Pavel A Dub

Oleg A Filippov

Natalia V Belkova

Mireia Rodriguez-Zubiri

Rinaldo Poli
email: rinaldo.poli@lcc-toulouse.fr

Experimental (IR, Raman) and computational analysis of a series of PtBr2 derivatives: vibrational coupling in the coordinated ethylene and Pt-Br modes

Keywords: Platinum, Chojnacki's anion, Zeise's anion, aniline complexes, olefin complexes, vibrational coupling

 as well as the trichlorido analogue of 1, ( n Bu4P)[PtBr3(C2H4)] (1 Cl ), have been investigated experimentally by both IR and Raman spectroscopy, and theoretically by geometry optimization and normal mode analysis by the DFT approach. An analysis of the normal modes of coordinated ethylene in compounds 1, 1 Cl , 2 and 3 followed by a potential energy distribution investigation shows extensive vibrational coupling between the (C=C) and s(CH2) A1 modes in two bands at around 1510-1520 cm -1 and 1230-1250 cm -1 , the latter one having greater (C=C) contribution. The w(CH2) A1 mode, the contribution of which to the above two bands is negligible, is responsible for a lower frequency band at 995-1005 cm -1 . A complete vibrational analysis, backed up by the DFT calculations, has also been carried out on the Pt-Br stretching vibrations of the tetrabromido complex 4, the tribromido complexes 1 and 5, and the dibromido complexes 2, 3 and 6, and on the Pt-Cl vibrations of the analogous complex 1 Cl . The study illustrates the advantages of coupling high level computations to the vibrational analyses in order to make unambiguous band assignments in IR and Raman spectroscopy.

Introduction

Ethylene is a D2h-symmetric planar molecule with 12 vibrational modes distributed as 3Ag(R) + Au(inactive) + 2B1g(R) + B1u(IR) + B2g(R) + 2B2u(IR) + 2B3u(IR) (R = Raman active, IR = infrared active), the reference frame being chosen with the z axis perpendicular to the molecular plane. [START_REF] Nakamoto | Infrared and Raman Spectra of Inorganic and Coordination Compounds, Part B[END_REF] These modes can be separated into 5 stretching modes for the C=C and the 4 C-H bonds (2Ag + B1g + B2u + B3u), 4 in-plane bending modes involving the HCH and CCH angles (Ag + B1g + B2u + B3u), and 3 out-of-plane bending modes (wagging; Au + B1u + B2g).

These modes, available in many textbooks, are also given in the Supporting Information for convenience. Two Raman-active 2 modes at 1623 and 1342 cm -1 are usually attributed [START_REF] Herzberg | Molecular spectra and molecular structure[END_REF][4][START_REF] Socrates | Infrared Characteristic Group Frequencies[END_REF][6][7][8][9][10] to the Ag-type C=C stretching vibration (νC=C) and the in-plane CH2-scissoring deformation (δs(CH2)), respectively. However, vibrational coupling is expected between fundamental molecular motions that are bases of the same irreducible representation and close in frequency, thus the two above-mentioned Ag-type modes (labelled q1 and q2) include both νC=C and in-plane bending motions with different contribution as highlighted in Scheme 1. In the higher frequency band, the C=C bond stretches while the HCH angles widen (and the CCH angles narrow), whereas the opposite combination (HCH angle narrowing and CCH angle widening together with C=C bond stretching) is observed in the lower frequency band. [START_REF]bands to pure νC=C and δs(CH2) vibrations without mentioning the possibility of mixing[END_REF] On the basis of an inelastic neutron scattering analysis, the contribution of νC=C in each of these band was quantified in terms of the potential energy distribution (PED): 69 and 46 in the high and low-frequency bands, respectively. 12 A high-level normal coordinate analysis (NCA) yields a PED of 69% νC=C, 14% δ(CCH) and 17% δ(HCH) for the band at 1609 cm -1 and 33% νC=C, 30% δ(CCH) and 37% δ(HCH) for the band at 1332 cm -1 . 13 Similar values have been reported by another group. 14 The Ag-type C-H stretching combination, which mainly contributes to a higher frequency band (3022 cm -1 ) 9 , does not significantly contribute to these two bands.

An IR-active band observed at 949 cm -1 is attributed to the B1u-type out-of-plane wagging mode (ρw(CH2)). This normal mode (labelled as q3) is the only B1u-type mode in D2h symmetry and is consequently not involved in vibrational coupling. Coordination of ethylene to a metal center, however, reduces the symmetry from D2h to C2v at the most (if the metal complex has two perpendicular mirror planes, as for instance in Zeise's salt). Thus, all three basic molecular motions (from now on simply abbreviated as ν,  and ρ) become of A1-type and may mix with each other in all the above-described normal modes, the amount of mixing correlating in principle with the local symmetry perturbation, namely with the extent of deviation from planarity. In addition to an anticipated red shift for the modes with strong ν components (q1 and q2), the symmetry reduction upon coordination opens the possibility of observing these modes by infrared spectroscopy (Ag(R) → A1(R, IR)).

1623 cm -1 1342 cm -1 949 cm -1 A g A g B 1u q 1 [ C=C ,  s (CH 2 )] q 3 [ w (CH 2 )] q 2 [ C=C ,  s (CH 2 )]
Scheme 1. Three vibrational frequencies and normal mode assignments for ethylene.

Two models were initially proposed for coordinated ethylene and subsequently used in normal coordinate analyses: the first one based on the widely accepted 15 Chatt-Duncanson approach 16,17 whereby the ethylene H atoms move significantly away from the C2H4 plane; the second one, introduced by Bokii and Kukina, based on a perfectly planar arrangement for the coordinated ethylene. 18 For a variety of Pt ethylene complexes (including Zeise's salt), the band observed at 1500-1520 cm -1 was assigned to , leading Chatt and Duncanson to conclude about the "conservation of the double bond character" upon olefin coordination. 16,17 This assignment has been adopted in a few subsequent reports. [19][20][21] Conversely, the same band was attributed by other authors 22 to δ on the basis of comparisons with experimental and computational studies on (deutero) cyclopropane 23 and ethylene oxide. 24 Later, two NCA on Zeise's salt were based on the Bokii-Kukina's model. 25,26 In the first one, the experimentally observed band at 1526 cm -1 (calc. value 1528 cm -1 ) was assigned to the Ag-type q1 combination, 25 whereas in the second one the observed band at 1518 cm -1 (calc. value 1644 cm -1 ) was interpreted as a pure ν vibration. 26 In contrast with these reports, however, another NCA using the Urey-Bradley force field assigned ν, "probably coupled with δ", to a band observed at 1243 cm -1 . 27 Numerous other vibrational studies of coordinated ethylene (to Pt or other metals) appeared later, occasionally without mention of vibrational coupling, with the assignment of ν to either the 1500 cm -1 or the 1200 cm -1 band. [START_REF] Hartley | Comprehensive Organometallic Chemistry[END_REF] In more recent work, the notion that ν and δ are coupled in two different normal modes q1 and q2 has become better appreciated. On the basis of new experimental measurements on Zeise's salt, Powell et al. concluded that ν contributes to both experimentally observed bands at ca. 1515 cm -1 and ca. 1240 cm -1 and suggested that the lower frequency one (q2) includes a greater proportion of ν relative to δ. [START_REF] Powell | [END_REF] This assumption was later confirmed by the already mentioned inelastic neutron scattering study, 12 which reported PEDs for  and δ in Zeise's salt of 47 and 61 in the 1515 cm -1 band and 50 and 30 in the 1240 cm -1 band, and also by a theoretical study. 13 Note that the relative contribution of ν changes on going from free ethylene (major contribution in the higher-frequency band) to coordinated ethylene (major contribution in the lower frequency band). However, the issue was not yet settled because until then the contribution from ρ had been neglected. A new PED analysis of Zeise's salt using a larger data set yielded decompositions into 60 (δ) + 20 (ν) + 20 (ρ) for the absorption at 1515 cm -1 and 60 (ν) + 25 (δ) (with no significant contribution from ρ) for that at 1240 cm -1 . 30 A later publication proposed that two sets of three bands (either at 1517, 1241 and 1023 cm -1 , or at 1517, 1410 and 1241 cm -1 ) can be assigned to the strongly coupled ν, δ and ρ modes. 31 However, it was concluded that "at this stage we are not able to decide which assignment is more realistic", although the second set was shown to give better agreement for complex Pt(C2H4)3.

