Low Symmetry in Molecules with Heavy Peripheral Atoms. The Gas

Sep 28, 2010 - When refining structures using gas electron diffraction (GED) data, assumptions are often made in order to reduce the number of require...
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Low Symmetry in Molecules with Heavy Peripheral Atoms. The Gas-Phase Structure of Perfluoro(methylcyclohexane), C6F11CF3 Graeme R. Kafka, Sarah L. Masters, Derek A. Wann, Heather E. Robertson, and David W. H. Rankin* School of Chemistry, UniVersity of Edinburgh, West Mains Road, Edinburgh, EH9 3JJ, U.K. ReceiVed: August 16, 2010; ReVised Manuscript ReceiVed: September 14, 2010

When refining structures using gas electron diffraction (GED) data, assumptions are often made in order to reduce the number of required geometrical parameters. Where these relate to light, peripheral atoms there is little effect on the refined heavy-atom structure, which is well defined by the GED data. However, this is not the case when heavier atoms are involved. We have determined the gas-phase structure of perfluoro(methylcyclohexane), C6F11CF3, using three different refinement methods and have shown that our new method, which makes use of both MP2 and molecular mechanics (MM) calculations to restrain the peripheral-atom geometry, gives a realistic structure without the need for damaging constraints. Only the conformer with the CF3 group in an equatorial position was considered, as ab initio calculations showed this to be 25 kJ mol-1 lower in energy than the axial conformer. Refinements combining both high-level and low-level calculations to give constraints were superior both to those based only on molecular mechanics and to those in which assumptions about the geometry were imposed. Introduction Gas electron diffraction (GED) is effectively the only method available for determining complete experimental structures of molecules that contain upward of 20 atoms in the gas phase. GED works well, provided the molecules have high symmetry. However, for structures with low symmetry, extra information is often required to allow reliable structure determinations. In the past, assumptions of local symmetry or about relative values of geometrical parameters were often made to reduce the number of refining parameters. These were applied most often to light atoms. For example, a methyl group often would be constrained to C3 or C3V local symmetry. However, ab initio calculations have shown that such assumptions often are not valid and that artificial constraints can have a serious and damaging influence on the resultant structure. Accordingly, several attempts have been made to eliminate the need for such symmetry assumptions. The MOCED (Molecular Orbital Constrained Electron Diffraction)1 and SARACEN (Structural Analysis Restrained by Ab initio Calculations for Electron diffractioN)2 methods were developed with this goal. MOCED uses ab initio values to constrain small differences between certain parameters, while SARACEN uses computed values as flexible restraints on refining parameters. Although these methods have enabled a far greater range of molecules to be studied using GED, studies still frequently rely on assumptions being made about the peripheral atoms in a structure. These constraints can significantly affect structures, particularly of sterically crowded molecules, where the outer atoms, usually hydrogen, may be displaced significantly by interactions with other atoms. Removing the symmetry constraints on the light atoms using the SARACEN method is possible in principle, but it would lead to a very large number of refining parameters, only a few of which would be sensitive * Corresponding author, [email protected].

to the GED data. Other parameters would simply refine to give values and standard deviations corresponding to those of the restraints. To overcome this problem, the DYNAMITE (DYNAMic Interaction of Theory and Experiment)3 method was developed. This uses low-level calculations (usually molecular mechanics (MM)) linked to the refinement program to update the positions of the light atoms dynamically throughout the refinement process. The need for symmetry assumptions about the peripheral atoms is therefore removed, allowing for complete asymmetry, if required, but the number of refining parameters is not increased. However, MM is based on a set of empirical parameters, so light atoms are not completely free to find their optimal geometries. Ideally, an ab initio computational method would be used for the dynamic updating of the light-atom positions. However, limitations of computing time mean that such methods cannot be implemented directly. For this reason we developed the SEMTEX (Structure Enhancement Methodology for Theory and Experiment)4 method. SEMTEX indirectly includes the results of ab initio calculations in the refinement process in the form of a calculated set of differences between these parameters and those from MM. The differences may be recalculated once or twice during the refinements, to ensure that the final structure is effectively constrained entirely by the high-level, ab initio calculations. Successful testing of the SEMTEX code on tri-tert-butylphosphine oxide, OPBut3, and tri-tert-butylphosphine imide, HNPBut3,4 illustrated that the technique was built on sound methodology. However, until now the method has only been used for peripheral hydrogen atoms and in relatively simple examples, where it was found to have only modest effects on the overall fit to the experimental data. In addition, the way the code was written meant that it was only applicable to peripheral atoms in a branched-chain structural environment. The next challenges for developing the SEMTEX method were therefore 2-fold. First, it was desirable to expand the scope

