Nearsightedness of Oxygen-Containing Functional Groups - The

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The Nearsightedness of Oxygen-Containing Functional Groups Jonathan Miorelli, and Mark E. Eberhart J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b08256 • Publication Date (Web): 15 Nov 2016 Downloaded from http://pubs.acs.org on November 20, 2016

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The Journal of Physical Chemistry

The Nearsightedness of Oxygen-Containing Functional Groups Jonathan Miorelli and Mark E. Eberhart∗ Department of Chemistry and Geochemistry, Colorado School of Mines, Golden, CO 80401, USA E-mail: [email protected] Phone: +1 (303) 273–3726

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Abstract Matter is nearsighted, i.e. for a fixed chemical potential the charge density is only sensitive to perturbations within a radius, R. While it is known that the resultant change in the density at point r0 from some perturbation at some other point R (∆n(r0 , R)) is a monotonically decreasing function, a plausible range of a chemically significant ∆n(r0 , R), and the value of R needed to cause these perturbations has not been well studied. Using the functional group, which upon satisfying the necessary atoms/bonds specific to that functional group retains a characteristic chemistry, this paper provides an initial study into the magnitude of both ∆n and R, the radius beyond which to affect a given property. Values for ∆n are shown to be robust across a variety of DFT functionals and provide a framework for the transfer of the functional group concept other disciplines, such as metallurgy.

Introduction Electronic matter is nearsighted. W. Kohn has provided both a qualitative 1 and quantitative rationale 2,3 in support of this observation in what is known as the NEM (nearsightedness of electronic matter) principle. This principle asserts that molecular and solid-state properties originate from the piecewise properties of overlapping atomic neighborhoods. For all intents and purposes an atom can only “see” nearby atoms. 4–7 Rigorously, NEM asserts that for fixed chemical potential the charge density is sensitive to changes in the external potential only within some radius R. Changes to the potential beyond R—no matter how large—do not significantly affect the charge density 2 . In other words, there is a monotonically decreasing function, ∆n(r0 , R), giving the density change at r0 due to a perturbation of any magnitude at R, such that limR→∞ ∆n = 0. Because many local properties derive from the electronic charge density, NEM can be restated as a size constraint on properties. That is, there must be some Rp above which—and some corresponding ∆np below which—a perturbation will change a property p by a small amount 2 ACS Paragon Plus Environment

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in comparison to the magnitude of the property itself. Knowledge of Rp across a wide spectrum of molecular types, materials, and properties, would be an invaluable pillar supporting the developing field of molecular and materials design. With this knowledge the designer could determine the extent to which compositional changes could meaningfully alter desired properties. Unfortunately, with only a few exceptions, this knowledge does not exist. One of the exceptions for which we possess knowledge of Rp comes from the field of organic chemistry, where molecular properties are recognized as emerging from the combined action of a diverse though finite set of functional groups 8 . Every functional group is characterized by a set of chemical properties that change only slightly as the environment in which it is embedded is altered. Within a NEM context a functional group is a structure characterized by an inner and outer radius, Ri and Ro respectively. Perturbations or structural alterations beyond Ro have no discernible affect on chemical and structural properties while perturbations inside Ri produce radical changes to these properties. Changes to the structure or composition in the region between Ri and Ro modify properties within some narrow envelope. The structure contained within Ri is the functional group and Ro we associate with Rp , where the properties of interest are the chemical and structural properties of the functional group. As pointed out by Pordan and Kohn 2 , without the functional group paradigm, it would have been practically impossible to understanding the physics and chemistry of large organic molecules and solids. Instead of trying to rationalize the properties of such systems as a whole, they have been studied and understood one “neighborhood at a time.” Because electronic matter is nearsighted, functional groups are present in all molecules and materials, though their extent will depend on the material and property of interest. Our objective is to identify the functional groups in materials where they are not currently recognized, for example in metals and alloys. We begin this search with a speculation that while Rp may vary from material to material, ∆np will be more or less constant for the same



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set of properties regardless of material. The first step in support of this speculation, which is the subject of this paper, is to calculate ∆np for a known set of organic functional groups and compare their magnitudes. In subsequent investigations we will determine the Rp of metals that give rise ∆np found here.

Methods The charge densities were calculated using ADF 2016.101. 9–11 All calculations used an allelectron triple zeta polarized (TZP) basis set using a “Very Good” Becke fuzzy cells integration. 12,13 The charge density was analyzed using the algorithm developed for ADF by Rodriguez. 14 Calculations were run using six different density functionals: the local density approximation developed by Vosko, Wilk, and Nusair; 15 the BLYP functional with the exchange term developed by Becke 16 and the correlation term by Lee, Yang, and Parr; 17–19 the PBE functional by Perdew, Burke, and Ernzerhof; 20 the M06-L and M06-2X functionals by Zhao and Truhlar; 21,22 and the B3LYP hybrid functional by Stephens, Devlin, Chablowski, and Frisch. 23 To investigate the magnitudes of ∆np we first need a test point within the charge density and observe how the charge density changes upon perturbation of the external potential (i.e. chemical substitutions). The test points chosen are the critical points (CPs) within the charge density — points at where the charge density achieves extreme values in all directions. 24 The charge density is a 3D scalar function and therefore contains four distinct kinds of critical points (CPs). These CPs are denoted by an index given by the number of principal positive curvatures minus the number of principal negative curvatures. For example, at a minimum, the curvature in principal directions is positive; therefore, it is called a (3, +3) CP. The first number is the number of dimensions of the space and the second is the net number of positive curvatures. A maximum is denoted by (3, -3), because all three curvatures are negative.