In more recent years additional publications have appeared in the literature where either one or two (but not three) bands were used to describe the C=C stretching vibration. For example, in a 1995 IR study of ethylene adsorption on Pt/Al2O3, only one band at 1205 cm -1 was chosen to represent ν (vibrationally coupled with ). 32 In another study limited to the 1515 and 1241 cm -1 bands, [START_REF] Maslowsky | Vibrational Spectra of Organometallic Compounds[END_REF] it was pointed out that the strength of the ethylene-metal interaction determines which motion is dominant in each normal mode and that there is a crossover in relative importance. In a SERS (surface-enhanced Raman spectroscopy) study of ethylene on Pt electrodes, the observed bands at 1495 and 1210 cm -1 were confidently contributed to vibrationally coupled ν (+δ) and δ (+ν). [START_REF] Mrozek | [END_REF] However, the authors state that "usual assignment of the higher and lower frequency bands to ν and δ, respectively, is largely formal and is sometimes reversed". 35 Finally, in two very recent contributions on Zeise's salt 36 and its tris-C6F5 analogue, 37 the authors reported three bands as having contribution from ν, but with no mention of the ρ mode. In the first of these contributionsa variable pressure studythe weak 1515 cm - 1 mode collapsed upon application of pressure, while a band at 1418 cm -1 with a negative pressure dependence was assigned to the ν (+) mode and a band at 1252 cm -1 with a positive pressure dependence was assigned to the δ (+) mode. 36 In the second paper, no absorption in the IR spectrum of compound [Pt(C6F5)3(C2H4)] -could be unambiguously assigned to ν, but B3LYP/LANL2DZ calculations predicted three bands associated with a combination of ν and δ at 1307 (symmetric), 1501 (asymmetric), and 1584 (symmetric). 37 Therefore, in spite of several publications on vibrational studies of coordinated ethylene, there are still many controversies with the incomplete application of previously established knowledge, plus the unresolved issue of the vibrational coupling between the  and modes on one side and the  mode on the other side. Another problem affecting the correct assignment of the vibrational modes could be related to the nature of the metal atom, with isostructural complexes possibly showing opposite trends for the different bands as was shown for example for Zeise's salt and its Pd-analogue. 38 In the course of a recent mechanistic investigation of the PtBr2-catalyzed hydroamination of ethylene and higher olefins, [39][40][41][42] we have been drawn to synthesize and fully characterize a number of Pt II -C2H4 compounds with different ligand sets, notably aniline, as well as other aniline complexes that do not contain ethylene. 43 A thorough investigation of these complexes by IR and Raman spectroscopy, coupled to high level DFT calculations, with particular focus on the vibrational modes that involve the ethylene ligand, allow us to shine more light on the vibrational coupling problem of coordinated ethylene. An analysis of other vibrations in the above compounds, notably the Pt-halogen stretching modes, will also be presented. This includes a previously unrecognized vibrational coupling and a band reassignment for the Pt-Br stretching vibrations.

Experimental Part.

IR spectra were recorded on a Perkin-Elmer Spectrum 100 FTIR spectrometer (neat/4000-600 cm -1 ) and on a Magna 750 Nicolet FTIR spectrometer (nujol/polyethylene: 600-50 cm -1 ) with 2 cm -1 resolution. Raman spectra (solid) were recorded on a LabRAM HR 800 (HORIBA Jobin Yvon) spectrometer. 13 C NMR investigations were carried out on a Bruker DPX300 spectrometer operating at 75.47 MHz. All complexes used in this study have been synthesized as described elsewhere. 43 Quantum chemical calculation were performed with the Gaussian03 suite of programs 44 using the B3LYP functional which includes the three-parameter gradientcorrected exchange functional of Becke [START_REF] Becke | [END_REF] and the correlation functional of Lee, Yang, and Parr which includes both local and non-local terms. 46,47 The basis set chosen was the standard 6-31+G*, which includes both polarization and diffuse functions that are necessary to allow angular and radial flexibility to the highly anionic systems, for all atoms of type H, C, N, and Br.

The Pt atom was described by the LANL2TZ(f) basis, which is an uncontracted version of LANL2DZ and includes an f polarization function and an ECP. 48 Frequency calculations were carried out for all stationary points in order to verify their nature as local minima and to obtain the frequency, absorption intensity and composition of all vibrational normal modes, under the gas-phase and harmonic approximations. The Gaussian03 output files where analyzed using ChemCraft software. 49 The normal coordinate analysis and PED calculations were performed for all gas-phase optimized complexes with the program DISP 50 by using equilibrium geometries and Cartesian force constants from Gaussian output files. DISP was used for transformation of the equilibrium geometries and the Cartesian force constants into the redundant internal coordinates and force constants with minimal off diagonal terms. PED was expressed as relative contribution of each internal coordinate to the potential energy of the given normal vibration. 5), and cis-[PtBr2(NH2Ph)2] (6) have been investigated experimentally by both IR and Raman spectroscopy, and theoretically by geometry optimization and normal mode analysis by the DFT approach.

Results and discussion.

Compounds ( n Bu4P)[PtBr3(C2H4)] (1), trans-[PtBr2(NH2Ph)(C2H4)] (2), cis- [PtBr2(NH2Ph)(C2H4)] (3), (PBu4)2[PtBr4] (4), (PBu4)[PtBr3(NH2Ph)] (
Compound ( n Bu4P)[PtCl3(C2H4)] (1 Cl ) has also been investigated for comparative purposes. The theoretical study was also carried out on free C2H4 at the same theory level for comparison. The DFT results were subsequently used to perform potential energy distribution (PED) analyses. In the next section, we shall describe the vibrational features (with particular focus on the q1, q2 and q3 vibrations) of the Pt(C2H4) moiety, which is present in compounds 1 Cl , 1, 2 and 3.

Subsequently, with shall analyze the Pt-halogen modes and finally other relevant vibrations. A full list of all computed vibrational frequencies and IR intensities is provided as Supporting Information.

(a) νC=C vibration of coordinated ethylene: two or three bands?

Experimental IR and Raman spectra in the 1600-980 cm -1 region for compounds 1, 2 and 3 are presented in Figure 1, Figure 2 and Figure 3, respectively. Those of compound 1 Cl are available in the Supporting Information. The frequencies of the bands that can be assigned to the three A1-type normal modes q1, q2 and q3 are reported in Table 1. As expected, these are located at ca. 1550, 1250 and 1000 cm -1 . The IR spectrum of compound (Bu4N)[PtBr3(C2H4)] has been previously reported, with a weak band at 1510 cm -1 in CH2Cl2 solution being assigned to ν. 31 Complex 2 was also previously investigated by IR spectroscopy. [START_REF] Foulds | [END_REF] A band observed at 1252 cm -1 , in perfect agreement with our data, was attributed to the ν mode without mention of vibrational coupling. Analysis of the DFT results confirms the band assignment of Table 1. The three above mentioned normal modes of compound 1 are shown in Figure 4. Corresponding views of those of the other three complexes are available in the Supporting Information (Figure S1). The calculated frequencies are greater than those observed experimentally for each compound, as is usually the case for calculations done with density functional methods. However, use of an appropriate "scaling factor" should in principle afford a good agreement with the experimental data. Indeed, the computed frequency ratios (1/2 and 1/3) are essentially identical with those obtained from the experimental data, further confirming the correctness of the band assignments.

In addition, the frequencies measured for q1 and q2 of compound 1 Cl are in good agreement with those described in several previous studies of Zeise's salt (see Introduction). This also means that the nature of the cation does not affect the Pt(C2H4) vibration to a large extent. On the other hand, there was not universal agreement on the location of q3. As stated in the Introduction, two sets of bands (at 1517, 1241 and 1023 cm -1 or at 1517, 1410 and 1241 cm -1 ) were considered as possibilities for q1, q2 and q3 in Zeise's salt, a preference being given to the latter set. 31 Our computational results, however, clearly identify the q3 mode as the lower frequency band (measured at 997 cm -1 for the PBu4 + salt). a IR = observed in the IR spectrum; R = observed in the Raman spectrum; the value in parentheses is that computed for the DFT optimized geometry.

b The Raman data for free C2H4 are taken from ref. [START_REF] Nakamoto | Infrared and Raman Spectra of Inorganic and Coordination Compounds, Part B[END_REF] .

q 1 1557 cm -1 q 2
1252 cm -1 q 3 1017 cm -1 The results of the PED analyses are also collected in Table 1. This analysis reveals that ν and  are heavily mixed in all cases in the higher frequency modes q1 and q2, and provide a small or negligible contribution to the lower frequency q3. Conversely, the ρ mode mostly contributes to q3 and only to a very minor proportion to q1 and q2. Thus, even though the deviation from planarity of the ethylene molecule upon coordination allows mixing between (ν + ) and ρ as discussed in the Introduction, this mixing remains in practice minimal. This is partly due to the small perturbation of the higher symmetry, and partly to the large frequency difference between the ν/ and ρ modes, although the coordination process has the effect of raising the q3 frequency by ca. 50 cm -1 and lowering the q1 and q2 frequencies by ca. 100 cm -1 , such as the (1-3) and

(2-3) values are significantly reduced. As found in most previous studies, the major contribution of ν is found in q2, whereas  contributes more heavily to q1. Thus, our analysis is fully consistent with previous results, 12 ,13,29 but it additionally provides a clearer picture about the location and mixing of the  vibration.

An analysis of the relative frequencies of q1 and q2 for the various compounds may provide information on the Pt-C2H4 bonding. As noted above, the  mode is more heavily contributing to q2, for which the relative frequency trend is 2 (1252 cm -1 ) > 3 (1236 cm -1 ) > 1 Cl (1230 cm -1 ) > 1

(1227 cm -1 ) for a total frequency range of 25 cm -1 . This trend suggests a C=C bond weakening along the same series. The mode q1 varies to a much smaller degree between the four compounds (10 cm -1 frequency range, see Table 1), and the trend is not exactly the same (2 > 1 Cl > 3 > 1), although the smaller range makes this assignment less reliable. Weakening of the C=C bond may result from either an increase of PtC2H4  back-bonding, or an increase of PtC2H4

 bonding, or both. It is not possible to make conclusions about the relative effect of each of these bonding components, although both are probably contributing because there is no clear correlation with the computed Mulliken charges on the ethylene C atoms. Note that the largest frequency change for q2 is observed on going from 2 to 3, corresponding to a change of the ligand trans to ethylene from aniline to Br. The frequency changes are smaller when the same ligand variation occurs in the cis position or when Br is changed with Cl.