10.1021/jp1077517  2010 American Chemical Society Published on Web 09/28/2010

Low Symmetry Molecules

Figure 1. Gas-phase molecular structure of C6F11CF3.

of the method so that peripheral atoms in environments other than branched chains could be treated. Second, the method should be applied to a molecule with atoms heavier than hydrogen on the periphery, for which the fit to the GED data would be very sensitive to the accuracy of the constraints on the geometrical parameters. In such a case it would be expected that the SEMTEX method would yield a substantial improvement over the DYNAMITE method, and refinements of both should be much better those in which assumptions about local symmetry were imposed. With these two considerations in mind, gas electron diffraction data were collected for perfluoro(methylcyclohexane), C6F11CF3, for which the peripheral fluorine atoms will account for the major part of the electron scattering. As a ring structure with peripheral fluorine atoms, and with little symmetry (just one mirror plane), it allows both challenges for the SEMTEX method to be tested. Experimental Methods Computational Studies. All calculations were performed with the resources provided by the National Service for Computational Chemistry Software (NSCCS),5 using the Gaussian 03 program.6 A search of the potential-energy surface using the RHF method and the 3-21G* basis set7 on all atoms located two conformers of C6F11CF3, with the methyl group in an equatorial position in one conformer and an axial position in the other. Both conformers were found to have Cs symmetry, with the CF3 group in a staggered conformation. The difference in energy between the conformers was calculated to be sufficiently high that only one conformer could be expected to be present in significant quantity in the experimental gas-phase sample mixturesthat with the trifluoromethyl group in the equatorial position. Therefore all subsequent geometry optimizations were carried out only on this conformer, at the MP2 level8 using the 6-31G*9 and 6-311+G* basis sets. All MP2 calculations were of the frozen-core type [MP2(fc)]. The structure with the lowest energy is shown in Figure 1. For the implementation of SEMTEX, the low-level geometry optimizations were performed using the TINKER molecular mechanics package with the MM3 parameter set.10 A force field was calculated using analytic second derivatives of the energy with respect to the nuclear coordinates obtained at the HF/6-31G* level. This was then used by the program SHRINK11 to provide estimates of the amplitudes of vibration (uh1) and vibrational corrections to distances (kh1) required for the GED refinement. The force field was also used to calculate vibrational frequencies for the optimized structure. All calculated

