Document [original]

Unusually Large Effects of Charge-assisted CH···F

Hydrogen Bonds to Anionic Fluorine in Organic Solvents:

Computational Study of 19F NMR Shifts versus

Thermochemistry

Martin Kaupp,* Caspar J. Schattenberg, Robert Müller, and Marc Reimann[a]

A comparison of computed 19F NMR chemical shifts and experi-

ment provides evidence for large specific solvent effects for

fluoride-type anions interacting with the σ*(CH) orbitals in

organic solvents like MeCN or CH2Cl2. We show this for systems

ranging from the fluoride ion and the bifluoride ion [FHF]to

polyhalogen anions [ClFx]. Discrepancies between computed

and experimental shifts when using continuum solvent models

like COSMO or force-field-based descriptions like the 3D-RISM-

SCF model show specific orbital interactions that require a

quantum-mechanical treatment of the solvent molecules. This is

confirmed by orbital analyses of the shielding constants, while

less negatively charged fluorine atoms (e.g., in [EF4]) do not

require such quantum-mechanical treatments to achieve rea-

sonable accuracy. The larger 19F solvent shift of fluoride in

MeCN compared to water is due to the larger coordination

number in the former. These observations are due to unusually

strong charge-assisted CH···Fhydrogen bonds, which mani-

fest beyond some threshold negative natural charge on fluorine

of ca. <0.6 e. The interactions are accompanied by sizable

free energies of solvation, in the order F@[FHF]>[ClF2]>

[ClF4]. COSMO-RS solvation free energies tend to moderately

underestimate those from the micro-solvated cluster treatment.

Red-shifted and intense vibrational CH stretching bands,

potentially accessible in bulk solution, are further spectroscopic

finger prints.

Introduction

CH bonds acting as hydrogen-bond donors have a long and

varied history going back to a 1937 suggestion by Glasstone to

explain the formation of mixtures of CX3H (X=Cl, Br, I) with

acetone or quinoline.[1] From the controversial early history of

such suggestions, we mention here only the X-ray diffraction

studies of short CH···O distances in crystals by Suton[2] and first

definitive IR experiments by Allerhand and Schleyer.[3] Mean-

while the existence of such interactions is very well established,

with too many facets and applications to be mentioned here in

detail. They even form the central basis for a book on weak

hydrogen bonds.[4] The latter implies that usually such inter-

actions tend to be weaker than regular hydrogen bonds with

more electronegative donor atoms like N, O, or F. And indeed,

often CH···O hydrogen bonds tend to exhibit blue-shifted CH

vibrations with reduced intensities and have been (improperly)

termed “improper hydrogen bonds”, as the charge-transfer

component is small, and electrostatic and rehybridization

effects can lead to shortened CH bonds with enhanced force

constants and reduced bond dipoles.[5,6]

However, the strength of CH···X hydrogen bonds can be

enhanced by various factors: a) a net positive charge on the

donor in cationic species, for example by protonation, metal

coordination or involvement in an ammonium-ion framework;[7]

b) employing sp2or sp hybridized carbon donors, which

increases their electronegativity;[8] c) a more gradual increase of

the electronegativity and donor strength by attaching electro-

negative substituents to the carbon atom (this explains the

predominant early observation of such interactions for halo-

forms); and d) a negative charge on the hydrogen-bond

acceptor.[9,10,11] All of these aspects have been utilized, for

example, in the design of supramolecular anion receptors,[12]

including those for halide ions, or, for example, in catalysis.[13]

The term “charge-assisted hydrogen bonding” has been used in

this context.[14]

While these types of studies of specific anion receptors

benefit from well-defined structural arrangements, the CH

bonds of many common solvents also should be expected to

form rather strong CH···X hydrogen bonds with anionic solutes.

This is supported by a number of recent computational studies

at various levels.[9,10,11] While little experimental solution data is

available, these computational studies indeed suggest strong

CH···X interactions to contribute to the microsolvation of anions

in many common organic solvents. This certainly should hold

for aliphatic CH groups not only in the haloforms (which have

been used in previous computational studies[9]) but also in

solvents like acetonitrile (MeCN) or dichloromethane (DCM),

which all bear electronegative substituents on the donor carbon

[a] Prof. Dr. M. Kaupp, C. J. Schattenberg, Dr. R. Müller, M. Reimann

Technische Universität Berlin

Institut für Chemie, Theoretische Chemie/Quantenchemie

Sekr. C7, Strasse des 17. Juni 135, 10623 Berlin (Germany)

E-mail: [email protected]

Supporting information for this article is available on the WWW under

https://doi.org/10.1002/open.202200146

article under the terms of the Creative Commons Attribution License, which

permits use, distribution and reproduction in any medium, provided the

original work is properly cited.

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atom. It should also hold for the more electronegative aromatic

CH groups as in benzene or toluene, even in the absence of

electronegative substituents,[15] but enhanced in their

presence.[16]

If we discard small, multiply charged anions,[10a] which are

unlikely to dissolve in organic solvents, fluoride-like species may

be expected to exhibit the largest CH···X solvent-solute

interactions,[9] as fluoride concentrates negative charge density

on the smallest conceivable volume. In a recent combined

experimental and computational study[17] of polyhalogen anions

[EFx](E=Cl, Br, I; X=2, 4, 6) we found that using suitable DFT

approaches and continuum solvent models allowed us to

reproduce well the 19F NMR shifts with X=4, 6 to within about

10–15 ppm but not with X=2. In the latter case our

computations underestimated the shifts systematically by about

50–60 ppm at our best DFT level used (with the LH12ct-

SsifPW92 local hybrid functional[18] and large basis sets). As

relativistic effects were found to be small, and such discrep-

ancies are clearly outside the expected accuracy of functional

and basis set,[19,20] we suspected that specific solvent interac-

tions in the experimentally used MeCN, that are not covered

adequately by the standard COSMO solvent model[21] used, are

responsible for the differences. We will show this to be the case

below by using microsolvated cluster models. The differences

between X=2 versus X=4, 6 in these systems intrigued us, as

they suggested that the negative charge on fluorine may

determine how well or how poorly standard solvent models

may reproduce these effects. Similar specific solvent interac-

tions can be inferred from recent ab initio molecular dynamics

studies of the bifluoride ion [FHF]in deuterated dichloro-

methane (CD2Cl2).[22] Here an explicit quantum-mechanical treat-

ment of solvent molecules was found as well to be necessary to

reproduce the experimental 19F NMR shifts in solution, even

though the main focus of that work was on the (a-)symmetry of

hydrogen bonding within the anion.

