Weak Interactions as Diagnostic Tools for Inductive Effects - The

Mar 25, 2015 - No broadly applicable and well-defined measure for the inductive effects of substituents (outside of the context of substituted benzene...
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Weak Interactions as Diagnostic Tools for Inductive Effects Kelling J. Donald,* Marina Tawfik, and Brandon Buncher Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, Virginia 23173, United States S Supporting Information *

ABSTRACT: No broadly applicable and well-defined measure for the inductive effects of substituents (outside of the context of substituted benzenes) exists. We assess the viability of two different forms of weak interactions as tools for this purpose. The responses of interatomic (I···N and Ge···N) separations in the halogenbonded and dative covalent complexes F3CI···Y and FH3Ge···Y, where Y = NH2R, afford a direct ordering of a diverse set of substituents, R, according to their influence on the availability of the N lone pair in the base (NH2R) for bonding. Despite their structural and electronic differences, the two bonding modes that we consider show good qualitative agreement on the electron-withdrawing inductive tendencies of substituents because of their sensitivity to the electronic environment at the donor site (the N center, in this case) on the base. The choice of the monosubstituted (NH2R) base minimizes steric interactions, resonance, and other electronic effects that could interfere with the bonding between N and the I or Ge centers in the complexes. We find, moreover, that the inductive tendencies for substituents in these complexes are, in general, not additive. Depending on the identity of R, the trisubstituted base (NR3) may actually reverse rather than enhance changes in the acid−base interactions that are achieved going from NH3 to NH2R. These outcomes are observed at the MP2(full) and the M06-2X levels of theory, for both halogen and dative bonding interactions. A conservative ordering of substituents according to the observed inductive tendencies is presented.

1. INTRODUCTION 1.1. Withdrawing and Donating Tendencies of Substituents. Inductive and resonance effects are two of the basic mechanisms by which substituents influence the nucleophilicity (or electrophilicity) of compounds. The terms ‘electron-withdrawing (or donating) power’ refer broadly to the influence that a substituent, R, can have on the electron density of a molecular fragment to which it is bonded. This characteristic probably cannot be quantified rigorously in a transferrable manner, however, since the effect of one substituent compared to another on the electron distribution in a given compound is unique to that particular compound. That is, two substituents, R1 and R2, can have similar inductive effects on the electron density in the rings in C6H5R1 and C 6 H 5 R 2 , but very different effects on the rings in C6H4(COOH)R1 and C6H4(COOH)R2. If the substituents are ortho to the −COOH group, for example, then R1 and R2 may have noticeably different effects on the ring if R2 is bulky or if (compared to R1) R2 interacts very strongly electrostatically with one or both of the O atoms on the −COOH group. Moreover, the list of substituents in order of their relative electron-withdrawing abilities in contexts where π-electron delocalization is important (for C6H5R, for instance) may be different from the list that one gets when π-type contributions are negligible or irrelevant (as in NH3R). Once the electronic context is defined, however, attempts may be made to quantify electron-withdrawing tendencies1,2 and to locate ad hoc boundaries and construct categories of strongly, moderately, or weakly withdrawing or donating species. One example of this © 2015 American Chemical Society

construction in practice is in the area of aromatic substitutions where synthetic experience and patterns that have emerged in the literature over decades, and which are routinely echoed in college textbooks, have led to a robust understanding of the relative efficacy of substituents in moderating the charge density at different positions on benzene rings. NH2, for example, is considered to be a strong electron donor, and NO2 is a strong electron-withdrawing group. For nonaromatic bases such as NH3 or H2O, substitutions can have a substantial inductive effect on the availability of the lone pair(s). The interaction of NH3 or H2O with an electron acceptor in an acid−base complex can be altered significantly, in fact, if one or more of the H atoms on the base is replaced by a strongly electron-withdrawing or -donating substituent. We showed recently, for example, that NF3 and N(CH3)3 form F3MI···NR3 halogen bonds that are noticeably longer and shorter, respectively, than the F3MI···NH3 analogue,3 and a similar situation has been found as well for M···N contacts in the dative type (F4M·NR3) complexes,4 where, in both types of complexes, M is a group 14 atom. We consider in this work a series of bases involved in (halogen-bonded and coordinate covalent (dative)) complexes of the forms just described, and we examine the ability of those weaker forms of bonding interactions to act as yardsticks in assessing the relative electron-withdrawing powers of subReceived: January 18, 2015 Revised: March 24, 2015 Published: March 25, 2015 3780