J. Phys. Chem. A, Vol. 114, No. 41, 2010 11023 frequencies were real, indicating that the structure represented a minimum on the potential-energy surface. Gas Electron Diffraction. The Edinburgh gas-phase electron diffraction apparatus12 was used to collect data, with an accelerating voltage of 40 keV (wavelength ca. 6.0 pm). Scattering intensities were recorded on Kodak Electron Image film at two nozzle-to-film distances, 97.4 and 260.8 mm, to maximize the scattering angle over which data were collected. Four films were exposed at each nozzle-to-film distance. In order to obtain suitable vapor pressures the sample was heated to 423 and 443 K for the long and short nozzle-to-film distances, respectively. The corresponding nozzle temperatures were 429 and 450 K. The weighting points for the off-diagonal weight matrices, correlation parameters and scale factors for both distances are given in Table S1 in the Supporting Information. Also included are the electron wavelengths, determined using the scattering patterns for benzene, which were recorded immediately after the sample patterns. The photographic films were scanned using an Epson Expression 1680 Pro flatbed scanner using a routine method described elsewhere.13 The data reduction and leastsquares refinement were carried out using the ed@ed program,14 with scattering factors developed by Ross et al.15 The SEMTEX Method for Peripheral Atoms in a Ring Structure. In order to apply DYNAMITE and SEMTEX to the fluorine atoms in C6F11CF3, it was necessary to expand the method to handle peripheral atoms in a ring environment. The set of parameters needed to describe the atoms in this case differs from that used for the hydrogen atoms in tert-butyl groups in the previously studied phosphine molecules.4 Instead of a bond length, bond angle, and torsional angle, the individual ring F-atom positions in C6F11CF3 were described using their C-F bond length and two CCF angles, one in each direction around the ring. These were then scaled back to the average parameter values from the ongoing GED refinement, as for the branchedchain cases previously studied. In this case, these refining parameters (see below) are rC-F (p2) for the distances, and two C-C-F angles (p4-5) described in more detail later. The F atoms in the CF3 group are still in a branched-chain local environment and could thus be treated in the same way as the H atoms in the phosphine refinements.4 Electron Diffraction Model. The structure was defined using a model with Cs symmetry, as indicated by the ab initio calculations described above. Seven independent geometric parameters were required, comprising two bond lengths and five bond angles and differences. These are listed in Table 1. The starting values used for the parameters in the model were the re values obtained from the MP2/6-311+G* calculation. The refinable parameter defining the core-atom (ring and methyl carbon-atom) bond lengths was the average C-C bond length (p1). Ab initio calculations showed that in principle there are many different C-C distances in the structure, but the differences are small, and they were therefore fixed in the electron diffraction model at values computed at the MP2/6311+G* level, thereby ensuring that the number of refining parameters was workable. For the core-atom bond angles, the average of all core-atom CCC angles (p3) was used, again with the small differences between them fixed to values calculated ab initio. Note that both the C(ring)-C(ring)-C(methyl) angles needed, with the C(ring)-C(methyl) bond length, to define the position of the methyl carbon atom were included in the average. Two parameters were also used to describe the chair conformation of the C6 ring. The midpoints between C(3) and C(5) and

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TABLE 1: GED Refined Parameters for the SARACEN, DYNAMITE, and SEMTEX Refinements of C6F11CF3a p1 p2 p3 p4 p5 p6 p7 a

parameter

MP2/6-311+G* (re)

SARACEN (rh1)

DYNAMITE (rh1)

SEMTEX (rh1)

rC-C rC-F ∠C-C-C average ∠C-C-F average ∠C-C-F difference C(1)/C(4) displacement averageb C(1)/C(4) displacement differenceb

154.5 134.0 112.5 108.7 1.2 134.4 1.2

154.9(2) 133.8(1) 113.2(3) 109.2(1) -0.3(4) 134.6(3) 1.2(5)

154.3(2) 133.9(1) 110.4(4) 109.4(1) 1.2(5) 139.3(5) 1.2(5)

154.8(2) 134.0(1) 113.1(3) 109.6(2) 1.2(5) 132.4(4) 1.0(5)

restraint

1.2(5) 1.0(5)

All bond lengths are in pm and angles in deg. b See text for full parameter definition.

between C(2) and C(6) were defined as X and Y, respectively. The average of ∠C(1)-Y-X and ∠C(4)-X-Y and the difference between them were then used to describe the displacements of each of C(1) and C(4) from the plane containing C(2), C(3), C(5), C(6), X, and Y. Three parameters were necessary to describe the starting positions of the fluorine atoms. These comprised the average C-F distance (p2), and the average and difference of the C-C-F angles (p4-5). There are two ∠C-C-F for each ring fluorine atom, and these can define the atomic position of each ring fluorine atom without the need to use ∠F-C-F. The average ∠C-C-F parameter (p4) is the average of the 22 ring ∠C-C-F and the three CF3 group angles. The difference parameter (p5) is defined as the average difference (larger value minus smaller value) between the two separate ∠C-C-F values for each ring fluorine atom. These three parameters provide a representation of the mean values for all nine F atoms in one half of the C6F11CF3 molecule. For the SARACEN refinement, the fluorine atoms were restricted to these average parameter values, modified where necessary by small fixed differences from the initial MP2 calculation, since to include each distance and pair of angles explicitly in the refinement would lead to an unworkable number of refining parameters. In the DYNAMITE and SEMTEX refinements, however, the absolute values for each individual atom were determined using the respective computational methods (MM3 and MP2) and then scaled to the values of these average parameters in the ongoing GED refinement. Results and Discussion Computational Methods. The structure of C6F11CF3 was determined ab initio. Initial calculations suggested two possible conformers, with the CF3 group in either the axial or equatorial position. However, the equatorial conformer was calculated to be 25 kJ mol-1 lower in energy than the axial conformer at the HF/3-21G* level, and it was therefore decided that only the latter conformer would be present in the experimental mixture in significant quantity. The molecular geometry of C6F11CF3 at the MP2/6-311+G* level can be found in Table 1. At the outset of the SEMTEX refinement process, the coreatom positions were fixed as calculated using DYNAMITE, and both MP2/6-311+G* and MM3 calculations were performed for the fluorine atoms. The resulting fluorine-atom parameters can be found in Table 2. SARACEN Refinement. The starting parameters for the rh1 refinement were taken from the theoretical geometry optimized at the MP2/6-311+G* level. All seven independent geometric parameters were refined, along with 13 groups of vibrational amplitudes. One geometric parameter was restrained [the C(1)/ C(4) displacement difference] at the value calculated using MP2/ 6-311+G*, with the uncertainty determined by the variation in this parameter during the series of calculations performed.

