Spin–Spin Coupling Constants for Getting - American Chemical Society

Article pubs.acs.org/JPCA

Revisiting NMR Through-Space JFF Spin−Spin Coupling Constants for Getting Insight into Proximate F‑-‑F Interactions Rubén H. Contreras,† Tomás Llorente,† Lucas Colucci Ducati,*,‡ and Cláudio Francisco Tormena§ †

Department of Physics, FCEyN, University of Buenos Aires and IFIBA-CONICET, C1053ABJ Buenos Aires, Argentina Institute of Chemistry, University of Sao Paulo − USP, P.O. Box 26077, 05513-970 Sao Paulo - SP, Brazil § Chemistry Institute, University of Campinas - UNICAMP, P.O. Box 6154, 13083-970 Campinas - SP, Brazil ‡

S Supporting Information *

ABSTRACT: At present times it is usual practice to mark biological compounds replacing an H for an F atom to study, by means of 19F NMR spectroscopy, aspects such as binding sites and molecular folding features. This interesting methodology could nicely be improved if it is known how proximity interactions on the F atom affect its electronic structure as gauged through high-resolution 19F NMR spectroscopy. This is the main aim of the present work and, to this end, differently substituted peri-difluoronaphthalenes are chosen as model systems. In such compounds are rationalized some interesting aspects of the diamagnetic and paramagnetic parts of the 19F nuclear magnetic shielding tensor as well as the transmission mechanisms for the PSO and FC contributions to 4JF1F8 indirect nuclear spin−spin coupling constants.

1. INTRODUCTION The main aim of this work is to obtain an in-depth insight into how proximate F---F interactions affect the F high-resolution NMR parameters improving their use for studying changes in the F electronic surroundings. This knowledge is expected to be important in the study of biochemical compounds marked with a fluorine atom.1 In a classic paper Mallory et al.2 reported 4JFF spin−spin coupling constants, SSCCs, in a series of 1,8-difluoronaphthalenes where in some of these compounds the relationship between 4JFF and the corresponding F---F distance, dFF, failed to show the expected exponentially decreasing trend typical for JFF SSCCs mainly transmitted through space.3,4 Shortly afterward, Peralta et al.4 reported that this unusual trend originated mainly in the paramagnetic spin−orbit term, PSO, one of the four Ramsey5 isotropic contributions to SSCCs, eq 1 n

J FF =

respect to the molecular framework. These considerations lead us to assume that some of the reported PSO contributions to 4 JFF SSCCs in peri-difluoronaphthalenes could be notably affected by this “geometric effect”.4 It is expected that not only the PSO term should show this “geometric effect” mentioned above, but it could also be important in other second rank tensor molecular properties like, for instance, the SD and DSO Ramsey contributions to SSCCs, and the diamagnetic and paramagnetic contributions to nuclear magnetic shielding tensors. In several cases such “geometric effect” can be easily rationalized employing a qualitative model for analizing SSCCs and nuclear magnetic shielding constants, which is described elsewhere.7−9 It is recalled that such geometric effect is not present in the FC term because this is the only isotropic contribution to indirect nuclear spin−spin constants.

n FC n SD n FSO n DSO 1 n Tr( J FF ) = JFF + JFF + JFF + JFF FF FF FF FF 3

2. COMPUTATIONAL DETAILS All molecular geometry optimizations were performed with the Gaussian10 suite of programs at the B3LYP11−13/EPR-III14 level of theory, as well as, all Ramsey contributions to 4JF1−F8 SSCC calculations in 12 peri-difluoronaphthalenes corresponding to measurements reported by Mallory et al.2 Diamagnetic and paramagnetic nuclear magnetic shielding tensors were calculated at the KT2/TZ2P level employing the ADF15 program. NBO analyses were performed with the NBO 5.0

(1) 6

On the other hand, in a previous paper, it was reported that in 2JFF SSCC in difluoromethane, its PSO contribution, which is substantial, presents an unexpected “geometric effect”, which is rationalized as follows. The PSO term corresponds to an unsymmetric second rank tensor, and consequently, when measurements are carried out in the isotropic phase, only the average of its trace contributes to the JFF isotropic value. However, most molecules are not isotropic and, consequently, the trace of any molecular second rank tensor property depends on the orientation of its principal axes system, PAS, with © 2014 American Chemical Society