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well. These two methods were chosen because they represent two very different approaches to describing the physics of the chemical systems under consideration. The cc-pVTZ allelectron basis sets27 have been employed for all elements except for iodine, which is the heaviest atom considered. For iodine, we used the scalar-relativistic energy-consistent small core (28 electron) Dirac−Fock (MDF) effective-core pseudopotential (ECP) and the corresponding (MDF cc-pVTZ-pp) basis set.28−30 All of the ab initio calculations in this work were performed using the Gaussian 09 suite of programs.31 The molecular structures and other atomic representations have been generated using ChemCraft software.32 Given the large number of electron-donating and -withdrawing groups considered in this work, only a few representative structures are included in the main text. Additional structural information for the systems studied in this work and additional graphics for some complexes with unusual bonding patterns are included in the Supporting Information.

stituents. Detailed analyses of the driving forces for the two kinds of interactions just mentioned are provided elsewhere,5−10 but a brief summary of the natures of those interactions is in order here for the ensuing discussion. 1.2. Weak Interactions. A halogen bond or X-bond (R′X··· Y), so-called because of its obvious analogy to the hydrogen bond (R′H···Y; ref 11), is a weak bonding interaction between (i) a halogen atom X (bonded to an electron-withdrawing group, e.g., R′− = F3C−) and (ii) an electron-rich center on a base, Y (such as the lone pair in NH3). In the F3CX···NH3 complex, the F3C− fragment induces a positive potential (an electron-deficient region) on the pole or cap of X outside the bonding region (indicated by the arrow in CX←) along the bond axis. This localized region of positive potential on X (the so-called sigma-hole) interacts with an electron-rich center on Y (N in NH3) to form the halogen bond (X···Y). Since polarizability increases going down group 17, the sigma-hole on X in R′X (for any given R′ group) increases as I > Br > Cl ≫ F.7 The formation of the dative F4M···Y type complexes in which the base, Y, is bonded to M at the axial position is favored as well by the presence of a sigma hole, in this case on the central M atom.4 In these systems, M is polarized by F such that a positive potential is generated on M opposite each F−M bond in MF4 (i.e., at the center of each face of the MF4 tetrahedron). A few instances of these dative-type complexes in which a base is coordinated axially to a saturated group 14 central atom have already been identified computationally.4,12,13 This wellestablished preference for the axial position is in conflict with classical expectations for ligands in inorganic chemistry14,15 but is supported strongly by both computational and experimental observations.16−23 Moving down group 14 toward M = Pb, the weak F4C···Y complexes that are held together by really weak pro-dative sigma-hole bonds evolve into strong dative covalent F4M·Y complexes as the M atom gets larger and more polarizable.4 The NH2R systems that we consider in this work, unlike substituted benzenes (C6H5R), for instance, for which Hammett substituent constants have been available for a long time,24 are expected to have very little contribution to the electron-withdrawing power from resonance effects. So, the acid−base interactions that we consider in this work provide a means for assessing almost exclusively the inductive influence of the substituents on central atoms. The inductive tendencies of some 21 substituents (relative to NH3) are examined using the halogen-bonded CF3I···NH2R and F4Ge·NH2R type complexes as our models systems. We consider more broadly as well the potential for generating a reliable relative scale for the withdrawing (donating) powers of monovalent σ-bonded substituents, and certain successes and significant limitations are identified. Through-bond and through-space interactions between the R groups in the NR3 bases guarantee that the inductive effects observed for R in NH2R are, in general, not even nearly additive. Complexes of the monosubstituted N bases, which are also less demanding computationally than the corresponding NR3 species, are viable and hitherto unexploited systems for the qualitative assessment of the relative inductive electron-withdrawing tendency of monovalent substituents.

