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The NMR Chemical Shift of a Helium Atom as a Probe for Electronic Structure of FH, F, (FHF) and FH –

–

2+

Elena Yu. Tupikina, Alexandra A. Efimova, Gleb S. Denisov, and Peter M. Tolstoy J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b10189 • Publication Date (Web): 27 Nov 2017 Downloaded from http://pubs.acs.org on November 30, 2017

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The Journal of Physical Chemistry

The NMR Chemical Shift of a Helium Atom as a Probe for Electronic Structure of FH, F–, (FHF)– and FH2+ E.Yu. Tupikina,a A.A. Efimova,a G.S. Denisov,a P.M. Tolstoyb,* a

– Department of Physics, St. Petersburg State University, Russia

b

– Center for Magnetic Resonance, St. Petersburg State University, Russia

*

– correspondence author, [email protected]

Abstract In this work we present the first results of outer electronic shell visualization by using a 3

He atom as a probe particle. As model objects we have chosen F–, FH and FH2+ species, as well

as hydrogen-bonded complexes FH···F– at various H…F– distances (3.0, 2.5, 2.0, 1.5 and equilibrium one ca. 1.14 Å). The interaction energy of investigated objects with helium atom (CCSD/aug-cc-pVTZ) and helium atom chemical shift (B3LYP/pcS-2) surfaces were calculated and their topological analysis was performed. For comparison, the results of standard quantum mechanical approaches to electronic shell visualization were presented (ESP, ELF, ED, ∇2ED). We show that the Laplacian of helium chemical shift, ∇2δHe, is sensitive to fluorine atom lone pair localization regions and it can be used for the visualization of the outer electronic shell, which could be used to evaluate the proton accepting ability. The sensitivity of ∇2δHe to lone pairs is preserved at distances as large as 2.0–2.5 Å from the fluorine nucleus (in comparison with the distance to ESP minima, located at 1.0–1.5 Å or maxima of ELF, which are as close as 0.6 Å to fluorine nucleus).

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Introduction The structure of electronic shell of molecules and ions plays a decisive role in the formation of non-covalent interactions. There has been a number of attempts to find parameters that could describe features of the electronic shell of isolated molecules and allow one to predict some characteristics of non-covalent intermolecular interactions formed by these molecules, such as the bond geometries and bond energies.1,2 Firstly, it was proposed to use such functions as molecular electrostatic potential (MESP),1,3 electron localization function (ELF)4,5 and electron density (ED).6,7,8 For example, an electron density map can serve as an indicator of the charge distribution in a molecule,9 its magnitude at the quantum theory of atoms in molecules (QTAIM) bond critical points of hydrogen bonds correlates with the binding energy7,10,11,12,13 and maxima of Laplacian of ED could be used to locate the lone pairs.8 The minima of electrostatic potential also indicate the directions of lone pair localization.1 Moreover, the minimum value of the electrostatic potential correlates with the interaction energy of the lone pair with a proton donor.4 Analysis of ELF extrema makes it possible to find the localization regions of lone electron pairs.4,14 However, both MESP and ELF are computed values which are hard to measure experimentally. Secondly, it was proposed to use test molecules, which are able to form weak non-covalent bonds with the investigated molecule, to probe its outer electronic shell properties. For example, hydrogen atom H, hydrogen molecule H2, methane CH4, 4-fluorophenol and other small molecules can act as such probes.15,16 Some experimentally measurable spectral parameters of the probe molecules (stretching vibration frequency of the proton donor νXH,16 chemical shift of the proton δH17,18 and other nuclei19,20,21,22) were used to describe the features of the electronic shell. For example, previously 2,4,6-collidine was used as a probe proton acceptor for a studied series of benzoic acids,23 and acetic acid CH3COOH was used as a probe proton donor for a studied series of pyridines.24 It was shown that NMR parameters (chemical shift and coupling constants) could be quite informative to describe the geometry of the hydrogen bond and thus the proton-accepting and proton-donating properties of the studied molecules. The disadvantage of 2 ACS Paragon Plus Environment

