Unusual Indirect Nuclear SpinâSpin Exchange Coupling through

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Unusual Indirect Nuclear Spin-Spin Exchange Coupling Through Solvated Electron Changzhe Zhang, Qi Luo, Shibo Cheng, and Yuxiang Bu J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b03249 • Publication Date (Web): 25 Jan 2018 Downloaded from http://pubs.acs.org on January 25, 2018

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The Journal of Physical Chemistry Letters

Unusual Indirect Nuclear Spin-Spin Exchange Coupling through Solvated Electron Changzhe Zhang, Qi Luo, Shibo Cheng, Yuxiang Bu* School of Chemistry and Chemical Engineering, Shandong University, Jinan, 250100, People’s Republic of China ABSTRACT: Solvated electrons have been found to exist in various media which also exhibit more intriguing properties such as superconductivity, nonlinear optical response and so on. However, how they affect the nuclear spin properties have not been proved. In this work, we present the first detailed study on solvated-electron-triggered indirect nuclear spinspin J-coupling using density functional theory calculations. Taking 19F as a probe, we verify the presence of unusual J couplings between two distant F atoms in HF-containing anionic clusters. These couplings occur “through solvated electron”, rather than through conventional covalent bonds or space. Solvated electron can serve as an additional channel to efficiently realize long-range J-coupling between far separated nuclei because of its dispersivity and Rydberg character. The coupling magnitude strongly depends on the unique distribution of solvated electron and its second-order interaction with solvating HF units.

This work

provides novel insights into the mediating roles of electrons, possibly opening up potential applications based on weakly bound electrons. TOC Graphic Unusual Indirect Nuclear Spin-Spin Coupling Occurring “through Solvated Electron” rather than through bond and through space eJ

FF

F-H···F-H···e···H-F

*

To whom correspondence should be addressed: [email protected] 1

ACS Paragon Plus Environment

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The indirect nuclear spin-spin coupling constant (J-coupling) in NMR spectroscopy is a sensitive antenna for detecting the features of electronic structure, geometry, and conformation of molecules and their assemblies

1-5

and has also found diverse

interdisciplinary applications in condensed matter as probes.1,6-16 The coupling information is exchanged between the coupled nuclei through intervening electrons between them in all possible pathways. Thus, the J-couplings sensitively depend on the states of such intervening electrons between the coupled nuclei, as characterized by the through-bonds and throughspace channels.8,17,18 The through-bonds coupling is closely associated with the bonding electrons in the chain linking the coupled nuclei and would be negligible in magnitude beyond three or four bonds. However, the through-space coupling is realized through the orbital overlap between the diffuse parts of lone-pair or nonbonding electrons (elp) on the spatially proximate atoms. Undoubtedly, for any channels J-coupling is accounted for by the Fermi contact, spin dipole, diamagnetic spin-orbit and paramagnetic spin-orbit interactions,19 and the delocalization characteristic of such mediating electrons is conceivably favorable to Jcouplings.20,21 As a unique kind of electron carriers, solvated electrons (esol) have been characterized experimentally and theoretically in various media and surroundings since its first discovery 2231

and are also evidenced to possess more intriguing properties and promising applications

due to their loose structures and Rydberg character. In particular, the discovery of some novel structures such as electrides

32-35

and electron clathrate hydrates

36,37

further unveils

their unique electronic properties with high thermal stability such as superconductivity,33,34 nonlinear optical properties,38,39 magnetic and spintronics,34,40 and so forth.

Thus, it is

anticipated that such loosely bound esol could provide an unexpected role in realizing or enhancing J-couplings.

2


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In fact, the NMR experimental information about esol was well documented, including the Knight shift for solvent nuclei in lithium-methylamine or sodium- and potassiumammonia solutions which is ascribed to the Fermi contact interaction of the nuclei with esol.4042

However, information about the effect of esol on the NMR parameters is still very scarce

and far less than that about the effect of valence electrons (e.g. through bonds). Thus, it is of fundamental interest to explore how a loosely bound esol affects the J-coupling and to clarify the role of an esol as a novel channel (or way) in realizing the J-coupling. This is because such solvated electrons involve a large type of weakly bound electron systems, e.g. solvated electrons in clusters, solutions, and solids, electrides, and electron clathrates, and play an important role in exhibiting more unique properties. As the most sensitive element in nuclear magnetic responses, fluorine (F) has been extensively utilized as the NMR probe of much more systems.43-47 Furthermore, F is the most electronegative element in the periodic table and its formed bonds with other elements have the largest polarity. Thus, the F-containing compounds have been extensively utilized as the binding motifs and carriers of excess electrons,48-50 and their electron adducts have also found some intriguing properties, e.g. large nonlinear optical response.38,39 Clearly, it is of great interest to investigate the J-coupling responses of the F-containing species to esol. In this letter, we report our findings about the J-coupling constants between F nuclei (JFF) triggered by esol in (HF)n− and HF-doped electron hydrates using DFT calculations and electron localization function and localized orbital locator analyses which have been widely used to characterize the electron delocalization quantitatively.51,52 The calculational details with relevant calculated results are given in the Supporting Information. It should be noted that the significance of quantum chemistry calculations is not only to explain experimental phenomena, but more importantly to predict the nature of science and to provide more valuable information for experimental science. In fact, many theoretical predictions have