The absorption frequencies 1 and 2 are found to correlate with the 13 C{ 1 H} NMR resonance of the ethylene ligand in CD2Cl2 solution, see Figure 5. Compound 3 could not be used for this study since it is insoluble in CH2Cl2. Although the validity of correlations based on only three points may be questioned, we note that analogous correlations have been highlighted

between the CO vibration of carbonyl compounds and the carbonyl 13 C NMR resonance. 52,53 For both bands, the compound showing the lower frequency (smaller force constant) is associated to the most upfield-shifted resonance. This appears consistent with a greater importance of  backbonding effects. Indeed, greater  back-bonding (as expected for the anionic compounds where the charge density on the metal is greater) would not only weaken the C=C bond (lower frequency for q1 and q2) but also increase the electron density on the olefin ligand, inducing an upfield shift of the 13 C NMR resonance. In conclusion, for all practical purposes a coordinated ethylene ligand has the  mode distributed essentially in two normal modes, usually observed around 1500 and 1200 cm -1 . The contribution to the mode at ca. 1000 cm -1 may be neglected because too small. On the other hand, attributing the  mode to only one band is incorrect, because mixing between  and  is always extensive. At any rate, the major contribution of  is found in the lower-frequency band at ca. 1200 cm -1 and not in the higher frequency one at ca. 1500 cm -1 , at least for the family of Pt II complexes investigated here.

The other 9 normal modes of the C2H4 are modified only in a minor way upon coordination to the Pt atom, see Supporting Information (Table S1). The band calculated at 1473 cm -1

(observed at 1406 cm -1 ) for compound 1 and related to that previously considered as a possibility for  in Zeise's salt 31 is clearly originating from an asymmetric CH2 scissoring mode (B1), derived from (B3u) of free ethylene. Note that this band is of B1 type in C2v symmetry, thus it cannot vibrationally couple with the A1-type q1, q2 and q3 modes.

(b) ν(Pt-C) vibrations.

The symmetric and antisymmetric motions of the Pt-C2H4 moiety [ν(PtC2)] were assigned on the basis of the theoretical calculations and are in close agreement with those previously reported for other Pt(C2H4) complexes. [START_REF] Nakamoto | Infrared and Raman Spectra of Inorganic and Coordination Compounds, Part B[END_REF]31 In all cases the measured frequencies were higher than the calculated ones, see Table 2. Both experimental and computed values are smallest for complex 2 and highest for 1 Cl . As expected, a stronger Pt-C2H4 interaction should be associated to a greater weakening of the C=C bond, thus yielding higher-frequency PtC2 modes and lower frequencies for the q2 mode where C=C participates the most. Indeed, the overall trend in the two PtC2 vibrational modes is opposite to that of 2 (1 Cl > 1 > 3 > 2), cf. Table 2 and Table 1. As can be seen in Table 2, these trends also perfectly correlate with the optimized Pt-C and C=C distances. out-of-plane (wagging) modes (A2u+B2u). 54 The far-IR and Raman frequencies of the [PtBr4] 2- complex in the PBu4 + salt (see Figure S2) are in good agreement with those previously reported for the n Bu4N + and K + salts 55,56 (see Table 3). However, some assignments made previously need to be reconsidered. A previously unrecognized vibrational coupling in the two IR-active Eu modes is revealed by the computational results, as shown in Figure 6. The higher frequency band calculated at 192 cm -1 (1Eu) consists mostly of  but also has a 6% component of , whereas the much weaker band calculated at 96 cm -1 (1Eu) has greater component from the bending mode and a 6% contribution from . The other 5 normal modes of the [PtBr4] 2-complex are shown in the compounds in the low-frequency region are available in the Supporting Information (Figures S4 and S5, respectively). Only the stretching modes, shown in Figure 7 for compound 1 Cl as an example, will be analyzed in detail (see Table 4). The in-plane bending modes, for which only partial and tentative assignment of the spectra could be made, are shown in the Supporting Information (Figure S6) together with the experimental IR and Raman spectra (Figures S4 andS5).

In several contributions reporting a vibrational analysis of T-shaped MX3 moiety, the three stretching modes are described as one axial (axial, A1) and two equatorial (a symmetric A1, eq,s, and an antisymmetric B1, eq,as) modes. However, like the A1-type C=C and s(CH2) modes described in part a, vibrational coupling is to be expected and indeed the calculations yield two A1 normal modes with contribution from all three Pt-X bonds. The higher frequency 1 mode is an in-phase motion of all three Pt-X bonds, whereas in 3 the two mutually trans Pt-X bonds move in-phase with respect to each other and out of phase with respect to the axial Pt-X bond (trans to the olefin). The B2 stretching mode (2) is an out-of-phase stretching of the mutually trans Pt-X bonds, with no contribution from the axial Pt-X bond. The contribution of axial and equatorial Pt-X vibrations to each of these modes is revealed by a PED analysis, the results of which are also reported in Table 4. It is interesting to compare the Cl/Br substitution (1 Cl vs. 1)

and also the C2H4/PhNH2 substitution (1 vs. 5). The highest frequency stretching mode is ν1 for 1 Cl and ν2 for 1, according to the calculations. On going from 1 to 5 (C2H4/PhNH2 substitution), however, ν1 becomes again the higher frequency mode. The ν3 mode is the lowest frequency stretching mode for all three complexes. Table 4. Experimental (IR/Raman) and calculated (gas phase) frequencies (cm -1 ) a for the ν(Pt-X) vibrations in compounds 1 Cl , 1 and 5.

Vibr. a IR = observed in the IR spectrum; R = observed in the Raman spectrum; the value in parentheses is that computed for the DFT optimized geometry. b Observed as a shoulder.

It is interesting to note that the axial and equatorial Pt-X bond stretches are heavily mixed in ν1 and ν3 for compound 1 Cl , much less so for compound 1, and not at all for compound 5. The new assignments backed up by our DFT calculations are compared with those previously published by other authors in Table 5. Only one of the previously published assignments for the [PtBr3(C2H4)] -complex (nBu4N + salt 56 ) is essentially in agreement with ours, except for the neglect of a small mixing of the symmetric equatorial PtBr2 vibration in the middle frequency mode and a similarly small mixing of the unique PtBr vibration in the low frequency mode. The other two studies 26,58 report only two of the three possible bands, with assignments in disagreement with ours. Concerning Zeise's salt, many different assignments have been made, all of them attributing the higher frequency band to either the symmetric or the asymmetric PtCl2 vibration. On the other hand, there is high mixing between symmetric PtCl2 and PtCl vibrations according to our calculations, and the strongest contribution to the higher frequency band is in fact provided by the latter.

c3. The neutral dihalo complexes 2, 3 and 6.

The vibrational properties of compound 2 have already been reported. [START_REF] Foulds | [END_REF]59 However, the study was limited to IR and only one stretching vibration was reported at 248 cm -1 . We find (see Table 6 and supporting figures S4 and S5) an intense band in the IR at the same frequency (also visible as a weaker band in the Raman spectrum at 249 cm -1 , calculated at 223 cm -1 ), which can be assigned to the asymmetric PtBr2 vibration on the basis of the calculations. On the other hand, two bands at 199 and 189 cm -1 are predicted by the calculations to be associated with the symmetric PtBr2 vibration, because of vibrational coupling with the aniline and ethylene ligand deformations. These are seen as two intense bands at 202 and 212 cm -1 in the Raman spectrum, whereas they are weaker in the IR spectrum (201 cm -1 with a lower intensity shoulder on the higher frequency side). A relatively strong band observed in the IR spectrum at 195 cm -1 (not visible in the Raman spectrum) can be assigned to a C2H4-Pt-NH2Ph bending mode (calculated at 185 cm -1 ). A band at 195 cm -1 (but none at 201 cm -1 ) was also reported in ref. 59 without assignment.

Table 6. Experimental (IR/Raman) and calculated (gas phase) frequencies (cm -1 ) for ν(Pt-X) and δ(Pt-X) vibrations in compounds 2, 3 and 6. 6). According to the calculations, the lower frequency band has the major component from the Pt-Br bond trans to ethylene (with the longer bond of 2.482 Å), with a small in-phase component from the other bond. The higher frequency band is an out-of-phase component with the major contribution from the Pt-Br bond trans to aniline (with the shorter bond of 2.449 Å). The small coupling between these two bonds is probably related to the electronic asymmetry of the molecule.

The vibrational properties of compound 6 have already been reported. 60 However, like in the case of compound 2, the study was limited to IR and only one stretching vibration was reported at 223 cm -1 . Like complex 3, we find complex 6 to feature two high intensity Pt-Br stretching vibrations both in the IR and in the Raman spectrum, at frequencies very close to those of 3 (see Table 6). However, contrary to 3, the electronic symmetry in 6 favors a strong coupling and thus symmetric and asymmetric combinations are observed, each having equal contribution from the two Pt-Br bonds. Note that for the trans arrangement in 2, the in-phase mode (νs(PtBr2)) is seen at lower frequency relative to the out-of-phase mode (νas(PtBr2)), whereas the reverse is true for the cis arrangement of 6.

