Metal–metal bonding, electronic excitations, and strong resonance Raman effect in 2D layered α-MoCl3

Covalent bonding between transition metal atoms is a common phenomenon in honeycomb lattices of layered materials, which strongly affects their electronic and magnetic properties. This work presents a detailed spectroscopic study of α-MoCl3, 2D van der Waals material with covalently bonded Mo2 dimers, with a particular focus on the Mo–Mo bonding. Raman spectra of α-MoCl3 were studied with multiple excitation laser lines chosen in different parts of the absorption spectrum, while polarization measurements aided in the symmetry assignment of the observed modes. Furthermore, far-IR measurements and (Density Functional Theory) DFT phonon computations were performed to complete vibrational assignment. Polarized absorption, PL, and photoelectron spectroscopy supported by DFT calculations were employed to understand the consequences of the Mo–Mo bonding for the electronic structure and the localization/delocalization balance in d3–d3 interactions. A coupling of dimerization-related structural and electronic properties was revealed in the strong resonance Raman enhancement of the Mo–Mo stretching mode at 153 cm−1 when the excitation laser matched the electronic transition between σ-bonding and antibonding orbitals of the Mo2 dimer (σ → σ*). The deeper understanding of the metal–metal bonding and identification of the vibrational and electronic spectroscopic signatures of the dimerization will be of great use for the studies of electron delocalization in magnetic van der Waals materials.


Introduction
Transition metal trihalides (MX 3 ) form a versatile group of 2D van der Waals materials with interesting bulk and nanoscale properties [1].The most famous examples are RuCl 3 and the chromium trihalides, which were intensely studied regarding exotic magnetic properties at low dimensions [2][3][4][5].Specific physical properties of these compounds originate from partially-filled nd-shell with nd m -electron localization in octahedrally coordinated metal cations and ensuing magnetic nd m -nd m interactions in a honeycomb lattice formed by edge-sharing MX 6 octahedra.
A competing phenomenon that may occur in such systems is the d-electron delocalization, producing bonding between neighboring metal atoms.Back in 1960, Goodenough pointed out that the face or edge-sharing arrangement of coordination octahedra may support strong metal-metal interactions, including an abrupt formation of covalentlybonded metal dimers below a certain phase transition temperature [6].While the original analysis was done for transition metal oxides, it should stand for halides as well.For 2D lattices, this phenomenon was also discussed in terms of Peierls-like distortion, which removes electronic instabilities by contracting the lattice along one of the layer axes and thus enforcing dimerization, and in terms of resonating valence bond state and valence-bond crystals or liquids [7][8][9][10][11][12].The delocalization-localization balance in layered transition metal compounds and the propensity for dimerization are very ubiquitous phenomena, which have a dramatic influence on their physical properties [13][14][15].Formation of dimers with metal-metal bonds in MX 3 group was observed in α-TiCl 3 [16,17], α-TiBr 3 [18,19], β-TcCl 3 [20,21], α-RuCl 3 [22,23], and α-MoCl 3 (figure 1) [24][25][26].While dimerization in RuCl 3 happens only under increased pressure, other listed halides can support M-M bonds under ambient conditions.Anisotropic dimer-containing phases are then stable below a certain phase transition temperature (217 K in α-TiCl 3 , 180 K in α-TiBr 3 , 585 K in α-MoCl 3 ), above which metal-metal bonds break and more symmetric hexagonal arrangements are obtained.This process also involves drastic changes in magnetic behavior since dimeric phases tend to be non-magnetic.In particular, despite the 4d 3 configuration of the Mo 3+ and the similarity to the magnetically active 3d 3 configuration of Cr 3+ in the chromium trihalides, α-MoCl 3 is diamagnetic at room and lower temperatures due to the formation of Mo-Mo dimers with the bond length of 2.76-2.78Å [24][25][26].These dimers break at temperatures above 585 K, causing an abrupt increase of Mo magnetic moment and elongation of the intermetallic distance to 3.36 Å [24,25].
Unusually high thermal and ambient stability turn α-MoCl 3 into an ideal object for dedicated studies of dimerization-related phenomena.Furthermore, its unconventional properties, when compared to other metal trihalides, are very interesting in the context of alloying and doping of 2D nanomaterials for property tuning.However, in contrast to most other transition metal trihalides, α-MoCl 3 is much less well investigated in its basic properties and only little is known about the details of Mo-Mo interactions in this material, even though dimerization and diamagnetism were discovered decades ago [24,26].In this work we performed a detailed spectroscopic and computational analysis of α-MoCl 3 with particular focus on the Mo-Mo bonding.Intertwining of structural and electronic properties necessarily involves phonon degrees of freedom, making vibrational and especially Raman spectroscopy a powerful tool in such an endeavor [18,[27][28][29][30]. Varying the Raman excitation laser wavelengths, we found that Mo-Mo stretching undergoes strong resonant enhancement when excitation matches electronic transitions between σ-bonding and σ * -antibonding orbitals of Mo-Mo dimers.Augmented with complete vibrational assignment as well as the data from absorption, photoluminescence (PL), and photoelectron spectroscopies, our findings reveal in-depth information on the Mo-Mo interactions in MoCl 3 and provide a reference for studies of dimerization-related phenomena in other transition metal trihalides.