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The two CPs of interest in this study are the saddle CPs: (3, −1) and (3, +1). The (3, −1) CP, which sits at the minimum along the charge density ridge connection nuclear CPs and is accordingly know as the “bond CP”. Similarly, the (3, +1) CP is required within ring structures (rings of bond ridges) and is known as the “ring CP”. 25,26 The CPs are characterized by both the magnitude and curvature of the charge density at the CP. The eigenvalues of the Hessian matrix (a rank 2 tensor giving the second-order partial derivatives of the charge density) provide the curvature at the CP. Comparisons between CPs (and hence ∆np ) are made by calculating the magnitude and curvature of the charge at the CP and comparing how these metrics change as chemical substitutions are made near the functional group. In essence, we are expanding the charge density in a Taylor’s series around CPs and comparing the changes to the low order coefficients of this expansion to gauge the variation of the charge density as a whole. It is of course possible to pick other points or values as metics, say the position of CPs of the Laplacian of the charge density. However, such choices are arbitrary and amount to nothing more than an alternative selection of points around which to expand the charge density. This selection will have little impact on the qualitative results of this study. Here we investigate four distinct kinds of critical point (CP): the bond CP associated with carbon-oxygen double bonds (carbonyls), the bond CP associated with carbon-oxygen single bonds (C–O), the bond CP associated with oxygen-hydrogen bonds (hydroxyls), and the ring CP in aromatic compounds. The geometry of the charge density (i.e. the magnitude and eigenvalues of the Hessian) at these CPs is given for molecules containing acid, ester, alcohol, and ether groups (see figure 1). The substituents (labeled as R and R’ in figure 1) are fully saturated carbon chains that vary from 1 carbon to 4 carbons long (methyl to n-butyl), with the lengths of substituent carbon chains kept equal (i.e. the length of R will equal R’ for any given molecule). The initial portion of the manuscript looks exclusively at hydrocarbon substituents while the latter half of the manuscript investigates the response of the density upon halogen substitution at the terminal carbon(s) of the side-chains. The



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aromatic molecules investigated are mono-substituted benzenes where the substituents are selected so as to provide a wide range of activating and deactivating groups with respect to electrophilic attack.

Results This study compares dozens of molecules calculated across 6 DFT functionals. The expansiveness of the data-set makes it too bulky to provide in full in the manuscript and hence what is shown in the tables below are the mean and standard deviation across the 6 DFT functionals for each CP. The full data set can be found in the accompanying supplementary information.

Hydrocarbon Substituted Carbonyl Table 1 gives the mean and standard deviation for the carbonyl bond CP in the methyl, ethyl, n-propyl, and n-butyl substituted acids, esters, and ketones. The three carbonyl environments have magnitudes of charge at the respective bond CP, n, between 0.41–0.42 a.u., the mean negative curvatures range from −0.98 to −1.15 a.u., and the mean positive curvatures range from 1.5–1.6 a.u. The standard deviations for the magnitude of the charge density at the bond CP for carbonyls are relatively small, around 0.8%. There is a higher deviation between DFT functionals for the values of curvature where the discrepancy comes from the M06 functionals, where λ1 , λ2 , and λ3 have average relative standard deviations of 1.8%, 2.5%, and 5.9%. Table 2 gives λ1 , λ2 , and λ3 for acetic acid, methyl acetate, and acetone and demonstrates how M06 values differ from the other functionals. Compared with the other bond CPs analyzed (hydroxyl and carbon-oxygen single bond), the carbonyl has the largest magnitude of n, the largest positive positive curvature (λ3 ), 6 ACS Paragon Plus Environment

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and the second largest negative curvature values (λ1 and λ2 ). The carbonyl bond CP where the carbonyl carbon also makes a carbon-oxygen single bond, i.e. the acid and ester groups, have larger magnitudes of the charge density, larger negative curvature values and smaller positive curvature values when compared with the ketone carbonyl. It is important to note, though, that the differences in curvature at the bond CP for the ester, acid, and ketone carbonyls (table 2) are smaller than the reported standard deviation. In spite of this, table 2 shows that the trends in curvature hold for a given DFT functional, i.e. acids and esters have a larger negative curvature compared to ketones.

Carbon-Oxygen Single Bond Tables 3 and 4 give the mean and standard deviation for the carbon-oxygen single bond CP in the methyl, ethyl, n-propyl, and n-butyl substituted acids, esters, alcohols, and ethers. Compared to the other bond CPs considered, the carbon-oxygen has the smallest magnitude of the charge density and curvatures. There is also a clear distinction between carbon-oxygen single bonds attached to carbonyls (acids and esters) and those where the adjacent carbon is not a carbonyl carbon (alcohols, ethers, and the β-carbon-oxygen bond in esters). The mean magnitude of the charge density for the carbonyl adjacent carbon-oxygen single bond ranges between 0.296–0.301 a.u. and it ranges between 0.24–0.26 a.u. for non-carbonyl adjacent — more than 4 standard deviations smaller than the acid and ester values. Carbonyl-adjacent carbon-oxygen single bonds also have higher magnitude curvatures compared to their noncarbonyl-adjacent counterparts. Compared with the bond CPs associated with carbonyl and hydroxyl bonds, the C–O bond CPs have the least amount of charge density and lowest magnitude curvature at the bond CP. The standard deviations for the carbon-oxygen single bond possess a similar trend to that seen in the carbonyl bond CP, with the charge density having a lower deviation than the curvatures. The relative standard deviation for the magnitude of the charge density is around 0.6%. The curvatures for the carbonyl-adjacent C–O bond CPs as well as λ1



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and λ2 for the non-carbonyl adjacent C–O bond CPs was around 1.3–2.5%. The relative standard deviation for the positive curvature on the non-carbonyl adjacent C–O bond CPs is considerably higher, around 5.5% (see table 4). As was the case in the carbonyl bond CP, the deviation in the magnitude of λ3 is due to variability between the M06 functionals and the other DFT functionals.