(d) (Pt-N) vibrations

In order to complete the analysis of Pt-ligand stretching vibrations, we halso also examined the Pt-N stretch for all complexes containing aniline. The calculated and experimental frequencies are summarized in Table 7. For all compounds, the Pt-N stretching vibration is strongly coupled with ring vibrations and thus substantially contributes to two different vibrational modes. These are shown in the Supporting Information for the specific case of compound 5 (Figure S7). For this reason, there is no clear correlation between either of the two frequencies and the calculated Pt-N bond length (also reported in Table 7). The previously reported vibrational analysis, limited to IR, of compound 2 attributes the Pt-N stretching vibration to a band observed 51 at 434 cm -1 whereas the analysis of compound 6 attributed to the Pt-N stretch bands at 367 and 290 cm -1 . 60 For each of compounds 2, 3 and 5, we observe a band in the 430-450 cm -1 region and also two bands around 550 cm -1 , one of which is probably related to the combination mode with (Pt-N) component. For compound 6, two bands of similar intensity are observed at ca. 450 cm -1 , whereas the 550 cm -1 region of the spectrum is similar to that of the other compounds. Table 7. Experimental (IR/Raman) and calculated (gas phase) frequencies (cm -1 ) for ν(Pt-N) and ν(C-N) vibrations in compounds 2, 3, 5 and 6.

Conclusion

Our spectroscopic analysis of a few PtBr2 derivatives, triggered by a theoretical study of these compounds in relation to their possible involvement in ethylene hydroamination catalysis, has led us to reconsider several spectra assignment made for these and related compounds in the 19 literature, including some relatively recent contributions. The main contributions of the present study have been the recognition of previously unsuspected vibrational couplings (notably for PtBrn fragments with n = 2, 3 and 4) and an analysis of its limitations (notably for the q1, q2 and q3 modes of coordinated C2H4). It has been shown that a satisfactory interpretation of the experimental spectra can be provided on the basis of high level DFT calculations. Given the ready availability of computational tools, it is now possible to reconsider previously dubious assignments of spectral features and put vibrational analysis on a more solid basis as a characterization tool for new compounds.

Figure 1 .

 1 Figure 1. Raman (a) and IR (b) spectra (neat) of compound 1.

Figure 2 .- 1 Figure 3 .

 213 Figure 2. Raman (a) and IR (b) spectra (neat) of compound 2.

Figure 4 .

 4 Figure 4. Two orthogonal views of the calculated normal modes q1, q2 and q3 for the anion of 1.

Figure 5 .

 5 Figure 5. Correlation between the normal mode frequencies of Band 1 (a) and Band 2 (b) and the olefin ligand 13 C NMR chemical shift for olefin complexes.

.

  The D4h-symmetric square-planar [PtBr4] 2-complex is expected to give rise to 9 vibrational modes, A1g(R) + B1g(R) + A2u(IR) + B2g(R) + B2u(inactive) + 2Eu(IR), which can be classified as 4 stretching modes (A1g+B1g+Eu), 3 in-plane bending modes (B2g+Eu) and 2

3 Figure 7 .

 37 Figure 7. Normal modes of vibration for the PtX3 moiety in compound 1 Cl . Compounds 1 and 5 exhibit related modes.

  a shoulder. b trans to ethylene. c trans to aniline.Complex 3 features two Pt-Br stretching vibrations that are seen as the most intense bands in the low-frequency region both in the IR and in the Raman spectrum (see Table

Table 1 .

 1 Observed and calculated a frequencies and PED analysis for the q1, q2 and q3 modes of the Pt(C2H4) moiety in C2H4 and in the Pt complexes 1 Cl , 1, 2 and 3.

	Vibr.	C2H4 b		1 Cl			1		2				3
		Freq.		% Freq.		% Freq.		% Freq.		% Freq.	%
	q1	1623 R (1701.9)	 HCH CCH 	62 23 15 0	1516vw IR 1516w R (1557.1)	 HCH CCH 	21 36 39 5	1510w IR 1512w R (1556.6)	 HCH CCH 	22 35 38 4	1519w IR 1520w R (1576.2)	 HCH CCH 	23 36 36 5	1513w IR 1515w R (1568.7)	 HCH CCH 
	q2	1342 R (1388.3)	 HCH CCH 	37 39 24 0	1230m (IR) 1230m (R) (1251.3)	 HCH CCH 	76 10 9 2	1227w IR 1226m R (1252.3)	 HCH CCH 	75 11 10 1	1252w IR 1254m R (1283.6)	 HCH CCH 	74 11 9 2	1236w IR 1236m R (1265.6)	 HCH CCH 
	q3	949 IR (974.2)	 HCH CCH 	0 0 0 100	997 (IR) 997w (R) (1019.0)	 HCH CCH 	0 0 14 90	995m IR 995w R (1016.7)	 HCH CCH 	0 0 14 90	1007m IR 1004m R (1050.3)	 HCH CCH 	0 0 14 88	1005m IR 1002m R (1037.1)	 HCH CCH 
	1/ 2	1.21 R (1.23)		1.23 IR 1.23 R (1.24)	1.23 IR 1.23 R (1.24)	1.21 IR 1.21 R (1.23)	1.22 IR 1.23 R (1.24)
	1/ 3	1.71 R (1.75)		1.52 IR 1.52 R (1.53)	1.52 IR 1.52 R (1.53)	1.51 IR 1.51 R (1.50)	1.51 IR 1.51 R (1.51)

Table 2 .

 2 Experimental (IR/Raman) and calculated frequencies (cm -1 ) for the ν(PtC2) vibrations and optimized Pt-C and C=C bonding parameters (Å). IR = observed in the IR spectrum; R = observed in the Raman spectrum; the value in parentheses is that computed for the DFT optimized geometry.

		1 Cl	1	2	3
		413w IR	403m IR	382w IR	386w IR
	νs(Pt-C2) (A1)	413m R	407m R	380w R	393m R
		(408)	(393)	(371)	(377)
		507w IR	498w IR	475w IR	482m IR
	νas(Pt-C2) (B1)	512m R	504m R	474w R	482w R
		(502)	(487)	(471)	(475)

a

Table 3 .

 3 Calculated and observed frequencies and assignments for [PtBr4]2-

	Calcd	symmetry	Assignment,		Observed frequency/cm -1
	freq. cm -1		PED
				Compd 4	NBu4 + salt a	K + salt b	K + salt c	K + salt d
				(IR and R)	(IR)	(R)	(IR)	(R)
	192	1Eu (IR)	94% ν + 6% δ	226vs	225vs (227)		231
	176	A1g (R)	Ν	203s		208	214, 204 e (208)
	159	B1g (R)	Ν	190s		194	n.l. f
	97	A2u (IR)	Ρ	110vwsh	104ms (105)		128
	96	2Eu (IR)	6% ν + 94% δ	104vw	112sh (112)		129
	93	B2g (R)	Δ	108m		106	189 (194)
	43	B2u (n.a.) g	Ρ

a From ref. 56: powder data for Raman, Nujol mull data (CHCl3 solution in parentheses) for IR. b From ref. 56: H2O solution. c From ref. 57: single-crystal IR-reflectance (transverse optical mode, 295 K). d From ref. 55: powder data, with solution values (D2O) in parentheses. e Observed as a nonsymmetrical doublet due to a Davydov splitting. f Not located. g Not active.

Table 5 .

 5 Comparison of Pt-X stretching band assignments. a Measurements carried out in Nujol mull unless otherwise stated. b Measured in H2O-HCl solution. c Measurement carried out under pressure. d Measured in CDCl3 solution. e C9H7NH = quinolinium.

	Compound	High frequency	Middle frequency Low frequency	Ref.
	Trichloride
	K[PtCl3(C2H4)]•H2O	339 PtCl2 as	331 PtCl2 s	310 PtCl	25
		338 PtCl2 s	327 PtCl2 as	309 PtCl	27
		335 PtCl2 s	328 PtCl	306 PtCl2 as	56
		336 PtCl2 s	330 PtCl	308 PtCl2 as	56b
		336 PtCl2 s	Not located	294 PtCl2 as	36c
		340 PtCl2 s	330 PtCl2 as	305 PtCl	26
	K[PtCl3(C2H4)]	338 PtCl2 s	334 PtCl	312 PtCl2 as	56
	nBu4N[PtCl3(C2H4)] d	338 PtCl2 s	332 PtCl	316 PtCl2 as	56
	nBu4P[PtCl3(C2H4)]	338 PtCl (58%)	332 PtCl2 as	314 PtCl2 s (58%)	This work
		+ PtCl2 s (41%)		+ PtCl (42%)
	Tribromide
	K[PtBr3(C2H4)]•H2O	246 PtBr2 as	227 PtBr2 s	Not located	58
	C9H7NH[PtBr3(C2H4)] e	Not located	218 PtBr2 as	198 PtBr	26
	nBu4N[PtBr3(C2H4)]	241 PtBr2 as	220 PtBr	201 PtBr2 s	56
	nBu4P[PtBr3(C2H4)]	241 PtBr2 as	221 PtBr (86%)	201 PtBr2 s (89%)	This work
			+ PtBr2 s (10%)	+ PtBr (11%)

a

Acknowledgement. We thank the CNRS and the RFBR for support through a France-Russia (RFBR -CNRS) bilateral grant № 08-03-92506, and the MENESR (Ministère de l'Éducation nationale de l'enseignement supérieur et de la recherche de France) for a Ph.D. fellowship to PD.

