Article Cite This: J. Org. Chem. 2018, 83, 15463−15469
pubs.acs.org/joc
Atomic Charges Kenneth B. Wiberg*,† and Paul R. Rablen*,‡ †
Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States Department of Chemistry and Biochemistry, Swarthmore College, Swarthmore, Pennsylvania 19081, United States
‡
J. Org. Chem. 2018.83:15463-15469. Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 12/21/18. For personal use only.
S Supporting Information *
ABSTRACT: The problem of deriving atomic charges from the results of ab Initio MO calculations has been studied by the use of several reported methods: Mulliken population analysis, the minimal basis set (MBS) procedure, the natural population analysis (NPA), two electrostatic potential fitting methods, M-K and ChelpG, the Hirshfeld population analysis, and CM5 (charge model 5), which is related to the Hirshfeld method. The first set of studies were concerned with hydrogen charges. It was found that the MBS charges were linearly related to the Hirshfeld charges. The Hirshfeld, CM5, and MBS methods, but not the others, provided an excellent correlation for H atomic charge with the H−C−H bond angle, and with calculated gas-phase acidity. The two methods that were linearly related and gave hydrogen charges in agreement with an experimental study of partially deuterated methanes are MBS and Hirshfeld. In order to see which of the two methods is the more satisfactory, the methanol dimer was examined. The calculated H bond energy was 6.2 kcal/mol, which was in good agreement with studies of hydrogen bonds. The Coulombic interaction for the O···H bond was estimated using the MBS and Hirshfeld charges. The latter gave a calculated energy of 3−6 kcal/mol, whereas MBS gave an energy of ∼35 kcal/mol. Clearly, the Hirshfeld method is more satisfactory and should be the method of choice. Hirshfeld,7 an X-ray crystallographer, started with a “promolecule” that had spherically symmetric neutral atoms at the coordinates of the atoms in the real molecule. Then, at any point about the real molecule and the corresponding point about the promolecule, the charge density is calculated. The charge for the real molecule is apportioned among the atoms in proportion to what each atom contributes to the promolecule at that same point in space. Integration of these partial charge densities gives the total charge at each atom. A variant of this approach (CM5) has been suggested by Truhlar and Cramer,8 in which the charges are modified so that they will reproduce the calculated dipole moment. All of these methods are commonly available in ab initio codes such as Gaussian.9 A very recent new model for calculating charges has been reported by Zhao, ete. al.,10 but we have not had any experience with it.
1. INTRODUCTION For many years, chemists have had a real interest in describing electron density distributions in terms of atomic charges.1 With the increasing power of computers and the increasing use of methods that include electron correlations such as MP2 and CCSD as well as relatively large bass sets such as aug-cc-pVTZ, we can now routinely obtain quite accurate density matrices as a part of geometry optimizations. Our problem is how to convert the density matrix into meaningful atomic charges. There is no quantum chemical operator that could effect this conversion. Therefore, it is necessary to use some model to get appropriate atomic charges. The first of these is the Mulliken population analysis.2 It has a number of problems especially since it is very sensitive to the basis set used. This was improved considerably by the natural population analysis (NPA) developed by Reed and Weinhold,3 which is based on their natural bond order (NBO) localization of molecular orbitals into bond orbitals. Another approach is the minimal basis set (MBS) method of Montgomery et al., in which the results of a large basis set calculation are mapped onto a minimal basis set followed by a Mulliken analysis.4 Merz and Kollman, noting that the electrostatic potential is a quantum-mechanically defined quantity, derived atomic charges (M-K) that “best fit” the electrostatic potential about a molecule.5 A similar approach was taken by Brenneman and Wiberg (ChelpG).6 A problem with methods that rely on fitting data is that there may be several “good” solutions and that there is no systematic way of finding the “best” one. Also, they sometimes have difficulty with retaining the symmetry of symmetrical compounds. © 2018 American Chemical Society