Received: February 24, 2014 Revised: June 8, 2014 Published: June 16, 2014 5068

dx.doi.org/10.1021/jp501929t | J. Phys. Chem. A 2014, 118, 5068−5075

The Journal of Physical Chemistry A

Article

Table 1. FC, SD, PSO, and DSO Calculated Contributions and Total 4JF1F8 SSCCs (Hz) Together with the Corresponding Optimized F1---F8 Distance (Å) for 4-X4- and 5-X5-Substituted 1,8-Difluoronaphthalenesa comp

X5

X4

FC

SD

PSO

DSO

total

exp

dF1···F8

1 2 3 4 5 6 7 8 9 10 11 12

HC H2C− OC− H H H H H H H CN CH3

CH −CH2 −CO H NH2 CH3 CN Cl Br NO2 CN CH3

23.5 26.9 26.6 54.7 64.7 64.4 63.1 64.4 65.9 84.4 83.2 94.2

3.7 −2.2 −2.2 0.0 −0.4 0.2 0.3 0.1 0.2 1.4 0.9 0.8

20.9 5.5 8.5 5.7 3.6 5.6 8.4 5.7 5.7 10.0 9.1 0.9

0.8 0.8 0.8 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

49.0 31.2 33.8 61.3 68.9 71.3 72.8 71.3 72.9 96.9 94.2 97.2

36.7 28.4 31.5 58.8 61.8 65.0 66.1 66.5 67.4 75.2 83.5 85.2

2.797 2.762 2.752 2.609 2.592 2.587 2.588 2.583 2.578 2.532 2.530 2.509

a

Total calculated 4JF1F8 SSCCs are compared with experimental values taken from ref 2. Compounds are numbered following the optimized dF1‑‑‑‑F8 distance decreasing trend.

Figure 1. Structures for compounds 1−12.

program16 (included in the Gaussian package of programs) at the B3LYP/EPR-III level.

four isotropic contributions to 4JFF SSCCs for compounds reported by Mallory et al.2 as well as the respective optimized F1---F8 distances. In general, calculated SSCCs are overvalued when compared with their experimental counterparts; however, total calculated SSCCs reproduce correctly the experimental trend. It is highlighted that studies presented in this work aim at obtaining an in-depth insight into factors defining NMR trends originated in F---F proximity interactions and not in obtaining the best agreement between calculated and measured SSCCs. For all 12 compounds included in Table 1, the largest contribution to 4JFF SSCCs comes from the FC term, the second largest being the PSO term. It is also observed that in the most strained compounds, 1, 2, and 3, the PSO relative importance in comparison with the corresponding total SSCC,

3. ANALYSIS OF 4JFF SSCCS IN 1,8-DIFLUORONAPHTHALENES In Table 1 are displayed the calculated FC, SD, PSO, and DSO contributions to 4JFF SSCCs for compounds 1−12 (Figure 1). It is obvious that SD and DSO terms are not worthy of being studied in detail. This is not the case for the PSO and FC terms where a detailed study of their transmission mechanisms could provide interesting insight into these compounds’ electronic structures. For this reason in the following two subsections only these terms are considered. a. Transmission Mechanisms for PSO Terms Contributing to 4JFF SSCCs. In Table 1 are displayed the calculated 5069