TABLE 2: C-F Bond Lengths and C-C-F Bond Angles for C6F11CF3 Calculated Using the MM3 and MP2/ 6-311+G* Methodsa rC(n)-F

∠C(m)-C(n)-F

C(m)-C(n)-F

MM

MP2

MM

MP2

C(1)-C(2)-F(7) C(3)-C(2)-F(7) C(1)-C(2)-F(8) C(3)-C(2)-F(8) C(2)-C(3)-F(9) C(4)-C(3)-F(9) C(2)-C(3)-F(10) C(4)-C(3)-F(10) C(3)-C(4)-F(11) C(5)-C(4)-F(11) C(3)-C(4)-F(12) C(5)-C(4)-F(12) C(2)-C(1)-F(18) C(6)-C(1)-F(18) C(1)-C(17)-F(20) C(1)-C(17)-F(21)

134.2 134.2 136.7 136.7 134.0 134.0 137.4 137.4 134.2 134.2 136.9 136.9 131.1 131.1 136.0 138.9

134.3 134.3 134.9 134.9 134.7 134.7 134.2 134.2 134.0 134.0 134.6 134.6 136.2 136.2 133.3 132.5

109.5 109.5 108.4 106.5 107.3 107.7 110.0 109.6 111.6 111.6 108.6 108.6 109.0 109.0 110.7 114.3

109.4 107.0 109.2 107.2 108.0 108.3 108.1 109.1 109.5 109.5 108.8 108.8 108.4 108.4 108.9 113.2

a All bond lengths are in pm and angles in deg. Internuclear distances are the calculated (re) values. See Figure 1 for atom numbering.

Eight amplitude restraints were also applied according to the SARACEN method, using the values obtained from SHRINK and uncertainties of 10% of their calculated values. The refined geometric parameters can be found in Table 1. The final R factors for the refinement were found to be RG ) 0.063 and RD ) 0.040. Interatomic distances and corresponding amplitudes of vibration are given in the Supporting Information along with final experimental coordinates from the SARACEN GED analysis. DYNAMITE Refinement. The starting parameters and force field were as for the SARACEN refinement, and all geometric parameters were refined according to this method. Once this was complete, the DYNAMITE code was activated and difference parameters defining the fluorine-atom positions were updated computationally, while the average parameters continued to refine. Consequently, the parameters associated with the fluorine atoms now represent refined average values over all such atoms in the structure. As for the SARACEN refinement, seven geometric parameters were refined, along with 13 groups of vibrational amplitudes. This time one additional geometric parameter was restrained (the ∠C-C-F difference parameter) and eight amplitude restraints were applied. The final R factors for the refinement were found to be RG ) 0.133 and RD ) 0.076. The refined GED parameters can be found in Table 1. Interatomic distances and corresponding amplitudes of vibration can be found in the Supporting Information, along with final experimental coordinates from the DYNAMITE GED analysis. SEMTEX Refinement. The starting parameters were as for the SARACEN and DYNAMITE refinements. The geometric

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Figure 2. Experimental and difference (experimental - theoretical) radial-distribution curves, P(r)/r, from the SEMTEX refinement of C6F11CF3. Before Fourier inversion the data were multiplied by s exp(-0.00002s2)/(ZC - fC)(ZF - fF).