Properties like NMR shifts are important probes of molecular

interactions, and the need to include solute-solvent interactions

quantum-mechanically in some but not in other cases signals a

more general challenge for computational studies in that field.

Consider, for example, a chemical reaction where the anionic

character on a fluorine atom (or on some other very electro-

negative atom) varies for different intermediates or transition

states. Then standard computational treatments using continu-

um solvent models will certainly not be adequate, and an

appropriate treatment of microsolvation becomes mandatory.

As we will see below, a force-field based treatment of the

solvent, as in QM/MM simulations or related approaches, is also

insufficient.

To obtain more insight, we use here microsolvated model

clusters for anionic fluorine species and select MeCN as organic

solvent and CH-bond donor, as it is often used to dissolve such

species (see Ref. [11] for a recent computational study of

interactions between one acetonitrile molecule and chloride). In

addition to the anions [ClFx](X=2, 4) that were part of the

abovementioned study,[17] we will evaluate such effects for the

free fluoride ion, and for the bifluoride ion. We will concentrate

on MeCN, to avoid complications due to halogen bonding, as is

possible for DCM. For the fluoride ion we will compare also to

aqueous solution, as experimental evidence suggests a larger

deshielding solvent effect on the 19F shift in organic solvents

such as MeCN compared to water,[23] which seems interesting to

understand.

Computational Details

Initial estimates of the average number of solvent molecules

expected around a given species were obtained using 3D-RISM-SCF

calculations,[24] where the solute is treated at the BP86-D3(BJ)/TZ2P

level[25,26,27] and the solvent at the 3D-RISM level based on OPLS

force field parameters, either using a united atom (UA) approach[28]

or the parameters obtained from the LigParGen web server[29,30]

employing 1.14*CM1A-LBCC[31] charges and the all-atoms (AA)

approach. All these computations used a modified version of our

recent 3D-RISM-SCF implementation[32] in the ADF engine[33] of the

AMS program package[34] – a code based on Slater-type-orbital

basis sets. These modifications are part of the 2022.1 release. In all

calculations, the 3D-RISM equations were solved on a Cartesian grid

with 128 points in each direction and a spacing of 0.25 Å using the

KH closure[35] and solvent susceptibility functions obtained from

DRISM calculations[36] employing the hypernetted chain (HNC)

closure.[37] The Lennard-Jones parameters of the solute atoms were

taken from Ref. [38], using special parameters for the H in FHF(σ=

1.0 Å, ɛ=0.056 kcal/mol). The electrostatic potential obtained from

the fitted electron density of the solute at the given DFT level has

been used.[32] The estimated average coordination number was

obtained by integrating the pair distribution function – either

spherically averaged around a fluorine atom or around the

molecular center of mass – up to the first minimum.

The computed average solvation numbers provided the basis for

fast meta-dynamics runs using the GFN2-xTB tight-binding

approach[39] as implemented in the CREST tool of the xtb

program.[40] Optimized structures from the latter simulations were

used as starting points for DFT structure optimizations of clusters of

the solute with varying numbers of solvent molecules. These

optimizations were done within a COSMO solvent environment (ɛ=

35.688 for MeCN, ɛ=78.355 for water) at MARIJ-BP86-D3(BJ)/def2-

TZVPP[41] level (MARIJ stands for “multipole-accelerated resolution

of the identity”), using the Turbomole program,[42,43] version 7.5.1

and newer.

Free energies of solvation were computed from the microsolvated

cluster energies following a cluster cycle[44] corresponding to the

reaction [X(MeCN)n]solv*

X(g)+[(MeCN)n]solv (and analogously for

F(H2O)n). Contributions to the free energies were obtained from

the optimized clusters by including their vibrational contributions

at the same level plus additional solvation contributions at COSMO-

RS(MeCN) level for X(MeCN)nas well as for (MeCN)n.[45] To this end,

additional single-point calculations at the COSMO and gas-phase

optimized structures were carried out. These calculations were

performed at MARIJ-BP86 level (omitting the D3(BJ) corrections)

with COSMO, setting an infinite permittivity and using the refined

COSMO cavity construction algorithm (keyword $cosmo_isorad),[45b]

as well as in the gas phase, employing def2-TZVPD[41a] basis sets for

all atoms. Based on these single-point calculations, subsequent

COSMO-RS computations to obtain ΔGsolv used the COSMOtherm

program, version C30_1201, and a BP-TZVPD-FINE level parameter-

ization (BP_TZVPD_FINE_HB2012_C30_1201). Electronic energy

contributions were refined by single-point energy calculations at

the DLPNO-SCS-MP2/aug-cc-pVTZ[46,47] level and, where computa-

tionally feasible for smaller clusters, at the DLPNO-CCSD(T)-F12/cc-

pVTZ-F12 level as reference.[48,49] These calculations used the ORCA

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program, version 4.2.1.[50] For comparison, electronic energies have

also been computed by single-point energy calculations at the

ωB97M-V/def2-TZVPP[51] DFT level. Furthermore, free energies of

solvation without the presence of explicit solvent molecules have

been computed directly with COSMO-RS at MARIJ-BP86/def2-

TZVPD level for comparison, using the settings given above. Free

energies were computed at standard conditions, i.e. 298.15 K and

0.1 MPa, and standard-state corrections were computed as SScorr=

RTln(Vm); Vm=24.46 moll1.