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look to be the most important to take into account, namely, the s % character at the F lone pair that, when rotated around the α axis, shows a significant overlap with the (C−F)* antibonding orbital, the C−F bond length, and the C−F s % character at the F site. In this qualitative PSO description, LMOs are considered to behave, under chemical interactions, like NBO orbitals as given by Weinhold et al.’s approach.17,18 Because within the NBO approach, bonds and their corresponding antibonding orbitals present the same s % characters, in this PSO term qualitative description, s % characters are weighed with the corresponding orbital occupancies.19 This description leads to the following conclusions. Whenever any chemical interaction either lengthens the C−F bond length or decreases the C−F bond s % character at the F atom, the corresponding PSO component decreases and, reciprocally, interactions either shortening the C−F bond length or increasing the C−F bond s % character at the F atom increase the respective absolute value of its PSO contribution. In this way, it is expected that the larger the LP2(F) s % character is, their PSO contribution to 4JF1F8 SSCC increases its absolute value. In Table 2 one observes that the LP2 s % character increases when the F1---F8 distance decreases in the respective compounds, i.e., when the LP2(F) steric compression increases. Comments made above on the C−F bond length are supported by comparing the calculated PSO terms in compounds 4, 5, and 10, i.e., 5.7, 3.6, and 10.0 Hz, respectively, Table 1. In fact, in 5 the NH2 group placed at the 4 position of the aromatic ring slightly inhibits the F1 mesomeric interaction increasing the C1−F1 bond length, whereas the NO2 group in 10, at the four ring position, enhances the F1 mesomeric interaction, reducing the C1−F1 bond length; i.e., they follow the trend quoted above. It is noteworthy that the LP2 nonbonding electron pair s % character increases monotonically when the F1----F8 distance decreases, Figure 2, confirming the assertion that steric compression on the fluorine LP2 nonbonding electron pair increases its s % character, as reported previously.8 In Table 2 are collected some geometric and NBO parameters considered relevant for rationalizing some PSO

is larger than in the remaining compounds. This observation is in line with results discussed previously.4 The dispersion of PSO values displayed in Table 1 is indicative that there are at least two different types of effects affecting the PSO trend, namely, the “geometric effect”6 and changes in the F electronic surroundings originating in usual chemical interactions, like steric, inductive, conjugative, and hyperconjugative interactions. Therefore, before considering in detail the “geometric effect”, it sounds adequate to get an idea on how the latter interactions affect the PSO term. This can be easily achieved using the qualitative approach described previously.7−9 Within this approach for samples measured in isotropic phase, the PSO contribution to 4JF1F8 SSCCs is given by (1/3) of the PSO tensor trace, eq 2, which in turn can be deconvoluted into occupied and vacant localized molecular orbital (LMO) contributions as given in eq 3, where ΩPSO is a positive constant chosen to yield in Hz the PSO contribution to 4 JF1F8; γF is the fluorine nuclear magnetogyric ratio; i and j, and a and b stand for occupied and vacant localized molecular orbitals, LMOs, respectively. LMOs are assumed to play the common chemical roles; i.e., occupied LMOs are assumed to represent inner shell orbitals, bonding orbitals or nonbonding electron pairs, and vacant LMOs, representing either antibonding or Rydberg orbitals. PSO JF1F8 = 4 PSO, αα JF1F8

1 3

PSOαα ∑ JF1F8

(2)

α 4

αα = −ΩPSOγF 2 ∑ JiPSO (F1,F8) a ,jb ia ,jb

(3)

where 4 PSOαα Jia ,jb (F1,F8)

α1 PSO, α = UiPSO, a ,F1 Wia ,jbUjb ,F8

(4)

Equation 4 can be described as built up from one “emissionreceiving” and one “transmission” systems given by UPSO,α ia,F1 and PSO,α Ujb,F8 , and 1Wia,jb, respectively. The former are determined by the electronic surroundings for the coupling nuclei whereas the latter depends on the whole electronic molecular structure. Besides, they are more important than the latter because studies of slight changes in the F electronic surroundings are the main aim of this work. U factors in eq 4 are written as eqs 5 and 6. These simplified expressions provide significant insight into factors affecting the electronic surroundings for each F coupling nuclei. α UiPSO, a ,F1 = ⟨i|

α UjPSO, b ,F8 = ⟨j|

( rF1⃗ × ∇⃗)α rF13

( rF8⃗ × ∇⃗)α rF83

| a⟩ (5)

|b⟩ (6)

In eqs 5 and 6 the numerator inside the brackets corresponds to the 90° rotation operator around the Cartesian α axis with origin in F1 and F8 nuclei, respectively. It is considered to be applied to occupied LMOs representing either bonds or lone pairs containing one of both F coupling nuclei. Therefore, substantial contributions to these terms will appear whenever an occupied LMO containing one of the coupling nuclei is rotated 90° around the α axis overlaps to a substantial extent with the respective (C−F)* antibonding orbital. It is observed that both expressions are very sensitive to factors affecting denominators inside the brackets. The following three factors