3. RESULTS AND DISCUSSION 3.1. Halogen and Dative Bonds as Probes for Inductive Effects. The influence of 22 different substituents (R groups in Table 1) on the availability of the electron density Table 1. Substituents (R Groups) Considered in This Work −H −F −Cl −Br −I −C6H5

−CH3 −CF3 −CCl3 −CF2CH3 −CHO −CN

−CH2CH3 −CHCH2 −COOCH3 −COOH −NH2

−NHCH3 −NHCHO −NO2 −OH −OCH3

on the atomic center to which they are bonded (N in NH2R) has been assessed. Most of the species that we consider have been selected for their prevalence as functional groups and their relevance as (ortho-para or meta) directing groups in organic reactions. 3.1.1. Weak Interactions. The inductive electron-withdrawing power of each of the substituents (Table 1) has been assessed indirectly by considering the perturbation of the (I···N and Ge···N) interatomic separations between the F3CI or FH3Ge molecule and the N center of the Lewis base, NH2R, to which the substituent (R) is bonded. Representations of the halogen-bonded CF3I···NH2R and the dative-type FH3Ge··· NH2R complexes are shown in Figure 1. These complexes were chosen because they are simple and relatively easy to handle computationally at the somewhat demanding MP2(full) level of theory with large basis sets in allelectron calculations (a pseudopotential is used only for iodine). Our research group has a strong interest and some experience as well in the computational analysis of so-called sigma-hole interactions,3,4,10 a general class of interactions that includes, but is not limited to, halogen bonding. In the latter case, the formation of a weak I···N bond in CF3I···NH2R is fostered by a positive potential induced on the pole of the iodine atom (opposite the C−I bonding region in CF3I) by the −CF3 group. In the FH3Ge·NH2R complex (on the right in Figure 1), which is the second form of interaction that we consider, the F substituent has a similar polarizing effect on Ge as F3C has on I in CF3I. In this dative bonding case, therefore, the sigma-hole emerges on the central Ge atom below the F−Ge bond. The

2. COMPUTATIONAL DETAILS The results reported in this work have been obtained at the Møller−Plesset (MP2(full)) level of theory,25 with a substantial amount of additional data obtained at the M06-2X level26 as 3781

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expected classically to occupy an equatorial and not the axial position.4,14,15 The coordinate covalent bond between FH3Ge and NH2R is expected to have substantial electrostatic and covalent contributions, with the proportions depending on the electrostatic potential at Ge and the availability of the lone pair on N for bonding. The availability of the lone pair, in turn, is dictated by the electron-withdrawing power of the substituent, R. As R becomes more polarizing, the lone pair shrinks and the Ge···N contact becomes weaker and longer, and the opposite effect is expected as R becomes more σ-donating. So, why have we chosen CF3I and GeH3F as the acceptors or Lewis acids for this investigation? Halogen bonds formed by CF3I are much stronger and more stable than the analogous SiF3I X-bonds and are comparable in strength to the corresponding Ge and Sn cases. PbF3I forms stronger MF3I··· Y halogen bonds than CF3I− for any given Lewis base, but the halomethanes are of greater practical interest in organic and inorganic chemistry, and CF3I is much less demanding computationally than the Pb analogue. For sigma-hole bonds to central atoms, the softer and larger Ge atom is far superior to carbon. The longer Ge−H bonds minimize as well both the potential for (i) steric clashes with the substituent on the axially coordinated base in the FH3M·Y complex (Figure 1) and (ii) secondary weak interactions such as hydrogen bonding between H sites on MH3F with an F atom on NF3, for instance. The F−Ge···N bonds have also been shown to be much stronger than the corresponding F−C···N bonds, but they are weak enough we find to be tuned significantly by changes to substituents on N.4 The computed bond distances obtained for over 70 complexes examined herein are listed in Table 2. We focus

Figure 1. Sample structures of the systems considered in this work. Complexes of the NR3 bases (where the two H atoms in NH2R are replaced) have been considered also. Electron-withdrawing R groups promote a contraction in the lone pair on N and weaken the bond between N and the acceptor site. An increases in rI−N or rGe−N is a consequence of this weakening, and donor R substituents have the opposite effect: contractions in rI−N and rGe−N.

presence of this sigma-hole promotes the formation of a dativetype Ge−N bond at the axial position (by a donation of electron density into an empty orbital on Ge that coincides with the sigma-hole, opposite the F−Ge bond). The location of the sigma-hole trans to the inducing F atom strongly favors the axial position for the base in the FH3Ge·NH2R complex. This axial preference is observed, in fact, in F4Ge·NH3 even though the less electronegative substituent (NH3 compared to F) is