Hydroxyl Table 5 provides the mean and standard deviation for the hydroxyl bond CP in the methyl, ethyl, n-propyl, and n-butyl substituted acids and alcohols. Of the CPs studied, the hydroxyl bond has the second largest magnitude for the charge density (∼0.35 a.u.), greatest magnitude for negative curvatures (∼ −1.6 a.u.), and second greatest positive curvature (∼ 1.4 a.u.). Unlike the carbonyl and carbon-oxygen single bond, the relative standard deviation for the magnitude of the charge density (∼0.9%) is larger that relative standard deviation for λ1 and λ2 (∼0.6%). Similar to the other bond CPs, the positive eigenvalue has the largest relative standard deviation of roughly 2%.

Halogen Substitution To investigate the magnitude of R0 for oxygen-containing functional groups a strong electronwithdrawing group was placed a variety of distances from the group resulting in a perturbation of the density (∆np ) at the relevant bond CPs. This was done by substituting various hydrogen atoms in the molecules discussed above with halogen atoms, specifically fluorine, chlorine, and bromine. Fluorinated analogues of the molecules discussed above can be found in tables S1–S4, chlorinated analogues can be found in tables S5–S8, and the brominated analogues can be found in tables S9–S12.


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Fluorine Substituted Carbonyl — Table S1 provides the carbonyl bond CP metrics for the CF3 substituted molecules. Comparisons between the CF3 values and their CH3 analogues (see figure 2 and table 1) shows that all four metrics, the magnitude of charge density, λ1 , λ2 , and λ3 have larger absolute values in the CF3 substituted molecules. For example, the mean magnitude of n increases from roughly 0.42 a.u. to 0.43–0.44 a.u.. Relative to the hydrocarbon substituted molecules the CF3 substituted acid shows the least change to the carbonyl bond CP with a 2% for n, λ1 , and λ2 and an 8% increase in λ3 . The CF3 substituted ester and ketone show larger increase in the bond CP metrics with increases around 4%–6% for n, λ1 , and λ2 and an 16%–18% increase in λ3 . It’s also interesting to note that the ketone, CF3 COCH3 , has values similar to that of the ester and acid carbonyl, showing that the presence of a single CF3 alters the geometry similar to how an electronegative oxygen perturbs the carbonyl bond CP. The ester functional group offers an interesting opportunity to see how placement of the fluorinated carbon affects the carbonyl bond CP. For instance consider the two molecules: CH3 COOCF3 and CF3 COOCH3 . When the CF3 is attached to the carbon-oxygen single bond of the ester, the bond CP metrics look similar to those found in the doubly CF3 substituted, CF3 COOCF3 . Yet, when that CF3 moiety is placed opposite the carbon-oxygen single bond, as is CF3 COOCH3 , the carbonyl more closely matches the hydrocarbon substituted CH3 COOCH3 . The relative standard deviations are similar to that for hydrocarbons with n, λ1 , λ2 , and λ3 having relative standard deviations around 0.8%, 2%, 3%, and 6%, respectively. As was the case for the hydrocarbon substituted carbonyl bond CPs, the larger deviation in λ3 is due to disagreement of the M06 functionals. Carbon-oxygen single bond — Figure 3 gives the magnitude of the charge density at the bond CP corresponding to the carbonyl-adjacent carbon-oxygen single bond in both the fluorinated acid and ester functionalities (see table S2 for tabulated magnitudes and curvatures). Unlike the hydrocarbon case, the C–O bond CP shows a distinct character in the 9 ACS Paragon Plus Environment


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acid compared to the ester functional group. The acid C–O bond CP, like the carbonyl bond CP, has a larger magnitude for the charge density and its curvature upon fluoridation of the α-carbon. The ester C–O bond CP, on the other hand, shows a decrease in both the magnitude and curvatures of the charge density at the bond CP. Comparing CH3 COOCF3 and CF3 COOCH3 shows the influence halogen placement has on the C–O bond CPs. Placing electron-withdrawing groups on either side of the bond, as is the case in CF3 COOCF3 , causes a decrease in the magnitude in the bond CP metrics, which is similar to the changes to the carbonyl-adjacent C–O bond CP present in CH3 COOCF3 . While having the electron-withdrawing groups concentrated on the carbonyl side of the bond, as is the case in CF3 COOCH3 , causes an increase in the magnitude of the charge density and its curvatures at the bond CP. The percent changes relative to the carbonyl adjacent C–O bond CPs reveal that the acid C–O bond CP has a similar percent changes to those seen in the acid carbonyl bond CP with a percent increase around 5% for n, 9% for λ1 , 6% for λ2 , and 11% for λ3 . The percent change to the carbonyl-adjacent ester possesses a more interesting trend. For the doubly substituted CF3 COOCF3 there is a decrease in the bonding metrics of −4% for n, −5% for λ1 , −3% for λ2 , and (excluding the outlying increase of 27% seen in the M06-2X functional) a decrease around −4% to −7%. As mentioned above, the unevenly substituted CF3 COOCH3 and CH3 COOCF3 show the most drastic changes. CF3 COOCH3 has a percent increase of 4%, 9%, 6%, and 15% for n, λ1 , λ2 , and λ3 respectively. While CH3 COOCF3 has a more dramatic percent decrease of −12% for n, −19% for λ1 , −15% for λ2 , −17% for λ3 . The non-carbonyl-adjacent carbon-oxygen single bond (see figure 4 and table S3) shows the same trend as acid carbonyl and acid carbon-oxygen single bond — the magnitude of the charge density and its curvatures increase in close proximity to the strong electronwithdrawing CF3 moiety. Unlike the carbonyl-adjacent C–O, mixed placement of electronwithdrawing and hydrocarbon groups causes a decrease in the magnitude and curvatures of the density for the O–CHx bond CPs. This is seen in both the O–CH3 bond in CF3 OCH3