Figure 2. Isotropic PSO value, β angle and LP2(F) s % character (Table 2) for symmetrically substituted compounds (1−4, 11, and 12). 5070



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eigenvectors differs from the “local” coordinate system just by a β angle rotation around the eigenvector perpendicular to the aromatic plane. From the above considerations it is obvious that the “geometric effect” is nil when the PSO1,8 tensor eigenvectors coincide with the “local” coordinate system. It is also obvious that in the local coordinate system the PSOZZ term is notably smaller (in absolute value) than the PSOXX and PSOYY components because, when LP1 is rotated around the Z axis, its overlap with any vacant LMO is notably smaller than those for the PSOYY and PSOXX principal axes because, when LP2 and LP3 are rotated around the Y and X axes, respectively, they overlap with the C−F antibonding orbital. This point is discussed in greater detail in section where rationalizing the F nuclear magnetic shielding tensor is discussed. Besides, in the present case, the steric compression between both fluorine atoms yields an increase in the LP2 s % character. This trend increases the PSOXX principal value when the F1---F8 distance decreases. Both the PSOXX and PSOYY eigenvalues increase when the F mesomeric interaction increases and vice versa because such interaction affects the C−F bond length. If the “local coordinate system” does not coincide with the PSO PAS system, eq 6, it is observed that for the PSOXX component the rF projection onto the nearest eigenvector is constant along the whole integral’s domain involved in the respective bracket. This projection increases the bracket in eq 6, approximately, like the (1/cos3 β) factor. From this qualitative description, the following trends are expected. For 0° ≤ β < 90°, the larger β is, the larger, in absolute value, is the PSOXX eigenvalue. As commented below in the discussion of the paramagnetic shielding tensor, the PSOZZ eigenvalues show a quite different trend. This PSOXX eigenvalues trend is consistent with the following conclusion, the very large PSO contribution, 20.9 Hz, to 4JFF SSCC in compound 1 (Table 1) is due mainly to the geometric effect owing to the departure of the X PSO eigenvector from its corresponding “local coordinates”, Figure 3. Such “geometric effect” originates mainly on the trend determined by eqs 5 and 6 defining the PSO “emissionreceiving” system. This suggests that in the same compounds, the paramagnetic eigenvalues for the F nuclear magnetic shielding constant should also be affected by this geometric effect. For this reason, in a section below such effect is discussed in detail. b. FC Transmission Mechanisms for 4JFF SSCCs. Interesting insight into molecular electronic structures from known FC terms can be obtained with the qualitative approach quoted above for the PSO term, complemented with an important well-known property; i.e., it is known that the FC term is transmitted through a molecular electronic structure like the Fermi hole.20,21 The FC term can also be deconvoluted into occupied and vacant localized molecular orbital (LMO) contributions as given in eqs 7 and 8, like commented in the subsection 3a for the PSO term,

Table 2. Calculated β Angles (deg) for Compounds 1, 2, 3, 4, 11, and 12 (Figure 3)a cmpd 1 2 3 4 11 12

X4

X5

HCCH H2CCH2 OCCO H H CN CN CH3 CH3

β (deg)

C−F

Fs%

LP2 s %

occ LP3

9°50′ 8°50′ 8°20′ 4°02′ 1°43′ 1°24′

1.344 1.348 1.339 1.346 1.337 1.347

29.71 29.46 29.81 29.50 29.76 29.46

0.06 0.08 0.08 0.17 0.28 0.38

1.917 1.924 1.967 1.920 1.911 1.922

a For the same compounds the C−F bond lengths (Å) as well as its s % character at the F atom, and the LP2 s % character together with LP3 occupancy are also displayed. It is observed that changes on LP2 occupancies (not shown) are negligible in spite of its s % character trend.

