Indirect Nuclear 15Nâ15N Scalar Coupling through a Hydrogen Bond

Article pubs.acs.org/JPCA

Indirect Nuclear 15N−15N Scalar Coupling through a Hydrogen Bond: Dependence on Structural Parameters Studied by Quantum Chemistry Tools Anežka Křístková,† James R. Asher,† Vladimir G. Malkin,†,‡ and Olga L. Malkina*,† †

Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia Faculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Paulínska 16, SK-91724 Trnava, Slovakia

‡

S Supporting Information *

ABSTRACT: NMR spin−spin couplings through a hydrogen bond in the free-base and protonated forms of the complete series of [15N2]-Nmethylated 1,8-diaminonaphthalenes have been analyzed using quantum chemistry tools. The dominating role of the overlap of the coupling pathway orbitals has been demonstrated. The correlation of the sum of the 13C NMR shifts of the naphthalene ring C(1,8) carbons directly attached to the interacting nitrogens with the J(N−N) values and the degree of methylation found earlier by G. C. Lloyd-Jones et al. [Chem.Eur. J. 2003, 9, 4523] have been reexamined. It has been found that the correlations of J(N−N) and [Δ∑C1,8] with the degree of methylation have different reasons. While the former is mostly connected with the structural changes due to the solvent effect, the latter is attributed to the changes in the paramagnetic contributions from the C−N and C−C bonds caused by the replacement of a hydrogen by a methyl group.

1. INTRODUCTION NMR spin−spin coupling through hydrogen bonds remains topical in experimental and theoretical studies (see, for example refs 1−3). Besides being a fascinating phenomenon by itself, it is also an important source of structural information for biomolecules. There are many publications discussing the factors affecting the J value: whether it correlates with the distance between the interacting nuclei or with the sum of distances from the proton to the coupled nuclei, etc. (see, for example, refs 4−11). The role of the overlap of the orbitals forming the hydrogen bond has also been discussed albeit implicitly, i.e., using geometry arguments concerning the orientation of the orbitals.12 However, relying on the proposed correlations without understanding their reasons is dangerous. Therefore, in this paper we are trying to elucidate the underlying mechanism of the dependences of couplings through a hydrogen bond on structural parameters. Some years ago, scalar coupling between the 15N centers in methylated 1,8-diaminonaphthalenes was examined by G. C. Lloyd-Jones et al.13 In this thorough study, the scalar couplings between hydrogen bonded nitrogen centers in the free-base and protonated forms of the complete series of [15N2]-Nmethylated 1,8-diaminonaphthalenes in [D7]DMF solution were determined experimentally. In the free-base and protonated series, a linear correlation between the J(N−N) value and the degree of methylation was found, though it was much less pronounced for the former. In the protonated series, © 2013 American Chemical Society

the values of J(N−N) varied smoothly from 1.5 to 8.5 Hz while the N−N distance remained almost constant. Thus no correlation between the J(N−N) value and the N−N distance was observed. To gain a better insight, the authors supplemented their experimental studies with density functional theory (DFT) calculations. Based on their experimental and computational observations, they suggested that in the protonated series “Fermi-contact between the two N centers is decreased upon formation of strong charge-dispersing intermolecular hydrogen bonds of the free N−H groups with the solvent”.13 It has been rationalized that the main reason is probably significant structural changes (rotation around the C− N bonds) due to formation of intermolecular hydrogen bonds with solvent. As a result, the mutual orientation of the hydrogen bond acceptor and donor became less favorable for the indirect spin−spin coupling between two interacting nitrogens leading to decreasing of J(N−N). This very interesting work of Lloyd-Jones et al.13 contains a large collection of systematic experimental data and provides an excellent foundation for studying the indirect nuclear spin−spin couplings through hydrogen bonds in these systems using advanced quantum-chemical tools developed by us recently.14 We have applied this variety of new quantum-chemical Received: May 10, 2013 Revised: August 29, 2013 Published: August 29, 2013 9235

dx.doi.org/10.1021/jp404650b | J. Phys. Chem. A 2013, 117, 9235−9244

The Journal of Physical Chemistry A

Article

calculations we denote with the superscripts ↑↑ and ↑↓, respectively. In addition to this, from DFPT we may also derive the following real-space function, the coupling deformation density (CDD) that is proportional to the difference between the total electron densities for parallel and antiparallel orientations of nuclear spins:

interpretation tools to the analysis of “through-space” transmission of indirect nuclear spin−spin couplings between two phosphorus nuclei mediated mainly by the overlap of the phosphorus lone pairs.15 In particular, we have visualized the spin−spin coupling pathways, analyzed the contributions to J(P−P) from localized molecular orbitals, introduced a quantitative measure of the overlap of lone pairs, and demonstrated the quantitative correlation between the value of J(P−P) and the overlap of phosphorus lone pairs.15 In the present work we will use these tools to verify the explanation proposed by Lloyd-Jones et al. of the trends experimentally observed in their work.13 The spin−spin couplings studied in ref 13 are strongly affected by solvent effects. However, since it is likely that the major solvent effect comes through structural changes,13 here we will concentrate on the analysis of the dependence of spin− spin couplings through a hydrogen bond on structural parameters. When comparing the J(N−N) couplings in the protonated and free-base series, we will try to separate the effects caused by the changes in the electronic structure (direct effect) and the structural changes (indirect effect) due to the presence of an additional proton in the protonated series. We will also analyze a very curious linear correlation observed in ref 13 between the sum of the 13C NMR shifts of the naphthalene ring C(1,8) carbons directly attached to the interacting nitrogens and the J(N−N) values and degree of methylation. The paper is organized as follows. The description of theoretical tools used for the analysis of spin−spin couplings is given in section 2. Section 3 provides computational details. Section 4 is devoted to discussions and it is split into six parts: Comparison of the Calculated and Experimental Values of J(N−N); Visualization of Spin−Spin Coupling Pathways; Direct and Indirect Effects of H+ on the Spin−Spin Coupling through a Hydrogen Bond; Analysis of LMO Contributions to J(N−N); Correlation between Spin−Spin Coupling and the Overlap of LMO Densities; Relationship between J(N−N) and the Sum of C(1,8) Carbon NMR Chemical Shifts . The main results of this work are summarized under Conclusions.

ρMN ( r ⃗) = =

≈

∂ 2E(λM , λN) ∂λM ∂λN

2λMλN ↑↓

In eq 2 ρ (r)⃗ and ρ (r)⃗ are the electron densities with nuclear spins oriented parallel and antiparallel, respectively; ρ↑↑ α (r)⃗ , ↑↓ ↑↓ ρ↑↑ β (r)⃗ , ρα (r)⃗ , and ρβ (r)⃗ label the corresponding α and β electron spin densities. The CDD represents the coupling pathway between the interacting nuclei, in that the magnitude of the CDD indicates how much the electron density at any location is affected by the interaction of the two nuclear magnetic moments. In quantum mechanics, the electron density is an observable; the CDD, as the difference between two electron densities, likewise represents an observable quantity and thus a physical reality (within the accuracy of the method used for the SCF calculation). Here we would like to note that other real-space functions suggested for visualization of spin−spin coupling pathways17,18 do not possess this feature. In contrast to CDD, these functions are constructed in such a way that their integral over the three-dimensional space gives the value of the spin−spin coupling constant (a kind of the “property density” suggested by Buckingham and Jameson19). Adding any function that integrates to zero would not change the value of the initial integral (i.e., the value of the spin−spin coupling constant), but the spin−spin coupling pathways may transform dramatically. In practice this means that the obtained picture very much depends on a particular implementation of these functions (for example, what kind of perturbation theory was used: implementations based on the linear response theory and DFPT yield completely different plots). 2.2. Perturbation-Stable Localization Procedure. One of the most popular techniques for analyzing a calculated property is to split its values into separate contributions related to different physical interaction mechanisms or associated with different parts of a molecule. The perturbation-stable localization procedure makes it possible to decompose the Fermi contact contribution to the J-coupling, as calculated by finite perturbation theory (FPT),20 into contributions from individual localized molecular orbitals. In FPT, the FC operator on one of the interacting nuclei is included as finite perturbation in the Hamiltonian. This perturbation results in the spin polarization of the electron density that propagates through a molecule and changes the α and β spin densities at the second nucleus. The expectation value of the FC operator on the second nucleus is then calculated to give the Fermi contact contribution to the spin− spin coupling constant. In order to decompose the perturbed (and therefore slightly different) α and β spin densities into contributions from matching localized molecular orbitals, the following procedure was suggested.14 First, some standard localization procedure (such as Boys21 or Pipek−Mezey22

λM = λN = 0

E(λM , λN) − E(λM , −λN) 2λMλN

[ρα↑↑ ( r ⃗) + ρβ↑↑ ( r ⃗)] − [ρα↑↓ ( r ⃗) + ρβ↑↓ ( r ⃗)] (2)

↑↑

2. INTERPRETATION TOOLS 2.1. Coupling Deformation Density. For elucidating the spin−spin coupling pathways, we will employ the visualization of the coupling deformation densitya quantity obtained using double finite perturbation theory (DFPT).16 In this method, the Fermi contact (FC) operators on the two coupled nuclei are simultaneously included as finite perturbations in the Hamiltonian, thus treating both interacting nuclei on an equal basis. The coupling constant is proportional to the bilinear derivative of the total energy with respect to the nuclear magnetic moments, which is obtained numerically: JMN =