2. HYDROGEN ATOM PROBLEM There are many cases in which we might like to know the charges at the hydrogen atoms in a molecule. This is particularly true when dealing with a CH···X Coulombic attraction.11 This relatively weak, ∼1 kcal/mol, interaction has been widely observed.11 In the case of a comparison between 3,5-dimethyl-1fluorocyclohexane and 3,5-ditrifluoromethyl-1-fluorocyclohexane, the CF3 group led to an increase in positive charge at the axial ring hydrogens. This led to an increased Coulombic attraction with the axial F that could be observed via equilibrium Received: October 25, 2018 Published: November 26, 2018 15463
DOI: 10.1021/acs.joc.8b02740 J. Org. Chem. 2018, 83, 15463−15469
Article
The Journal of Organic Chemistry Table 1. Charges at Hydrogens, MP2/aug-cc-pVTZ compound methane ethane ethene ethyne propane
propene
butadiene
cyclopropa benzene MeF MeCl MeOH
MeNH2
MeCHO
MeCN MeNO2 H2O NH3 MePH2
Me3P EtCl
EtF
ethlene oxide
H
Mullikan
MBS
NPA
M-K
CHELPG
HIR
CM5
H H H H Ha-3 Hb-4 Hc-7 Ha-4 Hb-3 Hc-5 Hd-8 He-7 Ha-3 Hb-4 Hc-5 H H H H Ha Hb H(O) Ha Hb H(N) Ha Hb H(CO) H Ha Hb H H Ha Hb H(P) Ha Hb Ha Hb CH2 Ha Hb CH2 H
0.3133 0.3003 0.4422 0.6213 0.2976 0.3033 0.2722 0.2728 0.5175 0.3407 0.3091 0.2966 0.3546 0.4218 0.3505 0.3864 0.4356 0.3134 0.3200 0.3450 0.3201 0.1915 0.3227 0.3378 0.1484 0.3311 0.3094 0.4795 0.3377 0.4177 0.3563 0.2146 0.2017 0.3097 0.3251 0.1104 0.2927 0.3050 0.3107 0.3303 0.2954 0.3364 0.3075 0.3092 0.4057
0.0745 0.0627 0.0936 0.1872 0.0618 0.0590 0.0535 0.0836 0.0897 0.0830 0.0756 0.0737 0.0900 0.0973 0.0899 0.0858 0.0940 0.0905 0.1143 0.0891 0.0651 0.3326 0.0493 0.0738 0.2288 0.1049 0.0915 0.0684 0.1263 0.1344 0.1365 0.3350 0.2347 0.0882 0.0851 −0.0444 0.0703 0.0793 0.0722 0.0832 0.1055 0.0717 0.0809 0.0811 0.0974
0.1988 0.1881 0.1788 0.2221 0.1942 0.1877 0.1805 0.1755 0.1849 0.1781 0.2044 0.1980 0.1784 0.1869 0.1869 0.2004 0.2011 0.1512 0.1980 0.1701 0.1485 0.4524 0.1524 0.0784 0.3413 0.2196 0.2195 0.0868 0.2387 0.2140 0.2184 0.4547 0.3488 0.2102 0.2129 −0.0468 0.2041 0.2168 0.2022 0.2040 0.1914 0.2020 0.2022 0.1449 0.1709
0.1358 0.0082 0.1645 0.2710 0.0643 0.0763 0.0618 0.2188 0.1881 0.0801 0.0890 0.0981 0.1841 0.1740 0.1389 0.1483 0.1116 0.0796 0.1919 0.0774 0.0098 0.3782 −0.0806 −0.0080 0.3331 0.1326 0.1129 −0.0377 0.1833 0.1542 0.1593 0.3408 0.2916 0.0221 0.0769 0.0904 0.1120 0.1302 0.0521 0.0638 0.0931 0.0589 0.0908 −0.0031 0.1588
0.0975 0.0006 0.1250 0.2228 0.0443 0.0348 −0.0655 0.1709 0.1482 0.0730 0.0161 0.0226 0.1553 0.1044 0.0814 0.1025 0.0775 0.0369 0.0847 0.0425 −0.0356 0.3751 −0.0969 −0.0255 0.3249 0.0893 0.0716 −0.0503 0.1115 0.1236 0.1307 0.3379 0.2896 −0.0527 0.0005 0.0736 0.0050 0.0223 0.0333 0.0423 0.0669 0.0520 0.0846 −0.0196 0.1208
0.0323 0.0282 0.0378 0.0897 0.0285 0.0274 0.0262 0.0327 0.0337 0.0343 0.0356 0.0349 0.0366 0.0379 0.0398 0.0367 0.0398 0.0423 0.0472 0.0408 0.0277 0.1468 0.0172 0.0320 0.0893 0.0466 0.0484 0.0343 0.0644 0.0557 0.0617 0.1457 0.0897 0.0356 0.0386 −0.0202 0.0297 0.0359 0.0386 0.0362 0.0422 0.0399 0.0382 0.0372 0.0449
0.0805 0.0794 0.0905 0.1435 0.0797 0.0791 0.0808 0.0860 0.0865 0.0898 0.0870 0.0873 0.0896 0.0998 −0.0961 0.0916 0.0959 0.0949 0.0995 0.1011 0.0855 0.3191 0.0750 0.0928 0.2763 0.1015 0.1006 0.0957 0.1174 0.1224 0.1269 0.3123 0.2723 0.0893 0.0930 0.0617 0.0844 0.0905 0.0900 0.0886 0.0977 0.0915 0.0907 0.0931 0.1060
Let us first compare the hydrogen charges calculated from a variety of models. Throughout this study, if the theoretical level used is not stated, it will be MP2/aug-cc-pVTZ, which should give fairly accurate density matrices. The data are shown in Table 1. The M-K and ChelpG calculations sometimes do not give symmetrically related atoms the same value. In these cases,