Experimental details
MoCl 3 powder was synthesized by reacting powders of Mo (99.95% metal basis, Alfa Aesar) and MoCl 5 (99.6%, abcr) in a ratio of 2.0:3.1 in an evacuated ampoule at 550 • C for 100 h.Remaining excess of MoCl 4 and MoCl 5 were removed from the product by sublimation in the same ampoule at 300 • C to room temperature in an open-ended one-zone furnace for 5 h before opening the ampoule under inert gas atmosphere and extracting the product.The purity of the obtained MoCl 3 was confirmed by powder x-ray diffraction (figure S1) performed with a 'STOE STADI-P' (STOE) with a Ge (111) primary beam monochromator in transmission geometry with Coradiation (λ Kα1 = 1.788 96 Å).A small amount of Sipowder was added before grinding of the powder as an internal standard.
Crystals of MoCl 3 were grown by chemical vapor transport as described in [25] using a two-zone furnace (LOBA, HTM Reetz GmbH).Since MoCl 3 crystals tend to bend and twin during growth, for spectroscopic measurements we used intergrown singlecrystals with domains of at least 10-30 µm size as judged by polarized micro-Raman and Vis-NIR measurements (figure S2).This size is considerably larger than the ∼1 µm diameter of the laser beam spot, thus ensuring that Raman and absorption spectra were measured on a single-crystalline domain.Since it was not possible to index these domains with x-ray diffraction, we relied on polarized optical measurements in alignment of the crystal along crystallographic axes.While these measurements did not allow us to distinguish a and b axes, the latter could be accomplished using additional information on spectroscopic transitions discussed in the manuscript.
Micro-Raman spectra were studied using a T64000 spectrometer (Horiba Jobin Yvon) with 1800 gr mm −1 gratings, liquid nitrogen-cooled Symphony CCD detector, and excitation at 532 and 660 nm by solid-state Torus lasers (Laser Quantum Novanta Photonics) and at 785 nm by BrixX diode laser (Omicron-Laserage Laserprodukte GmbH).Additional measurements with the excitation between 604 and 720 nm were performed with a tunable dye laser Matisse 2 (Sirah Lasertechnik) charged with 2-methyl-6-(4-dimethylaminostyryl)-4 H-pyran (DCM) dye and pumped by 532 nm laser Millennia (Spectra-Physics).To avoid spurious polarization effects during non-polarized Raman measurements of a single-crystalline sample, the laser beam was depolarized.In polarization-dependent measurements, the polarization plane of the laser was rotated with a polarization rotator.Further details on the settings of optical elements in non-polarized and polarized measurements are described in figure S3.
Far-IR and visible absorption spectra were recorded at room temperature in transmission mode using Vertex 80v spectrometer (Bruker).For far-IR measurements, fine powder of MoCl 3 was suspended in ethanol and drop-casted onto polyethylene IR sample card (International Crystal Laboratories), the spectrum was recorded with SiC Globar light source and DLaTGS detector with polyethylene window.For absorption measurements in the visible range, the light source and detector were changed to a tungstenhalogen lamp and Si-photodiode.Powder sample for absorption measurements was mixed with KBr, ballmilled (with FRITSCH Pulverisette 23) and pressed into a pellet.A single-crystalline sample was placed on KBr substrate, and the spectra were measured in transmission mode using Hyperion FTIR microscope.Complementary diffuse reflectance measurements of MoCl 3 powder pressed into BaSO 4 pellets were performed using Shimadzu UV-3101PC spectrometer.
PL measurements were performed in backscattering geometry using a microscope of home design and laser excitation at 488 nm (Omicron PhoxX diode laser).PL detection was done using Kymera 328i spectrograph (Andor) and Newton 920 CCD camera (Andor), calibrated versus black body radiation.The temperature of the sample was controlled with Janis ST-500 microscopy cryostat.PL lifetime measurements were performed using timecorrelated single-photon counting technique based on ID900 Time Controller (ID Quantique).The 488 nm Omicron PhoxX diode laser was modulated with the pulse width of 1 ns, and the ID230 NIR single-photon counter (ID Quantique) was used for broad-band time-resolved detection in the NIR range.
Photoemission spectroscopic measurements were performed using a laboratory-based system equipped with a Scienta R8000 analyzer, a He discharge lamp and an Al Kα excitation source.The measurements have been conducted at room temperature.
Crystals have been cleaved in situ by the scotch tape method and measured under a base pressure of 2 × 10 −10 mbar.

