p5_conformations - Chapter P5: Conformations of Molecules...

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Unformatted text preview: Chapter P5: Conformations of Molecules Introduction Up to this point in the text, we have talked about molecular structure solely in terms of bond lengths and angles, for example, the experimental structure of water in terms of two OH bonds of 0.96Ǻ and a HOH bond angle of 104.5o. For most molecules with four or more atoms, an additional set of variables needs to be considered. These are torsional or dihedral angles. For example, description of the geometry of hydrogen peroxide, HOOH, requires specification not only of an OO bond length, two OH bond lengths and two HOO bond angles, but also the HOOH torsional angle. H O O H The torsional or dihedral angle ABCD is defined as the angle the normal to plane made by ABC and the normal to the plane made by BCD. Variation of the HOOH dihedral angle in hydrogen peroxide over the range of 0 to 360o reveals two equivalent energy minima around 120o and 240o. While hydrogen peroxide exhibits only a single unique conformational isomer or conformer, for most molecules variation in dihedral angle over the full 360o range gives rise to more than one distinct conformer. For example, variation of the CCCC dihedral angle in n-butane from 0 to 360o gives rise to three conformers and two distinct conformers, an anti structure (dihedral angle of 180o) and a pair of equivalent gauche structures (dihedral angles around 60o and 300o). 1 H H3 C HC H C H H3C CH3 HC H H C H3 C H CH3 HC H C CH3 H H The average value of a property A for a molecule with more than one unique conformer follows from the Boltzmann equation. Summation is carried out over all conformers, ai is the value of the property for conformer i, ni is the number of times that it appears and Wi is its Boltzmann weight. A = ∑i ai ni Wi The Boltzmann weight depends on the energy of the conformer relative to the energy of the lowest-energy conformer, ΔEi, and on the temperature, T, in K. k is the Boltzmann constant. Wi = exp(-ΔEi/kT)/ ∑j nj [exp(-ΔEj/kT)] Distribution of Conformers for n-Butane: Obtain equilibrium geometries for both anti and gauche conformers of n-butane using the HF/6-31G* model. At what temperature does the minor conformer make up less than 1% of an equilibrium mixture? At what temperature does it make up more than 40%? Don’t forget that 360o rotation about the central CC bond leads to two equivalent gauche conformers. Where the energy difference between conformers is small, as is the case for n-butane, the average value of a property may differ significantly from that of the lowest-energy conformer. This explains why the measured dipole moment for n-butane is finite even though the dipole moment of the lowestenergy (anti) conformer is zero because of symmetry. 2 Dipole moment of n-Butane: Using the results from the previous problem, calculate the value of the dipole moment for a sample of n-butane at room temperature. To what value does the dipole moment go as the temperature is raised? Elaborate. The validity of the Boltzmann equation to establish average molecular properties is based on the assumption that the conformers are in equilibrium, that is, that they rapidly interconvert or that they interconvert on a scale that is rapid relative to the timescale of the experimental measurement. The speed with which conformational equilibrium occurs depends on the heights of the energy barriers separating the conformers. n-butane shows an energy barrier of only ~10 kJ/mol for change from gauche to anti conformers and ~15 kJ/mol for change from anti to gauche conformers. Experimental rotational barriers have been measured for a variety of simple systems including ethane (H3C-CH3) at 12 kJ/mol, methylamine (H3C-NH2) at 8 kJ/mol, methanol (H3C-OH) at 5 kJ/mol), methyl silane (H3C-SiH3) at 7 kJ/mol, methyl phosphine (H3C-PH2) at 8 kJ/mol and methane thiol (H3CSH) at 5 kJ/mol. Such small barriers are typical those involving single bonds with at least one carbon. Except where experiments are carried out at very low temperatures, they suggest that it would be very difficult to slow down (let alone stop) equilibration among conformers. Note that the rotational barriers for ethane, methylamine and methanol roughly follow the ratio of 3:2:1, that is, they appear to correlate with the number of bond eclipsing interactions. Note also, that this is not the case for second-row analogues methyl silane, methyl phosphine and methane thiol. Finally, it needs to be mentioned, that depending on the relative timescales of conformational equilibration and process involved in generating the observable, an experiment can either yield a single (average) value of a property or a set of values, each corresponding to a different conformer. Two important spectroscopic techniques illustrate the situation. The timescale of the process underlying NMR spectroscopy (nuclear spin relaxation) is long relative to that for conformational equilibration, meaning that an NMR spectrum represents an average of NMR spectra for different conformers. On the other hand, the timescale of the process underlying infrared spectroscopy (vibrational excitation) is short relative to that for conformational equilibration. This means that an infrared spectrum is actually made up of spectra of the individual conformers. Only a few conformers are likely to significantly contribute to the average (or likely to be seen individually). 3 Infrared Spectra of Acrolein Conformers: Acrolein (propenal, H2C=CC(H)=O) exists as a mixture of syn and anti conformers, with the latter dominating. O H H C C H H C H C C H H O C H Is it likely that these could be distinguished by way of their infrared spectra, in particular the frequency corresponding to the CO stretching motion? Obtain equilibrium geometries and infrared spectra for both conformers. Use the B3LYP/6-31G* model. While the anti conformer is planar, the syn conformer may not be, so start with a non-planar geometry. Which conformer is lower in energy? What percentage of a room-temperature equilibrium mixture corresponds to the higher-energy conformer? If it lower than 5%, what temperature would be needed to bring it to 5%? Compare the infrared spectra for the two conformers. Are the CO stretching frequencies sufficiently different (by 5 cm-1 or more) to allow them to be distinguished? Is there anything else that would help to distinguish the spectra? Elaborate. The properties of some molecules will be correctly described in terms of a single unique conformer. This is either because these molecules are rigid, or because all conformers are equivalent, or because one particular conformer is strongly preferred over all others. For example, ethylene is rigid, the two conformers of hydrogen peroxide are identical and the cis conformer of formic acid is strongly preferred over the trans conformer. H H O C H O O C O H Dipole Moment of Formic Acid: Use the HF/6-31G* model to obtain equilibrium geometries for both cis and trans conformers of formic acid. Use the Boltzmann equation to calculate an average dipole moment at room temperature. Is it dominated by one conformer or do both conformers contribute significantly? However, the majority of molecules exist in terms of a collection of several distinct conformers or shapes. These result from rotation about single bonds (as illustrated up to this point in the chapter), from constrained rotation about single bonds incorporated into rings, from inversion of pyramidal nitrogen and phosphorus centers and from pseudorotation about fivecoordinate centers. Except for very simple molecules with one or two degrees of conformational freedom, the number of unique shapes that can arise may not be obvious. Suffice it to say that this number increases rapidly with the number of single bonds and pyramidal and pentacoordinate centers and with the number and size of the rings, and may grow into the hundreds or even thousands of conformers. 