Table of Content Graphic

Supporting Information (Figure S3) and their calculated frequencies and symmetry labels are reported in Table 3. There are 3 higher frequency modes (192-159 cm -1 ), of which only one is active in the IR, followed by a large gap with the next group of 3 modes in a narrow range (97-93 cm -1 ), and a final inactive mode (B2u at 43 cm -1 ). The 1Eu mode is the most easily identified mode because it is the most intense band in the IR spectrum at 226 cm -1 , and corresponds to previously assigned bands for the K + and nBu4N + salts (see Table 3). 56,57 The two other high-frequency modes (A1g and B1g) are visible in the Raman spectrum at 200 and 188 cm -1 . These assignments appear reasonable because the calculated and observed frequency ratios are quite comparable (1Eu/A1g: calcd. 1.09; found 1.13.

1Eu/B1g: calcd. 1.21; found 1.20). In previous Raman studies, carried out only on the K + salt, the Ag mode was assigned also to a band in the same region of the spectrum at 208 cm -1 in aqueous solution, 55,56 or to two bands at 214 and 204 cm -1 due to lattice effects (Davydov splitting). 55 A band around 190 cm -1 was also observed in the previous studies but wrongly assigned to the B2g mode in one case.

For the next three bands, the assignment is more difficult given the narrow frequency range. Only one Raman active band is expected in this region and this was reported at 106 cm -1

for the K + salt in H2O solution. 56 Compound 4 shows this band at 108 cm -1 . The other two bands in this group, A2u and 2Eu, are IR active. Our measured spectrum shows a band at 104 cm -1 with a shoulder at ca. 110 cm -1 , similar to the spectrum reported for the nBu4N + salt. 56 According to the calculation, the 2Eu band is more intense than the A2u band (2.44 vs. 1.37), thus the assignment of the 104 cm -1 band to the 2Eu mode appears more consistent.

c2. The trihalo anions 1 Cl , 1 and 5.

In these compounds, the three Pt-X (X = Cl or Br) bonds afford three stretching modes, two in-plane bending modes, and two out-of-plane bending modes, the last two being mixed with the out-of-plane Pt-C2H4 bending motions. The experimental IR and Raman spectra of these


Passos Gomes

Dr Guangcan Xu

Dr Xiaolei Zhu

Dr Lise-Marie Chamoreau

Dr Yongmin Zhang

Dr Olivia Bistri-Aslanoff

Dr Sylvain Roland

Prof Igor

V Alabugin
email: alabugin@chem.fsu.edu

Prof Matthieu Sollogoub

Mapping C-H×××M Interactions in Confined Spaces: (a-ICyD Me )Au, Ag, Cu Complexes Reveal "Contra-electrostatic H-bonds" Masquerading as Anagostic Interactions

Keywords: Confinement, C-H metal interactions, anagostic interactions, H-bonds, cyclodextrins, coinage metals, NHC

What happens when a C-H bond is forced to interact with unpaired pairs of electrons at a positively charged metal? Such interactions can be considered as "contra-electrostatic" H-bonds, which combine the familiar orbital interaction pattern characteristic for the covalent contribution to the conventional Hbonding with an unusual contra-electrostatic component. Such remarkable C-H×××M attractive interaction became experimentally accessible within (a-ICyD Me )MCl, NHC-Metal complexes embedded into cyclodextrins.

Introduction

The alkane C-H bonds are poorly suited for coordination to a metal center. Because these non-polar, weakly polarizable, strong bonds are associated with a low energy orbitals 𝜎 "#, and the high-energy orbitals 𝜎 "# Figure 1. Structure of (a-ICyD)MX and numbering of sugar carbons (1 to 6) and of glucose units on the cyclodextrin (A to F) (top left). 3D representation of (a-ICyD)MX showing the MX complex embedded in a cyclodextrin cavity where H 5A interacts with M (top right). 1 H NMR of imidazolium (a-ICyD)H + (top) and (a-ICyD)CuCl (bottom) showing the characteristic deshielding of H 5(A,D) In the present work, we spectroscopically studied the O-methylated (ICyD Me ) version of the O-benzylated ICyDs, and obtained X-ray crystal structures showcasing the C-H×××M interactions in their cavity. We then computationally probed the response of C-H bond lengths to the proximity and orientation of the C-H bond relative to the metal center. We started by analyzing the parent CH 4 ×××metal complexes and then showed how the general trends for the C-H×××M interactions are transferred to the C-H bonds in the cyclodextrin cavities. In order to understand the nature of C-H×××metal interactions, we investigated the orbital interactions involved in these contacts using Natural Bond Orbital (NBO) and Natural Energy Decomposition analyses (NEDA). An unusual feature of these coinage M×××H-C interactions is that even though the metal center has non-bonding doubly occupied orbitals (i.e., the d-type lone pairs, vide infra) and can serve as a Lewis base, it also bears a significant partial positive charge. Hence, although the anagostic M×××H-C interactions with such "cationic Lewis bases" share the familiar 3c,4e-features with conventional hydrogen bonds, their electrostatic interaction with a typical H-bond donor should be drastically different. In the final part, we explore how the experimentally observed trends in the rigid X-ray geometries correspond to the anisotropic response observed for the C-H bond in computed geometries. In the present system, metal encapsulation inside the cyclodextrin cavity forces the C-H bond to point toward the metal and forms the C-H×××M contacts that can be considered as H-bonds that have an unusual "contra-electrostatic" component but still potentially attractive (Scheme 2).

Results and Discussion

Experimental analysis

A prerequisite for a detailed study of the electronic effects involving the coinage metal encapsulated in the cyclodextrin cavity of an ICyD ligand is to get a crystal structure. We have shown that the replacement of benzyl groups with methyls on ICyD ligands could lead to the crystallization of (a-ICyD Me )AgCl. 39 We also previously synthesized (a-ICyD Me )CuCl, (a-ICyD Me )AgCl, and (a-ICyD Me )AuCl and characterized them by NMR. They all displayed deshieldings of H 5 characteristic of the metal complex confined inside the cyclodextrin cavity. More precisely, in the three complexes, H 5(A,D) were the most deshielded (5.55-6.32 ppm). The gold complex displayed the strongest deshielding for this pair of H 5 (6.32 ppm) but also showed stronger deshieldings than silver and copper complexes for all other H 5 (Figure 2, Table1). (a-ICyD Me )CuCl, and (a-ICyD Me )AuCl crystals could now be obtained through slow diffusion of pentane and cyclohexane into a solution of the complex in CDCl 3 . Interestingly, though the (a-ICyD Me )AgCl, (a-ICyD Me )CuCl X-ray structures are C 2 -symmetrical and quasi isomorphous, the structure of (a-ICyD Me )AuCl is not. This dissonance seems to be due to a different packing in the solid-state. In solution, however, this phenomenon does not occur, and the three compounds are C 2 -symmetrical in the NMR. Adding the hydrogen atoms to the heavy atoms in these structures, we determined M×××H 5 distances as well as C-H 5 -M, H 5 -M-Cl angles, and N-C-M-H 5 dihedral angles (Table 2). All distances are in the same range, although slightly longer on average for Au, and the closest protons from the metal are also the most deshielded in the NMR.

(Å) C-H 5 - M angle H 5 -M- Cl angle H 5 -M- C-N dihedral d M-H 5 (Å) C-H 5 - M angle H 5 - M-Cl angle H 5 -M- C-N dihedral d M-H 5 (Å) C-H 5 - M angle H 5 - M-Cl angle H 5 -M-C- N dihedral H 5(A,D)
H

Computational Analysis

With the NMR analysis and the crystal structure of all three (a-ICyD Me )MCl complexes in hand, we started the computational study with a brief survey of the electronic structure of the NHC-Au-Cl system. The LUMO is at the NHC ligand with little contribution from the metal. On the other hand, the HOMO is an antibonding combination of one of the Au-d-orbitals with a lone pair of Cl. Since the metal center contributes more to the HOMO than to the LUMO, one can expect that the metal center will be mostly a donor partner in the donor-acceptor interactions. However, one has to bear in mind that the Au(I) also has a considerable positive charge (+0.37 e, from the Natural Population Analysis). The effect of this positive charge is reflected in the relatively low energy of the Au d-orbitals (HOMO-4 and below) (Scheme 3). The observation that the HOMO and the LUMO are located at the opposite parts of the molecule suggests that the donor-acceptor interactions of the C-H moiety with such metal complexes are likely to be quite anisotropic; i.e., their nature may strongly depend

Cu

on the exact position of the C-H bond relative to the ligands. This analysis was also performed for the Ag and Cu complexes, with similar trends observed. The LUMO energies are virtually identical since this orbital is mostly concentrated on the NHC moiety. Although the HOMO energies differ only slightly since the contribution of the metal to this MO is relatively low, the order of the HOMO energies (Au<Ag<Cu) does agree with the relative electronegativities of these elements. Interestingly, the atomic charges at the three metal centers (Ag>Cu>Au) do not follow the above trend as the HOMO energies. Furthermore, the energy of lower energy occupied MOs corresponding closely to d-orbitals at the metal center increases in the following order Ag<Au<Cu (Scheme 3). These observations suggest that the interaction between the metal and the ligand are complex and involve more than one component.