ρ↑↑ ( r ⃗) − ρ↑↓ ( r ⃗) 2λMλN

(1)

In eq 1, λM and λN are finite perturbation parameters that can be roughly associated with the absolute values of the magnetic moments of the interacting nuclei M and N. The energy difference is obtained via two separate self-consistent field (SCF) calculations, one with parallel nuclear spins and one with antiparallel nuclear spins. Quantities obtained from these two 9236



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relaxed geometries. In other words, for each fixed value of the bond or dihedral angle all other geometric parameters have been reoptimized. Calculations of spin−spin couplings, 13C NMR shieldings, and CDD have been done with a local modified version of the deMon program.28 In these calculations we employed the Perdew86 exchange-correlation functional29,30 and IGLO-III basis set.31 We have analyzed only the Fermi contact term, which is by far the dominant contribution to the spin−spin couplings under consideration. Localized molecular orbitals were obtained using the Pipek−Mezey localization scheme.22 The Pipek−Mezey localization was also used within the IGLO (individual gauge for localized orbitals) approach31 to calculate NMR shieldings. Visualization was performed with the Molekel program.32

localization) is applied to the unperturbed system, yielding the unperturbed localized molecular orbitals (LMOs). Then, the perturbed canonical molecular orbitals (MOs) are localized by unitary transformations which maximize the overlap between (occupied) perturbed and unperturbed LMOs (this is done separately for α and β orbitals). In short, we localize the perturbed MOs to ensure that the perturbed LMOs resemble as much as possible the LMOs of the original unperturbed closedshell system. This makes it possible to find matching pairs of the perturbed α and β LMOs according to their similarity to the unperturbed LMOs. Then the corresponding α and β contributions can be combined to give the LMO contributions to the FC term of the J-coupling. We will use this procedure to obtain the LMO contributions to J(N−N) discussed in section 4.4. 2.3. Overlap of LMO Densities. One of our goals of this work is to demonstrate, and if possible to quantify, a correlation between spin−spin coupling and the overlap of the coupling pathway orbitals. For this, a quantitative measure for the overlap of molecular orbitals must be established. The overlap integral between two molecular orbitals is of little use, as molecular orbitals (including localized MOs) are orthogonal:

∫ φi( r ⃗) φj( r ⃗) dV = 0

4. DISCUSSION 4.1. Comparison of the Calculated and Experimental Values of J(N−N). We start with a comparison of the calculated and experimental values of J(N−N). The optimized structures of the considered free-base systems are presented in Figure 1. We have decided to extend the set studied in ref 13

(3)

Therefore the following integral to measure the overlap between two molecular orbitals was proposed:15 Ω= =

∬ φi 2( r1⃗) δ( r1⃗ − r2⃗ ) Ωj2( r2⃗ ) dV1 dV2 ∫ φi 2( r ⃗) φj2( r ⃗) dV

(4)

In eq 4, φi and φj are localized molecular orbitals. If we consider two electrons occupying molecular orbitals φi and φj as independent particles, the integrand here represents the probability of finding them in the same element of volume. We would like to stress that the overlap of lone pair densities is determined using the unperturbed MOs. While spin−spin coupling cannot be described solely in terms of the unperturbed occupied orbitals, CDD and the introduced measure of the overlap of orbitals are related. It was shown15 that the coupling deformation density can be expressed as the linear combination of the products of the pairs of unperturbed orbitals (occupied−occupied, occupied− virtual, virtual−virtual). It was also shown that in cases of “through-space” spin−spin coupling modulated by the overlap of lone pairs the main term is the product of these lone pairs. The same product enters the expression for the introduced measure of the overlap of localized orbitals. This provides a mathematical explanation of the phenomenon long known by experimentalists: the value of spin−spin coupling may depend on how much the interacting lone pairs (or other coupling pathway orbitals) overlap each other.

Figure 1. Optimized structures of the neutral systems.