4 The majority of this chapter concerns molecules with only a single degree of conformational freedom. This immediately highlights one advantage of calculations over experiment. Experiments may only directly probe equilibrium structures (and only then if they are present in sufficient amounts to actually be observed) and, for very simple molecules, the barriers to conformational change. Calculations may examine all conformers, irrespective of their abundance and all interconversion barriers. Pathways may also be described, although as pointed out in Chapter P4 they contain a degree of ambiguity. We start by introducing a Fourier series as a simple tool to “dissect” the energy profile for rotation about a bond, and to “interpret” conformational energy preferences in terms that are familiar to chemists, most notably, steric crowding, dipole-dipole interactions and conjugation. Next, we examine conformational energy profiles for a small but diverse selection of simple molecules. Here, the focus is in seeing how the fundamental preferences (identified in the Fourier series) combine to give rise to an actual energy profile. We will also seek to identify commonalities among energy profiles for different molecules. The third goal of this chapter will be to judge the ability of both “limiting” (large-basis-set) and “practical” Hartree-Fock, B3LYP and MP2 models to properly assign the lowest-energy conformer and to reproduce the known Boltzmann distribution of conformers. As indicated earlier, rotation about single bonds is not the only type of conformational change, and we will provide examples constrained rotation in rings, inversion and pseudorotation. The chapter concludes by “answering” a question that at first glance appears to be obvious, but on more careful consideration reveals is not: “What is the important conformer? The process of changing from one conformer to another is in fact a chemical reaction, and maxima on a conformational energy profile are transition states. There are, however, two significant differences between a conformational change and a “normal” chemical reaction. First, chemical reactions typically have activation energies in the range of 100 to 300 kJ/mol, whereas the energy required for conformational change is almost always much smaller (on the order of a few to a few tens of kJ/mol). Second, with the notable exception of constrained rotation in rings, the reaction coordinate for conformational change is most often (but not always) well described in terms of a single recognizable geometrical coordinate, most commonly a torsion angle. The reaction coordinate for a normal reaction typically involves several geometrical coordinates changing in concert. 5 Interpreting Conformational Energy Profiles The energy profile for rotation about a single bond repeats itself in 360o. In fact, for many simple molecules, the rotation profile repeats itself in a fraction of 360o, typically 120o or 180o. For example, the energy profile for rotation about the carbon-carbon bond in ethane repeats itself in 120o, and full 360° rotation yields three identical energy minima and three identical energy maxima. Any description of rotation about the carbon-carbon bond in ethane must accordingly repeat itself at 120o intervals. One possibility is a single-term Fourier series. Etorsion (!) = ktorsion3 [1 - cos 3 (! - !eq )] Etorsion(ω) is the energy as a function of the torsion angle, ω (HCCH dihedral angle in the case of ethane), ωeq is the ideal torsion angle and ktorsion3 is a parameter. A single-term Fourier series will not suffice for most molecules, as it will also be necessary to account for terms that repeat themselves in intervals of 180o and 90o. Etorsion (!) = ktorsion1 [1 - cos (! - !eq )] + ktorsion2 [1 - cos 2 ( ! - !eq )] + ktorsion3 [1 - cos 3 (! - !eq )] ktorsion1 and ktorsion2 are additional parameters. Here, the first (one-fold) term accounts for the difference in energy between 0° and 180° arrangements, the second (two-fold) term accounts for the difference in energy between 0° (180°) and 90° (270°) conformers, and the third (three-fold) term accounts for the difference in energy between 0° (120o, 240o) and 60o (180o, 300o) conformers. 6 A Fourier series truncated to any order is an orthogonal polynomial. This means that the individual terms are linearly independent, and each may be interpreted on its own. For example, the one-fold terms in the Fourier series for both n-butane and 1,2-difluoroethane may be interpreted solely in terms of a preference for the anti arrangements (CCCC and FCCF dihedral angles of 180o) over syn arrangements (dihedral angles of 0o), irrespective of any other factors that may contribute to the overall energy profiles. E(CCCC) = -5 [1-cos(CCCC)] -2 [1-cos2(CCCC)] -8 [1-cos3(CCCC)] E(FCCF) = -8 [1-cos(FCCF)] -7 [1-cos2(FCCF)] -9 [1-cos3(FCCF)] For n-butane, the anti preference likely reflects the need to minimize crowding of methyl groups, whereas for 1,2-difluoroethane it likely reflects the need to reduce interactions of CF bond dipoles (fluorine is actually smaller than hydrogen). A chemist might refer to these preferences as due to steric and dipole-dipole effects, respectively. CH3 CH3 CH3 F VS. CH3 "crowded" "not crowded" F F VS. bond dipoles add F bond dipoles cancel Even for molecules as simple as n-butane and 1,2-difluoroethane, more than one term may contribute significantly to the Fourier series (and to the resulting conformational preferences). For example, two terms contribute strongly to the Fourier fit for n-butane and all three terms contribute roughly equally to the fit for 1,2-difluoroethane. In such cases, examination of the individual terms may provide the insight needed to understand a complex energy profile. A good example is provided by the energy curve for rotation about the CN bond in fluoromethylamine. Variation of the FCN: dihedral angle (: designates the non-bonded electron pair) from 0 to 360o gives rise to three energy minima. The lowest-energy 7 (anti) minimum corresponds to a dihedral angle of 180o and the two equivalent higher-energy (gauche) minima correspond to dihedral angles around 45o and 315o. This energy curve is qualitatively similar to that for n-butane, although there are significant quantitative differences. For one, the difference in energy between anti and gauche conformers in fluoromethylamine is much larger than the corresponding difference in n-butane. Also, the FCN: dihedral angles in the gauche conformers for fluoromethylamine differ from the idealized (staggered) values found in n-butane (~60o and ~300o). Finally, all three terms in the Fourier series for fluoromethylamine make sizable contributions, with the two-fold term (which makes only a modest contribution for n-butane) actually being the major contributor. E(FCN:) = -4 [1-cos(FCN:)] + 6 [1-cos2(FCN:)] -5 [1-cos3(FCN:)] Plots of the individual Fourier components provide clues to the overall shape of the energy curve. one-fold two-fold three-fold The one-fold term reflects the desire to arrange the dipoles associated with the CF bond and the lone pair such that they will subtract (180o) and not add (0o). This is the dipole-dipole effect noted previously for 1,2-difluoroethane. 8 The two-fold term favors coplanar (0o, 180o) over perpendicular (90o, 270o) arrangements. This may be interpreted as evidence for electron donation from the nitrogen lone pair into an empty σ* orbital associated with the CF bond. The resulting delocalization leads to stabilization. The three-fold term reflects the preference for staggered (60o, 180o, 300o) over eclipsed (0o, 120o, 240o) conformers. 