TABLE 3: C-F Bond Lengths and C-C-F Bond Angles for C6F11CF3 from the DYNAMITE and SEMTEX Refinementsa rC(n)-F (rh1)

∠C(m)-C(n)-F

[C(m)-C(n)-F]

DYNAMITE

SEMTEX

DYNAMITE

SEMTEX

C(1)-C(2)-F(7) C(3)-C(2)-F(7) C(1)-C(2)-F(8) C(3)-C(2)-F(8) C(2)-C(3)-F(9) C(4)-C(3)-F(9) C(2)-C(3)-F(10) C(4)-C(3)-F(10) C(3)-C(4)-F(11) C(5)-C(4)-F(11) C(3)-C(4)-F(12) C(5)-C(4)-F(12) C(2)-C(1)-F(18) C(6)-C(1)-F(18) C(1)-C(17)-F(20) C(1)-C(17)-F(21)

132.5 132.5 135.0 135.0 132.3 132.3 135.6 135.6 132.5 132.5 135.2 135.2 129.5 129.5 134.3 137.1

133.9 133.9 134.5 134.5 134.4 134.4 133.9 133.9 133.6 133.6 134.2 134.2 135.9 135.9 133.0 132.2

109.4 109.3 108.3 106.3 107.1 107.5 109.8 109.5 111.4 111.4 108.4 108.4 108.8 108.8 110.3 114.1

109.9 107.5 109.6 107.6 108.5 108.7 108.5 109.5 110.0 111.0 109.3 109.3 108.8 108.8 109.4 113.7

a

All bond lengths are in pm and angles in deg. See Figure 1 for atom numbering.

parameters were refined using first the SARACEN and then the DYNAMITE method. Once all seven geometric parameters and 13 groups of vibrational amplitudes were refined according to the DYNAMITE method, the SEMTEX code was activated. The core-atom positions were fixed and theoretical structures calculated at both the MP2 and MM3 levels of theory, and the differences in the peripheral-atom parameters for these two structures were then derived. During each subsequent refinement cycle, for each parameter, the peripheral-atom positions returned by the MM3 code were immediately modified by this set of differences. As in the SARACEN and DYNAMITE refinements, all seven geometric parameters were refined, along with 13 groups of vibrational amplitudes. Restraints were applied as for the DYNAMITE refinement. In the final refinement the R factors were RG ) 0.062 and RD ) 0.038. The molecular-scattering intensity curve for C6F11CF3 is given in Figure S1, and Figure 2 shows the radial-distribution curve for the refinement. The refined geometric parameters are given in Table 1. Table 2 gives the core-atom parameters determined using both MM3 and MP2, while Table 3 gives the final fluorine-atom parameters from both DYNAMITE and SEMTEX refinements. Interatomic distances and corresponding amplitudes of vibration are given in the Supporting Information (Table S2), along with the least-squares