(systems [1]−[6]) by adding bis(2-pyridyl)acetonitrile ([7]), where a large spin−spin coupling of about 10.6 Hz through a hydrogen bond was experimentally observed.33 This system has a rigid structure, and the spin−spin coupling through a hydrogen bond is not much affected by solvent effects. Therefore, [7] is very convenient for theoretical benchmark calculations. The optimized structures of the protonated systems ([1H+]−[6H+]) are shown in Figure 2. The calculated and experimental values of J(N−N) are collected in Table 1 and presented graphically in Figure 3a (for free-base systems) and Figure 3b (protonated systems). There is some difference between the theoretical results obtained in this work and in ref 13. The deviation can be attributed to different geometries (i.e., different conformations found during the geometry optimization), different exchange-correlation

3. COMPUTATIONAL DETAILS All calculations have been carried out at the density functional level of theory. Geometries have been optimized with the Gaussian 98 package23 employing the hybrid B3LYP exchangecorrelation functional24,25 and 6-31G(d,p) basis set.26,27 All resulting structures correspond to global or local minima of the energy surfaces. For studying the dependence of spin−spin couplings on the bond angle and on the dihedral angle, we used 9237



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Figure 3. (a) Comparison of calculated J(N−N) with experimental data for neutral systems [1]−[7]. (b) Comparison of calculated J(N− N) with experimental data for protonated systems [1H+]−[6H+].

conclude that if one neglects solvent effects the employed level of computations (the exchange-correlation potential and basis set) is adequate for our purposes. With an increasing degree of methylation, the number of free N−H units is decreased; consequently the spin−spin coupling through a hydrogen bond becomes less affected by solvent effects and agreement between theory and experiment improves correspondingly, especially in the protonated series, in accordance with the findings of LloydJones et al.13 The theoretical values obtained for the optimized (i.e., gas phase) structures exhibit no correlation with the degree of methylation, confirming that the experimentally observed correlation is a consequence of solvent effects. We agree with Lloyd-Jones et al.13 that the interaction with solvent changes the mutual orientation of the nitrogen lone pairs resulting in their less favorable position for transmitting J(N− N). In section 4.3 this statement will be confirmed by our analysis of the overlap of the nitrogen lone pairs. 4.2. Visualization of Spin−Spin Coupling Pathways. When analyzing spin−spin coupling through a hydrogen bond, questions about the spin−spin coupling pathways are often raised.33 It is interesting to know to what extent different parts of a molecule are involved in the indirect (i.e., through the electron density) spin−spin interaction of two particular magnetic nuclei. Visualization of the coupling deformation density (see section 2.1) allows one to answer this question directly.16 In Figure 4, we have plotted CDD for free-base systems [1], [3], and [6] (top row, from left to right) and their protonated counterparts [1H+], [3H+], and [6H+] (bottom row, again from left to right). In all pictures the isosurfaces are plotted for the same CDD value of ±0.1 au for better comparison. The smaller volumes of blue and red lobes in the top row reflect smaller values of the spin−spin coupling constant in the free-base series in comparison with the protonated analogues in the bottom row. The CDD plot for [6] (top right) is consistent with the smallest J(N−N) value

Figure 2. Optimized structures of the protonated systems.

Table 1. Comparison of Calculated and Experimental J(N− N) Values system

calcda

calcdb

exptlc

[1] [2] [3] [4] [5] [6] [7] [1H+] [2H+] [3H+] [4H+] [5H+] [6H+]

4.13 4.47 4.43 3.86 4.46 0.49 10.55 9.6 8.02 8.79 7.2 7.8 8.29

3.34 3.46 3.51 2.77 3.62 0.32

2.88 3.25 3.21 3.3 3.71 0 10.6 1.5 2.6

7.53 6.31 5.85 6.85 6.17 6.67

4.46 6.68 8.46

a

This work (PP86, III-IGLO). bReference 13 (BP86, DZP on C, H and O; TZ2P on N). cReference 13 except for [7]; for [7] the experimental value was taken from ref 33.

potentials, and basis sets employed. Still, when compared to the experimental values, the theoretical results of both works exhibit similar trends as discussed below. It is clear that, on the whole, the agreement of the theoretical results with experimental values for free-base systems is much better than for their protonated counterparts. The best agreement is obtained for systems [7], [6], and [6H+], i.e., systems without free N−H units to form intermolecular hydrogen bonds with solvent. We would like to emphasize almost perfect agreement with experiment for system [7]the most rigid and least distorted by solvent effects. Thus we can 9238



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To separate these effects, we have performed a series of calculations for the free-base systems employing the optimized structures for the protonated systems but with H+ removed. Figure 6 presents the comparison of the spin−spin coupling

Figure 4. CDD plots for structures [1], [3], and [6] (top row) and [1H+], [3H+], and [6H+] (bottom row).

being found for this system (the theoretically predicted value is 0.49 Hz, no coupling is observed in the experiment). In accord with the calculated J(N−N), the CDD for the optimized structures (i.e., corresponding to gas phase) does not correlate with the degree of methylation. It is interesting to note that for all systems (including [7] with record values of J(N−N) through a hydrogen bond33 see Figure 5) the spin−spin coupling between two nitrogens