constant measurements. The increased charge could also be seen in calculations.12 It has also been found that hydrogens are quite sensitive to electronic effects at the atom to which they have been attached. With only a small nuclear charge, it is readily possible to shift some charge either to or from a hydrogen atom.13 15464
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the average value is given. Some key structures are shown at the end of Table 1. It can be seen that for any one compound there is a large variety of calculated charges. The Mulliken charges for an alkane are the largest, and for methane, they would lead to a −1.25 e charge at the carbon. This does not correspond to the properties of methane, and these charges will not be further discussed. The next largest are those from NPA. Reed and Weinhold14 recognized that they were too large and provided an explanation. They might be linearly related to some other set of charges and so will be considered along with all of the other charges. It would be good to have some other quantity with which the charges could be compared. It is known that hydrogen charges are related to the % s character from the carbon to which they are attached.15 For an H−C−H group, the % s should be related to the bond angle. Figure 1 shows the correlation between the calculated charges and the bond angles. The Hirshfeld and CM5 charges give a very good fit in the plot, and since CM5 charges are closely related to the Hirshfeld charges, it is not surprising that the slopes are the same. MBS gives a slightly larger slope, and NPA gives a slightly smaller
Figure 1. Correlation between the H−C−H bond angle and the calculated charges.
Figure 2. Relation between the hydrogen charges obtained via different methods. 15465
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smallest and largest charges and had an intercept close to 0.0, 0.0. It is shown as Figure 2. The M-K and ChelpG charges were reasonably well correlated (slope = 1.025, R = 0.952), but there was no useful correlation between the M-K and the MBS or Hirshfeld charges. The NPA charges are also correlated with the MBS and Hirshfeld charges, but with considerably more scatter. The charges are about 0.08 e larger than the MBS charges. For the (P)H hydrogen, the NPA value comes close to the Hirshfeld value. The CM5 populations are surprisingly not well correlated with the Hirshfeld charges. The problem appears to be found with hydrogens that are bound to P, N, or O. The rest of the CM5 data give a fairly good fit to the Hirshfeld charges. It also seemed possible that the acidity of a C−H bond might be related to the charge at the hydrogen atom. At least in simple, closely related molecules, one might reasonably expect a greater charge on the hydrogen to be associated with enhanced acidity. A chemically useful definition of atomic charge should probably reflect this association. This hypothesis was examined by comparing the charge for a hydrogen atom to the proton affinity of the anion derived by removing that hydrogen atom as a proton. Essentially, these are the gas-phase acidities of the protons, but are computed as electronic energy differences rather than as free energy differences. The comparison is shown in Figure 3. It purposely includes only compounds in which delocalization of the anion, e.g., in a π system, or through proximity to a highly polarizable atom or group, is not possible. That is because such delocalization would enhance the acidity of the hydrogen, but would not be expected to increase the positive charge on the hydrogen in the neutral compound. As such, the relationship between charge and proton affinity would only be expected to hold in cases lacking such stabilization through delocalization in the anion. Figure 3 shows that the proton affinity correlates very strongly with the charge computed using the MBS and Hirshfeld methods (r2 of 0.99 and 0.93, respectively), as well as the CM5 procedure (r2 = 0.90). The other charge calculation methods, on the other hand, give rather poor correlations. This finding corroborates the conclusion