Excitation wavelength dependence of Raman spectra
Raman spectra of α-MoCl 3 measured at three excitation wavelengths are compared in figure 2(a).The spectrum excited with the 532 nm laser is dominated by a line at 153 cm −1 , which is one order of magnitude stronger than the other nine peaks detectable in the range of fundamental modes (100-400 cm −1 ).Among the low-intensity features, the most prominent is the peak at 295 cm −1 .Similar but less-detailed Raman spectra were reported for α-MoCl 3 in [25] and [41], which also applied 532 nm laser.Excitation with 458 nm laser in [42] resulted in a reduced relative intensity of the 153 cm −1 mode and increased intensity of the peak at 350 cm −1 .
A very different Raman spectrum was obtained with the 660 nm excitation (figure 2(a)).While all peak positions remained the same as in the 532 nm spectrum, their intensity distribution changed immensely.The most profound effect is the dramatic decrease of the peaks at 153 and 295 cm −1 , which become only seen as shoulders near stronger lines at 157 and 301 cm −1 .On the other hand, the feature at 329 cm −1 , which is barely detectable in the 532 nm spectrum, becomes the strongest peak when excited at 660 nm.Overall intensity distribution between the modes in the 660 nm spectrum appears more uniform than with green laser.When the excitation wavelength was changed to 785 nm, the Raman signal became noticeably weaker, while relative intensities again showed a considerable redistribution.The peaks at 301, 329, and 350 cm −1 became the strongest ones, while intensity of the features at 108 cm −1 and especially at 168 cm −1 waned considerably.
The variation of the Raman intensity with excitation wavelength points to a resonant character, which appears particularly strong at 532 nm.This observation is also supported by the analysis of the higherfrequency range, in which overtones and combinational modes can be seen (figure 2(b)).The 532 nm laser produces an overtone progression corresponding to the multi-quantum excitation of the 153 cm −1 mode.The peaks in the progression are considerably broader than peaks of fundamental modes, pointing to the short lifetime of the coupled electronic state.The second overtone in the progression cannot be well distinguished because of its overlap with the fundamental mode at 295 cm −1 , but further members up to the sixth can be clearly identified (figure 2(b)).Additional peaks can be also seen near the third and fourth overtones, but the increasing linewidth prevents more detailed analysis of these components.For the 660 nm excitations, a set of overtones and combinational modes in the range of double-quantum transitions (350-700 cm −1 ) can be seen as well, but their intensity is much lower than in the 532 nm spectrum, and there are no multi-quantum overtone progressions.
The resonance Raman scattering is caused by the match between the excitation laser and an electronic excitation, thus calling for the analysis of the electronic spectrum.The absorption spectrum of powder α-MoCl 3 in the visible and near-IR range is shown in figure 3 (similar but less resolved spectrum was measured by diffuse-reflectance technique, figure S4).The 532 nm (2.33 eV) laser indeed closely matches the strong and broad absorption band with the maximum at 545 nm (2.27 eV).At lower energy, the spectrum has weaker absorption peaks at 795 and 700 nm (1.56 and 1.77 eV), and another weak feature near 740 nm (1.95 eV), which is not well resolved because of the overlap with the tail of the band at 2.27 eV.The 660 nm (1.88 eV) laser does not match any of these transitions, and thus the spectrum is either nonresonant or only weakly coupled.785 nm (1.58 eV) laser line is close to the absorption peak at 1.56 eV, but the strong resonant enhancement is not induced, indicating that this electronic excitation is not efficiently coupling with vibrational modes.
Using an advantage of a tunable dye laser, we also measured Raman spectra while scanning the laser wavelength in 10 nm steps between 604 nm (2.05 eV) and 720 nm (1.72 eV).This excitation range covers photon energies from the foothill of the strong absorption band at 2.27 eV to the absorption peak at 1.77 eV through the unresolved absorption feature at 1.95 eV (figure 3).The spectra, normalized to the peak at 108 cm −1 for the convenience of comparison, are plotted in figure 4, while figure S5 plots  Absorption spectra were measured at 300 K for a powder pressed in KBr pellet and for a single crystal (SC) in two perpendicular polarizations (∥x and ∥y).The broad wavy background in SC spectra is caused by a thin film interference.PL spectrum was measured for a polycrystalline sample at 5 K, λex = 488 nm.See figure S11 for comparison of PL spectra measured between 5 K and 300 K. some intensity profiles.The relative intensity shows a clear variation with the excitation wavelength, but the changes are not as dramatic as observed when switching between 660 nm and 532 nm lasers (figure 2).604 nm, which is the shortest wavelength we could obtain with DCM dye, is apparently not close enough to the resonant absorption at 545 nm, and the Raman peak at 153 cm −1 remains weak.The peaks at 260 and 301 cm −1 vary their relative intensities almost ten-fold, reaching the maximum at 640-660 nm.The relative intensity modulation of the 329 cm −1 line is the most pronounced: it has the highest intensity at 660 nm, then reduces to a barely distinguishable feature at 720 nm, but then again becomes one of the strongest lines in the spectrum when excited at 785 nm (figure 2(a)).At the same time, the peak at 350 cm −1 remains nearly unaffected, while the line at 238 cm −1 , which is hard to see at shorter wavelengths, gains visible intensity only when excitation wavelengths exceeds 690 nm.Comparison of the spectra excited at 720 and 785 nm (figures 2(a) and 4) again reveals a considerable intensity redistribution, showing that the modulation of Raman intensity is not limited to the vicinity of electronic transitions at 1.95 and 1.77 eV.Overall, these changes indicate that the spectra excited between 604 and 785 nm have a pre-resonant character, but unlike in the 532 nm spectrum, we cannot identify a particularly strong resonant coupling between electronic excitations and one specific vibration.Instead, continuous changes are observed for all vibrational modes, the Raman resonance effects are subtler, and their interpretation requires deeper analysis of electronic transitions and vibrational modes.