Figure 6. Direct and indirect effects of H+ on spin−spin coupling through a hydrogen bond. Solid triangles, spin−spin coupling constants for the protonated series [1H+]−[6H+] (optimized geometries); open triangles, spin−spin coupling constants for the free-base series [1]−[6] (with “fixed” geometries obtained by removal of H+ from optimized structures for the protonated series); open circles, spin−spin couplings for the free-base series (optimized geometries).

constants calculated for these “fixed” (in a sense that the geometries were not adjusted for the removal of H+) structures and the values obtained for the optimized structures, both free base and protonated. The removal of H+ while the structures are kept fixed decreases the values of J(N−N) compared to the protonated series, creating a smooth monotonic dependence on the degree of methylation. The values of J(N−N) in these series are bigger than those in the free-base series but still smaller than those in the protonated one, confirming that both the direct and indirect effects increase the J(N−N) values. Judging by the graphs in Figure 6, the relative importance of these effects varies across the series. The indirect effect on the J(N−N) value is most pronounced for systems [1H+]and [6H +] and is practically negligible for [5H+]. At first glance it would be natural to expect the indirect effect to be primarily connected with the shortening of the R(N−N) distance, which varies from 0.09 to 0.12 bohr for systems [1]−[5] and is almost double for [6] (0.22 bohr). This may explain the large indirect effect on the J(N−N) value in [6] but leaves unclear the reason for almost the same magnitude of the indirect effect in [1]. Thus the change of the R(N−N) distance alone cannot explain the observed trends. The largest direct effect is observed for [5H+] and [6H+], and the smallest one is observed for [1H+]. However, before rationalizing the trends shown in Figure 6, one has to remember that the model structures with “fixed” geometries are not in their equilibria energy minima and therefore they have lower lying excited states compared to their optimized counterparts. This also affects the calculated values of J(N−N). In the language of the perturbation theory this means that the energy denominator (i.e., the difference between the one-electron energies of the occupied and vacant orbitals) becomes to some extent smaller for the model structures and this change may vary among the systems. A crude estimation of the changes in the energy denominator can be obtained from the comparison of the HOMO−LUMO gaps in the free-base systems with optimized and “fixed” geometries. The smallest change in the HOMO−LUMO gap is observed for [1] (about 0.71 au), and the largest is oberved for [6]

Figure 5. CDD plot for structure [7].

goes exclusively through a hydrogen bond. The electron density in other parts of these systems (including the naphthalene ring) is not involved in the interaction of the magnetic moments of nitrogens. This conclusion supports the notion of Lloyd-Jones et al.13 that the naphthalene ring is not responsible for the deviation between theoretically predicted and experimentally observed values of J(N−N). 4.3. Direct and Indirect Effects of H+ on the Spin−Spin Coupling through a Hydrogen Bond. Theoretically predicted J(N−N) for the optimized structures (that correspond to gas phase) in the protonated series are significantly larger than those in the free-base series. The same is true for the experimentally observed couplings when the degree of methylation is greater than 2. The presence of the additional proton can affect the coupling in two ways: (1) directly, i.e., by providing an additional positive charge attracting the lone pairs of the interacting nitrogens and thus facilitating the indirect nuclear spin−spin interaction of the 15N nuclear magnetic moments, and (2) indirectly through the changes in geometry, i.e., shortening the N−N distance and also changing the mutual orientation of the lone pairs which again can increase their overlap. 9239



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In the first series of calculations we have varied the H+−C9− C8 angle (see Scheme 1) from about 55.0 to 70.0° with the