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these methods is a considerably strong structure deformation of the investigated molecule by the probe particle. Using non-perturbing probes is experimentally difficult and computationally challenging, as the description of a weak interaction at high level of theory requires significant computational resources. Such calculations became possible only relatively recently. During the last decade a number of publications were devoted to the study of van der Waals

complexes

of

various

molecules

and

ions

with

helium

atom.25,26,27,28,29,30,31,32,33,34,35,36,37,38,39 For example, one can name studies of van der Waals complexes of a helium atom with neutral halogen atoms. At MP2/6-311++G(d) level the energy of complex He + Hal (Hal = F, Cl, Br) is negligibly small (less than the accuracy of the calculations) and significant changes in electron density do not occur.25 At CCSD/aug-cc-pVTZ level the energy of helium complexes with halogen anions is about 0.2 kcal/mol.26,27 Complex with hydrogen bond He···H···He is also discussed in the literature.28 Some works are dedicated to the study of interaction energy surfaces of halogen-halides (HF, HCl) with helium atom.29,30,31,32,33 These surfaces, calculated in polar coordinates (R, φ) and at high levels of theory, contain two shallow minima (~0.1 kcal / mol): from the hydrogen side (φ = 0°) and from the halogen side (φ = 180°), and a saddle point (φ ≈ 95°). A few papers are devoted to the study of interaction energy surfaces of helium atom with water molecule,35,36 hydrogen cyanide,37 acetylene.38 In Ref. 39 helium atom 3He was considered as a probe, whose NMR chemical shift,

δHe, and interaction energy with investigated molecules (fullerenes, nanotubes, graphene) was used to describe their electronic features. The δHe for helium atoms encapsulated into fullerene cages was also measured experimentally.40,41 Besides, the experimental relaxation characteristics of 3He interacting with the surfaces of such nanostructures as aerogel,42 PrF3 nanoparticles43 and geological samples of calcium carbonate,44 were measured. In this work we are focused on developing and testing of a quantum mechanical approach for constructing a 3D map of the outer electronic shell of molecules and molecular ions and their complexes with hydrogen bond. The main idea is using helium atom 3He as a probe particle. 3 ACS Paragon Plus Environment


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There are a couple of reasons for this choice. Firstly, helium atom is expected to deform minimally the probed electronic shell. Secondly, helium atom (in comparison with other noble gases) has the smallest size. Therefore, one can expected that it would be possible to monitor spacially small, localized features of the electronic shell. Thirdly, the helium atom as a probe has no internal degrees of freedom, which makes it easier to describe its position relative to the probed molecule. The key feature of our idea is the transition to spectroscopically observable parameters, namely, to 3He NMR chemical shifts, and linking the observables to the main features of the probed electronic shell. Such spectral diagnostics has potentially high sensitivity and information content, because spectral parameters are quite sensitive to the weak changes in the electronic shell,taking place during non-covalent interactions.45,46 As model objects (Figure 1) we chose fluoride anion F‒ (spherical symmetry), hydrogen fluoride molecule FH (C∞v), cation FH2+ (C2v), hydrogen bonded complex FH···F‒ at different fixed rHF‒ distances (3.0, 2.5, 2.0, 1.5 Å) and, finally, symmetric hydrogen-bound anion (FHF)‒ (D∞h) in its equilibrium geometry (H…F distance about 1.14 Å). The non-covalent interactions of such species with helium atom are expected to be rather strong due to the presence of highly electronegative fluorine atom, which is an advantage for testing out the idea of probing with helium. Besides, each of these species belongs to a different type of symmetry and fluorine atom in them is expected to have a different hybridization state or a different number of electron lone pairs. For example, upon the approach of F– to FH molecule the electronic structure of both moieties changes and for (F··H··F)‒ anion becomes symmetric.


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Figure 1. Schematic representation of the model systems studied in this work: (a) fluoride anion, (b) hydrogen fluoride, (c) cation FH2+, (d-h) FH···F‒ complex with rH···F‒ distance equal to (from top to bottom) 3.0 Å, 2.5 Å, 2.0 Å, 1.5 Å and equilibrium distance 1.14 Å.