Methane complexes as probes for C-H×××M interactions

Because the fundamental understanding for the interaction of C-H bonds with the NHC-MX systems is still lacking, we started this investigation by using methane, the simplest hydrocarbon with an sp 3 C-H bond. The symmetry of this molecule, as well as the absence of other functional groups that can interact with the metal complex considerably, simplifies the electronic situation, allowing one to concentrate on the intrinsic effects associated with the C-H×××Metal interaction. So, how does the C-H bond interact with the metal center? And how does this interaction respond to changes in distance and orientation of the two interacting partners? We have considered three geometric parameters illustrated in the scheme below: a) the H×××M distance, b) the H-M-Cl angle, and c) the H-M-C1-N dihedral (Scheme 4A). The changes of electronic structure, geometry, and stability of the complexes as a function of these three parameters are illustrated in this section.

Scheme 4. A:

The three geometric variables used for charting the supramolecular space for the C-H×××M interactions between methane and the NHC-M-Cl complexes. B: Unrestricted optimized geometries for the three complexes. Energies in kcal/mol.

We have also located the energy minima corresponding to the complexes. All three complexes have a negative enthalpy of formation (ca. 1.5 kcal/mol), indicating that these intermolecular interactions are attractive (Scheme 4B). Because the attraction is relatively weak, the entropic penalty for the formation for bringing two components together renders the Gibbs energy positive (ca. +4.5 kcal/mol). For the unstrained complexes, other electrostatic components contribute as well to the observed geometries. Of course, neither this entropic penalty will apply to our cyclodextrin systems where such interactions are intramolecular, nor the calculated geometric preference for the complexes be preserved on these shallow energy surfaces because the cyclodextrin systems impose their own geometric restrictions on the position of the carbohydrate C-H bonds. We can use geometric constraints (Scheme 4A) to explore the structural and spectroscopic consequences of C-H×××M contacts away from their intrinsic equilibrium geometries.

The H×××M distance:

The effect of H×××M distance was probed using a symmetric trajectory where both the C-H-M angle and the H-M-C1-N dihedral were constrained to 180 and 90 degrees, respectively. All other geometric parameters were allowed to change freely in the geometry optimizations. Under these constraints, the lowest energy was observed at the H×××M distance of ca. 2.9 Å. The binding interaction was weak, as illustrated by minimal changes in energy at the greater H×××M separations. Bringing the two interacting molecules closer led to progressive energy increase. This increase was initially small (~1 kcal/mol for the first 0.5 Å but exceeds 5 kcal/mol at distances shorter than 2.1 Å, where direct orbital interactions start to operate (Figure 3). The experimentally observed C-H×××M distances (≥ 2.5 Å) correspond to the region where the interaction energies are quite small. Interestingly, computations suggest that the penalty for CH×××M distance shortening is more significant for M=Au. This prediction is in good agreement with the slightly larger CH×××M experimental distances for the Aucomplex in comparison to the Cu-and Ag-complexes (Table 2). The absence of a welldefined energy minimum characteristic for conventional H-bonds (where the H-bond acceptor is an electronegative heteroatom) is consistent with the unfavorable electrostatic forces in the C-H×××M systems. In the latter case, both H and M have partial positive charges. With the electrostatic component opposite to that of the "normal" Hbonding, it is not surprising that, under these optimization constraints, the potential energy curve is not attractive.

The calculated C-H distance response to bringing the metal complex closer is small for the experimentally attainable H×××M distances. Interestingly, the effect is larger for the Aucomplex. The C-H bond starts to elongate as the H×××M distance becomes shorter (Figure 4). This behavior is different from the more conventional C-H×××Y H-bonding, where Y is a heteroatom with a lone pair. In the conventional cases, C-H bond contraction (blue-shifted H-bonds) is often observed first, followed by C-H bond elongation at the shorter H×××Y distances. 42 Evaluation of the total charge transfer revealed a surprising difference between the Au vs. Cu and Ag complexes. At the longer M×××H distances, the methane molecule is a donor in all three complexes. However, at the distances of ~2.5-2.7 Å, methane behaves as the net acceptor in the Au complex but remains a donor in the Cu, Ag complexes.

The net donor ability of the Au-complex is observed even though the Au atom has a charge of +0.3 e! Further compression of the M×××H distance leads to an increase in the positive charge at the Cu and Ag complexes as well but at much shorter distances. (Figure 5) The carbon atom also loses electron density, and the intrinsic polarization of the C-H bond changes as hydrogen becomes less positively charged and gains electron density.

Overall, hydrogen of the C-H bond becomes less positive as it gets closer to the metal. On the other hand, the carbon atom loses electron density. (Figures 6 and7) This behavior is the opposite of the conventional C-H×××Y bonding to a heteroatom. For example, hydrogen becomes more positively charged whereas carbon gains electron density as the H atom approaches the oxygen atom of water in the F 3 C-H×××OH 2 system. 42 Analysis of the hybridization of the C-H bond provides an interesting insight into the nature of the electronic reorganization in this system. Initially, at the distances greater than 2.3 Å, the carbon hybrid of the interacting C-H bond gets additional s-character. This rehybridization 40,41 is similar to that observed at the early stages of the formation of blue-shifted H-bonds. 42 At the shorter distances, however, the carbon orbital gains pcharacter. This part of the curve for the C-H×××M complexes is very different from what is observed for conventional H-bonding to electronegative heteroatoms where scharacter at the C-H bond carbon hybrid continues to increase at the shorter distances. These differences are associated with the aforementioned opposite trends in the C-H bond repolarization in the two types of complexes (Figure 8). We have also calculated the NBO changes in the population of the 𝜎 "# and 𝜎 "# * orbitals in order to deeper understand the effects of the electronic origin of C-H bond elongation. A priori, one can attribute the observed C-H bond elongation (that should correspond to a red shifting of the IR-stretching frequencies) to one of the two effects: a) increased donations from the Au-moiety to the C-H bond at smaller distances (i.e., the increased population of the antibonding 𝜎 "# * orbital) or b) donation from the C-H bond to the empty orbitals at gold (i.e., the decreased population of the bonding 𝜎 "# orbital). As the Au×××H distance shortens, the bonding orbital is depleted of electron density whereas the antibonding orbital gains electron density. Both changes indicate a decrease in the C-H covalency. The more significant change in the 𝜎 "# * population (0.08 e) relative to the 𝜎 "# population (0.03 e) suggests that the C-H bond is a net acceptor. Interestingly, the positively charged Au center, which is commonly used as a Lewis-acidic catalyst in organic reactions 33,34,[START_REF] Michelet | Homogenous Gold Catalysis[END_REF][START_REF] Hashmi | Modern Gold Catalysis Synthesis[END_REF][START_REF] Fensterbank | [END_REF][46][47][48][49][50][51][52] serves as a donor in this particular situation. Again, the Aucomplex is a better donor than its Ag and Cu counterparts (Figure 9). The reasons for the relatively low sensitivity to the torsional scan for each of the metals are stereoelectronic. The metal center has a manifold of d-orbitals of similar symmetry, which can serve as interaction partners for the C-H bond at a variety of dihedral angles. These orbitals are shown in Figure 12. As the C-H bond explores a new region of space by moving around the metal, it starts to engage in a new favorable orbital interaction as an old interaction gets weakened.

Comparison with the conventional H-bonds:

At this point, let us summarize the key trends of this study. DFT computations reveal that the C-H bond elongates as the H×××M distances shorten. From the electronic point of view, shortening of H×××M distances results in a decrease of the charge on H and an increase on C together with a net donation of the metal into the 𝜎 "# * . The penalty for small deviations from the perpendicular approach is not large -the range of geometries in the range of 75-115 degrees are separated by less than 1 kcal/mol in stability. Changes caused by reorientation of the C-H bond relative to the molecular plane of the complex, i.e., the variations in the NC 1 (carbene)-M-H dihedral angle are also minor due to "stereoelectronic promiscuity" of the fully filled metal d-orbital manifold. As the C-H bond rotates around the metal center, it finds new interaction partners in the metal lonepairs that can serve as hyperconjugative donors in the 3c,4e-interactions. However, differences between the three metals are considerable, as one would expect from the different charge and size of Cu, Ag, and Au.