Table 2. Bond Distances (in angstrom units, Å) of the Acid···Base (Y) Complexes Considered in This Worka X-bonding (Y = :NH3‑nRn)

dative (Y = :NH3‑nRn)

bases

CF3I−NH2R

CF3I−NR3

GeFH3−NH2R

GeFH3−NR3

−CH2CH3 −CH3 −NHCH3 −NH2 −C6H5 I H −OCH3 −CHCH2 −OH Br Cl −NHCOH −CF2CH3 F −CCl3 −CF3 −COOCH3 −NO2 −COOH −CN −CHO

2.873 2.875 2.900 2.902 2.949 2.960 2.967 2.973 2.978 2.980 2.986 3.014 3.018 3.050 3.070 3.073 3.135 3.155 3.161 3.169 3.176 3.207

2.765 2.764 2.959 2.812

2.444 2.446 2.457 2.384 2.602 2.607 2.606 2.554 2.646 2.515 2.622 2.648 2.649 2.753 2.676 2.809 2.854 2.883 2.899 2.921 2.895 2.964

2.384 2.334 2.399 2.356

b

2.867 2.967 3.078 3.347 3.025 2.926 3.018 c b

3.353 b

3.463 b

3.141 c c c

b

2.570 2.606 2.742 2.970 2.473 2.603 2.691 2.983 b

2.950 b

3.177 b

2.831 c

3.176 3.129

a The list is in order of the lengths of the halogen bonds in column 2. bThe trisubstituted complexes for these substituents were not considered for these bulky and computationally demanding substituents. cA direct interaction between I or Ge with the N center in the base is not observed in these complexes. See the Supporting Information for the structural details.

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only 4.34 cm−1). These observations indicate that the Ge bonds have a substantial covalent component relative to the halogen bonds of I and are more stable. As we mention above, discussions of the structure, stability, and experimental evidence for the existence of such dative-type and halogen-bonded complexes are provided elsewhere (see refs 3 and 4 and references therein). We focus in this work on the geometrical properties of the complexes, in particular, the influence of the substituents on the interatomic separations between the two coordinating molecular units of the complexes. The Cartesian coordinates for the complexes discussed are included in the Supporting Information. The sensitivity of weak interactions including halogen bonding and weak dative bonding interactions make them unique structural frameworks for use in assessing the inductive electron-withdrawing power of a wide range of substituents. In that context, the interatomic separations in the complexes are particularly useful molecular parameters against which to benchmark the electron-withdrawing power of substituents. The direct comparison of the interatomic separations between a given electron acceptor or Lewis acid and substituted bases provides a relatively straightforward way to determine where one substituent falls relative to another in terms of their electron-withdrawing or -donating abilities. The most significant limitation is the computational cost for geometry optimizations for large or electronically complicated substituents using reliable model chemistries. Geometrical parameters for small- and medium-sized molecules and complexes, however, can be obtained readily with good accuracy, even at moderately demanding levels of theory. The advantage of using geometrical parameters as our yardstick for inductive effects, therefore (instead of relying on dissociation energies or vibrational frequencies, for example), is that the latter properties for weakly bound complexes can be difficult to obtain accurately without employing very demanding model chemistries. Figure 3 illustrates the relationship between the Ge···N and I···N interatomic separations for 22 NH2R bases, each distinguished by the identity of R. The bases fall surprisingly well into a few different classes (or subgroups) that show linear relationships between the

primarily in this work on complexes involving monosubstituted base (NH2R) using ammonia as our reference, but we have determined the minimum energy structures for several of the trisubstituted complexes as well. We wanted to assess the extent to which the electron-withdrawing power of these substituents may be considered to be additive. As we will see presently, the trisubstituted systems turn out to be more complicated to handle than anticipated because of the preference in some cases for alterative bonding patterns, which are outside our interest in this work, and some significant R···R interactions as well. 3.1.2. Sensitivity of Weak Interactions to the Inductive Effects of Distal Substitutions. Sample structures for the systems considered (each with R = −CH3) in this work are shown in Figure 2. The larger bond energies of the Ge···N

Figure 2. Sample MP2(full) structures for different types of complexes, using the −CH3 fragment as our substituent of choice.