In this paper we present the test results of the concept – using the 3He helium atom as a probing particle. The goals were a) to calculate the three-dimensional map of the interaction energy of investigated fluorine-containing molecules with the probe particle and the corresponding 3He NMR chemical shifts; b) to perform the topological analysis of calculated 3D-surfaces (extrema positions, surface gradients and Laplacians) and c) to choose the spectral parameters which are more sensitive and informative for the electronic shell description. As noncovalent interactions often occur at rather large distances between the interacting partners, it is interesting to see how the relevant features of the other electronic shell could be visualized in a practical manner. Consequently, it will be possible to estimate the prospects of using the helium probe for studying the various features of electronic shells, especially direction of lone pair localization, in other objects as well.

Computational details



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Quantum mechanical calculations were carried out using Gaussian0947 software and computational resources were provided by Computer Center of Saint-Petersburg University Research Park.48 Visualization of all surfaces was carried out in MatLab R2016b package.49 For isolated molecules, the geometry optimization was performed at CCSD/aug-cc-pVTZ level50,51 with tight convergence criteria. Molecular electrostatic potential (MESP) and Electron Localization Function (ELF) were calculated from Gaussian wavefunction files in MultiWFN wavefunction analysis program.52 Due to the high symmetry of the studied molecules, the calculations were performed in a two-dimensional Cartesian grid of points (or two twodimensional grids in case of FH2+). The size of the grid was 4.5×4.5 Å (4.5×7.0 Å for FH···F‒ complexes) with step 0.05 Å in each direction. For the complexes of the studied molecules with 3He atom, the energy calculation was performed at CCSD/aug-cc-pVTZ level. Reliable energy calculations for systems with very weak non-covalent interactions, especially the interactions of primarily dispersive nature, such as the ones with Helium atom, should be performed at advanced levels of theory with large basis sets. We choose the combination CCSD/aug-cc-pVTZ as it was demonstrated to produce high precision results for various Helium complexes.27,29,53,54 Calculation procedure was as follows: interaction energy of investigated molecules with helium atom 3He was calculated sequentially in a set of points for different helium atom positions. Set of points for each molecule was chosen individually taking into the account size and the point group of symmetry. For sphericallysymmetric F– calculations were performed along a single axis; for the molecules with principal axis C∞ (FH, FH···F–, (FHF)–) it was sufficient to calculate the interaction energy in one plane; for FH2+ (C2v symmetry), in order to save computational time, instead of calculating the interaction energy in a 3D grid of points we have performed calculations in two perpendicular planes – the plane containing all three atoms (σv1) and orthogonal plane containing bisector of HFH angle (σv2) (Scheme 1a). For the calculations in the plane the helium atom was moved sequentially along the arc at a fixed distance from the point of origin. Then the distance was 6 ACS Paragon Plus Environment

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increased stepwise and the helium atom was moved again along the bigger arc, while at each point the interaction energy was calculated, as illustrated in Scheme 1 for (FHF)–. Step size along the azimuthal direction was 5°, along radial direction – 0.05 Å. The point of origin was placed at the fluorine atom for F– and FH2+ and at the hydrogen atom for FH···F– and (FHF)–. The size of the grid was 6.0×6.0 Å.

Scheme 1. (a) σv1 and σv2 planes for FH2+. (b) Schematic representation of probing grid.

Interaction energy was calculated as a difference between the energy of complex (AB) and the sum of energies of a free helium atom (A) and the investigated molecule (B) with basis set superposition error (BSSE) corrections [55]: ‫ܧ‬୧୬୲ ൌ ‫ܧ‬୅୆ െ ሺ‫ܧ‬୅ ൅ ‫ܧ‬୆ ሻ. The interaction energy values calculated initially in the polar grid were interpolated by cubic splines and recalculated for future analysis into a regular Cartesian grid (step 0.05 Å) using home-written MatLab scripts. The NMR shielding of helium atom 3He was calculated at B3LYP/pcS-2 level.56 The family of pcS-n (n = 0, 1, 2, 3, 4) basis sets are specially designed by Jensen for obtaining nuclear magnetic shielding. In Ref. 56 F. Jensen has stressed that these basis sets were developed for density functional methods and “are shown to perform significantly better than existing alternatives for a comparable computational cost”. Among DFT methods, the B3LYP functional 7 ACS Paragon Plus Environment


