dl35 c s personal Iris workstation. The semiempirical A M 1 calculated equilibrium geometries for nitromethane and its deprotonated anion are presented in Figures 2a and 2b, respectively. Note that the -CH2 group in the anion is perfectly planar, even though it is isoelectronic with ammonia, and Valence Shell Electron Pair Repulsion (VSEPR) theory would predict it to be pyramidal. Chemistry students rely heavily on VSEPR theory; however, one must always remember that it is based on simple arguments concerning attractions and repulsions and does not include important considerations &ch as orbital interactions and electron lunetic energy (or anyt h i n ., e else a u a n t u m mechanical). I n t h e case of the nitromethanide ion there is a considerable contribution by resonance form lb. Further evidence of the oarticioation of l b can be obtained by comparing the c F ~and NO bond lengths in the anion with those in CHsN02.
Solvation and the Depmtonation Coordinate of Nitroalkanes
We can simulate deprotonation by successively elongatingone of the CH bonds by, say, O.lOAincrements, and recording the A M 1 calculated heat of formation a t each point. I t is important, however, to allow the geometry of the rest of the molecule to relax. This is most conveniently accomplished through the use of a eonstrained optimization (31, in which a geometry optimization is carried out under the constraint that the CH bond length remains fixed a t a prespecified value. The results of a series of eonstrained optimizations representing the deprotonation of 'SPARTAN is a pmduct of Wavefunction, Inc., twine, CA.
nitromethane are presented in the first column of Table 1 and graphed in Figure 3. Note that this looks nothing like the "classic" energy versus reaction coordinate profile in Figure 1. The reason is simple. The calculated energies correspond to the gas phase reaction. As there is no energy minimum for a dissociated acid in the gas phase, the concept of an energy barrier is meaningless. Compare the minimum in the curve with the calculated energy a t the equilibrium geometry and you'll see that they are identical. The situation is markedly different when solvation effects are included in the calculation. Solvation effects may be included in a number of ways. In the supermolecule approach discrete solvent molecules are placed a t various locations and in various orientations about the solute molecule, and the entire molecular assembly is submitted for full geometry optimization. Although this may be the most straightforward way of incorporating solvent effects in the calculation, it is far from the most efficient. In order to employ the supermolecule approach properly (i.e., consider successive solvation shells, solvent structuring, etc.), as many as a hundred water molecules should be included (4). An alternative method is to use a dielectric continuum model, in which interactions between the solvent and charge distributions within the solute molecule are calculated without discretely including solvent molecules, eliminating the enormous computational effort involved in the supermolecule approach. Dielectric continuum methods are among the oldest models of solvation in computational chemistry, and new modifications are constantly evolving. Probably the most appropriate modification for semiempirical calculations, however, is that of Truhlar (5).In this method the interaction enerw ..- between the oolarizable solvent (water~and the quantum mechanically calculated charee distributions in the solute is simulated through f&tions containing parameters fit to experimental data, thus following a semiempirical formalism. Moreover, the interaction terms are incorporated into the SCF procedure, thereby optimizing the solute's electronic strucVolume 71 Number 5 May 1994
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-30 1 1
I 2 3 C-H D i s t a n c e ( A )
4
Figure 4. AM1 calculated aqueous deprotonation profile for nitromethane.