dative4 complexes versus I···N halogen bonds3 are evident from the relative magnitudes of the harmonic frequencies shown in the figure. The lowest vibrational frequencies for the I···N halogen bond in the CF3I···N(CH3)3, second from the right in Figure 2, is 2 orders of magnitude smaller than that of the corresponding Ge···N bond. For the monosubstituted case, too (on the left in Figure 2), the frequency for the Ge···N bond is some 90 cm−1 larger than that for the halogen bond (which is

Figure 3. Ge···N and I···N separations for 44 (F3CI···NH2R and FH3Ge···NH2R) complexes optimized at the MP2(full) level of theory. The substituent to which each number on the graph refers is shown on the right. This numbering scheme is used throughout this work. 3783

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The Journal of Physical Chemistry A interatomic separations for the two sets of (I···N and Ge···N) complexes. A few best fit lines have been added to the graph only to identify the apparent linear relationship between the I··· N and Ge···N interatomic separations (within each subgroup) and to emphasize the groupings of the complexes that automatically emerge from the plot. The subsets of complexes, which come as a surprise to us, tend to appear along the way (going from left to right across Figure 3) as the I···N and Ge··· N interatomic separation increases, but the reasons for the specific groupings that we observe are unclear. Moreover, the range of distances spanned by the individual subgroups that we have identified in Figure 3 overlap somewhat: no. 14 (F) and no. 16 (CCl3) in Figure 3 have nearly identical I···N distances but noticeably different Ge···N distances. So, the shifts between the subgroups in Figure 3 (comparing the blue and orange subsets, for instance) are dependent on both the electronwithdrawing power of the substituents as well as the extent apparently of the sensitivity of the particular form of interaction (I···N vs Ge···N) to the identity of R. The latter is a more subtle effect, but it becomes significant and yields slightly different orderings of acid−base separations (for the I···N vs the G···N cases) where the inductive strengths of substituents (nos. 14 and 16, for instance) are similar. A close look at the set of substituents in each subgroup in Figure 3 provides a way for us to understand the groupings observed. The blue series in Figure 3 hosts almost all of the polarized carbon substituents (such as CCl3, and COOH) and NO2 as well, which is isoelectronic with CO2−. The orange series contains all of the monatomic group 17 substituents (F, Cl, Br, and I), H, and the substituents with less polarized C and N atoms as well, which also have, incidentally, π-systems with which the lone pair on the central N may interact to some extent. The green series includes the least polarizing substituents, the good electron donors, which are well-known from organic chemistry. Interestingly, the polarization of the moderately electronegative C atom by one or more O or F atoms tends to yield electron-withdrawing substituents (R = CHO and CF3 in the blue subset in Figure 3) that are stronger (i.e., more withdrawing) than the very polarizing O or F atoms are on their own (i.e., for R = OH and F, which are both lower, in the green and orange sections, respectively, in Figure 3). We assign a different color (pink) in Figure 3 to the complexes with R = −NH2 (no. 3) and −OCH3 (no. 6) since those systems do not align well with any of the three subgroups identified in Figure 3. To be sure, there are a few other ways to look at Figure 3. Might species 7, 8, and even perhaps 9 in Figure 3 be associated instead with the upper (blue) series instead of the orange one? Might no. 10 be excluded from the blue series and treated as part of the lower series to which it is rather close? We probed the method dependence of the pattern observed in Figure 3 by reoptiomizing all 44 of the complexes at the M06-2X level of theory. This method has been shown to reproduce certain weak bonding interactions rather well and is computationally less time-consuming than the MP2 method in contemporary electronic structure calculation packages. The pattern that we observed at the MP2 level in Figure 3 is recovered remarkably well at the M06-2X level. The alignment of species 10 with the upper (blue) series and the location of −OCH3 (species 6 in pink) midway between the two lower series (in orange and green in Figures 3 and 4) and the −NH2 substituent (species 3, also in pink), significantly offset from the other electron-donating species (in the green series), are all

Figure 4. Ge···N and I···N separations for 44 (F3CI···NH2R and FH3Ge···NH2R) complexes optimized at the M06-2X level of theory. The numbers refer to the species list in Figure 3.

well-reproduced. The actual positions of the species in the various series are not identical to what we found at the MP2 level in Figure 3, but the relative influence of the substituents on the interatomic separations in the two types of complexes considered is completely clear at both levels of theory. 3.1.3. Direct Assessment of Method Dependence. Given the generally direct relationship between the variations in the I···N and Ge···N distances, an instructive approach for analyzing the data set is a comparison of the interatomic separations for the complexes at the two different levels of theory (Figures 5 and 6). Ideally, a linear relationship is