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with pcS-2 basis set is widely used for NMR calculation and the applicability of this combination is confirmed by many researchers.39,57,58,59,60 The grid and the calculation procedure for helium shielding were the same as for energy. NMR shieldings were converted into chemical shifts δHe using the shielding value of a free helium atom (σref = 59.8557 ppm) calculated at the same level of theory. The Laplacian of helium chemical shift ∇ଶ δHe was calculated from helium chemical shift δHe in regular Cartesian grid (i,j) using the discrete Laplacian approximation obtained by the finite-difference method:

∇ଶ ߜு௘ ሺ݅, ݆ሻ ൌ

ଵ

௛మ

ఋಹ೐ ሺ௜ାଵ,௝ሻାఋಹ೐ ሺ௜ିଵ,௝ሻାఋಹ೐ ሺ௜,௝ାଵሻାఋಹ೐ ሺ௜,௝ିଵሻ

ቂ

ସ

െ ߜு௘ ሺ݅, ݆ሻቃ,

where h – is a step size (0.05 Å). For further details about the calculation of electron density, Laplacian of electron density, nuclear independent chemical shift (NICS61,46) and gradient of helium chemical shift ∇δHe see Supporting Information.

Results and Discussion 1. Electronic properties of free molecules We start by briefly considering the electronic properties of isolated molecules. Below we present and discuss the distribution maps for MESP and ELF, while in Supporting Information the maps for electron density and its Laplacian could be found (Figures S1-S4), as well as maps for the nuclear independent chemical shift (Figures S5-S6).

1.1 MESP In Figure 2 the distribution maps of molecular electrostatic potential (MESP) for F‒, FH and FH2+ (in σv1 and σv2 planes) are shown. MESP value for F– anion reaches its minimum value 8 ACS Paragon Plus Environment

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(about –0.4 a.u.) at ca. 1 Å from the fluorine nucleus and increases up to zero at larger distances. For FH molecule the MESP minima (about –0.04 a.u.) form a toroid at 1.5 Å from the fluorine nucleus at 120° angle from the direction of the FH bond. In Figure 2 the cross-section of a toroid is seen as a pair of minima. This ring of minima indicates the direction and localization of three lone pairs of F atom, which are indistinguishable due to the symmetry requirements (C∞ axis). For FH2+ in both σv1 and σv2 planes MESP is less informative, as it contains no characteristic features, decreasing down to zero with increasing of distance from the molecule.

Figure 2. Molecular electrostatic potential (MESP) distribution maps for (a) fluoride anion F‒, (b) hydrogen fluoride FH, (c) FH2+ cation in σv1 plane (see text), (d) FH2+ cation in σv2 plane.

Figure 3 shows MESP distribution maps for FH···F‒ complexes for rH···F‒ = 3.0, 2.5, 2.0, 1.5 and 1.14 Å. At the largest rH···F‒ distance (Figure 3a) the system resembles non-interacting FH and F–, considered above. Upon the rapprochement of F– and HF the picture changes, eventually converging to a symmetric one for the equilibrium (F··H··F)– anion. In particular, from the FH side at rH···F‒ = 3.0 Å a toroid-shape minimum exists (–0.17 a.u.) and it becomes deeper with shortening of the rH···F‒ distance. From the F‒ side at rH···F‒ = 3.0 Å there is almost a spherically-shaped minimum (–0.37 a.u.) at ca. 1.1 Å from the fluorine nucleus, which becomes 9 ACS Paragon Plus Environment


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less deep with the decrease of rH···F‒. Overall, when two fragments get closer, the MESP surfaces at each side are transformed into a single D∞h symmetric shape with two toroid-shape minima (– 0.3 a.u.) around each of the fluorine atoms (Figure 3e). Therefore, in summary, for FH and FH···F‒ (and arguably for spherically-symmetric F–) the positions of MESP minima indicate potential directions of fluorine atom lone pair localization.

Figure 3. Molecular electrostatic potential (MESP) distribution maps for FH···F‒ complex with rH···F‒ distance (a) 3.0 Å, (b) 2.5 Å, (c) 2.0 Å, (d) 1.5 Å and (e) equilibrium distance 1.14 Å.