drawn from the earlier analyses that the MBS and Hirshfeld procedures in particular seem to give hydrogen charges that have desirable features and that make chemical sense. It would be interesting to have an experimental test that could distinguish between MBS and Hirshfeld charges. Since the MBS charges are 2.3 times the Hirshfeld charges, the charge for an oxygen-bound hydrogen is much larger for MBS (0.333 e) than Hirshfeld (0.147 e). With methanol, this would lead to a large difference in H bond energies. A structure for the methanol dimer was obtained via MP2/aug-cc-pVTZ optimization (Figure 4) (Table 2) and has a H···O nonbonded distance of 1.879 Å. A comparison of the energy of the dimer with that of with methanol at the same level gave a H bond energy of 6.2 kcal/mol, in good agreement with experimental estimates.17 A comparison of the O and H charges of the dimer with those of the monomer indicates that there is an electronic
Figure 3. Correlation between proton affinity and the calculated charges. The points, from left to right, correspond to ethyne, chloromethane, oxirane, ethene, fluoromethane, cyclopropane, methane, and ethane. The correlation coefficients (r2) of the best fit lines are Mulliken, 0.70; MBS, 0.99; NPA, 0.28; M-K, 0.73; ChelpG, 0.67; Hirshfeld, 0.93; and CM5, 0.90. The MBS, Hirshfeld, and CM5 charges thus gave a much better correlation than the other methods.
Figure 4. Methanol dimer.
slope with more scatter. One additional piece of information is that Signorell et al.16 have, via high-resolution infrared spectroscopic studies of partially deuterated methanes including band intensities, found that the C−H bond dipole has the sense C−−H+ and that the bond dipole is quite small. This leads us to think that the Hirshfeld charges might be the best for this purpose. Another possible correlation might be between the electronegativity of the X atom in MeX and the charge at the methyl hydrogens. However, the change in H charges was small and not well correlated with electronegativity. In order to obtain further information, we have made plots using one method as the y axis and another as the x axis. One combination, MBS vs Hirshfeld, gave a very good correlation that included the
Table 2. Atomic Charges in Methanol and in the Methanol Dimer, MP2/aug-cc-pVTZ MBS
Hirshfeld
compound
E
qO
qH
qO
qH
methanol methanol dimer
−115.529008 −231.067846
−0.5807 −0.5625
0.3326 0.3468
−0.2364 −0.1612
0.1468 0.0908
15466
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The Journal of Organic Chemistry component. Using the calculated charges in Table 2, the Hirshfeld charges lead to a H bond energy of 3.2 kcal/mol, whereas the MBS charges gives 35.5 kcal/mol.18 To try to eliminate the effect of the electronic interaction, we also calculated the Coulombic energy18 using the O and H charges of methanol, giving 6.2 kcal/mol for the Hirshfeld charges and 35.1 kcal/mol for the MBS charges. There is a clear preference for the Hirshfeld charges that agree with the experimental results for deuterated methanes where the charge is small16 and as well as the energy of the methanol dimer where the charge is relatively large. It seems appropriate to conclude this section by showing applications where the hydrogen charges proved very valuable. In a recent study of the anomeric effect, Wiberg et al. found the changes in charge going from the equatorial to the axial conformers of 2-fluoro-1,3-dioxanes (Figure 5) to be interesting.19
Table 4. Charges with Hydrogens Included with Heavy Atoms, MP2/aug-cc-pVTZ compound
group
Hirshfeld
CM5
MBS
NPA
methyl fluoride
CH3 F CH3 Cl CH3 OH CH3 O Me NH2 Me N Me N O Me C N Me PH2 Me PH2 Me CH O Me C O Me CH2 F Me CH2 Cl CH O NH2 CH3 C O NH2 CH2 O
0.1594 −0.1594 0.1076 −0.1076 0.0896 −0.0876 0.0867 −0.1734 0.0357 −0.0357 0.0347 −0.1042 0.1550 0.2290 −0.1920 0.1499 0.0707 −0.2206 −0.0113 0.0113 −0.0298 0.0895 0.0554 0.1759 −0.2313 0.0397 0.1649 −0.2443 0.0272 0.1343 −0.1615 0.0245 0.0852 −0.1097 0.1737 −0.2936 0.1120 0.0403 0.1629 −0.3060 0.1027 −0.0928 −0.1853