(about 1.23 au). The latter is another reason for the large indirect effect on the J(N−N) value in [6]. Since the lowering in energy of the excited states for the model structures with “fixed” geometries obscures the rationalization of the direct and indirect effects, we have decided to analyze separately the influence of these effects on the overlap of the orbitals playing a key role in J(N−N), i.e., the coupling pathway orbitals. In the free-base systems these are the nitrogen lone pairs, and in the protonated series they are the H-bond orbitals (the nitrogen lone pair and the N−H+ bond). It should be noted that the shape of the N−H+ bond very much resembles the shape of the nitrogen lone pair. The similarity between the LMOs representing the coupling pathway orbitals in the free-base series in the protonated series is also confirmed by the Mulliken population analysis (see Table S2 in the Supporting Information). In order to assess the mutual orientation and delocalization of the orbitals in question, we can schematically represent them as vectors drawn from the positions of the nitrogens to the centers of charge of the LMOs obtained as byproducts of the localization procedure. The angle between the vectors can tell us about the mutual orientation of these orbitals, and the vector lengths can be interpreted as a measure of their delocalization (or elongation). One can expect that delocalization of the coupling pathway orbitals and their mutual orientation toward each other will create more favorable conditions for their overlap and, in turn, should result in larger values of J(N−N). Interestingly, the length of the vectors practically does not depend on the degree of methylation (see Figure S1 in the Supporting Information). In the free-base series for both optimized and “fixed” geometries it is about 0.6 bohr. In the protonated series the H-bond orbitals become significantly delocalized with the length of the corresponding vectors being about 0.95 bohr. Apparently the positively charged proton attracts the electron density of these LMOs, making them more delocalized and increasing their overlap. As for the mutual orientation of the coupling pathway orbitals, it turned out to be mostly defined by the geometryin particular by the orientation of the N−H or N−Me units. In the free-base series with optimized geometries (i.e., when the N−H or N−Me units have fewer restrictions for adjusting their position), the angle between the lone pairs varies from about 116° (for [5]) to 174° (for [3]) (see Figure S2 in Supporting Information). In the case of using the “fixed” geometries, the range of the angle variation becomes noticeably smaller: from about 135° [1] to 145° [6]. The presence of the positively charged proton in the protonated series shifts up the angle between the lone pair and the N−H+ bond by about 10° (making the range span values from 144° for [1] to 153° for [6]) and facilitates their overlap. However, as we have seen, even the most favorable mutual orientation of the lone pairs such as in [3] does not necessarily result in big couplings. Other factors such as the delocalization of the lone pairs, the distance between the interacting nitrogens, and the closeness of the excited states play an important role. 4.4. Analysis of LMO Contributions to J(N−N). Since the largest deviation between the theoretically predicted and experimentally observed couplings was found for [1H+], and hence this coupling is probably the most sensitive one to the structural changes upon solvation, we decided to study the dependence of J(N−N) on the geometry for this system in more detail.

Scheme 1. The H+−C9−C8 Angle

step of 0.5° crudely simulating the movement of the proton between two nitrogens. For each value of the H+−C9−C8 angle all other structural parameters have been reoptimized. The energy profile along this path presents a typical doublewell potential (see Figure 7). The the J(N−N) value gradually

Figure 7. Dependence of total energy on the H+−C9−C8 angle for [1H+].

increases with the increase of the H+−C9−C8 angle reaching the maximum at about 62.57° (corresponding to the symmetric position of H+ with respect to two nitrogens) and decreases again (see Figure 8). The perturbation stable localization procedure allowed us to decompose the Fermi contact contribution to J(N−N) into contributions from individual LMOs. By far the largest

Figure 8. Dependence of LMO contributions to J(N−N) on the H+− C9−C8 angle. Sum (open triangles) is the sum of the selected contributions (i.e., the H-bond orbitals, C−N bonds, and C−H bonds). 9240



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value of the “through-space” spin−spin coupling between two phosphorus nuclei.15 It is interesting to see whether a quantitative correlation between the value of spin−spin coupling through a hydrogen bond and the overlap of the coupling pathway orbitals can be also established for [1H+]. Figures 10 and 11 present the correlation between the overlap of the H-bond orbitals and J(N−N) for the two

contribution came from the H-bond orbitals. Other noticeable contributions came from the N−H and N−C bonds. As seen in Figure 8 the shape of the dependence of J(N−N) on the H+− C9−C8 angle is defined by the contributions from the H-bond orbitals. The N−C and N−H bonds give almost constant negative contributions. The contributions from the naphthalene ring are negligible, in accord with the CDD plots and the reasoning of Lloyd-Jones et al.13 Thus, the contribution from the H-bond orbitals is the most important one in this series. In the second series of calculations we have varied the dihedral angle H−N−C8−C9 (i.e., changing the angle between the NH2 fragment and the naphthalene plane), simulating the rotation around the CN bond caused by intermolecular hydrogen bonds with solvent. The starting angle (about 121°) corresponds to the optimized (gas phase) structure. The LMO contributions and the total J(N−N) are shown in Figure 9. Again, the dominating contribution comes from the

Figure 10. Correlation between J(N−N) and overlap of the densities of coupling pathway orbitals with variation of the H+−C9−C8 angle.

Figure 9. Dependence of LMO contributions to J(N−N) on the H− N−C9−C1 dihedral angle. Sum (open triangles) is the sum of the selected contributions (i.e., H-bond orbitals, C−N bonds, and C−H bonds).