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1.2 ELF In Figure 4 the distribution maps of the electron localization function (ELF) are presented. The ELF map for the F‒ (Figure 4a) is rather featureless, monotonously decreasing with the distance from the fluorine nucleus. The ELF map for the FH molecule (Figure 4b) contains two maxima (localization attractors) – a sphere around the hydrogen and a toroid around the fluorine atom. The latter (non-bonding attractor, ELF = 0.9) coincides with the direction of the fluorine atom lone pair localization – about 105° from the FH bond direction and ca. 0.5 Å away from the fluorine nucleus [62]. Thus, the fluorine atom of FH molecule has approximately tetrahedral sp3 hybridization state (three lone pairs and one bonding pair). However, as in the case of MESP, due to the symmetry requirement (C∞ axis), the shape of the lone pair localization region is a toroid. We note, however, that ELF and MESP maps give information about principally different parameters and thus the angles and distances to the region interpreted as “lone pair localizations” do not coincide (compare, for example, Figure 2b and Figure 4b). The ELF map for the FH2+ cation (Figures 4c and 4d) also contains a basin with maxima, corresponding to the lone pairs of the fluorine atom. These basins are visible as two allantoid-shaped regions near the fluorine atom (round shape in σv1 plane, Figure 4c, and two flat allantoids in σv2 plane, Figure 4d). Indeed, FH2+ cation has C2v symmetry and two lone pairs are localized and lie on both sides of the molecular plane, not unlike the oxygen lone pairs in a water molecule. Therefore, in all studied cases the ELF maxima indicate fluorine atom lone pair localization basins (in contrast to MESP, for which there were no corresponding features in case of FH2+).



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Figure 4. Electron localization function (ELF) distribution maps for (a) fluoride anion F‒, (b) hydrogen fluoride FH, (c) FH2+ cation in σv1 plane (see text), (d) FH2+ cation in σv2 plane.

Figure 5 shows the ELF distribution maps for FH···F‒ complexes with rH···F‒ = 3.0, 2.5, 2.0, 1.5 and 1.14 Å. For rH···F‒ = 3.0 Å the ELF distribution is essentially a sum of slightly perturbed maps for isolated FH and F– fragments. With the shortening of the rH···F‒ distance the ELF distribution as a whole becomes more symmetric, and hence for the equilibrium geometry (F··H··F)– with rH···F‒ = 1.14 Å there are two identical toroid-shape regions of maxima (ELF = 0.9) near fluorine atoms. These regions correspond to six lone pairs of two fluorine atoms. The maxima are located quite close to the fluorine nuclei (0.5 Å) and lie at the angle ca. 120° with the molecular axis.


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Figure 5. Electron localization function (ELF) distribution maps for FH···F‒ complex with rH···F‒ distance (a) 3.0 Å, (b) 2.5 Å, (c) 2.0 Å, (d) 1.5 Å and (e) equilibrium distance 1.14 Å.

2. Probing the electronic shell with helium atom Now we switch to the interaction of the studied species with a helium atom. The helium atom was placed in a set of points around F–, FH, FH2+, FH···F– and (F··H··F)– as described in the Computational details section and shown in Scheme 1. At each point the interaction energy 13 ACS Paragon Plus Environment


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and 3He NMR chemical shift were calculated and the resulting maps of these parameters were analyzed.

2.1 Interaction energy In Figure 6 the distribution maps of the interaction energy with He atom for F‒, FH and FH2+ (σv1 and σv2 planes) are shown. The map for F‒ contains a minimum at 3.3 Å away from the fluorine nucleus (spherical minimum; marked with a dashed circle in Figure 6); the interaction energy in the minimum is –0.17 kcal/mol, which matches well with the results of Ref. 26, where the same complex was studied at a similar level of theory. The interaction energy map of FH with He has two minima along the FH direction – one on the hydrogen side (–0.10 kcal/mol, global minimum) and the other one on the fluorine side (–0.05 kcal/mol, local minimum), marked with grey dots in Figure 6b. Again, the positions and depths of these minima correlate well with the ones reported in the literature.31,32,33 The global minimum could be associated with the direction of potential hydrogen bond formation, whereas the local minimum could be interpreted as the average position between fluorine atom lone pairs, the σ-hole, which detects potential halogen bond formation direction. The FH2+ interaction energy map (Figure 6c and 6d) has two equal minima (–2.3 kcal/mol) approximately along each FH bond at ca. 2.4 Å from the fluorine nucleus. Whether the FH⋅⋅⋅He interaction should be called a hydrogen bond is a terminological question which we do not discuss here. In comparison, early computations for H2O–He complex have also shown minima along the OH directions,63 while more recent computations for H2O–He complex did not show any such minima.35,36