trends in compounds 1, 2, 3, 4, 11, and 12 where the F1----F8 segment bisector is a symmetry plane. A similar assertion holds for the aromatic plane. For this reason eigenvectors for the PSO(F) tensors are found just by symmetry considerations. The two PSO eigenvectors contained in the aromatic plane are, one along the F1----F8 direction, and the other perpendicular to the F1···F8 segment. The remaining one is perpendicular to the aromatic plane and is parallel to the F1----F8 segment bisector plane. It is highlighted that the β angle, determined by the C1− F1 and C8−F8 bond directions, is the main parameter defining the geometric effect on the isotropic PSO contribution in this series of compounds. Compounds 1, 2, and 3 seem to be particularly suited to study the “geometric effect” on the PSOF1,F8 tensor because they show the largest β angles. However, it is recalled that each PSO term displayed in Table 1 corresponds to one-third of the PSO trace, i.e., (PSOXX + PSOYY + PSOZZ)/3. It is obvious that the PSOZZ terms in these compounds are notably smaller than both PSOXX and PSOYY principal values and it does not follow the same trend as the β angle because in 3 the CO groups enhance the F mesomeric interactions with the respective aromatic rings, yielding a slight shortening of the CF bond length. The three PSO tensor eigenvectors contributing to 4JF1,F8 SSCC are shown schematically at the right-hand side of Figure 3. The “local system”, shown at the left-hand side of Figure 3, is defined by the right-handed Cartesian orthogonal system defined by X, along the LP2 lone pair, Y along the LP3 lone pair, and the Z axis along the C−F bond.6,7 It is observed that the right-handed system determined by the three PSO tensor

4 FC JF1F8

Figure 3. Understanding the geometric effect on the PSOF1,F8 tensor for compounds shown in Table 2. In (A) at the left-hand side is shown the F8 “local coordinates system”; and at its right-hand side the PSOF1 eigenvector system is shown. In (B) both axes systems are shown together. It is stressed that the Y axis is common to both coordinate systems and it points away from the reader.

4

= γF 2 ∑ JiFC (F ,F ) a ,jb 1 8 ia ,jb

(7)

FC FC FC = 3Wia ,jb[UiFC a ,F1Ujb ,F8 + Uia ,F8Ujb ,F1]

(8)

with 4 FC Jia ,jb (F1,F8)

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FC where Uia,F = ⟨i| δ(rF⃗ ) |a⟩ and 3Wia,jb = (3A − 3B)ia,jb−1 is the triplet polarization propagator matrix. It is recalled that in this case diagonal matrix elements are notably larger than nondiagonal ones. Because 3Aia,jb = (εa − εi)δabδij − ⟨aj|bi⟩ and 3Bia,jb = ⟨ab|ji⟩, in this qualitative analysis the εa − εi = Δa,i energy gap between the vacant a and the occupied i orbital energies is basic for understanding the relative importance among the different terms in eq 8. However, knowing the behavior of the Fermi hole, in some cases the Δa,i energy gap could be somewhat misleading. In fact, if two occupied LMOs overlap significantly, the FC term can be transmitted directly from one LMO to the other through exchange interactions taking place in the overlapping region, without requiring virtual orbitals for the FC transmission.22 The known behavior of the Fermi hole can also help visualizing hyperconjugative interactions as effective “carriers” for transmitting the Fermi hole from an occupied to a vacant LMO. At this point it is recalled that many times hyperconjugative interactions are dubbed as “charge transfer interactions” meaning that such charge is shared by two LMOs, one occupied and one vacant. Therefore, the FC part of several long-range couplings can be transmitted through a concatenated sequence of hyperconjugative interactions.23 In a former work24 the relationship between FC and Fermi hole transmissions was used to develop an approach dubbed as FCCP-CMO (Fermi Contact Coupling Pathways −Canonical Molecular Orbitals), which is based on the following grounds. The Fermi hole, originated in the Pauli Exclusion Principle, spans the whole region covered by a canonical molecular orbital. Therefore, nuclei of two atoms participating in the same CMO show an FC contribution to their SSCC as long as there is a significant electron density at their sites. Within the FCCPCMO method, CMOs are expanded in terms of NBOs using Weinhold et al.’s NBO 5.0 program.16 In this way it is very easy to realize if and how a CMO contributes to transmit a particular FC term of a given SSCC. The FCCP-CMO approach is applied for compound 4 to get insight into the FC transmission pathways in its 4JFF SSCC. To easily detect the main coupling pathways, the numbering of atoms is taken directly from the Gaussian-NBO programs, as shown in Figure S1 in the Supporting Information. This numbering differs from that shown in Table 1, but it has the advantage of making it very easy to connect both numbering systems. Four occupied CMOs are plotted and the rationalization of the respective coupling pathways is commented. The CMO expansions in terms of NBO orbitals are also displayed. The two different colors represent opposite phases (Figures S2 and S3, Supporting Information). Occupied CMO 14 (Figure S2A, Supporting Information) represents the overlap between both C−F bonds and LP1(F) lone pairs. Therefore, this CMO does not require any virtual CMO to transmit the FC term because, in this case, it is transmitted through exchange interactions. It is observed that Δ14,a corresponds to a very large energy gap for any vacant CMO. Occupied CMO 35 (Figure S2B, Supporting Information) corresponds to the FC transmission through the π electrronic system by the same mechanism. CMOs 14 and 35 represent a well-known SSCC transmission mecanism, which was discussed in many articles as well as review papers.25,26 Two different through bond transmission mechanism are depicted in Figure S3 (Supporting Information). Occupied CMO 22 (Figure S3A, Supporting Information) involves (i)