H-bond orbitals: the contributions from the N−C and N−H bonds are negative and smaller in magnitude. The sum of these selected contributions almost coincides with the total value of J(N−N), confirming that all other LMO contributions are negligible. With the increase of the dihedral angle the contribution from the coupling pathway orbitals and the total J(N−N) decreases, approaching the experimentally observed value. Our results support the explanation of Lloyd-Jones et al. of the discrepancy between the theoretically predicted and experimentally measured J(N−N) in the protonated systems: primarily, it arises from the neglect of the solvent effect on the structure of the considered systems. 4.5. Correlation between Spin−Spin Coupling and the Overlap of LMO Densities. In view of the significance of the spin−spin coupling through a hydrogen bond for the structure determination there have been many discussions concerning the factors affecting its value, whether it correlates with the distance between the interacting nuclei or with the sum of distances from the proton to nitrogens, etc.5,13,33,34 In this paper we are trying to elucidate the underlying mechanism of those correlations, i.e., to rationalize the dependence of couplings through a hydrogen bond on structural parameters. It is clear that the spin−spin coupling through a hydrogen bond is governed by the overlap of the H-bond orbitals and the geometry arguments work only because they determine the mutual orientation of these orbitals and their overlap. Recently we have introduced a measure of the overlap of two orbitals (see section 2.3) and found that it correlates very well with the

Figure 11. Correlation between J(N−N) and overlap of the densities of coupling pathway orbitals with variation of the H−N−C9− C1dihedral angle.

examples considered in section 4.4: for the simulation of the proton movement between two nitrogens (Figure 10) and for the rotation around the C−N bond (Figure 11). In both cases the correlation is strong: the larger the overlap of the densities of the two LMOs the larger the value of J(N−N). The correlation is practically linear in the first case, and there is some slight nonlinearity in the second case. In both cases there is no doubt that there exists a direct quantitative correlation between the overlap of the LMO densities and the value of spin−spin coupling. The overlap of the LMO densities gives us a quantitative measure of how favorable is the spatial arrangement of nuclei for the overlap of lone pairs and hence for the spin−spin coupling. It also explains the correlations between 2hJ(N−N) and the N−N distance for complexes with linear or nearly linear NH···N and N−H+···N intermolecular hydrogen bonds found by Del Bene and Bartlett.5 4.6. Relationship between J(N−N) and the Sum of C(1,8) Carbon NMR Chemical Shifts. As was already mentioned, Lloyd-Jones et al.13 observed a very curious linear correlation between the sum of the 13C NMR shifts ([Δ∑C1,8]) of the naphthalene ring C(1,8) carbons (i.e., 9241



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almost linear correlation of [Δ∑C1,8] with the degree of methylation is obtained. We have to conclude that the correlations of J(N−N) and [Δ∑C1,8] with the degree of methylation have different reasons. The first one cannot be explained without taking into account the structural changes due to intermolecular hydrogen bonds. The underlying mechanism of the second correlation is not connected with such geometric changes, or at least not entirely. To gain insight into the nature of the dependence of [Δ∑C1,8] on the degree of methylation, we have used the IGLO (individual gauge for localized orbitals) method31 to split the computed NMR shielding into contributions from the localized molecular orbitals. In contrast to J(N−N), the Hbond orbitals give no contribution to [Δ∑C1,8]. In the protonated series, only the contributions from the C−N, C1− C2, and C7−C8 bonds of the naphthalene ring depend noticeably on the presence of a methyl group. The whole dependence of [Δ∑C1,8] on the degree of methylation can be reproduced by contributions from these orbitals. As the next step, we have analyzed the diamagnetic and paramagnetic parts of those contributions. We have found that the diamagnetic part of these contributions almost does not depend on the methylation: the diamagnetic contribution from the C−N bonds changes from 19.4 ppm ([1H+]) to 19.8 ppm (for ([2H +]−[6H+]) and the diamagnetic contribution from C−C bonds monotonically decreases along the series from 66.8 ppm ([1H+]) to 65.8 ppm ([6H+]). Therefore, the diamagnetic contributions cannot be responsible for the observed correlation. Since these contributions are entirely determined by the ground state electron density, the correlation cannot be explained by simple electronic charge redistribution. Analysis of the paramagnetic contributions reveals their significant dependence on the methylation (see parts a and b in Figure 13 for the

those directly attached to the interacting nitrogens) and the J(N−N) values and the degree of methylation, which was especially pronounced for the protonated series (see Scheme 1). As an explanation, Lloyd-Jones et al. proposed two counteracting effects. Since a methyl group is more electron donating than a hydrogen, then with increase of the degree of methylation, C1 and C8 became more shielded and the sum of C(1,8) NMR shifts should decrease. From the other side, the intermolecular hydrogen bonding leads to delocalization of the positive charge of the ammonium center, and thus to “reduction in the net electron withdrawing effect exerted at C(1,8) of the naphthalene ring.”13 This should be accompanied by increasing [Δ∑C1,8]. Thus the intermolecular hydrogen bonds are suggested to be responsible for the correlation of [Δ∑C1,8] with the degree of methylation just as for the dependence of J(N−N) on the degree of methylation in the protonated series. To verify this explanation, we have calculated the C1 and C8 NMR chemical shifts with respect to naphthalene and compared them with the experimental data. These calculations have been performed for the optimized (gas phase) structures, and therefore no solvent effects and no intermolecular hydrogen bonds have been taken into account. The calculated results and the experimental values are collected in Table 2 and Table 2. Sum of 13C NMR C(1,8) Chemical Shifts with Respect to Naphthalene in the Free-Base and Protonated Series calcd

exptl

methylation deg

[1−6]