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(ether) and CF3 COOCH3 (ester). C–O bonds directly attached to the CF3 moiety show an increase in bond CP metrics, such as in CF3 OCF3 and the CF3 –OCH3 bond CP in the ether groups and in the ester CF3 COOCF3 . Percent changes to the non-carbonyl adjacent C–O bond CP shows the greatest change of all the bond CPs studied. The alcohol and CF3 COOCF3 ester C–O bond CPs had similar percent increases of 22%–28% for n, 56%–62% for λ1 , 54% for λ2 , and 32% for λ3 . Similar to what was seen for the carbonyl-adjacent ester C–O bond CP, CF3 COOCH3 saw a small decrease in the bond CP metrics (between -1% and -5% for all metrics). While the bond CP in CH3 COOCF3 , being closer to the CF3 moiety, saw a drastic increase of 18% for n, 49% for λ1 , 37% for λ2 , and 22% for λ3 . For the ethers studied, the CF3 OCF3 C–O bond CP has a smaller percent increase of around 14% for n, 35%–37% for λ1 and λ2 , and 27% λ3 . As was the case for the ester molecules, ethers with mixed substitution saw changes to the CPs dependent on the location of halogen substitution. For example, in CF3 OCH3 the C–O bond CP close to the CF3 group saw an increase in the bond CP metrics (28% for n, 63%–66% for λ1 and λ2 , and 31% for λ3 ) and the bond CP attached to the CH3 group saw a decrease in the CP metrics of -9% for n, -19% for λ1 , -15% for λ2 , and -7% for λ3 . The relative standard deviations for the fluorinated carbonyl-adjacent C–O bond CPs is similar to that of their non-fluorinated analogues (see table 3) with relative standard deviations around 1% and 3% for the magnitude and curvatures of the charge density, respectively. A notable exception is the larger relative standard deviation seen in the carbonyl adjacent CF3 COOCF3 of 14%, due to the outlying value from the M06-2X functional. Hydroxyl — The effects of fluoridation on the hydroxyl bond CP is shown in figure 5 (see also table S4). Inspection of figure 5 as well as comparing table S4 with table 5 shows that the addition of neighboring fluoride groups has no appreciable affect on the charge density at the hydroxyl bond CP, with the magnitudes and standard deviations remaining consistent between both the hydrocarbon molecules and their fluorinated counterparts. The percent differences for the fluorine containing molecules were all less than 2% and so on the same



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order as the relative standard deviations for the hydroxyl bond CPs.

Chlorine and Bromine Substituted Calculations involving chlorine and bromine substitutions show similar trends to the fluorinated molecules. The carbonyl and carbon-oxygen single bond CPs show an increase in the magnitude of the charge density and curvature at the CP. For instance, compare tables S5 and S9 with table S1, tables S6 and S10 with table S2, and tables S7 and S11 with table S3. The hydroxyl bond CP for the chlorinated and brominated molecules (tables S8 and S12) did not appreciably change relative to the hydrogenated hydroxyl bond CPs (table 5), similar to the hydroxyl bond CP in the fluorinated compounds. The magnitudes of the errors also closely match those seen in the fluorinated molecules. The only exception being the brominated non-carbonyl adjacent carbon-oxygen single bonds (table S11), which have relative standard deviations around double those seen in the fluorinated and chlorinated molecules. The magnitude of the relative standard deviations are still relatively small, though, with around 2% and 4% relative standard deviations for the magnitude and curvatures of the charge density respectively.

Finding Functionality As mentioned in the introduction the functional group is characterized by an inner and outer radius, Ri and Ro . A change to the external potential within Ri would result in significant changes to ∆n — e.g. changing the external potential (i.e. change the atoms in the group) such that a hydroxyl bond becomes a carbon-oxygen single bond, as would be the case in going from an acid to an ester or an alcohol to an ether. It would follow then that each bond CP type (carbonyl, carbon-oxygen single bond, and hydroxyl) is constrained to a specific range of geometric values within the charge density. The differences between bond CP types is greater than the variability seen by either the addition of halogen atoms or use of different DFT functionals. These differences are well represented by comparing the bond CP metrics


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for the CH3 substituted functionalities, provided in tables 1–5. Comparison of the mean values for the bond CP metrics demonstrates that the variability between different DFT functionals for the bond CP associated with a specific bond type (e.g. carbonyl) is small compared to the differences between bond types (e.g. carbonyl vs. hydroxyl) which are considerably larger when compared to the standard deviations. Another way to see the clear differences between the bond CPs of the bond types investigated involves comparing the respective first and third quartile values of the full data-set (hydrocarbon and halogen) we can get an idea of a reasonable range for the bond CP metrics for a variety of bonds. For example, comparing the smaller first quartile value for the carbonyl bond CP density to the larger third quartile value for the hydroxyl to get an approximation of the lower bound for the relative magnitudes of the two values and comparing the third quartile of n at the carbonyl bond CP with the first quartile of the hydroxyl bond CP provides an upper bound on the range (see table 6). Doing this we see that the magnitude of the charge density at the carbonyl bond CP is around 40%–68% larger than the C–O bond CP and 15%–23% larger than that of the hydroxyl bond CP. The magnitude of the negative curvatures for the hydroxyl bond is 150%–243% larger than the negative curvatures for the C–O and 44%–67% larger than the carbonyl negative curvatures. The magnitude of λ3 for the carbonyl bond CP is 140%–285% and 10%–30% larger than the C–O and hydroxyl bond CPs respectively. All of these differences are larger than the relative standard deviations reported above. Even the smaller differences seen between n and λ3 for the hydroxyl and carbonyl, as discussed in more detail below and shown in table 7, do not have overlap between the values for all of the bond CP metrics. In general the overall magnitude of the difference between CP metrics for the different bond types (i.e. carbonyl vs. carbon-oxygen single bond vs. hydroxyl) are equal-to or greater-than 0.05–0.06 a.u. (≥15% difference) for n and 0.3 a.u. (≥10% difference) for λ values. Considering the overlap between bond CP types for any of the four metrics (n, λ1 , λ2 , and λ3 ) across all six DFT functionals studied shows that the differences between the bonds