the overlap between both LP1(F) lone pairs and both C−F bonds, and (ii) one concatenated sequence of hyperconjugative interactions, C2−F1 → (C3−C14)*/C3−C14 → (C4−F5)* and the “back-donation” sequence, C4−F5 → (C3−C14)*/C3−C14 → (C2−F1)*. The following long hyperconjugation sequence can also be envisaged: C2−F1 → (C3−C14)*/C3−C14 → (C17− H18)*/C17−H18 → (C12−C8)*/C12−C8 → (C4−F5)*; its backdonation and the analogous ones involve the left-hand aromatic ring instead of the right-hand one. The FC coupling pathway is quite similar for occupied CMO 23 (Figure S3B, Supporting Information), but its efficiency is lower because the C−F bonds and the LP1 lone pairs appear with smaller coefficients than they do in CMO 22. Only two vacant CMOs contribute significantly to the transmission mechanisms requiring vacant CMOs, namely, CMO 75 amd CMO 77. They are plotted in Figure S4 (Supporting Information), where their expanssions in terms of vacant NBOs are also shown. The two vacant CMOs participate in the FC transmission for 4JFF SSCC in peridifluoronaphthalene, where not only the exchange interactions are involved in that treansmission. For this particular problem, significant contributions are found to correspond only to the (C4−F5)* and (C2−F1)* antibonding orbitals. In Figure 4 are plotted the FC contributions to 4JFF SSCC for compounds 1, 2, 3, 4, 11, and 12, the respective LP2 s %

Figure 4. LP2 s % character, β angle (deg), and FC contribution to 4JFF SSCC (in Hz) for compounds 1, 2, 3, 4, 11, and 12 are displayed. It is recalled that the FC term is the only isotropic contribution in eq 1.

character, and the β angle (Figure 3). It is observed that, when the overlap between both LP2 nonbonding electron pairs increases, the FC term follows a similar trend; i.e., such overlap becomes an efficient FC transmission mechanism when this s % increases. Results presented in this subsection show that the FC term contributing to 4JFF SSCCs in peri-difluoronaphthalenes involves several rather complicated coupling pathways.

4. FLUORINE MAGNETIC SHIELDING CONSTANTS IN SYMMETRIC 1,8-DIFLUORONAPHTHALENES The magnetic shielding constant tensor has contributions from both the diamagnetic and paramagnetic shielding second rank tensors, eq 9 5072



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D P σαβ(F) = σαβ (F) + σαβ (F)

(9)

The paramagnetic tensor is rationalized on similar grounds as the PSO tensor contribution to 4JFF SSCCs shown above;9 i.e., each tensor component is deconvoluted into LMOs, eq 10, where −Ωσ is a constant adequate to express each paramagnetic tensor component in ppm units. σ P, αβ(F1,8) = −Ωσ