0.5
1.0 1.5 C-H Distance
2.0
2.5
(A)
Figure 6. AM1 atomic charges along the nitromethane deprotonation coordinate in aaueous solution. Table 2. Semiempirical AM1 Atomic Charges Calculated at Various Positions along the Deprotonation Coordinate of Nitromehane
-200
I 1
2 3 C-H D i s t a n c e ( A )
4
Figure 5. AM1 calculated aqueous solvation enthalpy along deprotonation coordinate of nitromethane. ture to allow for the polarizing effects induced by the solvent. This method is known as AMlISM1 (at the time of this writing a slightly more sophisticated SM2 version was being developed by the same group), and has been shown to reproduce experimental aqueous solvation energies of organic molecules and ions with great accuracy. The second column in Table 1contains the AM1 calculated aqueous heats of formation for each point along the reaction coordinate. These data are plotted in F i w e 4. Note that a well-defined activation barrier now appears, and the shane of the cuwe is ouite reminiscent of Fieure 1. In a different solvent, the shape and height of the Garrier will undoubtedly he different. Indeed, the kinetics of most reactions are affected profoundly by the solvent in which they are run. Computational methods can readily afford deeper insight into the nature of chemical phenomena than cannot easily be acquired by experiment. For example, our calculations lead to an interesting conclusion about the meaning of proton dissociationin nitroalkanes. The difference in heats of formation between the solvated and gas-phase molecule is defined as the solvation enthalpy, AH. (4).The 418
Journal of Chemical Education
solvation enthalpy calculated at various points along our defined reaction coordinate appears in the third column of Table 1 and is plotted in Figure 5 . For CH bond lengths near the equilibrium geometly AHs is small. Most of the solvation energy is due to interactions with the nitro group. As the CH distance increases, AHs remains almost perfectly constant until a distance of about 1.55 A is reached, at which point AH. abruptly and dramatically increases. Because we know that water, as a solvent, interacts stmngly with localized charges, it follows that a sudden polarization of the pH bond probably occurs when the distance exceeds 1.55 A. The calculations are suggesting that this is the point where the CH bond "breaks"; at longer distances the hydrogen rapidly takes on characteristics of a solvated proton; whereas at shorter distances, it is a participant in a covalent bond. This notion is further supported by the calculated atomic charges. First, however, a brief word on the meaning of atomic charges. The concept of an atomic charge is quantum mechanically incorrect, as it violates the Heisenberg principle. Electrons in molecules cannot be "assigned" to individual atoms. Instead, it IS correct to define a function that descnbes the total electron denwty of the molecule, then "fit" a collect~on
of atom-centered point charges such that the electric field created bv the point c h a ~ e matches s as closelv " a s ~ossible . the field due lo the true quantum nicchamcal elcctrondcnsity 16,. We define these "ootimum" point rharces as the atomic charges. Figure 6 shdws the dependenceof the departing hvdroeen's atomic charge as a function of motion along the reacti& coordinate. Alio presented in this figure are the atomic charges of carbon and oxygen. The data for these plots are presented in Table 2. Figure 6 clearly illustrates the dramatic increase in positive atomic charge of the departing hydmgen between 1.5 and 1.6 A. Note also that the counterbalancing negative charge building up on the nitromethanide anion is delocalized heavily onto the oxygens, in accordance with canonical resonance structure lb. lsosurface Visualization of Electronic Structure Properties H!ciln illustrate this phcnomenon most convinringlg by observing the moleculilr electrostutic putential (YEP, as the CH bond is stretched. The MEP is related lo thc ouanturn mechanical charge density surrounding the molecule. The MEP is generated by calculating the interaction energy of a unit positive point charge a t a three-dimensional grid of loci evenly distributed around the molecule. Acommon way of visualizing the MEP is to display it a s a n isosurface (71, a three-dimensional graphic surface of cons t a n t value. Although the value chosen for the MEP isosurface (notated a s iso-MEP) is arbitrary, values between 10 and 50 kcal mol-' are generally displayed, a s they