9 Conformational Energy Profiles for Simple Molecules We next examine the conformational energy profiles about single bonds for a selection of simple molecules, fitting these to three-term Fourier series, and interpreting the results. The energy curves have all been provided from HF/6-31G* calculations. Higher-order terms typically do not contribute significantly for bond involving first and second-row main-group elements, although they may be important where heavier elements an in particular transition metals are involved. However, a three-term Fourier series is not able to … Methylamine and Ethylamine The geometry about nitrogen in methylamine, ethylamine and other organic amines is roughly tetrahedral. Three of the four tetrahedral directions point toward the directly-bonded atoms, while the fourth direction is occupied by a non-bonded pair of electrons (a lone pair). As a result, the nitrogen centers in amines are pyramidal and not planar. The energy plot for CN bond rotation in methylamine is quite similar to that shown previously for ethane; over 360o rotation, both show three identical energy minima corresponding to staggered structures and three identical energy maxima corresponding to eclipsed structures. That is to say, the CH single bonds in methylamine prefer to stagger the nitrogen lone pair in the same way that the CH single bonds in ethane prefer to stagger each other. The only significant difference between the two energy curves is a 50% reduction in the energy difference between staggered and eclipsed conformers (~8 kJ/mol in methylamine vs. ~12 kJ/mol in ethane). 10 As was the case of ethane, only the three-fold term in the Fourier series contributes significantly. Given the similarity of energy profiles for ethane and methylamine, it is not unexpected that the plot for CN bond rotation in ethylamine is qualitatively similar to that for n-butane. There are, however, significant differences. For one, the anti and gauche minima in methylamine have nearly the same energy. Also, the energy barrier connecting the two gauche conformers in methylamine (through a syn structure) is much smaller than the analogous barrier in n-butane. This suggests that destabilizing interaction of the nitrogen lone pair and a CC single bond is of less consequence than that between two CC bonds. Finally note that the three-fold term dominates the Fourier series describing CN bond rotation in ethylamine. E(HCN:) = 1 [1-cos(HCN:)] + 1 [1-cos2(HCN:)] -5 [1-cos3(HCN:)] Energy Profiles for 1-Chloropropane and 1,2-Dichloroethane: As described earlier, rotation about the central carbon-carbon in n-butane by 360o leads to an energy curve with three minima. The anti conformer (CCCC torsion angle = 180o) is ~4 kJ/mol lower in energy than the pair of identical gauche conformers (CCCC torsion angles ~120o and ~240o). The usual explanation for the preference is that a methyl group is larger than hydrogen, and unfavorable non-bonded contacts (steric effects) will be smaller for the anti conformer than for the gauche conformers. Finally, note that energy barriers separating anti and gauche conformers are small enough to ensure their rapid equilibration. 11 Use the HF/6-31G* model to obtain an energy profile for rotation about the central carbon-carbon bond for 1-chloropropane. Step from 0 to 180o in 20o increments. (It is not necessary to step all the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Is this profile similar to that for n-butane? Which conformer (anti or gauche) is preferred and by how much? What is the roomtemperature equilibrium distribution of the two conformers? What does the similarity or difference say about the non-bonded interaction of chlorine and methyl (in 1chloropropane) relative to the interaction of two methyl groups (in n-butane)? Use the HF/6-31G* model to obtain an energy profile for rotation about the carboncarbon bond in 1,2-dichloroethane. Is what you find consistent with previous results for n-butane and 1-chloropropane? Elaborate. Energy Profile for CO Bond Rotation in Ethanol: Obtain an energy profile for rotation about the central carbon-carbon bond in ethanol. Use the HF/6-31G* model and step from 0 to 180o in 20o increments. (It is not necessary to step all the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Which conformer (anti or gauche) is preferred and by how much? What is the roomtemperature equilibrium distribution of the two conformers? What does the similarity or difference say about the non-bonded interaction of the OH and CC bonds relative to the interaction of two CC bonds (in n-butane)? Hydrazine The energy profile for rotation about the NN bond in hydrazine by 360o closely resembles the curve for rotation about the OO bond in hydrogen peroxide presented at the beginning of this chapter. It incorporates two identical energy minima, corresponding roughly to the two possible arrangements with the non-bonded electron pairs on nitrogen (lone pairs) perpendicular, and two different energy maxima corresponding to arrangements in which they are coplanar. Both NH bonds eclipse as do the lone pairs in the higher-energy maximum (~44 kJ/mol above the minima). The other energy maximum is very broad and only ~13 kJ/mol 12 above the minima. It corresponds to a range of conformers centering on a structure in which the two lone pairs are anti to each other. E(ϕ ) = 11 (1-cosϕ ) + 14 (1-cos2ϕ ) + 4 (1-cos3ϕ ) The Fourier series is dominated by the one and three-fold terms. The former shows that the anti coplanar geometry (:NN: torsional angle = 180o) is favored over the corresponding syn coplanar arrangement (:NN: torsional angle = 0o). This both minimizes unfavorable steric interactions in the syn coplanar arrangement and leads to a canceling of local dipole moments associated with the nitrogen lone pairs. H HN H N H HN H N H H The large two-fold term in the Fourier fit shows that the way to minimize lone pair-lone pair interaction is to keep the lone pairs perpendicular. H HN H H H N HN H N H Energy Profile for NN Bond Rotation in Methylhydrazine: Use the HF/6-31G* model to obtain an energy profile for rotation about the nitrogen-nitrogen bond in methylhydrazine. Step from 0 to 360o in 20o increments and fit to a Fourier series. Compare and contrast the energy profile (and the fit) with that of hydrazine. How many energy minima does the curve contain? How many unique conformers of methylhydrazine are there? If there is more than one conformer, are any of the nonlowest-energy conformers likely to be sufficiently abundant at room temperature to actually be observed. (Use >1% as a cutoff.) Tetrafluorohydrazine: Obtain an energy profile for rotation about the NN bond in tetrafluorohydrazine and obtain a Fourier fit. Use the HF/6-31G* model and step (:NN: dihedral angle) from 0 to 180o in 20o increments. (It is not necessary to step all 13 the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Is this profile qualitatively similar to that for for insofar as the location of the energy minimum and the locations and heights of the rotational barriers? Which term(s) dominate the Fourier fit? Point out any significant differences between the two and provide a rationale. Dinitrogen Tetroxide: Dinitrogen tetroxide (O2NNO2) is an intermediate oxidation product of hydrazine. Are the two nitrogen centers coplanar or perpendicular (or somewhere in between)? To tell, obtain the equilibrium geometry using the B3LYP/6-31G* model. Start with a twisted geometry. Rationalize your result. Hydrogen Peroxide We return to hydrogen peroxide, the molecule that opened this chapter. As shown earlier, the energy curve for 360o rotation about the OO bond shows a pair of identical minima with HOOH torsional angles around 120o and 240o. These may be interconverted either via an anti (HOOH torsion angle = 180o) energy maximum that is only ~5 kJ/mol above the minima, or by a syn (HOOH torsion angle = 0o) energy maximum that is ~40 kJ/mol above the minima. The location (value of the dihedral angles) of the two energy minima in hydrogen peroxide warrants comment. Most chemists would picture the molecule as incorporating two sp3 hybridized (“tetrahedral”) oxygen atoms (as in water). Two of the hybrids would be used to construct the single bonds to other oxygen and to hydrogen, and the two remaining hybrids would be used to hold the two “equivalent” lone pairs. Such a hybrid model is consistent with the HOO bond angle of 102o obtained from HF/6-31G* calculations. However, same model also suggests that the observed 120o dihedral angle should lead to an eclipsing interaction involving one lone pair on each oxygen, and a pair of eclipsing interactions involving the other oxygen lone pair and an OH bond. Such an arrangement would, therefore, not be expected to be favorable. 