Polarized Raman measurements
To determine symmetry types of Raman modes, polarized Raman measurements were performed.The crystalline structure of α-MoCl 3 belongs to the C2/m (12) space group with C 2h factor group.The C 2 axis is oriented along Mo-Mo dimers parallel to the MoCl 3 layers, while the σ h plane is perpendicular to the Mo-Mo bonds.In Γ-point, α-MoCl 3 has 6 A g + 6 B g Raman-active modes, 4 A u + 5 B u IR-active modes, and A u + 2 B u acoustic phonons with zero frequency.In our back-scattering Raman measurements, the propagation direction of the incident and scattered light (z, z) is normal to MoCl 3 layers (figure 1(a)), while a and b crystallographic axes are parallel to x and y laboratory axes.This arrangement is denoted as z (αβ)z, where α and β are polarization of incident laser and scattered light, respectively, each chosen in xy plane.In the following discussion, z (αβ)z will be shortened to αβ.A g and B g modes can be distinguished by their polarization behavior, since B g should be silent in the parallel polarization (αβ = xx or yy), while A g -in the cross-polarization (αβ = xy or yx) [43]; see supporting information for discussion of Raman tensors of A g and B g modes and the angular dependence of their intensity.
Figure 5 shows the angular dependence of the Raman intensity obtained with the 660 nm excitation and 10 • -stepwise rotation of the laser polarization plane, while the analyzer was either set to x (figure 5(a)) or to y (figure 5(b)).The maps reveal strong changes of intensity profiles and distinguish two types of modes with antiphase angular dependence.Figures 5(c  and 301 cm −1 as their close frequencies resulted in overlapped peaks in non-polarized spectra. The symmetry assignment reveals that the 532 nm spectrum is dominated by totally symmetric modes (figure 5(d)).In the non-polarized spectrum, B g modes are barely seen, the strongest one being the B g (3) peak at 174 cm −1 .The predominant enhancement of A g modes and the overtone progression discussed above (figure 2(b)) suggest the Frank-Condon mechanism (A-term) [44], which is usually the main mechanism for the Raman resonance with allowed electronic transitions of high intensity.Furthermore, the yy-polarized scattering is at least five-fold stronger than in other polarizations, including xx, and the non-polarized spectrum thus mainly represents the yy-polarization.The resonant A g (2) mode at 153 cm −1 , which has a very strong yy peak, loses all its intensity in the xx-polarizarion and becomes comparable to other features and is even weaker than the A g (1) peak at 108 cm −1 .Likewise, A g (5) at 295 cm −1 with the second most intense yy peak reduces to a feeble feature in the xxpolarizarion.Evidently, the resonant scattering occurs only when the laser polarization is parallel to y, which therefore should be a polarization direction of the electronic excitation involved in the resonance.Note that dipole-allowed excitations of α-MoCl 3 are polarized either parallel to b axis along Mo-Mo bonds (A u symmetry type) or have their induced dipole moment in the σ h plane (B u symmetry type) and hence polarized perpendicular to Mo-Mo bonds and have nonnegligible components parallel to a.
Interestingly, although the 660 nm excitation is quite far from the strong absorption band at 545 nm, a residual resonance effect is still detectable in polarized spectra: While the peaks at 153 and 295 cm −1 are very weak in xx polarization, they gain reasonable yy intensity (figure 5(c)).Another peculiar feature is that the strong intensity of the B g (6) mode at 329 cm −1 in the non-polarized 660 nm spectrum stems mainly from yx polarization, in which this peak is very strong, while its xy intensity is not so prominent.