correlation matrix (Table S3) and Cartesian coordinates from the SEMTEX GED analysis (Table S4) and from the MP2/6311+G* calculations. Comparison of Different Refinement Methods. The gasphase structure of perfluoro(methylcyclohexane) has been examined using the SARACEN, DYNAMITE, and SEMTEX methods of structure determination. The use of SEMTEX has allowed the full range of peripheral-atom parameters to be defined, free of constraints that were necessary in the SARACEN refinement of the structure. For the SARACEN and the SEMTEX refinements, refined parameters for the central atoms are generally in good agreement both with one another and with the calculated MP2 structure. The mean C-C bonded distance refined to a value of 154.9(2) pm using SARACEN and 154.8(2) pm using SEMTEX, compared with 154.5 pm calculated at the MP2/6-311+G* level of theory. Angles also generally agreed to better than 1.0°. For example, the average C-C-C angle refined to 113.2(3)° using SARACEN and 113.1(3)° using SEMTEX, as compared with 112.6° from the calculated MP2 structure. The C-F distances and the average C-C-F angles given by the SARACEN and SEMTEX methods are also in good agreement. However, the ∠C-C-F difference differs considerably: -0.3(4)° for SARACEN compared with 1.2(5)° for SEMTEX. Comparison of these values with the value of 1.2° calculated at the MP2 level leads to the expected conclusion that the SEMTEX refinement describes the positions of the peripheral atoms better. The slight improvement in goodnessof-fit parameter exhibited by the SEMTEX refinement may reflect this difference. The most notable result is the very poor agreement between the DYNAMITE refinement and both the SARACEN and SEMTEX refinements, with a high R factor associated with the DYNAMITE refinement. This can be attributed primarily to the serious inconsistencies in the C-F bond lengths and CCF angles calculated using the MM program (Table 2). Several parameters resulting from the DYNAMITE refinement are out of line. For example, the average C-C distance refines to 154.3(3) pm using DYNAMITE and 154.8(2) pm with SEMTEX. This disagreement between structures is most evident in the average C-C-C angle parameter, which refines to similar values using SARACEN (113.2(3)°) and SEMTEX (113.1(3)°), but takes a completely different value in the DYNAMITE refinement, 110.4(4)°. This is most likely caused by the molecular mechanics calculating inaccurate positions for the peripheral F atoms, and consequently these erroneously placed peripheral atoms having a serious effect on the structure of the central C6 ring. The dihedral angle defining the puckering of the ring is also substantially different in the DYNAMITE and SEMTEX refinements (139.3(5)° and 132.4(4)°, respectively), influenced by the positions of the peripheral fluorine atoms. The peripheralatom parameters given in Table 3 give some indication of the differences between the MM and MP2 calculations in this casesfor example, ∠F(7)-C(2)-C(3) and ∠F(8)-C(2)-C(3) differ in value by 3.0° in the MM case and by only 0.1° in MP2. The difference in the final R factors for the DYNAMITE and SEMTEX refinements is extremely marked, RG ) 0.133 for DYNAMITE and RG ) 0.062 for SEMTEX. This study therefore illustrates very well the limitations of the molecular mechanics method as used in DYNAMITE, and provides a first definitive example of case where inclusion of ab initio peripheralatom data via the SEMTEX method makes a very significant difference to the overall quality of refinement.

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Comparison of Structure with that of Cyclohexane. The effects of fluorine substitution on the structure of cyclohexane16 are substantial. First, the ring bonds are lengthened, from 153.6(2) (rg) to 154.8(2) pm, reflecting the withdrawal of electrons from the carbon atoms, which therefore repel one another. Second, the ring CCC angles increase from 111.4(2)° to an average of 113.1(3)°, and the CCCC dihedral angles in the ring decrease from 55.9(1)° to an average of 50.4°. The last two effects (which are correlated with one another) could be attributed to repulsion of negatively charged fluorine atoms, but of course steric effects may also play a role. Overall, the ring is expanded and flattened when fluorine atoms replace hydrogens. Conclusions The structure of perfluoro(methylcyclohexane), C6F11CF3, has been determined using each of the SARACEN, DYNAMITE, and SEMTEX methods and the results compared. The goodnessof-fit parameter RG is similar for the SARACEN and SEMTEX refinements, with the SEMTEX method performing better in the prediction of the peripheral-atom locations. The most notable result is the relatively poor performance of the DYNAMITE method in determining this structure, producing markedly different geometries for the carbon-atom core, with an RG value greater than double those given by the other two methods. The refinement of the structure of C6F11CF3 therefore illustrates perfectly the need for the new SEMTEX method if accurate total structure determination of a wide range of molecules is desired. We recommend that it is used for any molecule with low symmetry and many non-hydrogen peripheral atoms. This class of molecules includes most fluorocarbons and their derivatives and all but the simplest carbonyl complexes. It may also be useful for borane, carbaborane, and metallaborane cages. Acknowledgment. We acknowledge the EPSRC for funding the electron-diffraction research (EP/C513649) and the NSCCS for providing computational resources. G.R.K. thanks the School of Chemistry, University of Edinburgh for funding a studentship. S.L.M. thanks the Royal Society of Edinburgh for a BP/RSE personal research fellowship. Supporting Information Available: Tables of experimental parameters for the SEMTEX GED analysis of C6F11CF3 (Table S1), refined and calculated root-mean-square amplitudes of vibration (Table S2), the least-squares correlation matrix for the refinement (Table S3), and Cartesian coordinates for the final experimental structure of C6F11CF3 (Table S4) and for the calculated structure at the MP2/6-311+G* level (Table S5) and molecular-intensity scattering curves and difference curves for

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