14 H H The Fourier fit provides a clue to what is going on. E(ϕ ) = 16 (1-cos ϕ ) + 9 (1-cos2 ϕ ) + 1 (1-cos3 ϕ ) First, it reveals that the three-fold term (corresponding to the difference between staggered and eclipsed structures) is not very important. Rather, the fit is dominated by the one and two-fold terms. The one-fold term (favoring of an anti coplanar geometry over a syn coplanar arrangement) has the same origin as the analogous one-fold term in hydrazine, that is, the desire to minimize the sum of local dipole moments. The two-fold term (favoring a perpendicular over a planar geometry) may be rationalized by recognizing that the two lone pairs on oxygen are different. The higher-energy (π) lone pair is perpendicular to the plane made by the two bonds to oxygen while the lower-energy (σ) lone pair lies in the plane. Minimizing interaction between the two high-energy π lone pairs is much more important that minimizing interaction between σ and π lone pairs. Lone Pairs in Water and Hydrogen Sulfide: Describe the two highest-occupied molecular orbitals of water as obtained from a HF/6-31G* calculation. Are they primarily bonding, non-bonding or antibonding? Is the highest-occupied orbital a σ orbital or a π orbital? Repeat your calculations and analysis for hydrogen sulfide. Point out (and rationalize) any significant differences between the two molecules. Dimethyl Peroxide: Obtain an energy profile for rotation about the OO bond in dimethyl peroxide and obtain a Fourier fit. Use the HF/6-31G* model and step from 0 to 180o in 20o increments. (It is not necessary to step all the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Is this profile qualitatively similar to that for hydrogen peroxide insofar as the location of the energy minimum and the locations and heights of the rotational barriers? Which term(s) dominate the Fourier fit? Point out any significant differences between the two and provide a rationale. Hydrogen Disulfide: Obtain an energy profile for rotation about the sulfur-sulfur bond in hydrogen disulfide and provide a Fourier fit. Use the HF/6-31G* model and step from 0 to 180o in 20o increments. (It is not necessary to step all the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Is this 15 profile qualitatively similar to that for hydrogen peroxide insofar as the location of the energy minimum and the locations and heights of the rotational barriers? Which term(s) dominate the Fourier fit? Point out any significant differences between the two and provide a rationale. Propene Unlike the previous examples which involved bonds connected by sp3 hybridized centers, the single bond in propene is between sp3 and sp2 centers. A plot of energy vs. the C=C-C-H torsion angle shows three identical minima and three identical maxima. This plot closely resembles that for ethane, and the associated Fourier fit like that for ethane is dominated by the three-fold term. Even the rotational barriers are similar (~8 kJ/mol vs. ~12 kJ/mol in ethane). The energy minima for both molecules correspond to arrangements in which CH bonds stagger. In the case of propene, this means that one of the methyl CH bonds eclipses the carbon-carbon double bond. The latter preference (single bonds eclipse double bonds) is quite general extending to CC, CN, CO and CS single bonds on the one hand and CN and CO double bonds on the other. 1-Butene: Use the HF/6-31G* model to obtain an energy profile for rotation about the central CC single bond in 1-butene. Step from 0 to 180o in 20o increments. (It is not necessary to step all the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Is this profile qualitatively similar to that for propene insofar as the location of the energy minimum and the locations and heights of the rotational barriers? Which term(s) dominate the Fourier fit? Point out any significant differences between the two and provide a rationale. cis-2-Butene: Starting from a structure of cis-2-butene in which both HCC=C dihedral angles to 0° (eclipsed), calculate and plot the energy with change in one of these dihedral angles from 0° to 180° in 20° steps. Use the HF/6-31G* model. Characterize the structure of the energy minima as staggered or eclipsed relative to 16 the CC double bond. Rationalize any difference between energy minima and maxima in cis-2-butene (the rotational barrier) with the corresponding quantity in propene. Acetic Acid Acetic acid incorporates to two rotatable single bonds and two different energy plots can be generated. The first corresponds to rotation of the methyl group, and assumes a structure in which the OH bond eclipses the CO double bond (see discussion following). The plot is nearly identical to that for propene. The three minima correspond to the methyl CH bonds eclipsing the CO double bond and three maxima correspond to these bonds staggering the CO double bond. The rotational barrier is <3 kJ/mol, much smaller than that in propene. The second energy plot is much more interesting. It is for rotation about the OH bond, and assumes that a CH bond eclipses the CO double bond (see previous discussion). There are two different energy minima, corresponding to syn (O=CCH torsional angle = 0o) and anti (O=CCH torsional angle = 180o) conformers, connected by two equivalent energy maxima (O=CCH torsional angles ~90o and ~270o). E(ϕ) = 14 (1-cos ϕ) + 21 (1-cos2 ϕ) +1 (1-cos3 ϕ) 17 The Fourier fit is dominated by the one and two-fold terms. The former accounts for the ~30 kJ/mol difference in energy between syn and anti conformers. The syn conformer is preferred in order that the local dipole moment of the C=O bond (+C=O-) and the local dipole moment due to the σ lone pair on the OH group act to cancel rather than to reinforce each other. This is reflected in a reduction in the total dipole moment from ~4.7 debyes in the anti conformer where the two local dipoles point in the same direction, to ~1.8 debyes in the syn conformer where they point in opposite directions. H O C H O O C H3C O H3 C The two-fold term reflects the fact that interconversion of syn and anti is difficult, and that arrangements in which the carbonyl group and the OH bond are coplanar are strongly preferred over arrangements in which they are perpendicular. This may be rationalized by suggesting that electron donation from the high-energy π lone pair on the OH group into the electron deficient carbon of the carbonyl group is energetically beneficial and is maximized where the two are coplanar. O C O The three-fold term is much smaller than the one and two-fold terms, suggesting that single bond staggering (and staggering of bonds and lone pairs) is less important than other factors. Methyl Acetate: Use the HF/6-31G* model to obtain an energy profile for rotation about the central CO single bond in methyl acetate, CH3C(=O)OCH3. Step from 0 to 180o in 20o increments. (It is not necessary to step all the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Is this profile qualitatively similar to that for acetic acid insofar as the location of the energy minimum and the locations and heights of the rotational barriers? Which term(s) dominate the Fourier fit? Point out any significant differences between the two and provide a rationale. Carbonic Acid: Three conformers in which all six atoms lie in one plane can be drawn for carbonic acid. 18 H H O H O C O C O H O O O C H O O H Use the HF/6-31G* model to obtain equilibrium geometries for all three. Which conformer is preferred? Is your result consistent with the preferences previously noted for acetic and methyl acetate? Elaborate. Does the ordering of dipole moments for the three conformers parallel the ordering of energies? Does what you find support or refute the previous interpretation given to the one-fold terms in acetic and methyl acetate? Elaborate. 