Figure 5. I···N interatomic separations for 22 acid−base complexes optimized at the M06-2X and the MP2 levels of theory. The numbers refer to the species list in Figure 3.

expected of the form rGe···N = m·rI···N + c, where m = 1 and c = 0 if both methods generate identical sets of bond distances for the series of complexes, or where m = 1 and c ≠ 0 if there is a systematic difference in the distances computed by one method relative to the other. For the halogen bond (I···N; Figure 5), the coefficient of determination (R2) is only 0.953, indicating a significant degree 3784

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After all, the H−N−H bond angles and the N−H bond lengths to lesser extents will respond to varying degrees to changes in R, especially for bulky or electron-rich R groups. Fortunately, however, the interatomic separations in both sets of complexes are sufficiently long as to make such interactions negligible such that we can ignore those unique features of the bonding in the complexes and still obtain from the two different methods a definite ordering of the substituents relative to each other according to their electron-withdrawing powers. Given the differences in the interatomic separations in Figures 5 and 6, the 22 substituents may be organized as follows in order of the relative influence of each R group on the computed MP2 and M06-2X I···N and Ge···N interatomic separations:

of inconsistency between the two methods in accurately capturing the bonding between I and N. An explanation for the differences in the results obtained at these levels of theory (a failure of the M06-2X method to capture fully the contribution of dispersion to the bonding, augmented perhaps by some overbinding at the MP2 level for these interactions) is outside the scope of this work. Yet, we find that the random discrepancies that are evident between the two methods in Figure 5 overlay a general increase of about 0.049 ± 0.025 Å in the I···N bond lengths going from the MP2 to the M06-2X method. The correlation is far better (with R2 = 0.985) for the much more covalent Ge···N bonding interactions. The average difference between the MP2 and the longer M06-2X bond lengths is relatively large (0.146 ± 0.021 Å), but, notice, with a standard deviation that is even a bit smaller than it is for the halogen-bonding case that we just mentioned. Moreover, Figure 6 shows that this deviation is more evenly distributed among the data points than it is in the halogen-bonding case. The deviations in the bond distances may arise therefore (in both Figures 5 and 6) from certain fundamental differences between the assumptions and degree of accuracy of the methods plus relatively small differences in how adequately each method treats the individual substituents as we go from one complex to another. Unfortunately, we do not have any slate of experimental results with which to compare these results, but we have been gratified by the quality of the correlation between these two very different (MP2 and M062X methods) methods, especially in Figure 6.

CHO > −COOH, −NO2 , −CN ≳ −COOCH3 > −CF3 > −CCl3 > − CF2CH3 > F > − NHCOH, (Cl > Br), −CHCH 2 > −OH, −C6H5, (I > H), −OCH3 > − NHCH3, −CH3, −NH 2 , −CH 2CH3

To obtain this series, the change in the I···N distances relative to the bond distances obtained when R = H, at the MP2 and M06-2X levels of theory (Figures 5 and 6), were averaged and used to order the substituents.33 This was done for the Ge···N interactions as well, and the two lists of distance (Tables S7− S9) were compared. In cases where the relative positions of the species were different in certain regions of the lists of I···N vs the Ge···N complexes (such as −COOH, −NO2 and −CN; see species 19−21 in Figures 5 and 6), the relevant species are separated in the list above by commas. In one case, for instance, the ordering is −NO2 and −CN, and −COOH (for I···N), and in the other case, it is −COOH, −NO2, and −CN (for Ge···N). For Cl vs Br and I vs H, the Cl and I substituents always have a bigger effect on the bonding than Br and H, respectively, within their respective subgroups, and this fact is indicated using parentheses in the series above. The differences in the ordering of the species using one level of theory vs another demonstrate the difficulty in rigorously quantifying electron-withdrawing power in the absence, at least, of any consensus on using a particular form of interaction at a specified level of theory as a reference. Of the two types of interactions considered in this work, the dative bonding interactions present as the better option since they span a wide range of distances for the same set of bases (Figures 5 and 6) and are ostensibly therefore more sensitive to changes in R. It is also less expensive computationally using all-electron basis sets since GeH3F has far less electrons than CF3I, even if a small core pseudopotential, such as that used in this work, is employed for I rather than an all-electron basis set. Our preference for the monofluorogermane system has been explained above, but the C and Si FH3M analogues may be considered for use instead in any alternative acid−base complex for characterizing the electron-withdrawing tendencies of substituents. 3.2. The Non-additivity of Inductive Effects. The potential additivity of inductive effects when several substituents (all identical, in this case) are bonded to a single atomic center may be assessed by comparing the interatomic separations in the complexes formed by NH2R and NR3 to the same Lewis acids. As mentioned above, the trisubstituted bases (NR3) were optimized and characterized as minima at the MP2(full) level of theory for several of the substituents