DFT calculations and vibrational assignment
DFT calculations were performed to further aid the interpretation of the experimental spectra.According The optimized coordinates were then used in vibrational calculations.Phonon bands along high symmetry paths in the Brillouin zone are shown in figure S7 in SI and reveal a modest dispersion except for acoustic branches.Hereafter will focus only on Γ-point phonons as they are most relevant for optical spectra.Γ-point vibrational frequencies of Ramanactive modes agree very well with the experimental values (table 1).We can thus confirm that all 12 Raman-active modes of α-MoCl 3 were identified and properly assigned to A g and B g symmetry types.
To complete the vibrational assignment of α-MoCl 3 , we also studied its far-IR spectrum (figure 6).A close match of experimental and computed frequencies is found here as well (table 1), although some of the IR absorption bands are rather broad, which does not allow exact assignment of computed modes with close frequencies.Three weak but sharp features at 145, 158, and 161 cm −1 are ascribed to B u (1), B u (2), and A u (1).The strong experimental band at 257 cm −1 corresponds to the computed frequencies of B u (3) and A u (2) modes.Next, a very strong and broad band with poorly resolved peaks at 292 and 302 cm −1 is matched by three computed vibrations of A u (3), B u (4), and A u (4) types.Finally, the medium-strong band at 400 cm −1 is unequivocally assigned to the stand-alone B u (5) mode.
Having identified all fundamental modes (table 1), we can proceed to their description in terms of involved structural elements based on the computed atomic displacements.Mo<(µ 2 -Cl) 2 >Mo rings featuring Mo-Mo bonds and shorter Mo-Cl bonds are stiffer than non-bonded rings, and their vibrations therefore tend to occur at higher frequencies.IR-active B u (5) and A u (4) modes at 400 and 302 cm −1 , as well as Raman modes A g (6) at 350 cm −1 and B g (6) at 329 cm −1 are all localized on the 'bonded' Mo<(µ 2 -Cl) 2 >Mo rings and involve their Mo-Cl stretching partially coupled with Mo-Cl-Mo deformation.The A g (6) mode can be also described as the ring breathing mode.
B g ( 4) is the lowest-frequency Mo-Cl stretching vibration, and starting from the B g (3) mode at 174 cm −1 and further down, stretching modes give way to deformational vibrations (observe the gap of 63 cm −1 between B g (4) and B g (3)).Six deformational modes are densely distributed in the narrow frequency window of 145-174 cm −1 .They have modest IR intensity (figure 6), but medium-strong Raman activity (figures 2 and 4), especially when the spectra are excited in the red part of the visible spectrum.Finally, two lowest-frequency modes, B g (1) at 103 cm −1 and A g (1) at 108 cm −1 , can be described as rotational motion (libration) of non-bonded (B g ) Of particular interest for this work is the understanding of the unique nature of the A g (2) mode at 153 cm −1 leading to its strong resonant enhancement.Analysis of vibrational displacements revealed that this mode has a sizeable involvement of Mo-Mo stretching coordinate (figure 2(b)).Although none of α-MoCl 3 vibrations can be described as pure Mo-Mo stretching because of the unavoidable mixing with other coordinates, the A g (2) mode appears to be the closest to this definition.A small contribution of Mo-Mo stretching is also present in A g (3), A g (5), and A g (6) (figure S8), but displacements of chlorine atoms in these modes are much more pronounced.
Molecular compounds with Mo-Mo bonds attracted considerable interest for decades.Particular extensively studied are the complexes with quadruple Mo-Mo bonds and short distances of only 2.05-2.15Å [45].Stretching Mo-Mo vibrations of such bonds are usually found in the range of 350-400 cm −1 [46].For instance, the quadruple Mo-Mo bond in the Mo 2 Cl 8 4− anion is 2.13-2.15Å short, and its stretching vibrational frequency is 340-350 cm −1 [47].Vibrational properties of Mo-Mo bonds of lower order are not well characterized.We are only aware of spectroscopic studies of the Mo 2 Cl 9 3− anion, which has the Mo-Mo bond length of 2.67(1) Å in Cs salt [48] and the Mo-Mo stretching frequency of 142 cm −1 [49].Both the bond length and the frequency are remarkably close to those in α-MoCl 3 .
The Tsuboi rule [50] states that the vibrational displacements of the modes enhanced in the resonance Raman spectrum are commensurate with the changes in the molecular geometry induced by the resonant electronic excitation.Thus, the resonant enhancement of the Mo-Mo stretching mode in α-MoCl 3 implies that the coupled electronic excitation should considerably change the Mo-Mo bond length and therefore is expected to affect the Mo-Mo bonding.In the next section, we will analyze the electronic structure and details of the Mo-Mo bonding in α-MoCl 3 .

Electronic structure and Mo-Mo bonding in α-MoCl 3
The DFT-computed electronic band structure of α-MoCl 3 near the Fermi level is plotted in figure 7(a).With two Mo atoms in the unit cell, α-MoCl 3 has ten bands derived mainly from Mo-4d AOs, of which three are occupied, while the computed bandgap is near 1.2 eV.Spin-density distribution (figure 7(b)) illustrates the antiferromagnetic arrangement of Mo magnetic moments in dimer fragments and the nonmagnetic overall ground state.At the same time, the lowest-energy 4d band represents the σ-type Mo-Mo bonding (figure 7(c), see figure S9 densities of other bands).Thus, Mo-Mo interaction in α-MoCl 3 The small dispersion of 4d-bands in α-MoCl 3 suggests rather local electronic interactions, allowing the use of a truncated model.Since non-periodic molecular codes offer more possibilities for wavefunction analysis, we used a molecular model of α-MoCl 3 , comprising the bioctahedral Mo 2 Cl 10 4− fragment (figures 8 and S10).Here, the large negative charge is necessary to ensure correct electron count, but the excess electrons in this relatively small ion would lead to an unbalanced Coulomb repulsion.The latter was accounted for by addition of four K + ions in the positions, where next Mo atoms would be in the crystal structure.DFT calculations were thus performed for the neutral K 4 Mo 2 Cl 10 structure (figure S10(a)) and gave similar energies and shapes of t 2gderved orbitals as in the periodic structure.
Mo-Mo t 2g 3 -t 2g 3 interactions feature a complex balance of delocalization, responsible for the covalent bonding, and localization, yielding localized spins with antiferromagnetic alignment [58].The true electronic wavefunction of such a system is necessarily multiconfigurational, [58] but the reasonable modeling still can be accomplished in the framework of DFT using broken-symmetry approximation, [59] which allows asymmetry of spin-up and spin-down orbitals while maintaining the single-determinant approach.Although this determinant is not an eigenfunction of the spin Hamiltonian, it usually provides a conceptually simple description and a semiquantitative estimation of exchange coupling [60][61][62][63].The balance between bonding and localization in the Mo-Mo dimer can be illustrated by analyzing the shape and spatial overlap of α(↑) and β(↓) orbitals (figure 8(b)).For the σ-bonding orbital, α and β counterparts are almost identical (overlap 95%), indicating that this orbital is a normal bonding MO.An opposite situation is found for the δ * -orbital, which has its α and β counterparts localized on different Mo atoms with a spatial overlap of only 5%.The δ * -orbital is thus non-bonding and contributes to the localized spins.An intermediate situation is realized for the πorbital, which exhibits an α/β overlap of 64% (note that the part of this value is from Cl atoms, while pure Mo-Mo is smaller).Spin-up and spin-down orbitals show a clear asymmetry, leading to the enhanced localization of opposite spins on different Mo atoms, but also maintain a certain symmetric part, contributing to the Mo-Mo bonding.Thus, π orbital participates in both bonding and localization, and the shape of the spin density isosurface on each Mo results from the combination of π and δ * orbital densities (figure S10(b)).Population characteristics depend on the computational method, but all point to a fractional spin localization.For instance, spin population of Mo atoms is 1.46 (Mulliken) or 1.71 (Bader) instead of 3, which would be observed for the completely localized t 2g 3 state, while the Mo-Mo bond order is between 1.07 (Bader) and 1.25 (Mayer) and thus exceeds a single bond but is far less than a double bond.