1,3-Butadiene The single bond in 1,3-butadiene involves two sp2 carbon hybrids. Organic chemists would assume that the two (“conjugated”) double bonds are coplanar, either cis or trans to each other. They would be half right! While trans-planar 1,3-butadiene is the global minimum on the energy curve, the cis-planar conformer is actually an energy maximum. There is a nearby energy minimum (CCCC torsional angle ~40o) that is ~12 kJ/mol higher in energy than the trans form. This structure represents a compromise between the desire for the two double bonds to be coplanar and the need to minimize non-bonded steric interaction of the terminal methylene groups. E(φ) = -4 (1-cosφ) +8 (1-cos2φ) -5 (1-cos3φ) 19 First, note that the overall quality of the Fourier fit is not as good as we have seen in previous examples. All three terms contribute significantly. The one-fold term likely reflects unfavorable interaction between the terminal CH2 groups and is consistent with the fact that, whereas the trans conformer is planar, the corresponding “cis” structure is twisted. The two-fold reflects the desire for π systems to be coplanar (conjugation). No simple “chemical” interpretation may be attached to the three-fold term. 2,3-Dimethyl-1,3-butadiene: Use the HF/6-31G* model to obtain an energy profile for rotation about the central CC single bond in 2,3-dimethyl-1,3-butadiene. Step from 0 to 180o in 20o increments. (It is not necessary to step all the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Is this profile qualitatively similar to that for 1,3-butadiene insofar as the location of the energy minima? Specifically, is there a trans coplanar minimum? Is there a cis minimum that is actually slightly distorted from planarity? Is the trans minimum lower in energy than the cis minimum? Which term(s) dominate the Fourier fit? Acrolein and Glyoxal: Use the HF/6-31G* model to obtain an energy profile for rotation about the central CC single bond in acrolein (H2C=C(H)-C(H)=O). Step from 0 to 180o in 20o increments. (It is not necessary to step all the way to 360o to identify the unique energy minima and to obtain the connecting barriers.) Is this profile qualitatively similar to that for 1,3-butadiene insofar as the location of the energy minima? Specifically, are the CC and CO double bond in the “cis” structure of acrolein coplanar or (as in the case of 1,3-butadiene) and the locations and heights of the rotational barriers? Which term(s) dominate the Fourier fit? Point out any significant differences between the two and provide a rationale. Repeat your calculations for glyoxal (O=(H)C-C(H)=O) and answer the analogous questions. Styrene: Styrene (C6H5-C(H)=CH2), while larger than 1,3-butadiene is simpler, as there is only a single way for the CC double bond and phenyl ring to be coplanar. As with 1,3-butadiene, most organic chemists assume that styrene is a planar molecule. Is it? Use the HF/6-31G* model to obtain an energy profile for rotation about the CC single bond. You only need to step from 0 to 90o (in 15o increments). Biphenyl: Is biphenyl (C6H5-C6H5) a planar molecule or does it assume a twisted geometry? Obtain the equilibrium geometry using theHF/6-31G* model starting from a structure that is slightly distorted from planarity. If you find that the two rings are not coplanar, obtain the geometry of molecule where they are coplanar (that is, start with a coplanar 20 structure) and calculate the energy barrier. How does it compare with the corresponding energy barriers in 1,3-butadiene and in styrene? λ max vs. Diene Conformation: A very simple way to model the energy of an electronic transition from ground to excited state (λmax in the UV/vis spectrum) is to assume that it parallels the difference in energy between the highest-occupied and lowest-unoccupied molecular orbitals (the HOMO-LUMO gap). To what extent does this gap (and λmax) for a diene depend conformation? To what extent does the change in the gap parallel the change in energy of the ground-state molecule with change in conformation? Obtain energy profiles for 1,3-butadiene and 2-methyl-1,3-butadiene, varying the CCCC dihedral angle in each from 0° to 180° in 20° steps. Use the HF/6-31G* model. For each diene, plot both the energy and the HOMO/LUMO gap as a function of dihedral angle and answer the following questions: At what dihedral angle is the HOMO/LUMO gap the largest? At what dihedral angle is it the smallest? Is there much difference in the HOMO/LUMO gap between cis and transplanar diene conformers? Does the variation in total energy closely follow the HOMO-LUMO gap or are the two uncorrelated? Molecules Incorporating Transition Metals Ferrocene and bis-Benzene Chromium: The two cyclopentadienyl ligands in ferrocene can either eclipse or stagger one another. `` The preference would be expected to be small both because the ligands are far apart and because the two conformers differ by a torsion angle of only 36o. Similarly, the two benzene ligands in bis-benzene chromium can either eclipse or stagger. Use the B3LYP/6-31G* model to obtain equilibrium geometries of both eclipsed and staggered conformers for both ferrocene and bis-benzene chromium. For each, indicate which conformer is favored. Are the energy conformer energy differences in these two molecules of the same order of magnitude as previously noted for main-group compounds, for example, ethane, or are they smaller or larger? CO OC C0 OC OC CO CO C0 CO CO CO CO OC CO O C Mn Mn CO OC OC OC CO 21 Conformational Changes from Constrained Rotation, Inversion, Pseudorotation In addition to “free” rotation about single bonds there are several other ways available for changes in molecular shape to occur. These fall into three broad catagories: constrained rotation, inversion and pseudorotation. Constrained Rotation Constrained rotation involves changes in the dihedral angles involving atoms in a ring. Six and seven-membered rings typically exhibit two or three distinguishable conformers, and larger rings almost always exhibit three or more conformers. Four and five-membered rings may also undergo constrained rotation, but the different conformers that result are typically very similar and difficult to distinguish experimentally. Constrained rotation generally involves changes in several dihedral angles either stepwise or in concert in order to pass from one conformer to another. As such, it is not as straightforward to describe the motion pathway connecting ring conformers as it is the motion connecting single-bond conformers. With few exceptions, the best that chemists have been able to do is to construct “cartoons” that satisfy what is known about the energies of the different conformers and the barriers separating them. More to the point of the present text, it will normally not be possible to construct the kinds of simple diagrams and fitting functions used up to this point to describe and interpret free rotation about single bonds. By far, the most famous example cyclohexane, a molecule