We can now discuss how different the observed behavior of the M×××H-CH 3 complexes is in comparison to the conventional X×××H-C hydrogen bonds where X is an electronegative heteroatom. Remarkably, although both types of supramolecular contacts lead to C-H elongation and a net donation of the metal or X into the 𝜎 "# * , the underlying electronic perturbations are dramatically different, in a few cases, even opposite! The most striking difference is related to the charges of C and H: the polarization (estimated from the square of contributing orbital coefficients in the C-H NBOs) of the C-H bond increases on H when M gets closer, while it is decreasing in classical X×××H-C H-bonds when X approaches H. From the electronic point of view, this unusual nature of the electrostatic component in the M×××H-CH 3 complexes renders them the opposite of the classic H-bonds. On the other hand, the covalent (i.e., hyperconjugative, or charge-transfer) component of H-bonding is qualitatively similar for the two types of supramolecular interactions. Anti-electrostatic H-bonds (Scheme 5) have been defined for an H-bond between two ions of like-charge, 53 here we have an Hbond between two atoms of like partial charge, we propose to call this interaction "contra-electrostatic" H-bond. We employed Natural Energy Decomposition Analysis (NEDA) [54][55][56][57] as an additional tool for analyzing the nature of the "contra-electrostatic" H-bonds in this study. Scheme 6a illustrates the total energy of M×××H interactions along with the NEDA decomposition into three terms (electrical, charge transfer, and repulsion) for the three CH 4 ×××M-NHC systems (with M = Au, Ag, and Cu). The electrostatic (electrical) term is further decomposed into its parts (static, induced polarization, and self-energy correction in Scheme 6b). For comparison, we also include the NEDA data for a conventionally H-bonded H 3 C-H×××NH 3 complex. Fortuitously, the total interaction energies for the three CH 4 ×××M-NHC systems are nearly the same (-1.4 kcal/mol). The numbers are slightly negative, indicating that the "contraelectrostatic H-bonds" are attractive when optimization is conducted without any restraints. Each of these complexes is slightly stronger than the CH 4 ×××NH 3 complex. When considering these differences, it is essential to remember that these interaction energies are global, originating from the multiple contacts between methane and different parts of the NHC-metal complex. However, a comparison of individual contributions to the total interaction energies does reveal an interesting difference between the three CH 4 ×××M-NHC systems and the CH 4 ×××NH 3 complex. For the "contra-electrostatic complexes," the contribution of the charge transfer term (originating from hyperconjugative orbital interactions) is more significant than electrostatic stabilization whereas, for the CH 4 ×××NH 3 complex, the contributions of electrostatic and charge-transfer (hyperconjugative) interactions are nearly the same.

The stabilizing electrostatic interactions are considerably decreased in the Cu and Ag complexes. Again, the Au-systems is different: both the overall stabilization and the overall destabilization are larger for the Au system than for the Ag and Cu systems, possibly due to Au's relativistic effects.

The difference in the electrical term can be further broken down into three components, as described in Eq. ( 1):

𝐸𝐿 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 = 𝐸𝑆 𝑆𝑡𝑎𝑡𝑖𝑐 + 𝑃𝑂𝐿 𝑃𝑜𝑙𝑎𝑟𝑖𝑧𝑎𝑡𝑖𝑜𝑛 + 𝑆𝐸 (𝑆𝑒𝑙𝑓 𝐸𝑛𝑒𝑟𝑔𝑦 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛) (1)
From the latter dissection, one can conclude that the difference in the Au system mostly originates from induced polarization dominating the electrical term (Scheme 6b). From that perspective, the higher polarizability of Au makes its complexes less "contraelectrostatic" than the Ag and Cu complexes.

Insights into the experimental observations -computational analysis of the full system:

Using the abovementioned insights, we can decipher the type of interactions revealed by the experimental data for the cyclodextrin-encapsulated metal complexes. Selected calculated 1 H NMR chemical shifts are given below for (a-ICyD Me )AgCl, (a-ICyD Me )CuCl, and (a-ICyD Me )AuCl complexes. The absolute values of the NMR shifts are well in line with the experimental ones (Table 1) for H 5(A,D) and overestimated by ~0.6 ppm for H 5(C,F) , so the relative trend is well reproduced. The particular experimental behavior of the AuCl complex is also apparent in the computations (Figure 13). Computational dissection of key electronic parameters for the C-H bonds in the vicinity of the metal center in the experimentally studied cyclodextrin complexes is reported below. From the inspection of C-H bond length dependence from the M×××H distance, it is clear that proximity to the metals leads to, at best, only a very slight elongation (Figure 14). Furthermore, this weak effect can be masked by other factors that affect by C-H bond length, e.g., intramolecular stereoelectronic effects such as the anomeric or the gauche effects. The relatively small effects are consistent with our computational data for the model systems described above and contrast the relatively large effects that metals proximity has on the NMR chemical shifts (Figure 13). NBO analysis of the stereoelectronic interactions that may be responsible for the observed NMR trends was performed for the crystal structure geometries in the active centers of the Cu, Ag, and Au-systems (Figure 14). This analysis illustrates the presence of multiple donor-acceptor orbital interactions with different geometric parameters and significant variations in the H×××M distances and the angles of approach. Due to the geometric differences, the interactions are not identical from the electronic viewpoint. Interestingly, the contacts with the most deshielded H 5(A,D) protons correspond to the largest donations from the metal lone-pairs to the 𝜎 "# * orbital. Encouragingly, the unusual effect of H×××M distances on charges is well-reproduced in this experimental system. Indeed, H 5(A,D) have lower charges than H 5(B,E) because they are closer to the metal center. Conversely, the C 5(A, D) atoms bear a greater positive charge than the C 5(B,E) . Hence, the combination of available experimental and computational data confirms that metal encapsulation inside the cyclodextrin cavity forces the C-H bond to point toward the metal, and reveal the attractive contra-electrostatic H-bonding. Finally, we have also performed the NEDA analysis on truncated systems that include the metal centers and the four closely located sugar moieties derived from the experimental data on the cyclodextrin cavity. Interestingly, the overall interaction energies were found to be attractive for each of the four contacts between the metal and the sugars (decoded as West, North, East, and South in Figure 15). The range of interaction energies for the twelve evaluated contacts varied considerably -from -1.4 to -6.5 kcal/mol. Remarkably, the greatest anisotropy of the interaction energies of the four sugar partners with the same metal center was found in the Au-system (-1.4 (West) vs. -6.2 (South) kcal/mol). In contrast, all four interactions were nearly identical for the Cu-system (-2.9 vs. -3.3 kcal/mol). The Au-and Ag-systems also show a more considerable variation in the relative magnitude of the individual repulsive and attractive (electrostatic, charge transfer = hyperconjugative) interactions than the Cu-system. Although the NEDA data are cumulative and reflect the interplay of multiple interactions, these data again illustrate the large variations in the nature of supramolecular interactions in these three systems.

Conclusion

Intrigued by the initial observation of unusual "anagostic" interaction between coinage metal complexes and introverted cavity protons of an NHC-capped cyclodextrin, we

E) (A) (B) (D) (E) (A) (B) (D) (E) (A) (B) (D) (
explored these interactions theoretically. Our computations reveal that when a C-H bond is forced to interact with unpaired electron pairs at a positively charged metal, the covalent and electrostatic components of H-bonding do not work together as they do in classic H-bonds. We consider such interactions as "contra-electrostatic" H-bonds, as they combine the familiar orbital interaction pattern of conventional H-bonding with an unusual contra-electrostatic component. Whereas the Coulombic attraction is strongly stabilizing in the conventional C-H×××X bonds where X is an electronegative main group element, electrostatics is destabilizing/repulsive in the C-H×××M contacts when M is Au(I), Ag(I), or Cu(I) of NHC-M-Cl systems. In larger systems, this destabilization can be masked by the combination of the secondary effects between the other parts of the two interacting partners, including weaker electrostatics and dispersion interactions. Crystal structures of NHC-capped O-methylated cyclodextrin metal complexes (a-ICyD Me )MCl (M=Ag, Cu, Au) allowed an experimental study of such intriguing C-H×××M contacts inside the cavities. Together with the 1 H NMR data and the computational analysis, this data illustrates the unusual properties of the Au-complex. Unlike the Cu and Ag systems, the greater polarizability of Au can alleviate the lower contribution of electrostatic stabilization in such "contra-electrostatic" H-bonded complexes. In an attempt to generalize this weak interaction to other systems, we ran a CSD search looking for similar structural features (d M-H <2.6 Å and 130°<C-H-M angle<180°) and found around a 100 hits. Among them, we could identify one structure studied by Glorius that presented similar NMR and X-ray features, 58 making us believe that a contraelectrostatic H-bond was at play in that case too. Considering the reactivity of these complexes as Lewis acids, [33][34][35][36][37] the recent work by Gabbaï showing that a positive charge in the proximity of Au atom could influence its reactivity 59 and the involvement of intra-cavity protons in stabilizing some transition states, 37 we hope that the correlations of NMR data and structural features of C-H×××M interactions will help one to understand how a catalytic cavity is shaped for many different combinations of metal and ligands. Such understanding can facilitate the future design of highly selective metal-catalyzed reactions in confined spaces.