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been latter proved to be correct, in good agreement with experiments. In particular, the DFT calculations have been extensively used to determine the electronic properties and have been verified to be powerful tool to explore the structures and properties of various systems including the indirect nuclear spin-spin coupling constants.4 In this work, our calculations reveal an intriguing finding that esol can serve as a novel channel for realizing JFF-couplings with unexpected magnitudes which is distinctly different from traditional through-space and through-bonds ones. As well-known, a cluster of polar molecules can trap excess electrons, forming stable anions in at least two ways: dipole bound and solvated. As evidenced experimentally in (HF)3−, an esol structure (e@(HF)1,2, Fig. 1a) is one of the observed forms with a vertical detachment energy (VDE) of 0.43 eV.29 Further calculations suggested that such an esol structure has extremely large nonlinear optical response, similar to other esol systems, which is due to its unique electronic state or loose distribution. Motivated by this, we computationally studied its J-coupling properties at the B3LYP/6-311+3+G(d,p)-bq-6-311+2+G(d) level and particularly examined if a loose esol could transmit the J-coupling information among the nuclei in this experimentally observed esol system. Surprisingly, a quite large JFF is obtained to be 193 Hz between two far separated F nuclei (dF···F=~5 Å) in two HF which directly solvate an excess electron (i.e. 3eJFF for the FH···e···HF unit, Fig. 1a). However, two other JFF are 174 Hz (2hJFF) through a H-bond channel and 25 Hz (5heJFF) through a complex channel, respectively. This 3eJFF value is close to 2hJFF (228.6 Hz at dF···F=2.29 Å) in FH···F− and even larger than

2h

JFF (123 Hz at dF···F=2.4 Å) in FH···F−···HF which was confirmed

experimentally,3,53 and considerably larger than |2hJFF| (40.7 Hz at dF···F=2.74 Å) in (FH)2 which are through H-bond channels.54 In particular, it is far larger than JFF (0.9 Hz) in its neutral counterpart after removing excess electron vertically and those (4hJFF = 0.9 and 0.07 Hz) between two solvent F nuclei in FH···F−···HF and FH···FH···HF, two analogues with 4


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similar dF···F (ca. 5.0-5.5 Å, Fig. 1a), where the center unit (F− or HF) is a bridge to transmit the F···F J-coupling information between two solvent HF. Similarly, for e@(HF)1,1 (Fig. 1a), although its dF···F is slightly long (~5.5 Å), its 3eJFF is still considerably large (105 Hz). No experimental values appear for calculated

3e

JFF of these esol systems.

3e

JFF in the esol systems are larger than

However, the fact that our

2h

JFF (123 Hz) and

4h

JFF (0.9 Hz) in

FH···F−···HF should be a sufficient evidence for the esol-based J-couplings. Although the nonbonding J-coupling is demonstrated to be distance-dependent,46 the remarkable differences in JFF for the above systems with almost equivalent dF···F are undoubtedly attributed to other factors instead of the distance factor. That is, the extremely large JFF values in the esol systems fully indicate that esol is really a better mediator for JFF-coupling than elp although it is a single electron, and the essence of different mediating roles of esol and elp is closely associated with their differences in the states, distributions, and properties. In other words, esol can act as a bridge to realize the spin information exchange between two separated nuclei, thus contributing to the enhancement of J-coupling via a novel esol-based way. In fact, J-coupling is governed by not only the channel length for the through-bond mechanism or direct contact distance for the through-space mechanism

46

but also the bond

angles.3,55 It is anticipated that 3eJFF should be also dependent on the pathway distance and angle because an excess electron may be solvated by more solvent molecules. Thus, we further calculated other (HF)3-6− esol clusters with zigzag structures, e@(HF)m,n (i.e. (FH)m···e···(HF)n with a dimer esol unit, FH···e···HF, and m and n denote the lengths of two ligand chains of excess electron), and polyhedral structures, e@(HF)Pn, where Pn denotes the number of ligands in polyhedral structures (Fig. 2).56 Although all 3eJFF are in the ranges of 836-260 Hz for four zigzag structures and 158-66 Hz for four polyhedral ones, only 3eJFF of the zigzag structures and 3eJFF(180) of the linearly aligned two HF in e@(FH)P5 and e@(FH)P6

5



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present a quasi-linear dependence on the straight distance between two coupled F nuclei (dF···F).