that is known to exist in a so-called chair geometry (that drawn in all organic chemistry textbooks). Here, all six carbons are equivalent and the twelve hydrogens are divided into two sets of six equatorial hydrogens and six axial hydrogens. A “normal” temperatures only a single resonance at 1.36 ppm relative to tetramethylsilane is seen in the proton NMR spectrum of cyclohexane, despite the fact that the equatorial hydrogens are chemically distinct 22 from the axial hydrogens. Only when the sample is cooled to -90oC does the spectrum show the expected pair of resonances (at 1.12 and 1.60 ppm). These two observations suggest that a low-energy process exists, leading to the interconversion of equatorial and axial positions in cyclohexane. ax eq eq* ax* In addition to the two (equivalent) chair conformers, cyclohexane possesses a third stable conformer, commonly known as a twist-boat. It is known experimentally to be ~25 kJ/mol higher in energy than chair cyclohexane, meaning that it makes up only 0.xx% of the total sample at room temperature. The temperature would need to lowered to xx K in order for twist-boat cyclohexane to make up 10% of a sample and thus be easily observed. One plausible mechanism for interconversion among chair conformers of cyclohexane involves the twist-boat conformer as an intermediate. An “animated” energy profile obtained from HF/6-31G* calculations shows what is going on. At the outset, the two ends (CH2 groups) of the chair conformer point in opposite directions. The end that points down moves upward, until five of the six carbons roughly lie in a single plane. This is the transition state (a so-called half-chair conformer). Further upward motion leads to the twist-boat intermediate. The process is reversed with the other CH2 group (starting from the twist boat). It moves down through a second half-chair structure and then to the other chair conformer. half chairs twist boat chair c hai r 23 Open the document chair-chair interconversion in cyclohexane and step through (or animate) the sequence of structures. Identify the two stable conformers (chair and twistboat) and the transition state (half-chair). Note that the overall process appears to occur in a stepwise fashion. Proton NMR Spectrum of Cyclohexane: Calculations can be used to assist in the assignment of experimental NMR spectra. A simple example is provided by lowtemperature proton NMR spectrum of cyclohexane, which as previously indicated shows resonances at 1.12 and 1.60 ppm. Use the HF/6-31G* model to say which resonance arises from the equatorial hydrogens and which arises from the axial hydrogens. Twist-Boat Cyclohexanes: Obtain equilibrium geometries for both chair and twist boat conformers of cyclohexane using the HF/6-31G* model. Is the energy difference between the two conformers consistent with the experimental estimate? Calculate the room-temperature equilibrium distribution of chair and twist-boat conformers. Is the higher-energy conformer likely to be seen? Elaborate. Repeat your calculations for 1,1-dimethylcyclohexane and 1,2-difluorocyclohexane. Is either likely to show a greater percentage of the twist-boat conformer than cyclohexane itself? Dipole Moments in Fluorocyclohexane: Fluorocyclohexane can adopt a conformation which either places the fluorine in an equatorial or axial position. Use the HF/6-31G* model to obtain equilibrium geometries for both conformers, and the use the Boltzmann equation to calculate an average dipole moment. Is the Boltzmann distribution dominated by one conformer or do both conformers contribute significantly? Distribution of Conformers at Equilibrium: Calculate the room-temperature equilibrium distribution of equatorial and axial conformers of methylcyclohexane and tert-butylcyclohexane. Use the HF/6-31G* model. What temperature would provide a 90:10 distribution of lower:higher energy conformer for each? Boat Cyclohexane: The actual process by which chair conformers of cyclohexane interconvert may actually be more complicated than that described above, and involve two (equivalent) twist-boat intermediates connected by a boat transition state. This picture suggests that the transition state connecting chair cyclohexane to the twistboat intermediate is higher in energy than the transition state connecting twist-boat intermediates. You already have obtained energies for chair and twist-boat conformers 24 from the HF/6-31G* model. Now, obtain data for the two transition states. For halfchair cyclohexane, start the structure with a structure with five carbons roughly in one plane; for boat cyclohexane, start with a structure in which opposing CH2 groups point in the same direction. Are your data consistent with this picture? Specifically, is the energy of the boat transition state lower than that of the half-chair transition state? CH Eclipsing Interactions in Cycloalkanes (no calculations required): The CH bonds in the chair form of cyclohexane are nearly perfectly staggered. On the other hand, it is not possible to completely stagger the CH bonds in seven-membered and larger cycloalkanes. As a consequence, it might be expected that hydrogenation of these compounds leading to the corresponding n-alkanes would be more exothermic than hydrogenation of cyclohexane. CnH2n + CH3(CH2)4CH3 CH3(CH2)n-2CH3 + C6H12 Build cyclohexane to cyclodecane and n-hexane to n-decane in a single document, and replace your structures with the corresponding T1 entries from the Spartan Molecular Database. Is hydrogenation of cycloheptane and larger cycloalkanes more exothermic than hydrogenation of cyclohexane? Is there a correlation between the energy of hydrogenation and the number of CH eclipsing interactions. (The T1 structures that you have employed correspond to the lowest-energy conformer.) Inversion Inversion is the name given to a process whereby a three-coordinate pyramidal center, most commonly a nitrogen or phosphorus center, passes through a planar or nearly planar transition state leading to an equivalent pyramidal form, for example, in ammonia. H H N H H H N H H H H N The inversion barrier (energy difference between pyramidal and planar forms) is typically very small (24 kJ/mol for ammonia), meaning that the process is hard to stop. Note, that unlike free and constrained rotation discussed earlier (and pseudorotation to be discussed in the next section), inversion will not normally lead to molecules with different energies. However, inversion of molecules where the pyramidal center is bonded to three different atoms or groups leads to a change in chirality at that center, that is, to the other enantiomer. In most cases, the low barrier to inversion means that a racemic mixture results. 