[1−6H+]

[1−6]

[1−6H+]

0 1 2 3 4

41.647 43.187 45.669 49.864 51.107

2.102 11.749 19.644 28.815 36.406

38.8 39.8 44.9 45.9 46.8

9.8 11 23.5 31.6 35.6

Figure 12. Comparison of sum of calculated C1 and C8 NMR chemical shifts with respect to naphthalene and experimental data.

presented graphically in Figure 12. In contrast to the spin−spin couplings where poor agreement between the computed and experimental values is observed (see Figure 3b), the chemical shifts computed for the gas phase structures reproduce the experimental values rather well for all systems except [1H+]. For this system, the solvent effect is expected to be the largest due the presence of four N−H units potentially capable of forming intermolecular hydrogen bonds with solvent. An

Figure 13. (a) Dependence of paramagnetic contribution from the two C−N bonds to [Δ∑C1,8] on the degree of methylation for the protonated series. (b) Dependence of paramagnetic contribution from the C1−C2 and C7−C8 bonds to [Δ∑C1,8] on the degree of methylation for the protonated series. 9242



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C−N and C−C bonds, respectively). For both types of bonds the paramagnetic contributions to [Δ∑C1,8] increase monotonically along the series by 12−13 ppm. We can conclude that the correlation of [Δ∑C1,8] with the degree of methylation is mostly defined by the paramagnetic contributions from the C− N and C−C bonds. These contributions are to a great extent influenced by the difference of one-electron energies between occupied and virtual orbitals. Since it is known that in DFT this difference gives a good estimation for excitation energies, we can say that the changes in paramagnetic contributions are connected to the changes in the excitation energies caused by substitution of a hydrogen by a methyl group.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +421-2-59410422. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge financial support from Slovak grant agencies VEGA (Grant 2/0148/13) and APVV (Grant LPP0326-09).

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5. CONCLUSIONS We have analyzed indirect nuclear spin−spin couplings through a hydrogen bond in the free-base and protonated forms of the complete series of [15N2]-N-methylated 1,8-diaminonaphthalenes using quantum chemistry tools developed by us. The theoretically predicted couplings have been compared with the experimental values obtained earlier by Lloyd-Jones et al.13 In the protonated series the agreement depended on the degree of methylation being very good for a fully methylated system and bad in the absence of the methyl group. The latter has been mainly attributed to the neglect of the structural changes due to intermolecular hydrogen bonds with solvent. This conclusion is in agreement with findings of Lloyd-Jones et al. We have also studied the dependence of J(N−N) on the H+−C9−C8 angle and on the H−N−C9−C1 dihedral angle in [1H+]. In both cases the H-bond orbitals gave the dominant contribution to the dependence. We have demonstrated the direct quantitative correlation between the value of J(N−N) and the overlap of the densities of these orbitals. This correlation explains the relationship between 2hJ(N−N) and the N−N distance for complexes with NH···N and N−H+···N intermolecular hydrogen bonds that are linear or nearly linear found by Del Bene and Bartlett.5 In cases of linear or nearly linear intermolecular hydrogen bonds, the overlap of the nitrogen lone pair and the N−H+ bond will depend linearly on the N−N distance. However, proposed by us, the correlation between the value of 2hJ(N−N) and the overlap of the LMOs is valid even for a nonlinear arrangement. Lastly, the correlation of the sum of the 13C NMR shifts of the naphthalene ring C(1,8) carbons directly attached to the interacting nitrogens with the J(N−N) values and the degree of methylation found by Lloyd-Jones et al.13 have been reexamined. It has been found that the correlations of J(N− N) and [Δ∑C1,8] with the degree of methylation have different reasons. While the former is mostly connected to the structural changes due to the solvent effect, the latter holds even for the gas phase geometries. This contradicts the explanation of Lloyd-Jones et al.13 We attribute the dependence of [Δ∑C1,8] on the degree of methylation to the changes in the paramagnetic contributions from the C−N and C−C bonds caused by the replacement of a hydrogen by a methyl group.

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Article

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ASSOCIATED CONTENT

S Supporting Information *

Different contributions to J(N−N) for systems [1]−[6] and [1H+]−[6H+], Mulliken population analysis of selected orbitals, graphs illustrating the direct and indirect effects of protonation on mutual positions of the coupling pathway orbitals. This material is available free of charge via the Internet at http://pubs.acs.org. 9243



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