Electronic spectra and the resonance Raman effect
Theoretical prediction of the electronic structure can be further ascertained by experimental electronic spectra.Direct access to occupied states is provided by photoelectron spectroscopy.Figure 9 shows the spectra measured with UV and x-ray excitations at 40.8 eV (He II) and 1486.6 eV (XPS), respectively.At low binding energies (−1 to −3 eV), the spectra exhibit a double-peak feature, which agrees well with the DFT-computed density of states and corresponds mainly to t 2g 3 states of Mo.The cross-section ratio Mo-4d/Cl-3p of 13.2 at 40.8 eV is considerably higher than the value of 2.3 at 1486.6 eV, and the Mo-derived structure is much better seen and resolved in the He II spectrum.The two peak components at −1.5 and −2.3 eV can be straightforwardly assigned to (π, δ * ) and σ bands, respectively.The 0.8 eV splitting of t 2g 3 states is in perfect agreement with the theoretical modeling (figure 7) and is caused by the stabilization of the σ-band by the Mo-Mo bonding.
The broad band at deeper binding energies, between −3 and −8 eV, is mainly derived from Cl-3p states.At lower energies these are contributed by chlorine lone pairs, which gradually give way to Mo-Cl bonding orbitals at higher binding energies.Mo contribution to the density of state increases accordingly and results in the peak at −6.3 eV in the He II spectrum.
Experimental access to unoccupied states is less straightforward and depends on the optical excitations, which at first requires symmetry analysis of the valence and conduction bands.As π and δ * orbital symmetries are B u and A u , while those of π * and δ orbitals are B g and A g , respectively, (π, δ * ) → (π * , δ) excitations will be either of A u (π → π * , δ * → δ) or B u (π → δ, δ * → π * ) types.All four are dipoleallowed and can be expected in the low-energy part of the absorption spectrum.This formal symmetry analysis gives information neither on the oscillator strength of these transitions nor on the composition of excited states, but it is reasonable to expect relatively low intensity, especially for the δ * → δ excitation, as it is de facto a localized d-d transition in the octahedral coordination forbidden by the Laporte rule.Besides, excitations of the same symmetry type most likely mix, while a picture of single-electron transitions between MO levels may be oversimplified.The model of exchange-coupled clusters might be more appropriate here [64], such as discussed in spectroscopic studies of Cs 3 Mo 2 Cl 9 salt with similar Mo-Mo bonding motif [49,[65][66][67], but extended theoretical analysis of (π, δ * ) → (π * , δ) excitations goes beyond the scope of this work.Nonetheless, combination of powder and polarized absorption measurements allows preliminary analysis of the spectrum in the (π, δ * ) → (π * , δ) range.As already discussed above, absorption spectrum of α-MoCl 3 exhibits three low-intensity features at 1.56, 1.77, and 1.95 eV.Single-crystalline measurements revealed strong polarization of the spectra (figure 3).The peak at 1.77 eV is polarized parallel to y.The peak at 1.56 eV has x polarization and is accompanied by a vibronic structure at 1.58-1.65 eV with both x and y components.Since Frank-Condon vibronic coupling proceeds via totally-symmetric modes and does not change the symmetry and polarization, we suggest that these vibrational features are partially induced by the Herzberg-Teller mechanism, which allows admixing of the vibrational modes of B g symmetry (B g × B u = A u ; B g × A u = B u ).Polarized measurements also revealed that the unresolved feature near 1.95 eV in the powder spectrum is caused by two transitions with different polarization.The weak and broad x-polarized band with the maximum at 1.95 eV overlaps with y-polarized feature at 2.05-2.10eV, seen as a shoulder to a much stronger transition at 2.3 eV.Thus, polarized single-crystal measurements revealed two x and two y-polarized transitions in the low-energy part of the spectrum.As discussed further below, x and y laboratory axes can be associated with a and b crystallographic axes, respectively, allowing assignment of A u (∥ y) and B u (∥ x) symmetry types.We can preliminary suggest that we identified all expected (π, δ * ) → (π * , δ) excitations, but the definitive statement should await for a detailed theoretical analysis considering the configurational composition of excited states.Besides, in our analysis we assumed that all observed transitions are spin-allowed, but given their low intensity, spinforbidden transitions cannot be fully excluded.
To identify the lowest excited state energy limits, we also performed PL measurements.PL spectrum of α-MoCl 3 excited with 488 nm laser showed a broad emission band at 867 nm (1.43 eV), at somewhat lower energy that the first absorption peak at 1.56 eV.The integral emission intensity is strongly temperature dependent and increased 20-fold when the sample was cooled from 300 to 5 K, while the spectral shape remained weakly affected by temperature and only became somewhat narrower with cooling (figure S11).PL intensity variation is paralleled by the increase of the PL lifetime from 1 µs at 300 K to 8.4 µs at 5 K (figure S12).These long lifetimes indicate that the emission is presumably a phosphorescence and proceeds from the triplet state via spin-forbidden pathway.Nonetheless, it allows to conclude that the absorption peak at 1.56 eV corresponds to the lowestenergy spin-allowed excitation.
As δ * -MO in α-MoCl 3 is non-bonding, δ * → δ and δ * → π * excitations are not expected to significantly change the Mo-Mo distance and couple with Mo-Mo stretching vibration.At the same time, π orbital has a certain true bonding contribution, and, therefore, π → π * and π → δ excitations might affect the Mo-Mo bond length.However, our Raman measurements with the laser wavelengths chosen close to the energies of all identified (π, δ * ) → (π * , δ) transitions did not produce resonance enhancement of the Mo-Mo stretching vibration (figure 4), suggesting that the effect is small.
Interpretation of intensive absorption at 2.27 eV is more ambiguous, because two excitation types are expected near this energy and probably overlap: the σ → σ * transition within the t 2g manifold, and the crystal-field excitation of the t 2g → e g type from the highest occupied t 2g states, that is, (π, δ * ) → e g (green arrows in figure 7(d)).Note that the crystal-field transition in various Mo x Cl y z− species usually occurs near 2.4 eV with high absorption intensity [68].The σ → σ * transition is of A u symmetry type, while excitations from (π, δ * ) to the lowest energy e g -derived π * -orbital with B g symmetry are of A u and B u types.Single-crystal measurements showed that the strong absorption band is mainly polarized parallel to y, but also highlighted the presence of a lower-intensity x-polarized peak at 2.5 eV, which could not be distinguished in the powder spectrum (figure 3).
While we cannot assign A u and B u symmetry types solely from absorption measurements, the resonance Raman data strongly suggest that the σ → σ * transition is at least a part of the strong absorption band.The σ-MO in α-MoCl 3 is genuinely bonding, and the σ → σ * excitation will either completely break the Mo-Mo bond in the excited state or at least increase its length considerably.This excitation is therefore the primary candidate for the resonant Raman effect, which strongly enhances the Mo-Mo stretching mode when using the 532 nm laser (figure 2).Since σ → σ * excitation transforms under A u symmetry type, we can use this fact to establish the relative orientation of crystallographic and laboratory axes (x ≡ a, y ≡ b) and assign A u and B u types for all electronic transitions.
We are not aware yet of such dimerizationinduced resonance Raman effects in other transition metal halides or in dimolybdenum complexes with low Mo-Mo bond orders, but similar phenomenon was observed in quadruple-bonded complexes of Mo and some other transition metals [69,70].As their metal-metal distance is very short (∼2.1 Å), the δ-MO is truly bonding and is usually the HOMO of the molecule.Raman excitation into the δ → δ * transition in such complexes resulted in the strong resonance enhancement of the M-M stretching mode and produced long Frank-Condon progressions, sometimes with more than 10 overtones.For instance, δ → δ * excitation in Mo 2 Cl 8 4− occurs at 535 nm, very close to the energy of the strong absorption band in α-MoCl 3 , and in resonance Raman conditions the Mo-Mo stretching mode of Mo 2 Cl 8 4− at 340 cm −1 produced progressions with up to 9-11 overtones [47,71].