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Figure 6. Interaction energy of helium atom 3He with (a) fluoride anion F‒, (b) hydrogen fluoride FH, (c) FH2+ cation in σv1 plane (see text), (d) FH2+ cation in σv2 plane.

Figure 7 shows the distribution maps of the interaction energy with He atom for FH···F‒ complexes with rH···F‒ = 3.0, 2.5, 2.0, 1.5 and 1.14 Å. The interaction energy map for FH···F‒ complex at rH···F‒ = 3.0 Å is very similar to the superposition of the corresponding maps for free FH and F‒: there is a low-energy region almost all the way around F– with the global minimum on the F-F axis (–0.17 kcal/mol) and a local minimum at the fluoride side of the FH moiety (– 0.10 kcal/mol). With shortening of the rH···F‒ distance the interaction energy map becomes more symmetric and for the equilibrium (F··H··F)– geometry there is a global minimum (–0.22 kcal/mol) at 90° angle from the FHF axis and ca. 3 Å away from the hydrogen atom. Two local minima (–0.18 kcal/mol) are symmetrically placed on FHF line near fluorine atoms at distances ca. 3 Å away from the fluorine atoms. Unfortunately, none of these minima could indicate the direction of fluorine atom lone pairs localization.



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Figure 7. Interaction energy of helium atom 3He with FH···F‒ complex with rH···F‒ distance (a) 3.0 Å, (b) 2.5 Å, (c) 2.0 Å, (d) 1.5 Å and (e) equilibrium distance 1.14 Å.

Speaking of the stability of Helium complexes in their equilibrium geometries (in local and global energy minima), one has to take into account the values of zero point energies (ZPE). We have calculated the ZPE corrections for all energy minima in every system considered. The results are collected in Supporting Information in Table S1 for 3He and, for the sake of 16 ACS Paragon Plus Environment

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completeness, in Table S2 for 4He. In all cases ZPE correction is significant in comparison with the depth of the corresponding minimum. For example, for F– the correction is 0.08 kcal/mol (here and below the values are given for 3He), while the depth of the minimum is 0.17 kcal/mol. For FH the ZPE correction is larger than the depth of the minimum for both the local and the global minimum, indicating that in such a shallow potential there might be no vibrational energy levels (more precise calculations including the exact shape of the 3D potential are needed in order to answer this question in more detail). For FH2+ the ZPE correction is smaller than the depth the energy minimum. Finally, for (FHF)– the depth of energy minima and the values of ZPE corrections change with the H…F distance from the situation similar to non-interacting FH and F– to the equilibrium (FHF)– geometry, for which the minimum depth is 0.22 kcal/mol and ZPE correction is 0.15 kcal/mol. In all cases, changing 3He to 4He (Table S2) does not influence the situation qualitatively.

2.2 3He chemical shifts In Figure 8 the distribution maps of 3He NMR chemical shift, δHe, for F‒, FH and FH2+ (σv1 and σv2 planes) complexes with helium atom are shown. Hereinafter: 3He NMR chemical shift means the change of 3He NMR chemical shift with respect to free helium atom, which has the absolute shielding of 59.8557 ppm. In all cases, in the region that might be called “the outer electronic shell” (ca. 1.5 Å and further from the fluorine nuclei) the chemical shifts are small, less than 0.05 ppm by the absolute value. For F– (Figure 8a), δHe values pass through the minimum at ca. 3 Å from fluorine nucleus – close to the equilibrium He···F– distance – and increase up to zero with the elongation of F···He distance. The distribution map of δHe for FH molecule (Figure 8b) contains two sets of minima. The first one is located at the fluorine side along the FH bond (–0.03 ppm) and the second one is a ring of minima around the FH bond ca. 3 Å away from the fluorine nucleus. Both these minima do not coincide with the direction of 17 ACS Paragon Plus Environment