Using the clusters optimized at MARIJ-BP86-D3(BJ)/def2-TZVPP/

COSMO level, calculations of 19F shieldings were done with a

number of different DFT functionals that have recently been

established to perform well for the 19F shielding and shift subset (47

nuclei) of the large coupled-cluster-based NS372 benchmark.[20]

That is, we used the three local hybrid functionals cLH12ct-

SsirPW92,[18] LH12ct-SsifPW92,[18] and LH20t[52] including their cur-

rent-density response[53,54] within Dobson’s scheme[55] (denoted

cLH12ct-SsirPW92, cLH12ct-SsifPW92 and cLH20t) and with gauge-

including atomic orbitals (GIAOs[56]) as implemented in the

Turbomole code, version 7.6. pcSseg-3 basis sets were employed

for all atoms, and the computations used COSMO (MeCN, ɛ=

35.688; H2O, ɛ=8.93), as well as the MARIJ approach for the

Coulomb contribution (using “universal” auxiliary basis sets[57]). We

will preferably focus on results obtained with the cLH12ct-SsirPW92

local hybrid functional. For free Fand for HF, it provides 19F

shielding constants that agree with high-level CCSD(T)/pcSseg-3[58]

results to within about 1 ppm, and for LiF to within ca. 3 ppm.[20] Its

mean absolute error for the full 19F subset of the recent NS372

benchmark is 9.7 ppm.[20] This should be compared to 5.2 ppm for

MP2 and to 9.0 ppm for the top-performing[20,59] double hybrid

DSD-PBEP86,[60] which both require substantially higher computa-

tional effort and indeed exhibit somewhat larger deviations from

the benchmark data for HF (in the latter case also for LiF). For

comparison we also used the BHLYP global hybrid functional[61] that

has previously been used often for 19F NMR parameter

computations[62] but does not perform as well as the three local

hybrids.[19,20,53,54] Computations without explicit microsolvation using

COSMO or the self-consistent version of COSMO-RS, D-COSMO-

RS,[63] were also done for comparison at the otherwise identical

levels. Additional computations of 19F shieldings using 3D-RISM-SCF

as solvent model without explicit solvent molecules used ADF/AMS

at BHLYP/QZ4P-J//BP86-D3(BJ)/TZ2P level.

To transform computed 19F absolute shielding constants σinto

chemical shifts δrequires a value for the absolute shielding σref of

the reference standard used experimentally. For 19F NMR this is

nontrivial, as a direct computation of the absolute shielding

constant of neat liquid CFCl3is required. In this work we decided to

indeed use reference shieldings for CFCl3computed directly at the

given level, using structures optimized at the MARIJ-BP86-D3(BJ)/

def2-TZVPP level with COSMO (ɛ=2.315 for liquid CFCl3[64]) to

model the liquid environment. Shielding computations also used

COSMO(CFCl3). The obtained reference values are: 186.3 ppm

(cLH12ct-SsirPW92), 189.5 ppm (cLH12ct-SsifPW92), 184.6 ppm

(cLH20 t), and 187.2 ppm (BHLYP).

We have carefully considered but ultimately not applied an

alternative scheme for obtaining a shielding for liquid CFCl3

indirectly via the secondary standard of gaseous dilute HF at 300 K

that we want to share here for scientists interested in computing

19F NMR shifts in other contexts: the relative shift of HF(g, 300 K)

with respect to neat liquid CFCl3can be inferred to be 217.02 ppm

from a relative shift of HF(g, 300 K) against SiF4(g, 300 K) of 46.85�

0.35 ppm,[65] and a more recent relative shift of SiF4(g, 300 K) versus

CFCl3(l, 300 K) of 170.17 ppm.[66] For the absolute shielding of HF(g,

300 K) we use a nonrelativistic value of 409.7 ppm computed from

an equilibrium shielding of 419.384 ppm obtained at CCSDTQ/CBS

level (with corrections for quintuple excitations) and 300 K rovibra-

tional corrections at CCSD(T)/CBS level of 9.677 ppm.[67] Using this

shielding value provides us with a reference shielding value of

192.7 ppm for neat liquid CFCl3. We assume that this is an

appropriate reference for shielding computations that neglect

relativistic effects, as we expect computed relativistic effects of ca.

+4.6 ppm[67] to be essentially atomic in nature (a so-called heavy-

atom effect on the heavy-atom shielding, HAHA[68]) and to therefore

cancel out by taking the experimental shift of HF(g) vs. CFCl3(l) into

account to obtain our reference shielding. When relativistic

corrections would be included in the actual shielding computations,

the reference value would have to be increased accordingly. Note

that this alternative reference shielding value is a few ppm larger

than the directly computed ones (see above), and it would thus

lead to slightly lower relative shifts. We note furthermore in passing

that all σref values discussed here are much lower than the MP2-

based gas-phase value of 217.9 ppm used in the MP2 computations

of fluoride solvent shifts in Ref. [23], explaining our more negative

shifts for free fluoride compared to the 260 ppm given in that

work.

Natural population analyses (NPA) and natural bond orbital

analyses (NBO)[69] for the clusters F(H2O)6and F(MeCN)8were

carried out at the BP86-D3(BJ)/def2-TZVPP level using the NBO3.1

routines available in the Gaussian16 program, revision A.03.[70] MO-

based analyses of the shielding constants computed at GIAO-BP86/

pcSseg-2//MARIJ-BP86-D3(BJ)/def2-TZVPP level with Turbomole

were carried out by interfacing to the in-house MAG code.[71]

Alternative analyses using localized MOs at IGLO-level (individual

gauges for localized orbitals[72]) were not as informative, and we will

thus concentrate on the GIAO-based canonical MO analyses. The

Turbomole MOs have been generated with convergence criteria

scfconv 109, convergence of the density matrix to 107, and

gridsize m5 (internal settings). Harmonic vibrational spectra for

cluster models were computed using the NumForce subroutine at

MARIJ/BP86-D3(BJ)/def2-TZVPP/COSMO level with displacements of

0.02 a.u. Spectra are obtained with Gaussian broadening and a full

width at half maximum of 4 cm1using the Gallier tool included in

Turbomole.

Results

Fluoride in acetonitrile compared to water

We start with the fluoride ion as the simplest solute. For Fin

MeCN our 3D-RISM-SCF computations suggest an average

coordination by 9–10 MeCN methyl groups in the first solvation

shell for both UA and AA approaches. All-atom calculations

show that a bit more than 1 in 3 of the attached H atoms is in

close contact with the fluoride ion (using a maximum F···H

distance of 2.7 Å), suggesting each methyl group to contribute

one CH bond oriented towards the fluoride (see Figures S1, S2

in Supporting Information for the computed radial distribution

functions). This rather large coordination number is indeed

confirmed by the GFN2-xTB MD simulations and preoptimiza-

tions, which show binding of up to eight or nine solvent

molecules in the first shell. DFT- and DFT-COSMO-optimized

clusters tend to retain this picture. The F-(MeCN)9cluster has all

nine MeCN molecules contributing to the coordination (Fig-

ure 1). For n=10, 11 we see only eight molecules coordinating

directly to fluoride, with 3–4 somewhat shorter CH···F contacts

of around 1.98 Å and the others somewhat longer, 2.04 Å (see

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Figure 1 and Table S1; for n=9 a somewhat different arrange-

ment with overall longer distances is found).