∑ σiP,a ,jαβb (F1,8) (10)

ia ,jb

P, α 1 P, β P, α 1 P, β αβ σiP, a ,jb (F1,8) = UiaF1,8 W ia ,jbUjn ,F1,8 + Uia ,F1,8 W ia ,jbUjbF1,8

(11)

with UiP,a α(F1,8) = ⟨i| ∑ ( rk⃗ × ∇⃗)α |a⟩

(12)

k

UiP,a ,Aα (F1,8) = ⟨a| ∑

( rk⃗ F1,8 × ∇⃗)α

k

rk F1,83

Figure 5. Calculated values for isotropic diamagnetic, paramagnetic, and total 19F nuclear magnetic shielding constant (ppm) for compounds 1, 2, 3, 4, 11, and 12.

|i ⟩ (13)

It is worth noting the similitude between eqs 13 and 6. However, it is recalled that σαβ(F) values for both fluorine atoms show monocentric character whereas the PSOF1F8 tensor is a bicentric quantity. It is recalled that eq 12, in general, is not gauge invariant, whereas eq 13 is gauge invariant. Considerations made above when we rationalize trends for the PSO term, include observing that eq 13 is by far more sensitive to fine details of the electronic surroundings around each F atom than eq 12. Therefore, in this qualitative description only eq 13 is taken into account for studying some features of the P “geometric effect” on the σαβ (F1,8) nuclear paramagnetic shielding tensor. On the other hand, because the σDαβ(F1,8) tensors could also depend on a similar “geometric effect”, an estimation on this dependence is made calculating the diamagnetic part of the shielding tensor, Table 3 and Figure 5.

are electron acceptor groups. An increase on LP2 s % character yields a concomitant increasing effect on the XX absolute value, whereas the corresponding YY eigenvalue is practically unaffected. Similar assertions hold for the “geometric effect”; i.e., XX eigenvalues increase in absolute value when the β angle increases, whereas YY eigenvalues are only slightly affected. Trends for ZZ eigenvalues are discussed below. At this point it must be recalled that the qualitative description given above, includes only one aspect of the “geometric effect”. In some cases it could be notably affected, among other effects, by changing substantially the overlapping region between the occupied and vacant LMOs due to requirements corresponding to the whole molecular system under consideration. The YY eigenvalues follow the trend described above as originating mainly on either inhibitions or enhancements for the fluorine mesomeric interactions with the aromatic system. This trend does not have the same visibility in the XX eigenvalues, although it can be appreciated in compounds 3 and 11. On the other hand, the XX eigenvalue trend is compatible with being dominated by the “geometric effect” in compounds 1−3 and by the LP2(F) s % character for compounds 11 and 12. For compound 4 a cooperative contribution between both effects can be envisaged. For fluorinated compounds where the C−F bond is along a molecular symmetry axis, when LP1(F) is rotated 90° along the Z axis, the overlap between LP1(F) and the (C−F)* antibonding is constant as long as electronic interactions do not affect either the LP1(F) or the F (in C−F) s % characters, the ZZ eigenvalue remains unchanged. However, it is noted that, in this case, the “geometry effect” works quite differently than on the XX eigenvalues. In fact, for the ZZ eigenvalue the “geometric effect” main consequence is to affect the region where the LP1F) overlaps with the (C−F)* antibonding orbital, which in compounds quoted in Table 4, such overlap should depend on the β angle.

Table 3. Calculated Isotropic Values for Diamagnetic and Paramagnetic Parts of the σ(F) Nuclear Magnetic Shielding Tensor in Compounds 1, 2, 3, 4, 11, and 12 compd

σ(F1) (iso)

diamagnetic

paramagnetic

1 2 3 4 11 12

276.8 289.4 264.6 279.7 266.1 282.8

479.8 479.6 479.7 479.7 480.0 479.9

−203.0 −190.3 −215.1 −199.9 −213.9 −197.0

It is observed that, in compounds quoted in Table 3, i.e., 1, 2, 3, 4, 11, and 12 the isotropic values for the 19F nuclear diamagnetic shielding tensors are notably insensitive to the X4 and X5 substitution. Therefore, in these particular compounds no “geometric effect” affects the diamagnetic part of the F nuclear magnetic shielding tensor. For compounds displayed in Table 3, eigenvalues for the nuclear paramagnetic shielding tensors are collected in Table 4. It is noted that absolute values for both the XX and YY eigenvalues must be similarly affected by the mesomeric F interactions; i.e., for X4 and X5 (Figure 1) electron donor substituents, a lengthening on the C−F bond length takes place, decreasing the absolute value of their eigenvalues. It is just the other way around if substituents X4 and X5 (Figure 1)