Concluding remarks
In this work, we performed a comprehensive vibrational and electronic spectroscopic analysis of α-MoCl 3 as a case study of 2D van der Waals material with metal dimers.The complete vibrational assignment allowed us to identify Mo-Mo stretching vibration, while studying the Raman spectra in a broad range of excitation wavelengths showed that this mode undergoes strong resonant enhancement when excited at 532 nm.Computational modeling and analysis of the electronic spectra showed that the resonant absorption is most likely the σ → σ * transition in the Mo 2 dimer.Also, the computational study revealed a complex balance between spin localization and metal-metal bonding.
Our results on α-MoCl 3 show that the strong resonance Raman effect caused by the M-M bond can be realized in transition metal trihalides and likely other transition metal compounds with M-M bonding because they all should develop at least a σbonding orbital and an antibonding σ * counterpart, and feature σ → σ * transition in the electronic excitation spectrum.For bonds of higher order, the resonance may occur at π → π * or even δ → δ * excitation, as observed in molecular compounds with quadruple M-M bonds.Since the resonance effect occurs when Raman spectrum is excited into this specific transition, the enhancement of the M-M stretching mode can simultaneously serve as the diagnostic feature of the dimerization and as the way to identify the dimerbased electronic transition.Transition metal oxides and halides with nd m configuration (m ⩽ 5) and face or edge-sharing coordination octahedrons frequently show a tendency to dimerization, either in ambient conditions or under applied pressure, which can strongly change their electronic and magnetic properties.The possibility to follow this transformation using spectroscopic approaches can be very useful in further exploration of these materials on the verge of phase transitions.Especially important this approach is expected to be in mixed-metal (alloyed) systems, for which diffraction structural studies can become quite ambiguous.
From a broader perspective, our results demonstrate that α-MoCl 3 is a special case of a 2D material with strong orbital effects [15].Such materials can show a plethora of physical phenomena near the order-disorder transition, when localized singlet dimers start to move and may form valence bond liquid [8,14,72].The strong electron-phonon coupling suggests that these states can be tuned by changing the number of layers or external stimuli, such as an external strain or pressure.Charge injection may also destroy some dimers and dilute their order with concomitant formation of new spin states.Grain boundaries, at which orientation of dimers change, likely host uncompensated spins with interesting magnetic properties.Another important consequence of our study can be in the field of photomagnetism.Pumping into the σ → σ * transition should break the M-M bonds in the excited state and thereby change the local interaction between metal atoms.In molecular compounds this effect is used to cleave metal-metal bonds in photochemical reactions [73], but in the solid state the overall framework will keep metal atoms in place, ensuring integrity of the whole structure.Instead, the crystal should undergo a photoinduced structural and magnetic phase transition in a region spatially localized to the excitation light beam, thus opening the way to photomagnetic manipulations [74].