The exergonicity of the free binding energies of the solvent

molecules in the F(MeCN)nclusters increases very quickly for

smaller n and then more slowly (Figure 2 and Table S2). The

curve dips at around n=7–9, confirming completion of the first

solvation shell at around this number. Note that the embedding

of both the clusters and the cluster of MeCN molecules without

fluoride by the COSMO-RS solvent model is required to obtain

these qualitatively correct curves, and it is mandatory to use a

“cluster cycle” (see Computational Details). If one uses a

“monomer cycle” according to the reaction [X(MeCN)n]solv*

X-

(g)+n[(MeCN)]solv rather than the cluster cycle, the most

negative free energies (Table S3) are obtained for smaller n

(around n=5 for F), and the curves then bend up towards

zero for larger n values. This incorrect behavior, which is shown

in Figures S3, S4 (without and with COSMO-RS embedding; see

also Table S3) in Supporting Information and is similar to curves

obtained for microsolvation of anions by CHF3,[9] is an artefact

of an exaggerated translational entropy for the monomer

treatment. The even slightly larger coordination number given

by 3D-RISM-SCF might be attributed to the somewhat larger

CH···F bond length (maximum of the RDF, Figure S1). What is

also noticeable is the rather steep negative slope from n=1 to

n=2, which is consistent with the steep positive slope in that

area for the 19F shift changes (Figure 2). A direct computation of

the solvation free energy of Fin MeCN with COSMO-RS,

without explicit solvent molecules, gives 375.2 kJmol1. This is

somewhat below the expected asymptote of the cluster-based

free-energy curve in Figure 2, and it agrees well with an

experimental solvation free energy range of 383 kJmol1to

389 kJmol1for Fin MeCN obtained from the known range

in aqueous solution (454 kJmol1[73] to 460 kJmol1[74]) and

the standard Gibbs free energy for the transfer of fluoride from

water to MeCN (+71 kJmol1at 298 K).[75] Given the uncertain-

ties involved in the explicit calculations on the microsolvated

cluster models (e.g., neglected dynamical averaging, see below,

or configurational entropies) as well as in the parametrization of

Figure 1. Examples of microsolvated clusters X(MeCN)nwith relevant sizes (structures optimized at COSMO-MARIJ/BP86-D3(BJ)/def2-TZVPP level).

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COSMO-RS, this may be considered close agreement. We note

in passing that DLPNO-CCSD(T)-F12 gives about 13 kJmol1

more negative solvation free energies for a given n than the

DLPNO-MP2 values used to draw the curves in Figure 2

(compare Figure S5 in Supporting Information for electronic

binding energies; BP86-D3(BJ) and ωB97X-D give still larger

binding energies; see also Table S2), bringing the micro-

solvated-cluster value to around 365 kJmol1, into even closer

agreement with the implicit COSMO-RS value and experiment.

We note in passing that only for fluoride, the COSMO-RS value

is more negative than the (COSMO-RS-embedded) microsol-

vated cluster value, while this reverts for the other anions

discussed below (see Figure S6).

The experimental 19F NMR shifts of fluoride in different

solvents have been studied by Christe and coworkers (based on

dissolving tetramethylammonium fluoride),[76] and by others,[77]

and have been summarized and compared to MP2 calculations

of fluoride with one coordinated solvent molecule (and up to

six coordinated molecules for water) in Ref. [23]. Interestingly,

the measured 19F shifts of fluoride in organic solvents are larger

(less negative) than those in water or in alcoholic solvents (e.g.

74 ppm in MeCN, 109 ppm in DCM, 119 ppm in water, and

149 ppm in MeOH). That is, the deshielding solvent contribu-

tion in MeCN is particularly large. It was pointed out that these

solvent shifts do not correlate with the binding energies of the

corresponding solvent molecules to fluoride.[23] The MP2

calculations of the monocoordinated clusters reproduce the

trends but of course underestimate the solvent shifts. Our

computed shifts for n=8 (65.9 ppm) and n=9 (82.8 ppm) at

LH12ct-SsirPW92/pcSseg-3 level bracket the 74 ppm[23] exper-

imental shift value in solution and are clearly within the

expected accuracy margin of the method.[20] This corresponds

to a remarkable solvent shift of more than 200 ppm.

The shifts at n=8, 9 are thought to realistically reflect the

most probable situation in solution. This is borne out by

additional computations for all clusters obtained in xTB meta-

dynamics simulations with 12 MeCN molecules, which we

summarize in Figure S7 in Supporting Information. Energies at

either the BP86-D3/def2-TZVPP/COSMO level used for the

optimizations, or in LH12ct-SsirPW92-D3/pcSseg-3/COSMO sin-

gle-point calculations to match the level used for the shift

computations, clearly show that clusters with n=8, 9 provide

the lowest energies, by about 10 kJmol1compared to n=7

(the few n=6 clusters have even higher energies). The BP86-D3

energies favor somewhat structures with n=8, giving shifts

centered around ca. 65 ppm. The LH12ct-SsirPW92-D3 ener-

gies favor more structures with n=9, which lead to shifts closer

to 80 ppm. I.e. the two coordination numbers give shifts

slightly above or below the experimental value of 74 ppm

and generally match experiment to within the accuracy of the

method used in the shift computations. They are reasonably

well represented by the single-structure results shown in

Figure 2, given that the shifts for a given n only show a small

spread with different structures. This supports the approxima-

tion of using the “best” static cluster in this case, an

approximation made also for the other ions, given that to carry

out full MD simulations for all cases is beyond the scope of the

present work. We note that during revision of this paper,

Spicher et al.[78] reported a new, automated workflow for the

generation of microsolvated clusters, called “quantum cluster

growth”. Such algorithms provide more freedom to include

Figure 2. A comparison of computed solvation free energies ΔGsolv (DLPNO-SCS-MP2/aug-cc-pVTZ/COSMO-RS//MARIJ-BP86-D3(BJ)/def2-TZVPP[/

COSMO(MeCN)] level using a cluster cycle) and 19F NMR chemical shifts (GIAO-cLH12ct-SsirPW92/pcSseg-3/COSMO(MeCN)//MARIJ-BP86-D3(BJ)/def2-TZVPP/

COSMO(MeCN) level) of microsolvated anions in MeCN as a function of cluster size. See Supporting Information Table S2 for thermochemical data, Table S4

for NMR shifts, and Table S3 for comparative thermochemical data using a monomer cycle. Experimental shifts and shift ranges are shown at the right-hand

y-axis.