5. CONCLUSIONS In this work JFF SSCCs and F nuclear magnetic shielding constants are chosen as “probes” to get insight into changes in the molecular electronic structure of some difluorinated 5073



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Table 4. Calculated Eigenvalues for the σP(F) Paramagnetic Nuclear Magnetic Shielding Tensor (ppm) in Compounds 1, 2, 3, 4, 11, and 12 s % LP2 1 2 3 4 11 12 a

0.06 0.08 0.08 0.17 0.28 0.38

βa 9° 8° 8° 4° 1° 1°

50′ 50′ 20′ 02′ 43′ 24′

|Δ|b

XX

YY

ZZ

σP(F)

46.8 48.3 47.5 41.6 28.9 37.4

−280.2 −261.7 −297.7 −268.9 −286.4 −262.8

−233.4 −213.4 −250.2 −227.3 −257.5 −225.4

−95.3 −95.7 −97.4 −103.6 −97.7 −102.9

−202.9 −190.3 −215.1 −199.9 −213.9 −197.0

See Figure 2. bΔ = XX − YY.

■

compounds. With the exception of the Fermi contact term of SSCCs all other parameters show unsymmetrical second rank tensor character. For this reason it is important to know the respective eigenvector orientations. It is observed in compounds displayed in Table 1 that only in six of them their eigenvector orientations can be found just by inspection. In fact, in compounds 1, 2, 3, 4, 11, and 12 there are two orthogonal symmetry planes. The following observations are worth highlighting. (i) When the F1---F8 distance is shortened, there is a rather strong steric interaction between both LP2 nonbonding electron pairs, yielding an increase in their respective s % character. It is noted that such steric compression does not change the NBO occupancies of both LP2(F) lone pairs. This suggests that in halogen atoms the LP2 s % character can be employed to gauge semiquantitatively the steric compression exerted on it. (ii) The large calculated PSO term for JF1F8 SSCC in compound 1 is notably contributed from the “geometric effect” reported previously.6 (iii) The isotropic value of the diamagnetic shielding tensor, σD(F) is notably insensitive to substituents placed at the “para” position. This assertion suggests that the diamagnetic tensor is insensitive to stereoelectronic interactions. However, it seems to be affected by inductive interactions, which are known to decay rapidly with the number of bonds separating the electronegative center to the probe.27 (iv) Taking into account data included in Table 4, the qualitative analysis performed separately for different paramagnetic shielding tensor eigenvalues can provide interesting information on the electronic molecular structure around F atoms. Data discussed in Table 4 allow one to observe how different eigenvalues are affected by the “geometric effect”. (v) The analysis presented for the FC term corresponding to 4 JFF SSCCs in compound 4 shows that the so-called “through-space” FC transmitted component presents some subtle aspects that are, in general, not considered in the current literature.

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AUTHOR INFORMATION

Corresponding Author

*L. C. Ducati. Phone: +5511 3091-3816. E-mail: ducati@iq. usp.br. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.C.D. and C.F.T. are grateful to FAPESP for financial support (2011/17357-3) and for a fellowship (L.C.D 2010/15765-4), and to CNPq for a fellowship (C.F.T.). R.H.C. gratefully acknowledges economic support from CONICET (PIP 0369) ́ and UBACYT, Programación Cientifica 2011-2014. Using resources of the LCCA-Laboratory of Advanced Scientific Computation of the University of São Paulo.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Atom numbering scheme and CMO diagrams (Figures S1− S4). Full citation for ref 10. This material is available free of charge via the Internet at http://pubs.acs.org. 5074



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Spin–Spin Coupling Constants for Getting - American Chemical Society

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