Computational details

We employed the B3LYP functional (with an ultrafine integration grid of 99,590 points) for all calculations. We used the following basis set scheme (BS1): H, C, N, O and Cl (6-311++G**); and Au/Ag/Cu (Def2-TVZPP, with Effective Core Potential). [START_REF]Basis sets for Au, Ag, Cu were obtained from the Basis Set Exchange[END_REF] Grimme's D3 version (with Becke and Johnson's damping) for empirical dispersion 61 corrections were also included. X-ray structures were refined by the optimization of hydrogen atoms, first with GFN2-xTB, and then reoptimized with B3LYP(D3BJ)/BS1 and an ultrafine integration grid. Natural Bond Orbital [62][63][64][65][START_REF] Weinhold | Encyclopedia of Computational Chemistry[END_REF] analyses (with NBO6 67 program) were performed in order to correlate orbital interactions at the metal center with the chemical shifts of protons and the lengths of participating C-H bonds. Additionally, NBO analyses for the full systems were performed at the B3LYP(D3BJ)/LanL2DZ with an ultrafine integration grid. To guarantee that our analysis solely corresponds to the explored variable, we have used several geometric constraints for the scans. For example, in the H 3 C-H×××metal distance scans, we constrained other angles and dihedrals (i.e., the C-H-M angle and the H-M-C1-N dihedral) that could influence the outcome, as described in the main text. NBO analysis transforms the canonical delocalized molecular orbitals from DFT calculations into localized orbitals that are closely tied to the chemical bonding concepts. Each of the localized NBO sets is complete and orthonormal. The filled NBOs describe the hypothetical, strictly localized Lewis structure. The interactions between filled and antibonding orbitals represent the deviation from the Lewis structure and can be used to measure delocalization. For example, delocalizing interaction can be treated via the 2 nd order perturbation energy approach as 𝐸(2) = 𝑛 𝑖 𝐹 𝑖𝑗 2 𝛥𝐸, where n i is the population of a donor orbital, F ij is the Fock matrix element for the interacting orbitals i and j, and 𝛥𝐸 is the energy gap between these orbitals. Natural Energy Decomposition Analysis (NEDA) calculations were performed (at the B3LYP(D3BJ)/LanL2DZ/(int=ultrafine) level of theory) on both H 3 C-H×××M-NHC and H 3 C-H×××NH 3 systems, and on the truncated pieces of full systems where only one sugar interacts with the Cl-M-NHC system. This type of analysis proved useful when interrogating the system for different types of interactions between the sugar pieces of cyclodextrins and the metal centers. NEDA is an energy partitioning procedure for molecular interactions. [START_REF]orbitals ensures that the sets of eigenvectors for different fragments are mutually orthogonal. The charge distributions described by the perturbed wavefunctions arise from electric field quantum mechanical effects experienced by the fragments within the complex. A localized wavefunction[END_REF] Electrical interaction (EL), charge transfer (CT), and core repulsion (CORE) contributions are evaluated for self-consistent field (SCF) wavefunctions. [START_REF]Definitions according to the NEDA manual[END_REF] The total interaction energy is then given by 𝐸 = 𝐸𝐿 + 𝐶𝑇 + 𝐶𝑂𝑅𝐸, in kcal/mol. NMR shielding tensors were computed with the Gauge-Independent Atomic Orbital (GIAO) method, [START_REF] Cheeseman | [END_REF] at the (SMD 71 =CHCl 3 )/B3LYP(D3BJ)/LanL2DZ/(int=ultrafine) level of theory. 1 H chemical shifts were taken with respect to the usual reference of TMS at the (NMR=GIAO) B3LYP/6-311+G(2d,p) level of theory. All DFT and NBO6 calculations were performed with the Gaussian 09 rev. D01 software package. [START_REF] Frisch | Gaussian[END_REF] GFN2-xTB calculations were performed with Grimme's xtb (version 6.1). [START_REF] Ehlert | [END_REF] NEDA calculations were performed with NBO7 74 linked to Gaussian 16 rev. C01. [START_REF] Frisch | Gaussian[END_REF] Threedimensional structures and orbital plots were produced with CYLView 1.0.1, [START_REF] Legault | [END_REF] IQmol 2.8.0, 77 Chemcraft 1.8, 78 and UCSF Chimera. [START_REF]Some of the molecular graphics in this work were produced with UCSF Chimera, developed by the Resource for Biocomputing, Visualization, Informatics at the University of California[END_REF]

Scheme 2 .

 2 Scheme 2. Comparison of orbital and electrostatic contributions to C-H×××M interactions and conventional H-bonds

Figure 2 .

 2 Figure 2. Left: 1 H NMR spectra of (a-ICyD Me )CuCl, (a-ICyD Me )AgCl and (a-ICyD Me )AuCl (400 MHz, CDCl 3 ) 39 ; Right: X-ray crystal structure of (a-ICyD Me )CuCl, (a-ICyD Me )AgCl and (a-ICyD Me )AuCl from CDCl 3 /pentane/cyclohexane H 5 s are shown as pale grey spheres.

Scheme 3 .

 3 Scheme 3. The molecular orbitals for the investigated NHC-M-Cl systems (M=Au, Ag, Cu).

Figure 3 .

 3 Figure 3. Relative energies for the CH 4 ×××M (M = Au, Ag, Cu) distances. For Ag and Cu, the repulsive part of the distance scan starts at the shorter H×××M distances.

Figure 4 .

 4 Figure 4. Effect of the M×××H distance at the C-H bond length.

Figure 5 .

 5 Figure 5. Effect of the M×××H distance at the total natural charges of methane and NHC-M-Cl.

Figure 6 .

 6 Figure 6. Effect of the M×××H distance at the natural charges of methane's C and H specifically.

Figure 7 .

 7 Figure 7. Polarization of the C-H bond (% electronic density at H) as a function of the M×××H distance.

Figure 8 .

 8 Figure 8. s-character at C in the C-H bond (%) as a function of the M-H distance.

Figure 9 .

 9 Figure 9. Electronic population of 𝜎 "# (left) and 𝜎 "# * (right), both as a function of the M-H distances

Figure 10 .

 10 Figure 10. Left: relative energies for the Cl-M-H angle scans. Right: effect of the Cl-M-H angle at the C-H bond length. (M = Au, Ag, Cu).

Figure 11 .

 11 Figure 11. Left: relative energies for the N-C 1 -M-H dihedral angle scans. Right: effect of the N-C1-M-H dihedral angle at the C-H bond length. (M = Au, Ag, Cu).

Figure 12 .

 12 Figure 12. Hybridization, population, and energy level of gold's non-bonding orbitals in NHC-Au-Cl.

Scheme 5 .

 5 Scheme 5. Schematic representation of different trends in conventional H-bonds and "contraelectrostatic" H-bonds presented in this work.

Scheme 6 .

 6 Scheme 6. Natural Energy Decomposition Analyses (NEDA) of CH 4 ×××M-NHC systems (with M = Au, Ag, and Cu), and for H 3 C-H×××NH 3 complex as a conventional H-bond system. Left: The three components of NEDA (electrical, charge-transfer (ct above), and repulsion) are shown individually as well as the total interaction energy. Right: The electrostatic (electrical) term is further decomposed into its parts (static (ES above), induced polarization (POL above), and self-energy (SE above) correction).

Figure 13 .

 13 Figure 13. Selected calculated chemical shifts of (a-ICyD Me )AgCl, (a-ICyD Me )CuCl, and (a-ICyD Me )AuCl.

  notation matches those H atoms in Fig.2

Figure 14 .

 14 Figure 14. Computational analyses of full systems with Cu, Ag, and Au. The Cl atom and non-important H atoms were omitted for clarity in the picture. Only NBO interactions above the 0.05 kcal/mol threshold were included. A. Comparison of M×××H distances vs. C-H distances, with a focus on the region where the metal interacts with most C-H bonds (for r M×××H between 2.4 and 3.1 Å), suggests a very weak C-H bond elongation. B. NBO and natural charge analyses for interactions between C-H within the region of interest and the Cu atom. No orbital donations from the metal to the C-H 5(B,E) bonds. C. NBO and natural charge analyses for interactions between C-H within the region of interest and the Ag atom. Strongest donation from the metal center to the C-H 5A bond. D. NBO and natural charge analyses for interactions between C-H within the region of interest and the Au atom. No orbital donations from the metal to the C-H 5E bond, strong interactions in the C-H 5A, and C-H 5D bonds.

Figure 15 .

 15 Figure 15. NEDA of trimmed full systems with Cu, Ag, and Au and their respective sugar pieces. Nonimportant H atoms were omitted for clarity. The three components of NEDA (electrostatic, charge-transfer, and repulsion) are shown individually as well as the total interaction energy. A. Trimmed full system with four sugars A, B, D, and E. For NEDA analyses on each quadrant contained the pair Cl-M-NHC (fragment 1) and its sugar (fragment 2); the other two sugars (C and F) were removed. B. NEDA analyses for interactions between each sugar within the region of interest and the Cl-Cu-NHC center. C. NEDA analyses for interactions between each sugar within the region of interest and the Cl-Ag-NHC center. D. NEDA analyses for interactions between each sugar within the region of interest and the Cl-Au-NHC center.

Table

Table 2 .

 2 Distances and angles from X-ray crystal structures (Hydrogen atoms were placed at calculated positions in the model)39

	d
	5
	M-H

Acknowledgments I.V.A and G. P. G. are grateful for the support of the National Science Foundation (Grant CHE-1800329). G. P. G gratefully acknowledges Canada's Natural Sciences and Engineering Research Council (NSERC) for the Banting Postdoctoral Fellowship. Part of computational resources was provided by NSF XSEDE (TG-CHE160006), and FSU Research Computing Center. G. P. G. thanks Professor Alán Aspuru-Guzik (University of Toronto, Vector Institute for Artificial Intelligence) for the support and Compute Canada for computational resources. NEDA computations were performed on the niagara supercomputer at the SciNet HPC Consortium. SciNet is funded by: the Canada Foundation for Innovation; the Government of Ontario; Ontario Research Fund -Research Excellence; and the University of Toronto. X.L. and G.X. thank the CSC for a PhD grant. P.B.A, S.R., M.S. thank the LabEx MiChem part of French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, and Cyclolab (Hungary) for a generous supply of a-cyclodextrin. We thank Dr. Robert Pollice and Dr. Kjell Jorner (University of Toronto) for valuable discussions. The first version of this manuscript has been posted as a preprint on ChemRxiv. 80

Supporting Information

Experimental and additional computational details reported in this work are available in the SI. The geometries and other relevant files for this work can be freely obtained at https://github.com/gabegomes/anagostic_contra-electrostatic_H-bonds. This material is available free of charge via the Internet at http://pubs.acs.org.