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conformer averaging in a computationally affordable manner,

and we will investigate its use in our ongoing work.

Shifts for DFT-optimized clusters have been computed with

increasing cluster size up to n=9 (Table S4, Figure 2). In

Ref. [23] the solvent deshielding was linked to the larger

shielding anisotropy in the monosolvated complexes used to

model the effects. However, as we see in Table S5, the

anisotropy only reflects the unsymmetrical coordination (see

Figure 1 for some example cluster structures) and overall

decreases with increasing coordination number, albeit in an

uneven way due to the symmetry and structure of the given

static solvate complex used. Yet, the isotropic shifts increase up

to n=6, 7 before levelling off only slightly for n=8, 9 (Figure 2).

Moreover, the computed shielding anisotropies for the larger

clusters are much smaller (Table S4) than the overall solvent

shifts (Table S4, Figure 2) and thus cannot be the major reason

for the latter. Indeed, in isotropic solution the shielding

anisotropy of a fluoride ion will vanish in the dynamical

average. The mechanism by which solvation leads to low-

frequency shifts thus clearly must operate also in the absence

of anisotropy, and we will analyze it in more detail below.

In aqueous solution, which we also studied for comparison,

3D-RISM-SCF suggests an average of six hydrogen bonds from

water molecules to fluoride (see Figure S8), while previous ab

initio MD simulations give results closer to n=5.[79] Other

microsolvated cluster models even suggest n=4 to be the

predominant number of OH···F hydrogen bonds in the first

solvation shell.[80] Our computations on F(H2O)ncluster models

embedded in COSMO-RS surroundings show the Gibbs free

energies of solvation to still drop after n=6, but in an irregular

fashion (Figure S9, Table S6 in Supporting Information), even

though closer inspection of the clusters suggest that indeed

only four water molecules are coordinated to Fin the larger

clusters. This suggests that the contributions from the COSMO-

RS model are somewhat smaller than those contributed by

adding more explicit solvent molecules to the clusters in the

second solvation shell. However, the large scatter in the curve

suggests that the static clusters in any case do not provide an

as good description as they did for MeCN (see above). Free

solvation energies approach the experimental range of around

460 kJmol1(see above) but do not quite get there (Table S6,

Figure S9). The “pure” COSMO-RS value of 437.2 kJmol1

agrees well with the cluster-based numbers but is also slightly

too small in absolute value. We note in passing, that also in this

case the free energies of the “monomer cycle” agree much less

with experiment (Table S6) than those of the “cluster cycle”

shown in Figure S9.

The 19F shifts increase sharply for small n and seem almost

saturated at around n=6 (Figure S9, Table S7). At this n, the

chosen cLH12ct-SsirPW92/pcSseg-3 level provides a shift of

150 ppm. Further deshielding by up to 10–15 ppm is seen for

the larger n values. This brings us to around 130 ppm to

140 ppm, still somewhat below the experimental shift of

119 ppm of fluoride in aqueous solution.[23] Overall, the

solvent shift of around 140–150 ppm is in any case overall less

pronounced than the more than 200 ppm we find for MeCN

(see above). An explanation will be provided below.

Computations of Fwith only a COSMO or D-COSMO-RS

solvent model fail completely to capture the solvent shifts, both

in MeCN and in water. They give less than 2 ppm solvent shift

for both solvents (1.4 ppm in water for COSMO, 1.7 ppm for

D-COSMO-RS). A 3D-RISM-SCF treatment of the solvents does

not give any solvent effects on the 19F shifts. This is to be

expected, since the spherical symmetry of the solute gives a

spherical solvation potential, which in turn creates no polar-

ization of the electron density of the fluoride ion compared to

the gas phase.

That is, as previously noticed for the gas-liquid 17O shift of

water,[32] electronic coupling of the solute and solvent orbitals

in the magnetic field must play a decisive role for the solvent

shifts in such strong-interaction cases. We have analyzed these

effects in more detail using the F(MeCN)8and F(H2O)6clusters

(the latter cluster with S6symmetry, taken from Ref. [23], is not

a minimum but gives a good overall solvent shift and renders

analyses relatively transparent). We first note that the solvent

shifts arise purely from paramagnetic shielding contributions σp

(Table S8). For further analyses, we have used a breakdown into

orbital contributions using the implemented tools in the MAG

code,[71] at the quantitatively less accurate GIAO-BP86/pcSseg-

2[58] level (the more accurate functionals are not implemented

in that code). For the F(H2O)6cluster, the deshielding

compared to free fluoride ion is distributed over a substantial

number of occupied canonical MOs (some MO plots are

provided in Figure S10 in Supporting Information). All of them

have some fluorine p-orbital character mixed with various water

oxygen-based orbitals. This reflects the similar electronegativity

of fluorine and oxygen, which places their valence orbitals in a

similar energy range and thus leads to extensively delocalized

canonical MOs for the cluster. While it confirms extensive

solute-solvent orbital mixing, further analyses in terms of

occupied-virtual MO couplings turn out to be complicated.

Analyses are more straightforward for the F(MeCN)8cluster,

where the fluorine p-orbital character concentrates more in the

three highest, almost degenerate occupied canonical MOs,

which indeed dominate the large deshielding compared to free

fluoride (in particular the HOMO and HOMO-1; see Figure 3 for

MO plots). The dominant contributions to σpfrom occupied/

virtual MO couplings arise from these three occupied MOs and

from three virtual MOs. The latter do indeed have substantial

σ*(CH) character in the CH-bonds coordinating to fluoride,

albeit mixed with π*(C�N) character of these coordinated

MeCN molecules (Figure S10). Alternative analyses using Boys-

localized MOs[81] within an IGLO[72]-BP86-based scheme confirm

the dominance of occupied LMOs with fluorine p-orbital

character, but the couplings tend to be smeared over a larger

number of (canonical) virtual MOs, rendering the analyses less

transparent. Overall, our analyses clearly confirm couplings

between fluorine lone pair orbitals and low-lying solvent based

virtuals for MeCN solvates. This holds also analogously for the

interpretation of the 19F solvent shifts of the other species

covered in this work (see below). We will not discuss extensive

shielding analyses for these other species. We note here already

that both the free solvation energies and the shift effects in

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MeCN are largest for fluoride compared to the solutes discussed

further below.