0.1896 −0.1896 0.1189 −0.1189 0.1378 −0.1378 0.1421 −0.2842 0.1177 −0.1177 0.1285 −0.3854 0.2640 0.0448 −0.1544 0.1676 0.1728 −0.3404 0.0338 −0.0338 0.0195 −0.0584 0.0701 0.2163 −0.2865 0.0575 0.1793 −0.2943 −0.0346 0.1560 −0.1906 0.0303 0.0892 −0.1195 0.2981 −0.3417 0.0437 0.0322 0.2493 −0.3493 0.0322 0.1322 −0.2642
0.3760 −0.3760 0.3009 −0.3009 0.2481 −0.2481 0.2437 −0.4874 0.1445 −0.1445 0.1322 −0.3966 0.3275 0.4725 −0.4000 0.1743 0.1378 −0.3121 −0.0411 0.0411 −0.0728 0.2184 0.0491 0.4398 −0.4889 0.0397 0.4439 −0.5178 0.0304 0.3599 −0.3903 0.0508 0.2705 −0.3213 0.5942 −0.5716 −0.0226 0.0515 0.5839 −0.6003 0.0351 −0.2381 −0.4761
0.3828 −0.3828 0.0737 −0.0737 0.2723 −0.2723 0.2809 −0.5618 0.1504 −0.1504 0.1705 −0.5115 0.2227 0.4439 −0.3333 0.0382 0.2745 −0.3127 −0.2357 0.2357 −0.2624 0.7868 −0.0245 0.5193 −0.4948 −0.0263 0.5250 −0.5125 0.0022 0.3887 −0.3865 0.0231 0.0565 −0.0795 0.6031 −0.5727 −0.0309 −0.0348 0.6428 −0.5872 −0.0209 0.2545 −0.5090
methyl chloride methanol Me2O methylamine Me3N MeNO2
MeCN
Figure 5. 2-Fluoro-1,3-dioxanes.
MePH2
Table 3. Hirshfeld Charges at the F−C−H Group and the Ring O of 2-Fluorodioxanes
Me3P
isomer
qF
qC
qH
qO
axial equatorial change
−0.1587 −0.1262 −0.0325
0.2023 0.1972 0.0051
0.0518 0.0275 0.0243
−0.1610 −0.1649 0.0039
MeCHO
Me2CO
EtF
As can be seen in Table 3, the change in charge between the two isomers is found largely in the H−C−F group where the hydrogen donates charge to the fluorine. Hyperconjugation has been the common explanation for the lower energy of the axial-F compound,20 but the ring oxygen contributes only a small amount to the charge at fluorine, whereas, if hyperconjugation was the most important interaction, the charge should have come mainly from the oxygen. The polar contributions leading to stabilizing the axial form are shown in Figure 6. There are two Coulombic terms
EtCl
formamide
acetamide
ethylene oxide
seen by examining the charge distribution. We have examined this for three cases: propene, 2-fluoromethylamine, and formamide. In each case, the hyperconjugative interaction can be turned off by bond rotation, and the rotational barriers are 2, 8, and 17 kcal/mol, respectively (see Supporting Information). With propene, there is a transfer of 0.0013 e from the methyl group to the double bond on going from the TS to the GS. For fluoromethylamine, the TS to GS charge shift is 0.040 e from the nitrogen lone pair to the CF* orbital, and for formamide, the corresponding charge shift is 0.115 e from the nitrogen lone pair to the CO* orbital. The charge shift increases as the rotational barrier increases. It should be noted that the X−Y−Z group is different. In difluoromethane21 and in methoxymethanes,21 there is little vicinal hyperconjugative stabilization. There cannot be a net charge shift because a charge transfer from the first X to Y−Z*
Figure 6. Charge changes between equatorial and axial isomers and Coulombic interactions. (Only one pair is shown.)
involving a positively charged axial proton at C4 and C6 and the negatively charged axial fluorine and two additional interactions between the positively charged hydrogen at C2 and the negatively charge ring oxygens. In general, in hyperconjugative interactions such as in an X−Y−Z group, where X has a lone pair or the equivalent that can act as a donor and the YZ* bond can act as an acceptor (X not equal to Z), there will be a charge transfer that can be 15467
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Figure 7. Correlation between the calculated charges where hydrogens are combined with their heavy atoms.
will be canceled by the shift from the second X to the first X−Y* orbital. Thus, any hyperconjugative interaction must be a second-order effect.
charges, but the deviations are too large for this to be useful. The same is true with NPA vs CM5. In choosing between MBS and Hirshfeld charges, we can return to the choice given for the hydrogen charges. The Hirshfeld charges were the clear choice because the O and H charges led to hydrogen bond energies that agreed with the experiment, whereas this was not true for the MBS charges. Again, we conclude that the Hirshfeld charges are more satisfactory.