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that make up a functional group, and hence the differences between the functional groups themselves, is greater than the difference between different DFT functional. Table 7 gives the relevant minimum and maximum values calculated for a given bond CP types across all molecules and functionals (full tables of the bond CP metrics for all calculations can be found in the supplementary information). Note the absence of overlap between bond CP metrics across all bond CPs and DFT functionals studied. For example, the carbon-oxygen single bond with the most charge at the bond CP still has less charge than the hydroxyl with the least charge at the bond CP. In turn, the hydroxyl bond CP with the most charge is still less than the carbonyl bond CP with the least charge. This demonstrates that the differences in the charge density between the different bond CP types is greater than the difference for a given bond CP calculated across a variety of functionals.

Halogen Proximity and Rp Now we wish to further develop the idea presented in the introduction that there exists some outer radius (Ro ) for functional groups, or more specifically that there exists some radius (Rp ) beyond which perturbations to the external potential do not appreciably alter a given property. We expect that the values of Rp to vary depending on the property of interest. For example, preliminary data suggests that Rp for transport related properties is substantially larger than Rp for structural properties. For this reason the property (and associated Rp ) being investigated are those associated with the chemical changes seen in oxygen-containing functional groups in close proximity to a strong electron-withdrawing group — e.g. higher hydroxyl acidity and larger carbonyl affinity for nucleophiles. Using the perturbing effects of halogen atoms on the charge density we can get an approximation for the size of Rp . For the all bond CPs studied the charge density metrics return to their base-line values (hydrocarbon values) when the fluoride group is placed beyond 2 carbon lengths from the CP of interest. Comparing tables 1 and S1 shows that the acid, ester, and ketone return to hydrocarbonlike CP metrics for the CF3 (CH2 )2 substituted molecules. A similar trend is seen comparing


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table 3 to S2 and table 4 to S3, showing that the C–O bond CP also returns to hydrocarbon values once the fluoride atoms are more than two carbon bond lengths away. The exact same trends are seen for the chlorine and bromine substituted molecules, the bond CPs respond when the chlorine or bromine atoms are substituted within 2 carbon bond-lengths and when the halogens are placed on carbons beyond that distance the CP metrics match those seen in the hydrogen substituted molecules. The hydroxyl bond CP showed no discernible difference upon halogenation, hence the values in tables 5, S4, S8, and S12 are consistent across all molecules.

Aromatic Ring Points Table 8 provides the magnitude and eigenvalues of the charge density at the ring point for a variety of mono-substituted benzenes. Examining the values shows that substitution does not have a discernible impact on the CP metrics at the ring CP. The calculated values between functionals has a relative standard deviation similar to those seen for bond CP with around 2%, 3%, 1%, and 2% for nRCP , λ1 , λ2 , and λ3 , respectively.

Summary Comparing bond CPs across a number of oxygen-containing functional groups shows that while no two DFT functionals provide exactly the same charge density, the differences between functionals is relatively small, with differences often being within a few percentage points. For inductive electron-withdrawing effects (halogen substitution) on oxygencontaining functional groups there was a consistent range for ∆np . For while the percent change to the bond CPs varied considerably when comparing bond CP types, the overall magnitude of the changes were all below 0.05–0.06 a.u. for n and 0.3 a.u. for λ. The effective Rp was on the order of two carbon bond-lengths (∼ 3˚ A). Beyond Rp the presence or lack of fluorine groups is nearly indistinguishable from that of the hydrogenated molecules.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

There are a number of important implications from these results. First, the charge density is a robust property as there is often little variability between different DFT functionals in the charge density at the bond and aromatic ring CP. More importantly, though, this work provides a framework with which to seek-out functionality within systems where such a concept is currently lacking. Future work will investigate the variability of the charge density within metallic systems to see if there are groups of metal atoms that possess similar values for ∆n and Rp .

Supplementary Information The supplementary information for this manuscript contains a text document containing 12 supplementary tables (SI Tables.pdf) and an Excel spreadsheet containing the full data-set analyzed for this manuscript (Full CP Data.xls).

Acknowledgments Support of this work under ONR Grant No. N00014-10-1-0838 and under ARO Grant No. 421-20-18 is gratefully acknowledged. We would also like to gratefully acknowledge the use of the BlueM supercomputer at Colorado School of Mines which was instrumental in calculating converged geometries for a number of the larger molecules.


Page 16 of 38

Page 17 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1: Generic structures for the functional groups studied.



Comparing CH3 and CF3 Substitution: Carbonyl 0.45 0.44 0.43 0.42 0.41 0.40 0.39

Acid

Ester CH

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

CH2CX3

(CH2)2CX3

0.38 CX3

Charge at Bond CP [e- bohr-3]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 38

Ketone

CF

Figure 2: A comparison of the mean magnitude of the charge density at the bond CP corresponding to the carbonyl bond in hydrogenated (CX3 = CH3 ) and fluorinated (CX3 = CF3 ) molecules. Note how the charge density at the bond CP for the fluorinated molecules agree with the hydrogenated values once the fluorinated carbon is at or beyond two carbon 18bars represent the standard deviation of the bond lengths away from the carbonyl. Error ACS Paragon Plus Environment magnitude of the charge density.

Comparing CH3 and CF3 Substitution: CO-O

Acid

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

CH2CX3

(CH2)2CX3

0.32 0.31 0.30 0.29 0.28 0.27 0.26 CX3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 19 of 38

Ester CH

CF

Figure 3: A comparison of the mean magnitude of the charge density at the bond CP corresponding to the carbonyl-adjacent carbon-oxygen single bond in hydrogenated (CX3 = CH3 ) and fluorinated (CX3 = CF3 ) molecules. Note how the charge density at the bond CP for the fluorinated molecules agree with the hydrogenated values once the fluorinated carbon 19 from the carbonyl-adjacent carbon-oxygen is at or beyond two carbon bond ACSlengths Paragonaway Plus Environment single bond. Error bars represent the standard deviation of the magnitude of the charge density.