Bifluoride anion

Turning to the bifluoride ion FHF, we note that its solvation in

CH2Cl2and CCl4has been subject to recent AIMD simulations.[22]

While that work had its main focus on changes to the potential

of the strong hydrogen bond within the solute, computed 19F

shift results clearly also confirmed appreciable deshielding in

both solvents even for symmetrical structures of the solute, on

which we focus in the present work. Note that those authors

found that the average coordination of CH bonds to the

fluorine atoms tended to be close to two for each of the

fluorine atoms,[22] corresponding to n=4 in the present context.

It was speculated that steric interactions between the coordi-

nated solvent molecules determine average dihedral angles

between their CH···F vectors and thereby limit the average

coordination.

Here we focus on solvation in MeCN. 3D-RISM-SCF suggests

an average number of CH···F interactions n=10 when integrat-

ing to the minimum after the second maximum (Figure S2b, the

second maximum includes the sites coordinating to the other F

atom, assuming 1 in 3 H sites to form a CH···F contact), that is,

five hydrogen bonds per fluorine atom. Integrating only to the

first minimum results in an average of 3 close interactions

(again assuming 1 in 3 H sites to form a CH···F contact). The

GFN2-xTB preoptimizations and the subsequent DFT and DFT+

COSMO optimizations with up to 12 solvent molecules agree

with this notion, as maximally 10–11 short CH···F contacts below

2.3 Å are found, and there is a tendency of solvent molecules to

bind in a second solvation shell when higher coordination

numbers are explored (Table S1 in Supporting Information). The

DLPNO-SCS-MP2-based free energies behave similarly as for F

but progress more slowly down to ca. 290 kJmol1(Figure 2,

Table S2), while DLPNO-CCSD(T)-F12 gives even about

20 kJmol1more negative free energies. COSMO-RS without

explicit solvent molecules provides a somewhat less negative

free solvation energy of 263 kJmol1, again (see above for

fluoride) in agreement with the observation that the free

energies of the microsolvated cluster models still grow more

negative at n=14, even though this involves already solvent

molecules in a second shell. That is, the “pure” COSMO-RS

treatment seems to underestimate slightly the overall binding.

“Monomer-cycle” free energies again exhibit an incorrect

behavior (Table S3, Figures S4, S5)

The 19F NMR shifts tend to increase slowly up to n=10, 11

(Figure 2, Table S4), where they reach ca. 135 ppm (compared

to experimental shifts of 145 ppm to 148 ppm[82]), a solvent

shift of about +84 ppm compared to the gas-phase anion

(Table S4), less than half the solvent shift found for fluoride (see

above). This may be compared to an average solvent 19F shift in

CH2Cl2of +79 ppm from the AIMD simulations in Ref. [22].

COSMO and D-COSMO-RS give a solvent shift of about 3 ppm,

3D-RISM-SCF of less than 2 ppm, both methods again failing

completely to capture the orbital couplings and thus the

explicit solvent effects on the shifts, as can be expected. Note

that we have not varied the asymmetry of the FHF moiety, in

contrast to the AIMD simulations in Ref. [22], which showed a

coupling of an asymmetry in that nominally symmetrical

hydrogen bond and an asymmetric solvation shell. We conclude

thus that the bifluoride ion also exhibits large solvation shifts in

MeCN, but less so than fluoride, consistent with the overall

smaller binding/solvation energies.

ClF2compared to ClF4

For the ClF2anion, which originally stimulated our interest in

these types of interactions of fluoride-type fluorine atoms with

the CH-bonds of organic solvents,[17] 3D-RISM-SCF gives a lower

average number n=2 of close CH···F interactions (see also

Figure S2, assuming 1 in 3 H sites to form a CH···F contact) than

for the related FHFanion, where an identical analysis gives n=

3 (see above). The second minimum in the RDF would

accommodate 9 contacts. Overall, the RDF shows less pro-

nounced structure than for FHF. This trend is consistent with

the cluster models, which provide only up to 6–7 short F···H

distances below 2.3 Å, with additional solvent molecules

moving further away from the fluorine sites (Table S1 in

Supporting Information). The computed free energies for the

microsolvated clusters nevertheless also go down further, even

at n=12, beyond 260 kJmol1(Figure 2, Table S2), where they

have clearly not yet converged. “Pure” COSMO-RS suggests a

free solvation energy of 240.9 kJmol1, so the shape of the

curve is again consistent with the microsolvation beyond the

first solvent shell providing a slightly larger stabilization than

Figure 3. Structure of the optimized F(MeCN)8cluster used and isosurface

plots (0.03 a.u.) of relevant occupied and virtual canonical molecular orbitals

contributing to the 19F shielding tensor.

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the COSMO-RS embedding. Overall the solvation energies are

only slightly smaller than those discussed above for FHF.

The solvent effects on the 19F NMR shifts still increase slowly

up to n=11 (Figure 2, Table S3) where the calculations would

suggest them to be about 73 ppm, also only slightly less than

those for FHF(see above). However, possibly adding further

solvent molecules to the second solvation shell beyond n=6, 7

leads to an unbalanced coordination sphere. It thus seems

prudent to focus on the shifts obtained for n=6, 7. Then we

arrive at shifts between 115 ppm and 121 ppm, which is

reasonably close to the experimental shift of 125 ppm. This

corresponds to a somewhat smaller and more realistic and still

appreciable solvation shift of 47–53 ppm. COSMO and D-

COSMO-RS give a solvent shift of 4.8 and +0.5 ppm,

respectively, while 3D-RISM-SCF gives about +5 ppm. All of

these methods are thus again unable to recover most of the

actual solvent shifts. We note that our previous computations

using COSMO(MeCN) in Ref. [17] for this and related EF2anions

left deviations from the experimental shifts in solution of about

50–70 ppm using a similar local hybrid (LH12ct-SsifPW92, still

without current response). The present computations clearly

show that this is due to the orbital couplings caused by specific

CH···F hydrogen bonds not being covered by implicit or force-

field-based solvent models.

In that same work, the 19F shifts of anions EF4in MeCN

could be reproduced to within ca. 10 ppm using a COSMO

model for the solvent.[17] This suggests that the specific CH···F

interactions are much less pronounced for the tetrafluoro

species (as well as for the hexafluoro anions studied in the

same paper), and it was argued that this reflects a less negative

charge on fluorine (see below). 3D-RISM-SCF indeed suggests

only an average of 1.5 close CH···F contacts for ClF4in MeCN

overall for the four fluorine sites, and a much shallower RDF

overall than for the other three anions (Figure S2). This is

consistent with a much less structured solvation shell. While

cluster models can be constructed for many more solvent

molecules, they tend to feature only 6 short contacts below

2.3 Å (Table S1), about 8–10 below 2.5 Å. The free binding

energies still go down at n=12 (DLPNO-SCS-MP2 ca.