25 Nitroamide: Two opposing factors compete to determine the equilibrium geometry of nitroamide, O2N-NH2. One is the preference for the amino group to be pyramidal and not planar and the second that delocalization of the lone pair on the amino group into the nitro group is best accommodated by a planar geometry. Is nitroamide planar or non planar? Use the B3LYP/6-31G* model to decide. Start from a non-planar structure. If it is non-planar, what is the barrier to inversion? To answer, you need to determine the geometry of planar nitroamide and calculate the energy difference between non-planar and planar structures. Inversion in Cyclic Amines: Pyramidal inversion at nitrogen that is part of a three or four-membered ring might be expected to be more difficult that inversion of an acyclic amine. This is because the transition state incorporates a planar nitrogen center (ideal bond angles of 120o) which is more difficult to achieve if one of the angles is constrained to ~60o or ~90o. Use the HF/6-31G* model to obtain geometries for dimethylamine (to act as a reference), aziridine and azetidine and their respective inversion transition states. H3 C N H H H N N CH3 H2C H2 C CH2 CH2 C H2 Calculate inversion barriers (difference between pyramidal and planar forms) for the three molecules. Is the barrier in aziridine significantly larger than that in dimethylamine? Is the barrier in azetidine midway between those in dimethylamine and aziridine, or is it much closer to one of them? Rationalize you result. Pyramidal Inversion in Phosphine and Trifluorophosphine: Phosphine (PH3) is also pyramidal and inverts via a planar transition state. Obtain both the equilibrium geometry and transition state using the HF/6-31G* model. Is this barrier smaller, larger or about the same as that for ammonia? Provide a rationale if it is markedly different. Repeat your calculations for trifluorophosphine (PF3). Rationalize any significant increase or decrease in inversion barrier relative to that for phosphine. Pyramidal Inversion of Sulfoxides: The anti-ulcer drug esomeprazole (Nexium) is the S enantiomer of an older unresolved drug. While both enantiomers are active, the R enantiomer is metabolized faster than the S enantiomer (the pure S compound lasts longer lasting than the racemic mixture). 26 Esomeprazole does not contain any chiral carbon centers, and the two enantiomers differ only because of the fact that the sulfoxide group is pyramidal and not planar. Were racemization to occur at room temperature (via inversion at sulfoxide), the pure S enantiomer would not be any more effective than the racemate, and the “new” compound would not provide additional market value. In order for racemization not to happen, the inversion barrier needs to be >150 kJ/mol and preferable > 200 kJ/mol. Estimate the barrier to racemization in espmeprazole using methyl vinyl sulfoxide as model compounds. First obtain the “correct” equilibrium geometry (with a pyramidal sulfoxide group), and then a geometry for the transition state (with a planar sulfoxide group). For the latter, start with a planar structure (with Cs symmetry) to avoid having to do transition-state search. Use the HF/6-31G* model. What is the energy required for inversion in methyl vinyl sulfoxide? Do you results suggest that racemization of esomeprazole via inversion is likely to occur at room temperature? Elaborate. Pseudorotation Pseudorotation exchanges equatorial and axial positions in fivecoordinate, trigonal-bipyramidal centers, for example, the five-coordinate phosphorous center in phosphorous pentafluoride. equatorial F F axial F equatorial P F F axial Here, the process involves simultaneously decreasing (from 180o) the FPF angle involving two axial fluorines and increasing (from 120o) the FPF angle involving two of the equatorial fluorines. This leads to a structure in which what were the two axial fluorines and two of the equatorial fluorines form the base of a square-based pyramid. This is the transition state. Continuing the motion returns to the stable trigonal-bipyramidal geometry but with axial and equatorial fluorines exchanged. Repeated pseudorotation moves fully scramble the fluorines. F F P F F F F P F F F F HF/6-31G* calculations confirm that the transition state for pseudorotation in phosphorous pentafluoride adopts a square-based pyramid structure and shows a barrier of ~25 kJ/mol. The latter is consistent with failure of 19F 27 NMR spectroscopy to distinguish between equatorial and axial sites even at temperatures as low as -100o C. 19 F NMR Spectrum of Phosphorous Pentafluoride: Use the B3LYP/6-31G* model to calculate the equilibrium geometry and 19F NMR spectrum of phosphorous pentafluoride. Are the chemical shifts for equatorial and axial fluorines distinct? Provide and average and compare with the experimental shift (xx ppm). Structure of PF3Cl2: PF3Cl2 can exhibit three possible structures, with two, one or no fluorines in axial positions. Use the B3LYP/6-31G* model to assign the lowest-energy structure. Is your result consistent with the fact that the “high-temperature” 19F NMR spectrum of PF3Cl2 exhibits only a single resonance (split into doublets due to 19F-31P coupling)? Elaborate. Calculate the transition state for pseudorotation between the lowest and second lowest energy isomers. Is your result consistent with the fact that the “hightemperature” 19F spectrum shows two resonances, (one a doublet of doublets and the other a doublet of triplets)? Elaborate. Pseudorotation in Iron Pentacarbonyl: Like PF5, iron pentacarbonyl, Fe(CO)5, adopts a trigonal bipyramidal geometry with distinct equatorial and axial positions. Use the B3LYP/6-31G* density functional model to calculate geometries for both trigonal bipyramidal (D3h symmetry) and square-based pyramid (C4v symmetry) forms of iron carbonyl. (Even though the latter is presumed to be a transition state, if you start with a C4v symmetry structure, this will be maintained in the geometry optimzation.) Calculate the activation energy for pseudorotation. Is it significantly higher than that for PF5? Is it likely that the 13C NMR spectrum likely to exhibit one or two resonances? Elaborate. Competing Processes The fact that single-bond rotation (including constrained rotation) and inversion processes have similar energy requirements suggests that they may “compete”. A good example of this is provided by dimethylisopropylamine, the proton NMR spectrum of which at 170K shows two different resonances corresponding to methyl groups but four different CH3 resonances at 93K. This suggests that the molecules prefers an AG (or GA) conformation in which one methyl group on nitrogen is anti (A) to the hydrogen on the isopropyl group and the other is gauche (G), and that equilibrium between the AG and GA forms is rapid. Were the symmetrical (GG) conformer to be the dominant from, then only two resonances would be observed irrespective of temperature. 28 The experimental result is supported by HF/6-31G* calculations. These show that GA (AG) conformer is xx kJ/mol low in energy that the GG conformer, corresponding to an equilibrium distribution GA:GG of xx:yy at 170K and xx:yy at 93K. Interconversion of GA and AG conformers may occur directly or in a two step process involving the GG conformer as an intermediate. There are two possibilities in the former case. Either the transition state may involve a planar nitrogen center (inversion) or a structure in which both pairs of methyl groups eclipse. In the latter case, the transition state (leading to and away from the GG conformer) has only one pair of methyl groups eclipsed. Experiments are not able to distinguish which pathway is actually preferred, or whether both occur. 29 Limiting Behavior of Hartree-Fock, B3LYP and MP2 Models for Assigning Lowest-Energy Conformation and Accounting for RoomTemperature Conformer Distributions We first set out to establish the limiting behavior of Hartree-Fock, B3LYP and MP2 models with regard to properly assign lowest-energy conformation and to account for conformational energy differences. As with previous comparisons involving equilibrium geometries and vibrational frequencies (Chapter P2), reaction energies (Chapter P3) and transition-state geometries and activation energies (Chapter P4), this will allow us to separate the effects of the LCAO approximation from effects arising from replacement of the exact many-electron wavefunction by an approximate Hartree-Fock, B3LYP or MP2 wavefunction. While it is not possible to actually reach the limit, it is possible to use a sufficiently large basis set such that the addition of further functions to the basis will have only a small effect on calculated equilibrium geometry. The cc-pVQZ basis set has been employed as a standard for acyclic systems and the cc-pVTZ basis set has been employed for cyclic systems. As previously commented, cc-pVQZ is about as large a basis set as can be applied for geometry calculations on molecules with more than