3e

JFF(120), 3eJFF(109), and 3eJFF(90) in all other cases considerably deviate from the fitting

line about 3eJFF(180) (Fig. 3a). Even if the pathway channel is considered to pass the center of esol, the data points still deviate from the corresponding fitting line. This observation clearly indicates that dF···F is not only factor in accounting for 3eJFF. In particular, for all these esol structures, if excess electrons are vertically removed, the calculated JFF values of their unrelaxed structures are quite small (0.05-9.1 Hz), suggesting that the elp-based through-space contribution to total JFF is negligible. Further, the above conclusions are confirmed at the wave-function-based theory level (e.g. the HF method) as well as other functional methods (e.g. the X3LYP and M062X functionals), and similar trends are reproduced (Table S2). Thus, we can exclusively predict that the state, distribution character, and interaction with solvating HF of esol play a dominant role in realizing 3eJFF-couplings. Since the J-coupling between two nuclei is indirectly realized through the intervening electrons which directly couple the two nuclei via the Fermi contact interaction, the electron could distribution between the two nuclei certainly affects the J-coupling.

Thus, we

examined relevant orbital distributions of mediating electron(s) (i.e. valence electrons, elp or esol) in them (Fig. 1a). Clearly, JFF-coupling is exchanged through elp in either FH···FH···HF or FH···F−···HF, while it is through a single esol in either e@(HF)1,1 or e@(HF)1,2. Compared with the compact valence elp on the bridging F of FH···FH···HF and FH···F−···HF which poorly contribute to JFF-couplings, esol presents more diffuse character, and is also not strongly associated with any particular atom, remaining relatively far away from the molecular backbone or atomic nuclei. More importantly, such an esol not only resides in the cluster void as a Rydberg entity but also partially permeates the solvent layer and even localizes at the solvating HF in their antibonding orbitals (σ*F-H).

6


Undoubtedly, such

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permeation characteristic of esol is a virtual prerequisite of strong 3eJFF-couplings realized by esol, as confirmed by a comparison with the case for the vertically esol-detached structures. To obtain further insights into the mediating role of esol, we here make an electron localization function analysis on spatial distribution of esol qualitatively, examining if or how the distribution covers the coupled F nuclei. Fig. 1b shows the cross-section representations at the X-Y plane of electron localization functions for different clusters. Significant amounts of electron density are accumulated around every H-F units which correspond to valence electrons of HF for all clusters. More interestingly, large electron localization function values exist between two solvating HF in e@(HF)1,1 and e@(HF)1,2 and their distributions are also relatively expanded compared with those around the HF units (Fig. 1b), indicating a better condition for J-coupling. In contrast, the electron localization function between any two units in FH···FH···HF or FH···F−···HF is very small, indicating poor spin communication for Jcoupling, as confirmed in Fig.1c by another view of the electron localization function distribution for these clusters. For example, there are peaks in the electron localization function distribution for e@(HF)1,2. Two side peaks correspond to the electron distributions around two solvating HF, while the middle one denotes the esol distribution and its tail parts actually expand to the vicinity of two solvating HF, thus supporting 3eJFF. Similar analyses by the localized orbital locator (Fig. S3) also confirm the esol-triggered strong 3eJFF-couplings. Further, the natural bond orbital analysis is employed to understand

3e

JFF-couplings

quantitatively. We particularly focus on the interactions between the bridging electrons (esol versus elp in HF and F−) with solvating HF in two aspects (Fig. 4): Second-order interaction energy (E(2)) and energy gap (∆E) between the bridging electrons and σ*F-H of solvating HF. Essentially, electron delocalization from the bridging electrons to σ*F-H is an overall measure of the above two factors and can be characterized by the σ*F-H occupancy (Occ(σ*F-H)). As shown in Fig. 4, esol in e@(HF)1,1 or e@(HF)1,2 is in energy closer to σ*F-H than elp in

7



FH···FH···HF or FH···F−···HF, and thus ∆E(esol→σ*F-H) is quite smaller than ∆E(elp→σ*F-H) and E(2) for esol→σ*F-H is larger than that for elp→σ*F-H correspondingly. As an overall result, Occ(σ*F-H) (0.07, 0.22) in e@(HF)1,1 and e@(HF)1,2 are considerably larger than those (0.03, 0.01) of FH···F−···HF and FH···FH···HF.