251 kJmol1), but this also again involves second-shell micro-

solvation (Figure 2, Table S2), and the “pure” COSMO-RS value

of 223.6 kJmol1indicates again less binding. For both ClF2

and ClF4the “monomer cycle” is again unsuitable (Table S3,

Figures S3, S4).

The solvent effects on the 19F shifts in ClF4are much

smaller than those for ClF2, peaking at about 18 ppm at n=9,

while at a more realistic n=6 the solvation shift is 10 ppm

(Figure 2, Table S4), leading to a shift of 78 ppm compared to

the experimental value of 67 ppm. This explains why even a

COSMO-based calculation without explicit inclusion of solvent

molecules gave already reasonable agreement with experiment

in Ref. [17]. In the present work, COSMO gives a solvent shift of

4.9 ppm, D-COSMO-RS 2.0 ppm, 3D-RISM-SCF (OPLS-AA) ca.

+11 ppm.

NMR shifts of solvent nuclei

While the effects on the shifts of the coordinating MeCN

molecules will be difficult or impossible to observe experimen-

tally, due to the expected fast exchange on the NMR time scale

and the likely dominance of the bulk solvent signals, we

summarize the computed data nevertheless in Tables S9–S13 in

Supporting Information. As one might expect, the effects due

to the charge transfer from the anion to a given solvate

molecule decrease with increasing cluster size, as the effects are

somewhat “diluted” over more interactions. The 1H shifts of the

coordinating hydrogen atoms are computed to have increased

shifts compared to the noncoordinating ones by about 2–

3 ppm for F, by about 0.8 ppm for FHFand by about 0.4 ppm

for ClF2(Tables S9, S10), while noncoordinating hydrogens

show very small deviations from an (MeCN)ncluster. The

computed methyl and nitrile 13C shifts are within less than

1 ppm from a pure solvent cluster (CH3CN)8(Tables S11, S12),

the nitrile 15N shifts within less than 2.5 ppm (Table S13). Any

ion-induced shifts for these nuclei are thus even less likely to be

observable experimentally.

IR spectroscopic fingerprints for the interaction

While weak CH···X hydrogen bonds tend to give blue-shifted CH

stretching frequencies in vibrational spectra,[83] the larger

charge transfer into the σ*(CH) orbitals for stronger charge-

assisted interactions with anionic acceptors is expected to lead

to strongly red-shifted bands with enhanced intensity.[5,6] This

should certainly hold for simple halide ions in organic solvents,

and the only question is, whether these shifted bands are

sufficiently strong in comparison with the bulk spectra. As an

exploratory computational examination, we have computed the

harmonic vibrational spectra of the F(MeCN)8cluster in

comparison with clusters of the heavier halides Cland Brand

a cluster (MeCN)8without a halide ion as a rough approximation

for the bulk liquid. The simulated spectra at BP86-D3(BJ)/def2-

TZVPP/COSMO level are compared in Figure 4. It is clear that

Figure 4. Computed harmonic IR Spectra of X(MeCN)8clusters (X=F, Cl, Br)

in comparison with an (MeCN)8cluster (BP86-D3(BJ)/def2-TZVPP/COSMO).

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the halide ions generate red-shifted, very intense CH stretch-

ing bands that are not present in the (MeCN)8cluster (nor in an

isolated MeCN molecule). Both the red-shift by several

hundreds of cm1and the intensity increase by an order of

magnitude are clearly most pronounced for fluoride. Such

bands might well be observable even in the presence of the

bulk vibrations. We note in passing that similar computational

frequency and intensity shifts have also been found for

molecular complexes of halide ions with fluoro- or chloroform,

with fluoride again causing the largest effects.[10d]

Comparison of charge transfer and polarization in F(MeCN)8

and F(H2O)6clusters by NPA/NBO analyses

The fact that the 19F NMR solvent shifts of fluoride in MeCN are

larger than in water prompted us to compare the amount of

charge transfer in the respective cluster models by NBO

analyses (BP86/pcSseg-2//BP86-D3(BJ)/def2-TZVPP level, Ta-

ble 1). Nuclear shieldings are a response property and thus do

not necessarily follow the ground-state charge on the NMR

atom of interest.[84] Still, such charge analyses can be useful.

Interestingly, the negative NPA charge on fluorine is indeed

smaller for the MeCN-based cluster. However, the average

charge transferred to one solvent ligand is slightly larger for the

aqueous cluster (0.026 e) compared to the MeCN-based cluster

(0.023 e), and it is the larger number of solvent molecules that

are able to coordinate for the organic solvent that overall

depletes somewhat more charge from the fluoride than for the

aqueous case (note that the actual n in water may be 4 or

5,[79,80] so the disparity in the average coordination may even be

slightly larger than for the chosen cluster sizes).

For the latter, we see a redistribution of negative charge to

the water oxygen atoms within the coordinated molecules, and

the coordinating hydrogen ends up with an even more positive

charge than for a free water molecule. This behavior is

consistent with the behavior for a typical hydrogen bond, which

enhances the ionicity of the bond within the hydrogen-bond

donor. That is, in addition to moderate charge transfer from the

solute to the solvent molecules, charge becomes more

polarized within the coordinating solvent, accumulating more

negative charge on oxygen (which in turn will enhance further

interactions with the next solvent shell, not covered by the

cluster model). The same observations can be made for the

MeCN case: in addition to the charge transfer from fluoride to

the solvent molecules, the charge within the solvent molecules

becomes more polarized, accumulating charge on the nitrogen

and methyl carbon (C2) atom, while depleting charge from C1

and the hydrogen atoms, particularly on the coordinating ones

(H1). This underscores the character of a strong CH···F hydrogen

bond with an essentially conventional build. Perturbation-

theoretical analyses of the interactions between the strictly

localized NBOs and the composition of the resulting natural

localized MOs[69] (NLMOs) confirm expectations that the charge

transfer from fluoride to the solvent molecules involves

donation into the σ*(HO) and σ*(HC) antibonding orbitals of

the coordinating OH or CH units, respectively, consistent with

the MO couplings responsible for the 19F solvation shifts (see

above).