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fluorine lone pair localization. However, there are certain surface convexities at 120° angle from the FH bond direction, which indicate that further topological analysis of δHe surface might reveal more information about the fluorine lone pair localization. For FH2+ the δHe map (Figures 8c and 8d) has allantoid-shaped region with minima (ca. –0.01 ppm deep) on the side of protons at 4.5 Å from the fluorine atom, perpendicular to the plane of the molecule and passing through the bisector of the HFH angle.

Figure 8. Chemical shift of 3He atom δHe near (a) fluoride anion F‒, (b) hydrogen fluoride FH, (c) FH2+ cation in σv1 plane (see text), (d) FH2+ cation in σv2 plane.

Figure 9 presents the distribution maps of δHe for FH···F‒ complexes with He atom with rH···F‒ = 3.0, 2.5, 2.0, 1.5 and 1.14 Å. For rH···F‒ = 3.0 Å the map looks somewhat like a distorted superposition of the corresponding maps for FH and F‒: there is a global minimum (–0.06 ppm) at the FH side, while near the fluoride anion the chemical shift has positive values. Upon shortening of the rH···F‒ distance the picture gradually changes into the one for the equilibrium (F··H··F)– geometry. The δHe map becomes symmetric, having two equal minima (–0.06 ppm) on the continuation of the F-F axis and a symmetric cone of deschielding placed perpendicular to F-F axis. 18 ACS Paragon Plus Environment

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Figure 9. Chemical shift of 3He atom δHe near FH···F‒ complex with rH···F‒ distance (a) 3.0 Å, (b) 2.5 Å, (c) 2.0 Å, (d) 1.5 Å and (e) equilibrium distance 1.14 Å.

In summary, Figures 8 and 9 show that the absolute values of δHe are sensitive to the position of 3He around the studied molecule, but the maps of δHe do not appear to be especially informative in terms of such details of the outer electronic structure as, for example, fluorine lone pair localization. Here by the “informativity” we mean the utility of the chemical shift maps 19 ACS Paragon Plus Environment


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as a quick way to assess the electronic structure by a naked eye. Nevertheless, we believe that valuable information could be mathematically retrieved from the absolute values of δHe. For this purpose, we have tried two approaches: to account for the contribution of nuclear-independent chemical shift (NICS; see immediately below) and to consider the first and second derivatives of

δHe (see the Section 2.3). It is possible to reason that helium chemical shift is determined by two factors – firstly by the vicinity of the helium atom to the species, and secondly by the interaction of the electronic shells. The first contribution could be evaluated by computing the NICS values (the property describing the chemical shift of a virtual nucleus without charge and electrons, which is placed at a given point). NICS calculations were first introduced in Ref. 64, and later used, for example, for studying the aromaticity65 and proton shielding/deshielding upon approaching to proton acceptor sites.46 We have plotted maps of the δHe – NICS values, which was expected to reflect the part of shielding exclusively due to the interactions of electronic shells of helium atom and a studied species (see Figures S7 and S8 in Supporting Information). However, visually the δHe – NICS maps appeared to be not more informative than the initial maps of δHe. As mentioned above, it is possible that additional topological analysis of δHe distribution maps would help to visualize the direction and localization of fluorine lone pairs. Such analysis is done in the next section.

2.3. Laplacians of 3He chemical shifts Next, we attempted to carry out topological analysis of δHe distribution maps. The distribution maps for the gradient of δHe (see Figures S9 and S10 in Supporting Information) did not reveal any particularily interesting features and we have turned the attention to the Laplacians. In Figure 10 the distribution maps of the Laplacian of helium chemical shift ∇2δHe for F‒, FH and FH2+ (σv1 and σv2 planes) are shown. The values of ∇2δHe for F‒ are close to zero 20 ACS Paragon Plus Environment

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(within the margin of computational error). The ∇2δHe distribution map for FH has two regions containing higher values of ∇2δHe: a conical region near the fluorine atom (in Figure 10 it is visible as two lobes protruding from the fluorine) and the other region near the hydrogen atom. The position and direction of the conical region coincides with the direction of fluorine atom lone pair localization – about 120° from the direction of the FH bond. In a similar way, by looking at the map of ∇2δHe for FH2+ (Figure 10c and d) one can notice that the regions of high values are located either alone the FH bonds or along the direction of the lone pair localization.