Figure 1 .
Figure 1.Fragments of the crystal structure of α-MoCl3 (C2/m space group) with the view along (a) b axis and (b) c axis, Mo atoms are plotted in magenta, Cl atoms are green, unit cell boundaries are visualized in light blue.Arrows in (a) show direction of light irradiation in Raman, absorption, and photoluminescence measurements.

Figure 2 .
Figure 2. (a) Raman spectra of α-MoCl3 crystal excited with 532, 660, and 785 nm laser lines in the frequency range of fundamental modes.(b) Raman spectra excited with 532 and 660 nm and showing the frequency range of overtones/ combinational modes; black arrows in the upper panel indicate overtone positions of the resonant mode νR at 153 cm −1 .Insets show vibrational displacements for the modes with the strongest intensity in 532 nm and 660 nm spectra.

Figure 3 .
Figure 3. Absorption (Abs.) and photoluminescence (PL) spectra of α-MoCl3.Vertical arrows mark positions of laser lines used in Raman measurements (solid-state lasers at 532, 660, and 785 nm, and a DCM-dye laser tuned between 604 and 720 nm).Absorption spectra were measured at 300 K for a powder pressed in KBr pellet and for a single crystal (SC) in two perpendicular polarizations (∥x and ∥y).The broad wavy background in SC spectra is caused by a thin film interference.PL spectrum was measured for a polycrystalline sample at 5 K, λex = 488 nm.See figureS11for comparison of PL spectra measured between 5 K and 300 K.

Figure 4 .
Figure 4. Raman spectra of α-MoCl3 excited with dye laser tuned between 604 and 720 nm in 10 nm steps.For the sake of comparison, each spectrum is normalized to the intensity of the peak at 108 cm −1 .
) and (d) shows xx, yy, xy and yx polarized spectra measured with 660 nm (figure 5(c)) and 532 nm (figure 5(d)) lasers.In accordance with the symmetry analysis, the angular dependence and Raman spectra in parallel and cross-polarized geometries allow a very straightforward assignment of A g and B g modes (figures 5(c) and (d)).Polarization data appeared especially useful for distinguishing A g modes at 153 and 295 cm −1 from the B g modes at 157

Figure 5 .
Figure 5. Polarization dependence of Raman intensity studied with excitation at 660 nm.Laser polarization plane was rotated in 10 • steps, while the spectra were measured for vertical (a) and horizontal (b) positions of the analyzer, corresponding to z (αx)z and z (αy)z measurement geometries.Color scale corresponds to Raman intensity (in counts).Dashed lines denote the slices at φ = 0 • (α = x) and φ = 90 • (α = y) shown in (c); individual spectra at different values of φ are compared in figure S6. (c), (d) polarized Raman spectra (xx, yy, xy and yx) of α-MoCl3 crystal excited at 660 nm (c) and 532 nm (d).Also shown are non-polarized spectra (measured with depolarized laser) and assignment of Ag and Bg symmetry types.Note the five-fold intensity downscaling of the yy polarization in (d).

Figure 6 .
Figure 6.Far-IR spectrum of α-MoCl3 (fine powder on a polyethylene substrate, T = 300 K).Vertical bars indicate DFT-computed Γ-point frequencies of IR-active phonons of Au and Bu symmetry types.

Figure 9 .
Figure 9. Valence band photoelectron spectra of α-MoCl3 measured with the excitation at 1486.6 eV (XPS) and 40.8 eV (He II) and compared to DFT-computed total electron density of states (DOS) and Mo-projected density of states (pDOS Mo).Note that the cross-section ratio Mo-4d/Cl-3p is 2.3 for XPS and 13.2 for He II.Calculated DOS is shifted in the energy scale to match PES data.

Table 1 .
DFT-computed experimental vibrational-frequencies of α-MoCl3 in Γ-point and the description of vibrational modes.