Page 20 of 38

Comparing CH3 and CF3 Substitution: C-O 0.31 0.29 0.27

0.25 0.23

Alcohol

Ester CH

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

(CH2)2CX3

CH2CX3

0.21 CX3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Ether

CF

Figure 4: A comparison of the mean magnitude of the charge density at the bond CP corresponding to the (non-carbonyl-adjacent) carbon-oxygen single bond in hydrogenated (CX3 = CH3 ) and fluorinated (CX3 = CF3 ) molecules. Note how the charge density at the bond CP for the fluorinated molecules agree with the hydrogenated values once the 20 fluorinated carbon is at or beyond two carbon lengths away from the carbon-oxygen ACS Paragon Plusbond Environment single bond. Error bars represent the standard deviation of the magnitude of the charge density.

Comparing CH3 and CF3 Substitution: Hydroxyl 0.37 0.36 0.35 0.34

Acid

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

CH2CX3

(CH2)2CX3

0.33 CX3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 21 of 38

Alcohol CH

CF

Figure 5: A comparison of the mean magnitude of the charge density at the bond CP corresponding to the (non-carbonyl-adjacent) carbon-oxygen single bond in hydrogenated (CX3 = CH3 ) and fluorinated (CX3 = CF3 ) molecules. Note how the charge density at the bond CP for the fluorinated molecules agree with the hydrogenated values once the 21 fluorinated carbon is at or beyond two carbon lengths away from the carbon-oxygen ACS Paragon Plusbond Environment single bond. Error bars represent the standard deviation of the magnitude of the charge density.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6: Table of Contents image.


Page 22 of 38

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Table 1: Bond CP data for carbonyl hydrocarbons. n

23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Acids CH3 COOH CH3 CH2 COOH CH3 (CH2 )2 COOH CH3 (CH2 )3 COOH Esters CH3 COOCH3 CH3 CH2 COOCH2 CH3 CH3 (CH2 )2 COO(CH2 )2 CH3 CH3 (CH2 )3 COO(CH2 )3 CH3 Ketones CH3 COCH3 CH3 CH2 COCH2 CH3 CH3 (CH2 )2 CO(CH2 )2 CH3 CH3 (CH2 )3 CO(CH2 )3 CH3

e− [ bohr −3 ]

Hydrocarbon Carbonyl Data e− λ1 [ bohr sd sd −5 ]

−

−

e λ2 [ bohr −5 ]

sd

e λ3 [ bohr −5 ]

sd

0.4242 0.4233 0.4233 0.4231

0.0033 0.0033 0.0033 0.0033

-1.153 -1.149 -1.149 -1.147

0.021 0.021 0.021 0.021

-1.005 -1.004 -1.004 -1.003

0.025 0.025 0.025 0.025

1.584 1.588 1.589 1.584

0.090 0.091 0.092 0.092

0.4216 0.4200 0.4196 0.4197

0.0032 0.0032 0.0032 0.0032

-1.133 -1.128 -1.126 -1.126

0.021 0.022 0.022 0.021

-0.997 -0.992 -0.992 -0.992

0.025 0.025 0.024 0.025

1.563 1.565 1.564 1.567

0.092 0.091 0.091 0.090

0.412513 0.411404 0.410963 0.410903

0.003398 0.003493 0.003377 0.003369

-1.090 -1.081 -1.077 -1.077

0.021 0.018 0.018 0.019

-0.986 -0.986 -0.985 -0.985

0.024 0.024 0.024 0.024

1.63 1.63 1.633 1.63

0.10 0.10 0.099 0.10

ACS Paragon Plus Environment


Table 2: Eigenvalues for the bond CP in the methyl substituted acid, ester, and ketone — acetic acid, methyl acetate, and acetone, respectively.

λ1 λ2 λ3

LDA -1.1405 -1.0086 1.5161

λ1 λ2 λ3

LDA -1.1222 -0.99966 1.4950

λ1 λ2 λ3

LDA -1.0852 -0.99413 1.5465

24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 24 of 38

CH3 Substituted Carbonyl Curvatures CH3COOH BLYP PBE M06-L B3LYP -1.1577 -1.1394 -1.1276 -1.1874 -1.0152 -1.0006 -0.95913 -1.0350 1.5053 1.5450 1.7032 1.5381 CH3COOCH3 BLYP PBE M06-L B3LYP -1.1382 -1.1207 -1.1079 -1.1677 -1.0054 -0.99112 -0.95181 -1.0265 1.4830 1.5232 1.6856 1.5159 CH3COCH3 BLYP PBE M06-L B3LYP -1.0973 -1.0649 -1.0713 -1.1233 -0.99935 -0.97896 -0.94213 -1.0137 1.5466 1.5831 1.7584 1.5911


M06-2X -1.1636 -1.0114 1.6948 M06-2X -1.1439 -1.0049 1.6739 M06-2X -1.0995 -0.98481 1.7569

Page 25 of 38

Table 3: Bond CP data for carbon-oxygen single bonds in hydrocarbons. Specifically this table contains C-O bonds that are themselves attached to a carbonyl — which occurs in both acids and esters. Hydrocarbon Carbonyl-Adjacent Carbon-Oxygen Single Bond Data e− e− e− sd sd sd n [ bohr λ1 [ bohr λ2 [ bohr −3 ] −5 ] −5 ]

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Acids CH3 COOH CH3 CH2 COOH CH3 (CH2 )2 COOH CH3 (CH2 )3 COOH Esters CH3 COOCH3 CH3 CH2 COOCH2 CH3 CH3 (CH2 )2 COO(CH2 )2 CH3 CH3 (CH2 )3 COO(CH2 )3 CH3