Clearly, these large Occ(σ*F-H) should be

responsible to strong 3eJFF-couplings in two esol systems. Further, in two groups of large anionic clusters ((HF)n−, n=4-6, Fig. 2), the zigzag structures, e@(HF)m,n, can be viewed as extension by elongating two H-bond chains of e@(HF)1,1. Clearly, elongation of the zigzag (HF)n chain increases its dipole moment and electron-binding ability, and thus esol is tightly bound featuring increased VDE and shortened dF···F. In particular, the electron delocalization degree increases with considerable electron permeation into two solvating HF as evidenced by their electron localization function distributions (Fig. 2) and 3eJFF increases correspondingly. For example, from e@(HF)1,1 to e@(HF)2,2 to e@(HF)3,3, dF…F decreases from 5.5 Å to 4.2 Å to 3.67 Å, while VDE increases from 0.45 eV to 1.2 eV to 3.2 eV. The electron localization function distribution in between the esol peak and valence electron peaks of solvating HF noticeably increases due to delocalization of esol (Fig. 1 and 2), and Occ(σ*H-F) increases from 0.07 to 0.28 to 0.55. Clearly, these changes account well for the remarkable enhancement of 3eJFF from 105 Hz to 532 Hz to 836 Hz. Similar trend is also observed in asymmetric zigzag structures (e@(HF)1,m, m=2,3,5, Fig. S5-S8) but with a reduced variation magnitude due to only single chain elongation. Asymmetric arrangements lead to asymmetric distributions of esol with large fraction close to and considerably large Occ(σ*H-F) in the solvating HF in long chain (0.07/m=1 versus 0.22, 0.27, and 0.29 for m=2,3,5) and basically unchanged Occ(σ*H-F) (ca. 0.07-0.09 for all) in short chain, and thus a mild increase of 3eJFF (105/m=1 versus 193, 260, and 270 Hz for m=2,3,5).

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For the other JFF between the far apart F atoms which cross the esol region in the nonsolvating HF, for example,

7he

respectively, far smaller than

JFF and

11he

JFF in e@(HF)3,3, they are 3.5 Hz and 0.02 Hz,

3e

JFF (836 Hz). This observation indicates that esol does not

support super long-range JFF-coupling. This is because a large fraction of esol is enclosed in a limited region between two solvating HF and only a small part penetrates into the solvating HF units, as evidenced by small Occ(σ*F-H) (0.04, 0.004) of two non-solvating HF, which clearly imply very weak 7he/11heJFF-couplings. For the e@(FH)Pn (n=3-6) polyhedral structures (Fig. 2), we checked their couplings.

3e

JFF-

A common character of these esol structures is that they have one or more

nonlinear coupling modes. In general, Occ(σ*F-H) decreases (0.15, 0.12, 0.08 (axis-direction), 0.07) as n increases in part due to the sharing of esol by more solvating HF, and 3eJFF decreases (i.e. 158 Hz, 143 Hz, 75 Hz/3eJFF(180), 66 Hz/3eJFF(180)) from e@(HF)P3 to e@(HF)P6. However, unexpectedly, two 3eJFF are different for the highly symmetric e@(FH)P6 (Oh), i.e. 3eJFF(90) (44 Hz) < 3eJFF(180), although dF…F (4.0 Å, the straight-line distance) for the former is considerably shorter than that (5.7 Å) for the latter. In fact, the bent channel operates to realize the JFF(90) coupling for this case. But, even if the channel is considered to pass through the cluster center (also the center of esol) as a bent one also with a path length of 5.7 Å, it still cannot explain the difference between

3e

JFF(90) and

3e

JFF(180). This observation suggests that the

channel bending is an unfavorable factor which slightly decreases 3eJFF compared with that in the straight-line channel, as proved in experimental studies on 3JFF in the cis/trans ethylenic and N2F2 compounds (3JFF(cis) < 3JFF(trans)).57,58 As for the D3h-symmetric e@(HF)5, although the case is slightly complicated which includes three coupling types featuring different angles, they totally are close to those in both e@(HF)P3 (D3h) for 3eJFF(120) and e@(FH)P6 for 3eJFF(180) and 3eJFF(90) but with reduced Occ(σ*F-H). We also examined the dependence of 3eJFF on the

9



bending angle (∠F···e···F) and found that ∠F···e···F considerably affects 3eJFF through adjusting the esol distribution (Fig. S10). In short, although dF···F, angle and electron localization function distribution along the coupling pathway could yield effects on