Figure 6. Ge···N interatomic separations for 22 acid−base complexes optimized at the M06-2X and the MP2 levels of theory. The numbers refer to the species listed in Figure 3.

Hierarchies for the relative strengths of the electronwithdrawing powers of substituents necessarily depend on the kind of interaction that we considered. Aspirations toward any universal (i.e., transferrable) quantitative index for the electronwithdrawing power of substituents may not be realistic. In the case of the halogen-bonded complexes, for example, the interaction of the lone pairs on the iodine center with H atoms of the base (NH2R) will vary somewhat as R changes, and so, too, will any interaction between the three hydrogen atoms on Ge in the case of the Ge···N interactions. 3785

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interactions. The Ge···N bond length jumps by more than half of an angstrom when the three hydrogen atoms on N are replaced by fluorines. The reason for the unexpected reversal of the decrease in I··· N distance for R = NHCH3 going from n = 1 to 3 (Figure 7a) is not clear, but even in the Ge system, a peak appears for that case as well compared to the adjacent systems in Figure 7b. So the additional substituents do not have a dramatic effect there either, even if they lead to a small shift in the same direction (when R = NHCH3 for the Ge···N distance) compared to the n = 1 case. Another blatant reversal is observed as well for −OCH3 in the Ge case (Figure 7b), where the Ge···N bond contracts (relative to Y = NH3) for the monosubstituted case (in black in Figure 7b) and lengthens in the trisubstituted case. For the electron donors on the left in Figure 7, some small additional shrinkage of both the I···N and Ge···N bonds is generally observed, but nothing as dramatic as the expansions induced on the right by F and CF3, especially. This asymmetry in the effects observed on the sigma-donor side of the graph (left) and the sigma-acceptor side (right) in Figure 7a,b may be a consequence of the expected rapid increase in Coulomb repulsion as chemical bonds contract. Nonetheless, the qualitative similarities in the trends in Figure 7a,b for the two different types of interactions suggest that the obvious absence of any general additivity of inductive effects is inherent to the natures of the bases and is not an artifact of the method or any particular mode of interaction. Especially for bulky or electronically complicated substituents (where R is large and has several lone pairs, extensive π-systems, or even low-lying acceptor orbitals into which the lone pair on N can delocalize), one cannot assume additivity or even that the net inductive effect will change monotonous in any given direction as the number of a particular R group on the donor site (N in this case) changes.

considered in this work (Table 1). Figures 7a,b shows the bond distances obtained for the mono- and trisubstituted bases for 28 complexes.

4. SUMMARY AND OUTLOOK Weak interactions allow us to assess the relative sigma electronwithdrawing (and -donating) power of monovalent substituents in a straightforward way. Several primarily organic R groups have been shown to have noticeable effects on the internuclear separation between nitrogen centers in (monosubstituted amine) bases and the acceptor sites on I and Ge centers in halogen-bonded and dative covalent complexes. A rigorously defined and reliably quantitative scale for electron-withdrawing power will likely be quite difficult to achieve. The effect of substituents depends significantly on the specific electronic environment in which they exist and the number of substituents involved. We find in this work, for instance, that an increase in the number of electron-withdrawing or -donating substituents does not necessarily lead to a direct enhancement of the effects observed with a single substitution. Put another way, inductive effects are not generally additive or even cumulative. As a rule, however, substituents that are smaller or more compact may be expected to exhibit some cumulative effects as the number of that substituent on a given atomic center increases: CH3 on the donor side, for example, and F and CF3 on the withdrawing side. Large, bulky, and branching substituents are unpredictable. Steric effects and through-bond interactions such as electron delocalization across substituents that are mediated by the atomic center (N in this case) involved in the acid−base interaction may substantially alter the acid−base interaction. In fact, N(CN)3 and N(CHO)3, for example, are both completely planar molecules due precisely to that kind of

Figure 7. Computed relative I···N interatomic separations (a) and the Ge···N interatomic separations (b) with the NH2R and NR3 bases. The case where R = H (i.e., NH3) is used as our zero reference. All of these data were obtained at the MP2(full) level of theory.