The interactions for the other anions are analogous albeit

less pronounced, regarding both the charge-transfer and the

polarization within the MeCN molecules, consistent with the

reduced negative fluorine NPA charges for the free gas-phase

anions of 0.756 (FHF), 0.591 (ClF2) and 0.529 (ClF4).

Conclusions

The element fluorine occupies a special place in the Periodic

Table, not only as the most electronegative element but also

due to its compact charge concentration within a small radial

space. Once the accumulation of negative charge becomes very

large, the resulting fluoride-like units exhibit particularly strong

CH···F hydrogen-bonding interactions with the CH-bonds of

organic solvents, which are not captured by the usual

continuum solvation models nor by force-field-based models. In

this work we have largely concentrated on acetonitrile, but the

effects are clearly observable for other CH-bond containing

solvents as well, CH2Cl2or the haloforms being other examples.

Computational studies have already pointed out that

anionic acceptors Xcan enhance CH···Xinteractions to the

extent that they have to be considered strong, charge-assisted

hydrogen bonds (see literature pointed out in the Introduction).

The focus of the present work has been on the extremely large

and characteristic solvent effects on 19F NMR shifts generated

by these types of hydrogen bonds. It had been known that 19F

solvent shifts of fluoride in many organic solvents are larger

than in aqueous solution. Our analyses show that this is largely

due to the fact that a solvent like acetonitrile can form more

CH···F hydrogen bonds to fluoride than possible in aqueous

solution (8–9 rather than 4–6). In contrast to previous

interpretations, it is this larger number of (slightly weaker)

hydrogen-bonding interactions that leads to a larger solvation

shift, in spite of an overall somewhat smaller solvation free

energy. This is why Christe had noted that the 19F shift of

fluoride cannot be used as an indicator of its “nakedness”.

However, we do confirm that for a given solvent the 19F

solvation shifts of different anionic fluorine species correlate

with the magnitude of their solvation free energies, which are

Table 1. Relevant NPA charges of atoms and fragments for the solvent

complexes and the free solvent molecules (BP86/pcSseg-2//BP86-D3(BJ)/

def2-TZVPP)[a]

MeCN F(MeCN)8H2O F(H2O)6

Q(F) – 0.819 Q(F) – 0.843

Q(N) 0.308 0.368 Q(O) 0.905 0.975

Q(C1) +0.263 +0.294 Q(H1)[b] +0.452 +0.484

Q(C2) 0.733 0.785 Q(H2) +0.452 +0.465

Q(H1)[b] +0.259 +0.308

Q(H2) +0.259 +0.264

Q(H3) +0.260 +0.264

Q(MeCN) 0.000 0.023 (8x) Q(H2O) 0.000 0.026 (6x)

[a] Averaged over the eight and six solvent molecules, respectively.

[b] Hydrogen atom coordinating to fluoride in the cluster.

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in turn determined by the strengths of the CH···F hydrogen

bonds that correlate with the amount of negative charge on

the given fluorine atom. That is, both the solvation 19F shifts

and the solvation free energies in acetonitrile decrease along

the series F@FHF>ClF2>ClF4studied in the present

work. The 19F solvation shifts reach astounding +227 ppm for

Fand clearly require a proper quantum-chemical treatment of

microsolvation to be reproduced accurately. In contrast, the

effects of microsolvation are close to +10 ppm for ClF4, where

the negative charge is more delocalized and thus smaller on a

given fluorine atom. In the latter case these specific solvation

effects are still relatively close to the error margins of even

rather advanced DFT approaches but might be needed

accounting for in more accurate benchmark-level treatments.

And more delocalized fluoridic ions will exhibit even less

pronounced effects of microsolvation. But already for ClF2, the

19F solvation shifts of 50–60 ppm are far outside practically

achievable DFT accuracies and thus clearly have to be dealt

with.

None of the implicit or force-field-based solvent models

studied here, COSMO, D-COSMO-RS or 3D-RISM-SCF, can

reproduce these microsolvation effects on the 19F shifts, as

these involve a coupling of solute and solvent orbitals in the

magnetic-field response. This clearly requires an accurate

quantum-mechanical treatment of the directly bound solvent

molecules. In the present work, we have pre-generated the

static DFT cluster models used for the computation of both

shifts and solvation free energies by cheap tight-binding (xTB)

meta-dynamics methods available in Grimme’s CREST program,

followed by DFT optimizations. In the present case of relatively

simple anionic species, this has still led to probably reasonable

estimates of the microsolvation effects. Clearly, matters will

become less tractable for routine computational treatment for

more complicated systems that one may encounter in various

chemical applications (also for other electronegative elements

like oxygen or chlorine when they exhibit large negative

charge). This puts more emphasis on improved and expedient

methods for the generation of microsolvated clusters (as, for

example, the recent QCG algorithm, see above), short of the

costs of full AIMD simulations, to be used in mechanistic studies

of chemical reactions where the “fluoridic” character may vary

along a reaction coordinate. Thermochemistry and kinetics of

such reactions are expected to be strongly affected by differ-

ential microsolvation contributions not only in protic but also in

“aprotic” organic solvents. In contrast to the NMR shift case, in

this case we have semi-empirical methods like COSMO-RS as

reasonable albeit not perfect alternatives to obtain estimates of

solvation free energies. Finally, microsolvated cluster models

are also required to access computationally the fingerprints that

such CH···X hydrogen bonds may cause in the vibrational

frequencies and intensities of CH vibrations of the coordinated

solvent molecules.

Supporting Information Summary

Tables with additional data on structures, thermochemistry and

NMR chemical shifts, Figures on 3D-RISM-SCF radial distribution

functions, cluster models, free energies and NMR shifts as

functions of cluster size, relevant MOs for analyzing solvent

NMR shifts.

Acknowledgments

We acknowledge financial support from the CRC1349 funded by

the Deutsche Forschungsgemeinschaft (German Research Founda-

tion; Gefördert durch die Deutsche Forschungsgemeinschaft (DFG)

– Projektnummer 387284271–SFB 1349). We thank our experimen-

talist colleagues in SFB1349 on “Fluoro-Specific Interactions” for

motivating our interest in this topic.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

The data that support the findings of this study are available in

the supplementary material of this article.

Keywords: NMR chemical shifts ·solvation effects ·hydrogen

bonding ·density functional theory ·solvation free energy

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Manuscript received: June 27, 2022

Revised manuscript received: July 26, 2022

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