3e

JFF, Occ(σ*F-H) may be viewed as an overall

measure of the mediating role of esol in exchanging JFF-coupling information. Fig. 3b presents a high correlation between 3eJFF and Occ(σ*F-H) for all esol systems, which clearly suggests the coupling mechanism and essence of the esol-triggered noticeable enhancement of 3eJFF. To examine generality of the esol effect, we compare three HF-doped anionic hydrates (e@(H2O)22(HF)2, e@(H2O)12(HF)4, e@(H2O)6(HF)2, Fig. 5 and Table S6). The middle one (e@(H2O)12(HF)4) supports a network permeating state 59 in which four HF are in the middle and are covered by the permeating electron, while the other two support the internal states of esol. Their eJFF values were calculated to follow the order of e@(H2O)22(HF)2 (583 Hz) > e@(H2O)12(HF)4 (96 Hz) > e@(H2O)6(HF)2 (4.9 Hz), in agreement with the Occ(σ*F-H) order (0.32, 0.1 and 0.05) and their electron localization function and orbital distributions although they have distinctly different structures. Upon excess electrons are vertically removed, all JFF values of the unrelaxed structures become very small (2.6, 3.2 and 0.04 Hz), fully indicating a virtual mediating role of esol. Similar observations in fluorohydrocarbons also support the above analyses (Fig. S11 and Table S5). In summary, 3eJFF-couplings in (HF)n− anionic clusters and HF-doped electron hydrates are systematically studied through DFT calculations. Our findings indicate an unusually major mediating role of esol on JFF-couplings and unveil a unique esol-based exchange coupling mode. In contrast to traditional through-bonds and through-space channels, esol can also serve as a bridge to communicate the far separated nuclei and to realize long-range Jcouplings because of its dispersivity and Rydberg character. The strong mediating role originates from the state and distribution of esol and its second-order interaction with solvating

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HF σ*F-H orbitals and Occ(σ*F-H) although dF···F and angles also affect 3eJFF-couplings. The electron localization function distributions are used to visualize the 3eJFF-coupling differences among the esol systems. Our studies show a novel J-coupling channel through esol with remarkable coupling magnitude and provide new insights into the mediating roles of electrons, possibly opening up potential applications based on weakly bound electrons.

ASSOCIATED CONTENT (S) Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jpclett.*******. The calculated structures and electronic properties of different (HF)n− anionic clusters, comparison of the JFF-coupling constants between the excess electron-trapped perfluorocyclopropane and its corresponding neutral system, and the calculated structures and properties of HF-doped hydrate clusters, (HF)n(H2O)m−, (PDF).

AUTHOR INFORMATION Corresponding Author *byx@@sdu.edu.cn Notes The authors declare no competing financial interest ACKNOWLEDGMENTS Acknowledgments for support of this work are made to NSFC (21573128, 21373123, and 21773137), and also for National Supercomputer Center in Jinan and High-Performance Supercomputer Center at SDU-Chem.

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Figure 1. Schematic structures and electronic distribution functions. (a) The schematic structures with the coupling modes with orbital distributions (isovalue=0.04); (b) the electron localization function distributions at the X-Y plane and (c) those along the F···F straight connecting line (as the transverse axis) for four representative clusters. The positions of the coupling subunits (F-H······H-F) are also shown.

Figure 2. Structures and electronic distribution functions. The zigzag and polyhedral structures with main coupling modes (the digits in brackets are the bending angles) and esol orbital distributions (red-green), and the electron localization function distributions along the F···F straight connecting line (as the transverse axis) and the σ*F-H occupancies for six esol clusters with different structures. The positions of the coupling subunits (F-H···H-F) are also shown. 19



900

900 e@(HF)3,3

800

800

e@(HF)2,2

600

600 JFF (Hz)

500 e@(HF)1,5

400 300 200

e@(HF)3,3

700

700

JFF (Hz)

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

Page 20 of 21

e@(FH)P4(109)

e@(HF)1,3

100

e@(FH)P5

e@(FH)P6(90)

0 3.5

4.0

400

e@(FH)P6

e@(HF)1,5

300 200

e@(FH)P3(120)

e@(HF)2,2

500

e@(HF)1,3 e@(FH)P4

e@(FH)P3 e@(FH)P5 e@(FH)P6

100 0

4.5

5.0

5.5

0.0

6.0

0.2

dFF(Å)

0.4

0.6

0.8

1.0

1.2

Occ(σ*F-H)

Figure 3. Calculated JFF coupling constants. Dependences of 3eJFF(180) on dF…F, together with some discrete data points for 3eJFF(

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