The distances in Figure 7a,b have been plotted relative to the bond distances (the zero line on the y axis) for the cases where R = H. The halogen-bonded and dative NH3 complexes are employed, thus, as references for us for the influence of each (electron-withdrawing or -donating) R group on the I···N and Ge···N separations, respectively. The changes in the I···N and Ge···N interatomic separations in Figure 7a,b mirror each other remarkably well given the differences in the structural properties and energetic profiles of the two modes of interaction. In general, the interatomic separations do not change proportionally or even in the same direction when the number of substituents is tripled. In some cases, the additional substitutions (going from NH2R to NR3) actually reverses the effect observed in the monosubstituted case. The −Br substituent (Figure 7) is a case in point, even if the changes relative to NH3 are quite small. For −NO2 and −OH, the additional substitutions on the N center have almost no effect at all, whereas significant enhancements are observed for −CHCH2, −F, and −CF3. For −CHCH2, the I···N separation increases by about 0.4 Å, and in the latter two cases, the effect is more than doubled for both types of 3786

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electron delocalization, which is absent in the pyramidal NH2R. If such secondary effects are removed or diminished by employing simple model system with the mono- (rather than the di- or tri-) substituted base, then it is possible to categorize any common monovalent substituent, 22 of which we consider here, with regard to its relative electron-withdrawing power. Halogen-bonding and sigma-hole interactions, in general, which already have emerging roles in inorganic and other areas of chemistry, may be employed with significant success, we find, in a formal qualitative taxonomy of the electrophilicity and inductive effects of substituents in sigma bonds. In that regard, we find the overall trend CHO > −COOH, −NO2, −CN ≳ −COOCH3 > −CF3 > −CCl3 > −CF2CH3 > F > −NHC OH, (Cl > Br), −CHCH2 > −OH, −C6H5, (I > H), −OCH3 > −NHCH3, −CH3, −NH2, −CH2CH3 across both forms of (I···N and Ge···N) interactions that we considered.

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ASSOCIATED CONTENT

S Supporting Information *

Alternative local minimum energy structures that did not exhibit direct I···Y or Ge···Y bonding interactions, Cartesian coordinates of the (MP2(full) and M06-2X) optimized halogen-bonded and dative complexes considered in this work, tables of computed I···Y and Ge···Y interatomic separations, relative separations, and data derived therefrom as part of our analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 804-484-1628; Fax: 804-287-1897; E-mail: kdonald@ richmond.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Our work was supported by the National Science Foundation (NSF-CAREER award CHE-1056430) and NSF-MRI grants (CHE-0958696 (University of Richmond (UR)) and CHE1229354 (the MERCURY consortium)). K.J.D. thanks UR for a sabbatical leave; this research was supported in part by an appointment to the U.S. Department of Energy (DOE) Higher Education Research Experiences (HERE) for Faculty at the Oak Ridge National Laboratory (ORNL) administered through the Oak Ridge Institute for Science and Education (ORISE). K.J.D. thanks Valentino Cooper for hosting him at ORNL.

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REFERENCES

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The Journal of Physical Chemistry A (28) Peterson, K. A. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. I. Correlation Consistent Basis Sets for the Post-d Group 13−15 Elements. J. Chem. Phys. 2003, 119, 11099− 11112 (for Sn and Pb). (29) Peterson, K. A.; Shepler, B. C.; Figgen, D.; Stoll, H. On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and Their Anions. J. Phys. Chem. A 2006, 110, 13877−13883 (for I). (30) The energy-consistent triple-ζ (cc-pVTZpp) basis sets used were accessed via the Web site of the Institute for Theoretical Chemistry at the University of Stuttgart. (31) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2013. (32) Andrienko, G. A. ChemCraft; http://www.chemcraftprog.com/. (33) Averages and the resulting ordering of the substituents according to the effects on the I···N and Ge···N distances are shown in Tables S7−S9, Supporting Information.

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