3. ATOMIC CHARGES WITH HYDROGENS INCLUDED WITH THE ATTACHED ATOMS The above discussion has been concerned with just the hydrogen charges. We now wish to examine a wider range of atomic types. It is common to include the charges at the attached hydrogens, and this will be done in this section. The same range of charge definitions will be used, except the Mulliken charges and those derived from electrostatic potentials will be dropped. The calculated charges are summarized in Table 4. The best correlation was between the MBS and Hirshfeld charges as shown in Figure 7. The points that deviate significantly from the correlation line have a N atom as a common feature. It is not possible at this time to determine whether the deviation is due to the MBS charges or due to the Hirshfeld charges. Surprisingly, there is considerable scatter in the plot of CM5 vs Hirshfeld charges, despite the apparent relationship between them. NPA led to a fair correlation with the Hirshfeld
4. DEPENDENCE ON LEVEL OF THEORY The calculations discussed above were all carried out at the MP2/aug-cc-pVTZ level. It appeared useful to have a comparison with the results for other theoretical levels. The charges for all of the compounds in Table 1 were obtained using MP2/ 6-311+G*, B3LYP/aug-cc-pVTZ, and B3LYP/6-311+G* (see the Supporting Information). With the large basis set, there was only a small difference between the MP2 and B3LYP calculated Hirshfeld charges. The average absolute deviation was only 0.0008 e. The use of the smaller basis set led to somewhat larger deviations. MP2 using the two basis sets gave a deviation of 0.0034 e, whereas, with B3LYP, it was 0.0030 e. 15468
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5. SUMMARY The calculated atomic charges at hydrogen has been examined using 7 different methods: Mulliken population analysis, natural population analysis (NPA), mapping the result of a large calculation onto a minimal basis set followed by a Mulliken analysis (MBS), Merz−Kollman fitting of charges to electrostatic potentials (M-K), and a related method, ChelpG, Hirshfeld population analysis, and Charge Model 5 (CM5). Two of these methods gave a very good linear relationship with each other, and with various other parameters, such as hybridization and carbon acidity, that are expected to correlate with atomic charge: MBS and Hirshfeld. Experimental results from high-resolution spectroscopic studies of deuterated methanes and known energies for H···O hydrogen bonds were used to find that the Hirshfeld charges are more satisfactory. Examples have been provided showing how the hydrogen charges are useful in studying conformational differences and energy differences. 6. CALCULATIONS All calculations were carried out using Gaussian 16.9 The density = current option was used to ensure that the MP2 density was in fact used for the computation of charges. Geometries were optimized without constraint at the same levels of theory that were used for the determination of the atomic charges. In cases where symmetrically related atoms yielded slightly different charges (due to numerical noise), averages are reported. It might be noted that the Hirshfeld charges calculated using Gaussian 16 are slightly different than those from Gaussian 09.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.joc.8b02740. Calculations for propene, fluoromethylamine, and formamide, Hirshfeld H charges using MP2/6-311+G*, B3LRP/aug-cc-pVTZ, and 6-311+G*, and atomic coordinates and energies of all compounds (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. ORCID
Kenneth B. Wiberg: 0000-0001-8588-9854 Paul R. Rablen: 0000-0002-1300-1999 Present Address ∥
K.B.W.: 865 Central Avenue, Apartment A404, Needham, MA 02492, USA. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Wiberg, K. B.; Rablen, P. R. A Comparison of Atomic Charges Derived via Different Procedures. J. Comput. Chem. 1993, 14, 1504− 1518. (2) Mulliken, R. S. Electron Population Analysis 0n LCAO-MO Molecular Wave Functions. J. Chem. Phys. 1955, 23, 1833−40. (3) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735−746. 15469
DOI: 10.1021/acs.joc.8b02740 J. Org. Chem. 2018, 83, 15463−15469