−

e λ3 [ bohr −5 ]

sd

0.2971 0.2961 0.2958 0.2957

0.0016 0.0016 0.0016 0.0016

-0.6716 -0.6635 -0.6629 -0.6627

0.0117 0.0119 0.0119 0.0120

-0.6342 -0.6311 -0.6298 -0.6293

0.0146 0.0145 0.0142 0.0143

0.6377 0.6368 0.6357 0.6343

0.0080 0.0081 0.0081 0.0081

0.3010 0.2996 0.2996 0.2997

0.0017 0.0017 0.0017 0.0017

-0.6855 -0.6739 -0.6742 -0.6742

0.0124 0.0125 0.0128 0.0128

-0.6340 -0.6299 -0.6298 -0.6300

0.0154 0.0140 0.0147 0.0146

0.6620 0.6541 0.6532 0.6530

0.0090 0.0090 0.0091 0.0091



Table 4: Bond CP data for carbon-oxygen single bonds in hydrocarbons. Specifically this table contains C-O bonds that are not attached to a carbonly carbon — which are found in alcohols, ethers, and esters. Hydrocarbon Carbon-Oxygen Single Bond Data e− e− e− n [ bohr sd λ1 [ bohr sd λ2 [ bohr −3 ] −5 ] −5 ]

−

sd

e λ3 [ bohr −5 ]

sd

Alcohols

26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 26 of 38

CH3 OH CH3 CH2 OH CH3 (CH2 )2 OH CH3 (CH2 )3 OH CH3 (CH2 )3 CH2 OH Ethers CH3 OCH3 CH3 CH2 OCH2 CH3 CH3 (CH2 )2 O(CH2 )2 CH3 CH3 (CH2 )3 O(CH2 )3 CH3 Esters CH3 COOCH3 CH3 CH2 COOCH2 CH3 CH3 (CH2 )2 COO(CH2 )2 CH3 CH3 (CH2 )3 COO(CH2 )3 CH3

0.25440 0.25185 0.25392 0.25242 0.25678

0.00073 0.00065 0.00073 0.00071 0.00078

-0.497 -0.4949 -0.495 -0.4894 -0.499

0.011 0.0096 0.011 0.0099 0.010

-0.488 -0.478 -0.487 -0.483 -0.495

0.011 0.010 0.010 0.010 0.010

0.452 0.450 0.452 0.450 0.460

0.026 0.028 0.027 0.028 0.024

0.26159 0.25903 0.25970 0.25869

0.00087 0.00078 0.00083 0.00083

-0.519 -0.516 -0.518 -0.514

0.012 0.010 0.010 0.010

-0.500 -0.490 -0.492 -0.488

0.011 0.011 0.011 0.011

0.466 0.463 0.463 0.461

0.024 0.026 0.025 0.026

0.2416 0.2372 0.2382 0.2375

0.0010 0.0011 0.0011 0.0011

-0.447 -0.434 -0.436 -0.434

0.013 0.012 0.012 0.012

-0.440 -0.428 -0.431 -0.427

0.012 0.012 0.012 0.012

0.443 0.436 0.436 0.435

0.020 0.023 0.022 0.022


Page 27 of 38

Table 5: Bond CP data for hydroxyl (O-H) bonds in hydrocarbons. n

27

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Acids CH3 COOH CH3 CH2 COOH CH3 (CH2 )2 COOH CH3 (CH2 )3 COOH Alcohols CH3 OH CH3 CH2 OH CH3 (CH2 )2 OH CH3 (CH2 )3 OH CH3 (CH2 )3 CH2 OH

e− [ bohr −3 ]

Hydrocarbon Hydroxyl Data e− e− λ1 [ bohr λ2 [ bohr sd sd −5 ] −5 ]

−

sd

e λ3 [ bohr −5 ]

sd

0.3502 0.3501 0.3502 0.3502

0.0034 0.0034 0.0034 0.0034

-1.669 -1.668 -1.668 -1.667

0.010 0.011 0.011 0.011

-1.6376 -1.637 -1.637 -1.6364

0.0094 0.011 0.010 0.0098

1.367 1.366 1.365 1.366

0.026 0.027 0.027 0.027

0.3587 0.3585 0.3577 0.3591 0.3606

0.0033 0.0033 0.0033 0.0036 0.0037

-1.675 -1.672 -1.6629 -1.682 -1.6912

0.011 0.011 0.0097 0.010 0.0097

-1.623 -1.622 -1.6125 -1.6300 -1.6395

0.011 0.011 0.0096 0.0094 0.0091

1.407 1.399 1.386 1.389 1.392

0.027 0.027 0.027 0.029 0.029

Table 6: Inter-Quartile Range values. Bond CPs First and Third Inter-Quartile Range n λ1 & λ2 λ3 C-O Q1 0.255764 -0.65276 0.456155 Q3 0.298072 -0.48764 0.638398 C=O Q1 0.415448 -1.13517 1.54649 Q3 0.43002 -0.99989 1.758484 O-H Q1 0.350262 -1.67556 1.352751 Q3 0.358365 -1.63434 1.396515



Table 7: Minimum and maximum calculated values for the bond CP types investigated. C–O denotes the carbon-oxygen single bond CP, O–H denotes the hydroxyl bond CP, and C=O denotes the carbonyl bond CP. Note how there is not overlap for any of the bond CP metrics for any bond CP type. Relevant Minimum and Maximum Bond CP Values Value Molecule DFT Functional

28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 28 of 38

n max C–O min O–H max O–H min C=O λ1 and λ2 min C–O max C=O min C=O min O–H λ3 max C–O min O–H max O–H min C=O