produce images compact enough to resemble the shape of the molecule. An iso-MEP affords a wav of visualizine the shape of the electric field emanating fEom a molecuG (or ion) created by its charge distributions. Hence, the isoMEP will have a large radial extent in regions where the electric field is relativelv. high and will remain close to the nuclear framework in regions of low electric field. Obviously, the iso-MEP can be disdaved either a s a revulsive surface (positive value) or a s -mattractive surfa&(negative value), providing. - the chemist with complimentary information. A series of MEP isosurfaces for t h e dissociation of CHBNOzappears in Figure 7. I n these images the repulsive iso-MEP is represented by the solid surface, whiie the attractive iso-MEP is displayed a s a mesh. This kind of graphical representation is becoming increasingly popular in the research community, and offers obvious pedagogical advantages over the "old-fashioned" table of numbers. The pictures in Figure 7 drive the point home. In these images, we are looking down the C-N bond, with the methyl group facing us. Somewhere between 1.5 and 1.6 A. a n a b r u ~ t change occurs in the electronic structure of the &olecule.'A large electrostatic potential accumulates on the .. wsitive . departing hydrogen, with the counterbalancing negative ch:lrge distributed throurrhout the remainder of the mole~ u l e . the ~ ~ departing s h&ogen becomes a free proton, its repulsive iso-MEP approaches a maximum. A fundamental question remains to be answered. It is clear that the abrupt increase in AHs results from the sudden charge separation of the CH bond, but to what extent does the presence of the solvent assist i n the onset of the polarizat;on') To answcr thls questlon wc look at the same scrics ofrso-MEP surfaces, this timc calculated wthout Including solvation effects (the gas-phase calculations). These pictures, shown in Finwe 8, clearly demonstrate that the solvent actually induces the charge separation. Conclusions Modern electronic structure programs operating on s comprise a nowerful state-of-the-art e r a ~ h i c workstations learning tool foF &emistry undergraduatks and'are now sur~risinelvaffordable. G r a ~ h i c areoresentation l of &emicafphen&kna affords a n eiTective and enjoyable method for students to a r a w othcrwisc diff~culttopics. Presenting a n electronic prope&y (in our case, the molecular electmy static potential) by representation a s a high-resolution graphic isosurface provides the student with a natural way
Figure 7 . Molecular electrostatic potential isosurfaces (30kcal mod) for aqueous nitromethane in sequential stages of deprotonation.C-H interatomic distance increases progressively by 0.10 A from upper lefl (1.10 A) to lower right (1.90 A). The solid image represents the repulsive isoMEP, while the mesh illustrates the attractive isoMEP.
Figure 8. MEP isosurfaces for the deprotonation of nitromethane, Similar to Figure 7, except in the gas phase. Volume 71
Number 5 May 1994
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of visualizing abstract concepts. Modern graphical molecular builders take the tedium out of constructing input files for quantum mechanical calculations. Sophisticated graphical interfaces now allow all phases of an electronic structure calculation to be ~erformedinteractivelv.. encouraging experimentation on the part of the students. SPARTAN (or a combination of programs providing equivalent power), originally designed as a research tool, is now enjoying widespread use in the teaching of quantum chemistw at the undermaduate level. The fear of learnine (and -. teaching) computational chemistry is finally in its grave!
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Literature Cited 1. Fm a more indepth description oftheuses of mmputati6nalmethoda ~ e IaIHehm, : W.J.; &dm, L Seh1eyer.P 7.R.; Paple, J.AAbInitio M&culor Orbi01 m o m ; Wiley-lntersience: New York, 1966. (h) Dewar, M. J. S. The Molecular Orbital Theory of Org-ic Chemistry; McCraw-Hill: New Yo*, 1969.
2. Dewar, M. J. S.; Zaehish, E. C ;He* 107,3902.
E. F;Stewart. J. J. P.J . Am Chem. Soe. 1886,
3. Baker.J.J. Cornputof. Chem. 19% 13,240. 4. Pul1man.A. Qunnfum ThPory ofChemiealRmefiona 1980.2.1.
5. Cramer, C.J.;Truhlsr, D. G.J Am Chem S o c 199l. 113, ?S05. 6. Chirlian,L.E.;R a n d , M. M . J. Computot Chem. 1987.8,8% 7. Fielder, S. PhD thesis, 1993, Univeraityof California, Irvine.