Figure 10. Laplacian of 3He chemical shift ∇2δHe near (a) fluoride anion F‒, (b) hydrogen fluoride FH, (c) FH2+ cation in σv1 plane (see text), (d) FH2+ cation in σv2 plane.

The ∇2δHe map for FH···F‒ at rH···F‒ = 3.0 Å (Figure 11a) from the FH side looks like the map for isolated FH molecule, whereas from the F– side there is a two broad lobes of ∇2δHe maxima. Upon shortening of the rH···F‒ distance the ∇2δHe map becomes more symmetric and eventually for the equilibrium (F··H··F)– two identical conical-shaped regions are visible pointing at ca. 120° from the FHF axis, and thus coinciding with the directions of fluorine atoms lone pairs localization.



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Figure 11. Laplacian of 3He chemical shift ∇2δHe near FH···F‒ complex with rH···F‒ distance (a) 3.0 Å, (b) 2.5 Å, (c) 2.0 Å, (d) 1.5 Å and (e) equilibrium distance 1.14 Å.

The ∇2δHe maps for FH···F‒, shown in Figure 11, also support this interpretation: at rH···F‒ = 3.0 Å the map looks like the superposition of FH and F– maps with little deviations; upon shortening of the rH···F‒ distance the ∇2δHe map becomes more symmetric and eventually for the


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equilibrium (F··H··F)– two identical conical-shaped regions are visible pointing at ca. 120° from the FHF axis, and thus coinciding with the directions of fluorine atoms lone pairs localization.

Conclusions In this computational work we have probed with a helium atom the structure of the electronic shell of a series of species having fluorine atom in various hybridization states with different number of lone pairs: F–, FH, FH2+ and FH⋅⋅⋅F– complex at different H…F– distances. The outer electronic shell of fluorine, which, for example, determines the ability of this atom to act as a proton acceptor in hydrogen-bonded complexes, was mapped using the chemical shift of the probing 3He atom, δHe. We show that for all studied systems the topology of the δHe maps, namely, the maps of the δHe Laplacian, ∇2δHe, can be used to visualize the direction and localization of the fluorine lone pairs (see Figures 10 and 11). Note, that the construction of the ∇2δHe maps does not add any information which would not be already there in the initial maps of the absolute values of δHe. However, optically, for a human eye, the ∇2δHe maps reveal the lone pair localization in much clearer way than the δHe maps. While similar information could be obtained by other well-established computational methods (such as MESP and ELF mapping), the benefit of using a helium probe is the visualization of the electronic shell at larger distances, more relevant for the non-covalent interactions: the ∇2δHe features are pronounced at distances not less than 2 Å, in comparison with the characteristic distanced of 0.5 Å for ELF or 1.0–1.5 Å for MESP. At the moment it is not clear which molecular properties could influence the shape and values of ∇2δHe in the protondonating direction of the FH bonds; it would be interesting to test it on a larger and more diverse set of objects.



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Supporting information The Supporting Information is available free of charge on the ACS Publications website. The electron density (ED) maps for F‒, FH, FH2+ (Figure S1) and FH···F‒ (Figure S2). The Laplacian of the electron density (∇2ED) maps for F‒, FH, FH2+ (Figure S3) and FH···F‒ (Figure S4). The nuclear independent chemical shift (NICS) maps for F‒, FH, FH2+ (Figure S5) and FH···F‒ (Figure S6). The difference of δHe and NICS maps for F‒, FH, FH2+ (Figure S7) and FH···F‒ (Figure S8). The gradient of δHe for F‒, FH, FH2+ (Figure S9) and FH···F‒ (Figure S10).

Acknowledgements This work was supported by the RFBR grant 17-03-00497. The calculations were performed in the Computer Center of Saint-Petersburg University Research Park.


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