0.33441 0.34079 0.36281 0.40462

CF3 –OCH3 CF3 COOH CH3 (CH2 )3 CH2 OH CCl3 (CH2 )3 COO(CH2 )3 CCl3

B3LYP LDA B3LYP M06-L

-0.84408 -0.93698 -1.24294 -1.59760

CF3 –OCH3 CCl3 (CH2 )3 CO(CH2 )3 CCl3 CH3 COOCF3 CH3 (CH2 )2 OH

B3LYP M06-L B3LYP BLYP

0.83481 1.30400 1.44302 1.48298

CF3 COOCF3 (C3 F7 )2 CHOH CH3 OH CH3 COOCH3

M06-2X LDA BLYP BLYP


Page 29 of 38

Table 8: Ring CP data for a variety of aromatic compounds. e− [ bohr −3 ]

29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


C6 H6 C6 H5 CH3 C6 H5 NH2 C6 H5 OH C6 H5 F C6 H5 Cl C6 H5 Br C6 H5 CF3 C6 H5 CN C6 H5 NO2 [C6 H5 NH3 ]+ [C6 H5 OH2 ]+

n 0.02461 0.02445 0.02422 0.02426 0.02444 0.02454 0.02464 0.02455 0.02430 0.02476 0.02462 0.02492

sd 0.00049 0.00049 0.00049 0.00050 0.00051 0.00050 0.00049 0.00051 0.00050 0.00051 0.00052 0.00054

Ring CP Data e− sd λ2 [ bohr −5 ] -0.01858 0.00053 0.08671 -0.01827 0.00052 0.08338 -0.01780 0.00053 0.08107 -0.01783 0.00056 0.08208 -0.01802 0.00059 0.08492 -0.01821 0.00042 0.08517 -0.01854 0.00054 0.08628 -0.01859 0.00054 0.08699 -0.01832 0.00053 0.08630 -0.01882 0.00057 0.0862 -0.01852 0.00057 0.0853 -0.01873 0.00063 0.0842

e− λ1 [ bohr −5 ]


sd 0.00100 0.00092 0.00088 0.00084 0.00092 0.00094 0.00097 0.00098 0.00096 0.0010 0.0010 0.0011

−

e λ3 [ bohr −5 ] 0.0868 0.0891 0.0892 0.0885 0.0870 0.0872 0.0868 0.0871 0.0865 0.0882 0.08847 0.0911

sd 0.0010 0.0010 0.0011 0.0011 0.0010 0.0012 0.0010 0.0010 0.0010 0.0010 0.00099 0.0011


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

References (1) Kohn, W. Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms. Phys. Rev. Lett. 1996, 76, 3168–3171. (2) Prodan, E.; Kohn, W. Nearsightedness of Electronic Matter. Proc. Natl. Acad. Sci. USA 2005, 102, 11635–11638. (3) Prodan, E. Nearsightedness of Electronic Matter in One Dimension. Phys. Rev. B 2006, 73, 085108. (4) Bader, R. F. W. Chemistry and the Near-Sighted Nature of the One-Electron Density Matrix. Int. J. Quant. Chem. 1995, 56, 409–419. (5) Riess, J.; M¨ unch, W. The Theorem of Hohenberg and Kohn for Subdomains of a Quantum System. Theor. Chem. Acc. 1981, 58, 295–300. (6) Bader, R.; Becker, P. Transferability of Atomic Properties and the Theorem of Hohenberg and Kohn. Chem. Phys. Lett. 1988, 148, 452 – 458. (7) Mezey, P. G. The Holographic Electron Density Theorem and Quantum Similarity Measures. Mol. Phys. 1999, 96, 169–178. (8) McNaught, A. D.; Wilkinson, A. IUPAC. Compendium of Chemical Terminology, 2nd ed.; Blackwell Scientific Publications, Oxford, 1997. (9) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931–967. (10) Fonseca Guerra, C.; Snijders, G. J.; te Velde, G.; Baerends, J. E. Towards an Order-N DFT Method. Theor. Chem. Acc. 1998, 99, 391–403.


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(21) Zhao, Y.; Truhlar, D. G. A New Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006, 125, 194101. (22) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215–241. (23) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623–11627. (24) Matta, C. F. Modeling Biophysical and Biological Properties from the Characteristics of the Molecular Electron Density, Electron Localization and Delocalization Matrices, and the Electrostatic Potential. J. Comput. Chem. 2014, 35, 1165–1198. (25) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press, 1994. (26) Zou, P. F.; Bader, R. F. W. A Topological Definition of a WignerSeitz Cell and the Atomic Scattering Factor. Acta Crystallogr., Sect. A 1994, 50, 714–725.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Generic structures for the functional groups studied. 245x287mm (96 x 96 DPI)



Comparing CH3 and CF3 Substitution: Carbonyl 0.45 0.44 0.43 0.42 0.41 0.40 0.39

Acid

Ester CH

CF


Ketone

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

CH2CX3

(CH2)2CX3

0.38 CX3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 38


Comparing CH3 and CF3 Substitution: CO-O

Acid

Ester CH

CF


(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

CH2CX3

(CH2)2CX3

0.32 0.31 0.30 0.29 0.28 0.27 0.26 CX3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Page 35 of 38

Page 36 of 38

Comparing CH3 and CF3 Substitution: C-O 0.31 0.29 0.27

0.25 0.23

Alcohol

Ester CH

CF


Ether

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

(CH2)2CX3

CH2CX3

0.21 CX3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




Comparing CH3 and CF3 Substitution: Hydroxyl 0.37 0.36 0.35 0.34

Acid

Alcohol CH

CF


(CH2)3CX3

(CH2)2CX3

CH2CX3

CX3

(CH2)3CX3

CH2CX3

(CH2)2CX3

0.33 CX3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Page 37 of 38


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Table of Contents Image 578x337mm (96 x 96 DPI)


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Nearsightedness of Oxygen-Containing Functional Groups - The

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