a few non-hydrogen elements. The cc-pVTZ basis set is more widely applicable and can be expected to yield nearly identical results. Table P5-1 compares room-temperature conformer distributions for a variety of molecules calculated from Hartree-Fock, B3LYP and MP2 models with the cc-pVQZ basis set with experimental distributions. All molecules are very small and have only two stable conformers. Aside from practical concerns dealing with the calculations, it should be noted that reliable experimental data are typically available only for very simple molecules. Discussion … 30 Table P5-1: Room Temperature Boltzmann Conformer Ratios from “Limiting” Hartree-Fock, B3LYP and MP2 Models molecule low energy/ high-energy conformer n-butane anti/gauche 85 82 72 76 1-butene skew/cis 74 66 54 59 trans/gauche 100 100 99 99 acrolein trans/cis 98 97 97 95 n-methyl formamid e cis/trans 82 83 89 92 1,3-butadiene formic acid % low-energy conformer Hartree-Fock B3LYP MP2 expt. cis/trans 100 100 100 100 1,2-difluoroethane gauche/anti 60 81 78 72 1,2-dichloroethane anti/gauche 96 94 91 86 ethanol anti/gauche 60 49 53 55 methylcyclohexane equatorial/axial 98 99 95 95 fluorocyclohexane equatorial/axial 57 62 51 57 chlorocyclohexane equatorial/axial 84 82 60 70 2-chlorotetrahydropyran axial/equatorial 98 100 100 95 31 Behavior of Practical Hartree-Fock, B3LYP and MP2 Models for Assigning Lowest-Energy Conformation and Accounting for RoomTemperature Conformer Distributions Except for very small molecules, Hartree-Fock, B3LYP and MP2 models with large basis sets such as cc-pVQZ and cc-pVTZ are not currently practical. These (and even larger) basis sets are primarily of value in judging the limits of the underlying models. Two smaller Gaussian basis sets will be examined, 6-311+G** and 6-31G*. The latter may be routinely applied to molecules with weights up to 400-500 amu, while the former is restricted to molecules with weights up to 300-400 amu. Table P5-2 compares room-temperature conformer distributions for a variety of molecules calculated from Hartree-Fock, B3LYP and MP2 models with the 6-31G* and 6-311+G** basis sets with experimental distributions. The same set of molecules used previously to uncover the limiting behavior of the three models are examined here. Discussion … 32 Table P5-2: Room Temperature Boltzmann Conformer Ratios from Practical Hartree-Fock, B3LYP and MP2 Models molecule low energy/ high-energy conformer n-butane anti/gauche 84 1-butene Hartree-Fock 6-31G* 6-311+G** 79 B3LYP 6-31G* 6-311+G** 79 MP2 6-31G* 6-311+G** expt. 82 76 70 76 skew/cis 76 67 67 67 70 70 59 trans/gauche 99 100 100 100 99 99 99 acrolein trans/cis 95 97 95 98 93 98 95 n-methyl formamide cis/trans 86 86 76 84 84 88 92 formic acid cis/trans 100 100 100 100 100 100 100 1,2-difluoroethane gauche/anti 30 58 67 79 30 79 72 1,2-dichloroethane anti/gauche 96 96 95 94 96 92 86 1,3-butadiene ethanol anti/gauche 54 63 37 50 54 50 55 methylcyclohexane equatorial/axial 98 98 97 98 96 95 95 fluorocyclohexane equatorial/axial 37 54 42 58 24 54 57 chlorocyclohexane equatorial/axial 84 82 82 76 76 70 70 2-chlorotetrahydropyran axial/equatorial 99 99 100 100 99 99 95 33 Identifying the “Important” Conformer Up to this point in the chapter, we have assumed that the “important” conformer is the lowest-energy conformer. This is appropriate if what is of interest is the property of a system at equilibrium or the product of a reaction under thermodynamic control. More generally, a Boltzmann average of all conformers needs to be constructed, although in practice conformers with energies more than about 10 kJ/mol above the lowest-energy conformer will not contribute significantly to the average at normal temperatures. There are, however, situations where the important conformer will not necessarily be the lowest-energy conformer, at least the lowest-energy conformer of the isolated molecule. Conformational equilibrium may be influenced by environmental factors, for example, molecules in crystalline solids or small molecules bonded to proteins. Here, changes in conformation from those preferred by the isolated molecule may be necessary to ensure effective crystal packing or to reflect specific interactions with a protein. For example, according to 6-31G* calculations, the lowest-energy conformer of the anti breast cancer drug gleevec (shown as a tube model) is quite different from the conformer found in the protein (ball-and spoke model). Another situation is where the “important” refers to chemical reactivity for a process under kinetic control rather than thermodynamic control (see discussions in Chapter P4). A simple example is provided by the DielsAlder cycloaddition of 1,3-butadiene with acrylonitrile. + CN CN As detailed earlier in the chapter, 1,3-butadiene exists primarily in a trans conformation with the cis conformer being approximately 8 kJ/mol less stable. This means that (at room temperature) only about 5% of butadiene molecules will be in a cis conformation and able to react. The fact that the 34 reaction does occur is a consequence the Curtin-Hammett Principle. This states that because energy barriers separating conformers (typically 4-30 kJ/mol) are much smaller than those for chemical reaction (typically 100200 kJ/mol), conformers reach equilibrium much more rapidly than they react. In the case of the Diels-Alder reaction, equilibration between the higher-energy cis conformer and the lower-energy trans conformer is much faster and will be replenished throughout the reaction. chemical reaction "high-energy process" E equilibration among conformers "low-energy process" While it is clear that the products of kinetically-controlled reactions do not necessarily derive from the lowest-energy conformer, the identity of the reactive conformer is not evident. One reasonable hypothesis is that this is the conformer which is best “poised to react”, that is, the conformer that initially results from progression backward along the reaction coordinate starting from the transition state. Rates of Diels-Alder Reactions: 1,3-butadiene undergoes Diels-Alder cycloaddition with acrylonitrile more slowly than does cyclopentadiene. CN CN + CN CN + Is this simply a consequence of the fact that, whereas the double bonds in cyclopentadiene are properly disposed for reaction, additional energy is needed to move from the favored trans conformer of butadiene to a cis (or nearly cis) conformer? Alternatively, is cyclopentadiene inherently more electron rich than butadiene and, therefore, a more reactive diene? Use the HF/6-31G* model to establish the energy difference between the trans and (nearly) cis conformers of 1,3-butadiene. Use the 6-31G* model to obtain transition state geometries for Diels-Alder reactions of both 1,3-butadiene and cyclopentadiene with acrylonitrile, and then the 6-31G* model to obtain energies. Calculate activation energies for the two reactions using these data (along with energies for the reactants obtained in the previous step). Is your result in accord with the observation that the reaction with cyclopentadiene is faster? Is the 35 difference in activation energies between the two reactions of comparable magnitude to the difference in energies between trans and (nearly) cis-1,3-butadiene? Obtain electrostatic potential maps for cis-1,3-butadiene and cyclopentadiene, and display side-by-side using the same color scale. Which appears to be the more reactive diene? Explain your reasoning. Is your result consistent with the previous comparison of activation energy conformer energy differences? Elaborate. 36 ...
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This note was uploaded on 02/22/2010 for the course CHEM N/A taught by Professor Head-gordon during the Spring '09 term at University of California, Berkeley.

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